Seismic waves in a self-gravitating planet

NASA Astrophysics Data System (ADS)

Brazda, Katharina; de Hoop, Maarten V.; Hörmann, Günther

2013-04-01

The elastic-gravitational equations describe the propagation of seismic waves including the effect of self-gravitation. We rigorously derive and analyze this system of partial differential equations and boundary conditions for a general, uniformly rotating, elastic, but aspherical, inhomogeneous, and anisotropic, fluid-solid earth model, under minimal assumptions concerning the smoothness of material parameters and geometry. For this purpose we first establish a consistent mathematical formulation of the low regularity planetary model within the framework of nonlinear continuum mechanics. Using calculus of variations in a Sobolev space setting, we then show how the weak form of the linearized elastic-gravitational equations directly arises from Hamilton's principle of stationary action. Finally we prove existence and uniqueness of weak solutions by the method of energy estimates and discuss additional regularity properties.

Viscoacoustic anisotropic full waveform inversion

NASA Astrophysics Data System (ADS)

Qu, Yingming; Li, Zhenchun; Huang, Jianping; Li, Jinli

2017-01-01

A viscoacoustic vertical transverse isotropic (VTI) quasi-differential wave equation, which takes account for both the viscosity and anisotropy of media, is proposed for wavefield simulation in this study. The finite difference method is used to solve the equations, for which the attenuation terms are solved in the wavenumber domain, and all remaining terms in the time-space domain. To stabilize the adjoint wavefield, robust regularization operators are applied to the wave equation to eliminate the high-frequency component of the numerical noise produced during the backward propagation of the viscoacoustic wavefield. Based on these strategies, we derive the corresponding gradient formula and implement a viscoacoustic VTI full waveform inversion (FWI). Numerical tests verify that our proposed viscoacoustic VTI FWI can produce accurate and stable inversion results for viscoacoustic VTI data sets. In addition, we test our method's sensitivity to velocity, Q, and anisotropic parameters. Our results show that the sensitivity to velocity is much higher than that to Q and anisotropic parameters. As such, our proposed method can produce acceptable inversion results as long as the Q and anisotropic parameters are within predefined thresholds.

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.

Imaging of the internal structure of comet 67P/Churyumov-Gerasimenko from radiotomography CONSERT Data (Rosetta Mission) through a full 3D regularized inversion of the Helmholtz equations on functional spaces

NASA Astrophysics Data System (ADS)

Barriot, Jean-Pierre; Serafini, Jonathan; Sichoix, Lydie; Benna, Mehdi; Kofman, Wlodek; Herique, Alain

We investigate the inverse problem of imaging the internal structure of comet 67P/ Churyumov-Gerasimenko from radiotomography CONSERT data by using a coupled regularized inversion of the Helmholtz equations. A first set of Helmholtz equations, written w.r.t a basis of 3D Hankel functions describes the wave propagation outside the comet at large distances, a second set of Helmholtz equations, written w.r.t. a basis of 3D Zernike functions describes the wave propagation throughout the comet with avariable permittivity. Both sets are connected by continuity equations over a sphere that surrounds the comet. This approach, derived from GPS water vapor tomography of the atmosphere,will permit a full 3D inversion of the internal structure of the comet, contrary to traditional approaches that use a discretization of space at a fraction of the radiowave wavelength.

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.

REVIEWS OF TOPICAL PROBLEMS: Instabilities of a multicomponent plasma with accelerated particles and magnetic field generation in astrophysical objects

NASA Astrophysics Data System (ADS)

Bykov, Andrei M.; Toptygin, Igor'N.

2007-02-01

A system of MHD equations for the description of a magnetized nonequilibrium astrophysical plasma with neutral atoms and suprathermal (in particular, relativistic) particles is formulated. The instabilities of such a plasma, which arise from the presence of neutral and relativistic components, are considered. It is shown that the presence of nonthermal particles interacting with the thermal plasma component via regular and fluctuating electromagnetic fields is responsible for the emergence of specific mechanisms of MHD wave generation. The main generation mechanisms of static and turbulent magnetic fields near shock wave fronts in the Galaxy and interplanetary space are analyzed. We discuss the application of the generation effects of long-wave magnetic fluctuations to the problems of magnetic field origin and relativistic particle acceleration in astrophysical objects of various natures.

Alpha models for rotating Navier-Stokes equations in geophysics with nonlinear dispersive regularization

NASA Astrophysics Data System (ADS)

Kim, Bong-Sik

Three dimensional (3D) Navier-Stokes-alpha equations are considered for uniformly rotating geophysical fluid flows (large Coriolis parameter f = 2O). The Navier-Stokes-alpha equations are a nonlinear dispersive regularization of usual Navier-Stokes equations obtained by Lagrangian averaging. The focus is on the existence and global regularity of solutions of the 3D rotating Navier-Stokes-alpha equations and the uniform convergence of these solutions to those of the original 3D rotating Navier-Stokes equations for large Coriolis parameters f as alpha → 0. Methods are based on fast singular oscillating limits and results are obtained for periodic boundary conditions for all domain aspect ratios, including the case of three wave resonances which yields nonlinear "2½-dimensional" limit resonant equations for f → 0. The existence and global regularity of solutions of limit resonant equations is established, uniformly in alpha. Bootstrapping from global regularity of the limit equations, the existence of a regular solution of the full 3D rotating Navier-Stokes-alpha equations for large f for an infinite time is established. Then, the uniform convergence of a regular solution of the 3D rotating Navier-Stokes-alpha equations (alpha ≠ 0) to the one of the original 3D rotating NavierStokes equations (alpha = 0) for f large but fixed as alpha → 0 follows; this implies "shadowing" of trajectories of the limit dynamical systems by those of the perturbed alpha-dynamical systems. All the estimates are uniform in alpha, in contrast with previous estimates in the literature which blow up as alpha → 0. Finally, the existence of global attractors as well as exponential attractors is established for large f and the estimates are uniform in alpha.

A method of boundary equations for unsteady hyperbolic problems in 3D

NASA Astrophysics Data System (ADS)

Petropavlovsky, S.; Tsynkov, S.; Turkel, E.

2018-07-01

We consider interior and exterior initial boundary value problems for the three-dimensional wave (d'Alembert) equation. First, we reduce a given problem to an equivalent operator equation with respect to unknown sources defined only at the boundary of the original domain. In doing so, the Huygens' principle enables us to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time. Next, we discretize the resulting boundary equation and solve it efficiently by the method of difference potentials (MDP). The overall numerical algorithm handles boundaries of general shape using regular structured grids with no deterioration of accuracy. For long simulation times it offers sub-linear complexity with respect to the grid dimension, i.e., is asymptotically cheaper than the cost of a typical explicit scheme. In addition, our algorithm allows one to share the computational cost between multiple similar problems. On multi-processor (multi-core) platforms, it benefits from what can be considered an effective parallelization in time.

Rogue periodic waves of the modified KdV equation

NASA Astrophysics Data System (ADS)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-05-01

Rogue periodic waves stand for rogue waves on a periodic background. Two families of travelling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and two-fold Darboux transformations of the travelling periodic waves, we construct new explicit solutions for the mKdV equation. Since the dn-periodic wave is modulationally stable with respect to long-wave perturbations, the new solution constructed from the dn-periodic wave is a nonlinear superposition of an algebraically decaying soliton and the dn-periodic wave. On the other hand, since the cn-periodic wave is modulationally unstable with respect to long-wave perturbations, the new solution constructed from the cn-periodic wave is a rogue wave on the cn-periodic background, which generalizes the classical rogue wave (the so-called Peregrine’s breather) of the nonlinear Schrödinger equation. We compute the magnification factor for the rogue cn-periodic wave of the mKdV equation and show that it remains constant for all amplitudes. As a by-product of our work, we find explicit expressions for the periodic eigenfunctions of the spectral problem associated with the dn and cn periodic waves of the mKdV equation.

Statistics of extreme waves in the framework of one-dimensional Nonlinear Schrodinger Equation

NASA Astrophysics Data System (ADS)

Agafontsev, Dmitry; Zakharov, Vladimir

2013-04-01

We examine the statistics of extreme waves for one-dimensional classical focusing Nonlinear Schrodinger (NLS) equation, iΨt + Ψxx + |Ψ |2Ψ = 0, (1) as well as the influence of the first nonlinear term beyond Eq. (1) - the six-wave interactions - on the statistics of waves in the framework of generalized NLS equation accounting for six-wave interactions, dumping (linear dissipation, two- and three-photon absorption) and pumping terms, We solve these equations numerically in the box with periodically boundary conditions starting from the initial data Ψt=0 = F(x) + ?(x), where F(x) is an exact modulationally unstable solution of Eq. (1) seeded by stochastic noise ?(x) with fixed statistical properties. We examine two types of initial conditions F(x): (a) condensate state F(x) = 1 for Eq. (1)-(2) and (b) cnoidal wave for Eq. (1). The development of modulation instability in Eq. (1)-(2) leads to formation of one-dimensional wave turbulence. In the integrable case the turbulence is called integrable and relaxes to one of infinite possible stationary states. Addition of six-wave interactions term leads to appearance of collapses that eventually are regularized by the dumping terms. The energy lost during regularization of collapses in (2) is restored by the pumping term. In the latter case the system does not demonstrate relaxation-like behavior. We measure evolution of spectra Ik =< |Ψk|2 >, spatial correlation functions and the PDFs for waves amplitudes |Ψ|, concentrating special attention on formation of "fat tails" on the PDFs. For the classical integrable NLS equation (1) with condensate initial condition we observe Rayleigh tails for extremely large waves and a "breathing region" for middle waves with oscillations of the frequency of waves appearance with time, while nonintegrable NLS equation with dumping and pumping terms (2) with the absence of six-wave interactions α = 0 demonstrates perfectly Rayleigh PDFs without any oscillations with time. In case of the cnoidal wave initial condition we observe severely non-Rayleigh PDFs for the classical NLS equation (1) with the regions corresponding to 2-, 3- and so on soliton collisions clearly seen of the PDFs. Addition of six-wave interactions in Eq. (2) for condensate initial condition results in appearance of non-Rayleigh addition to the PDFs that increase with six-wave interaction constant α and disappears with the absence of six-wave interactions α = 0. References: [1] D.S. Agafontsev, V.E. Zakharov, Rogue waves statistics in the framework of one-dimensional Generalized Nonlinear Schrodinger Equation, arXiv:1202.5763v3.

The Capra Research Program for Modelling Extreme Mass Ratio Inspirals

NASA Astrophysics Data System (ADS)

Thornburg, Jonathan

2011-02-01

Suppose a small compact object (black hole or neutron star) of mass m orbits a large black hole of mass M ≫ m. This system emits gravitational waves (GWs) that have a radiation-reaction effect on the particle's motion. EMRIs (extreme-mass-ratio inspirals) of this type will be important GW sources for LISA. To fully analyze these GWs, and to detect weaker sources also present in the LISA data stream, will require highly accurate EMRI GW templates. In this article I outline the ``Capra'' research program to try to model EMRIs and calculate their GWs ab initio, assuming only that m ≪ M and that the Einstein equations hold. Because m ≪ M the timescale for the particle's orbit to shrink is too long for a practical direct numerical integration of the Einstein equations, and because this orbit may be deep in the large black hole's strong-field region, a post-Newtonian approximation would be inaccurate. Instead, we treat the EMRI spacetime as a perturbation of the large black hole's ``background'' (Schwarzschild or Kerr) spacetime and use the methods of black-hole perturbation theory, expanding in the small parameter m/M. The particle's motion can be described either as the result of a radiation-reaction ``self-force'' acting in the background spacetime or as geodesic motion in a perturbed spacetime. Several different lines of reasoning lead to the (same) basic O(m/M) ``MiSaTaQuWa'' equations of motion for the particle. In particular, the MiSaTaQuWa equations can be derived by modelling the particle as either a point particle or a small Schwarzschild black hole. The latter is conceptually elegant, but the former is technically much simpler and (surprisingly for a nonlinear field theory such as general relativity) still yields correct results. Modelling the small body as a point particle, its own field is singular along the particle worldline, so it's difficult to formulate a meaningful ``perturbation'' theory or equations of motion there. Detweiler and Whiting found an elegant decomposition of the particle's metric perturbation into a singular part which is spherically symmetric at the particle and a regular part which is smooth (and non-symmetric) at the particle. If we assume that the singular part (being spherically symmetric at the particle) exerts no force on the particle, then the MiSaTaQuWa equations follow immediately. The MiSaTaQuWa equations involve gradients of a (curved-spacetime) Green function, integrated over the particle's entire past worldline. These expressions aren't amenable to direct use in practical computations. By carefully analysing the singularity structure of each term in a spherical-harmonic expansion of the particle's field, Barack and Ori found that the self-force can be written as an infinite sum of modes, each of which can be calculated by (numerically) solving a set of wave equations in 1{+}1 dimensions, summing the gradients of the resulting fields at the particle position, and then subtracting certain analytically-calculable ``regularization parameters''. This ``mode-sum'' regularization scheme has been the basis for much further research including explicit numerical calculations of the self-force in a variety of situations, initially for Schwarzschild spacetime and more recently extending to Kerr spacetime. Recently Barack and Golbourn developed an alternative ``m-mode'' regularization scheme. This regularizes the physical metric perturbation by subtracting from it a suitable ``puncture function'' approximation to the Detweiler-Whiting singular field. The residual is then decomposed into a Fourier sum over azimuthal (e^{imϕ}) modes, and the resulting equations solved numerically in 2{+}1 dimensions. Vega and Detweiler have developed a related scheme that uses the same puncture-function regularization but then solves the regularized perturbation equation numerically in 3{+}1 dimensions, avoiding a mode-sum decomposition entirely. A number of research projects are now using these puncture-function regularization schemes, particularly for calculations in Kerr spacetime. Most Capra research to date has used 1st order perturbation theory, with the particle moving on a fixed (usually geodesic) worldline. Much current research is devoted to generalizing this to allow the particle worldline to be perturbed by the self-force, and to obtain approximation schemes which remain valid over long (EMRI-inspiral) timescales. To obtain the very high accuracies needed to fully exploit LISA's observations of the strongest EMRIs, 2nd order perturbation theory will probably also be needed; both this and long-time approximations remain frontiers for future Capra research.

Control of the transition between regular and mach reflection of shock waves

NASA Astrophysics Data System (ADS)

Alekseev, A. K.

2012-06-01

A control problem was considered that makes it possible to switch the flow between stationary Mach and regular reflection of shock waves within the dual solution domain. The sensitivity of the flow was computed by solving adjoint equations. A control disturbance was sought by applying gradient optimization methods. According to the computational results, the transition from regular to Mach reflection can be executed by raising the temperature. The transition from Mach to regular reflection can be achieved by lowering the temperature at moderate Mach numbers and is impossible at large numbers. The reliability of the numerical results was confirmed by verifying them with the help of a posteriori analysis.

Nonlinear PP and PS joint inversion based on the exact Zoeppritz equations: a two-stage procedure

NASA Astrophysics Data System (ADS)

Zhi, Lixia; Chen, Shuangquan; Song, Baoshan; Li, Xiang-yang

2018-04-01

S-velocity and density are very important parameters in distinguishing lithology and estimating other petrophysical properties. A reliable estimate of S-velocity and density is very difficult to obtain, even from long-offset gather data. Joint inversion of PP and PS data provides a promising strategy for stabilizing and improving the results of inversion in estimating elastic parameters and density. For 2D or 3D inversion, the trace-by-trace strategy is still the most widely used method although it often suffers from a lack of clarity because of its high efficiency, which is due to parallel computing. This paper describes a two-stage inversion method for nonlinear PP and PS joint inversion based on the exact Zoeppritz equations. There are several advantages for our proposed methods as follows: (1) Thanks to the exact Zoeppritz equation, our joint inversion method is applicable for wide angle amplitude-versus-angle inversion; (2) The use of both P- and S-wave information can further enhance the stability and accuracy of parameter estimation, especially for the S-velocity and density; (3) The two-stage inversion procedure proposed in this paper can achieve a good compromise between efficiency and precision. On the one hand, the trace-by-trace strategy used in the first stage can be processed in parallel so that it has high computational efficiency. On the other hand, to deal with the indistinctness of and undesired disturbances to the inversion results obtained from the first stage, we apply the second stage—total variation (TV) regularization. By enforcing spatial and temporal constraints, the TV regularization stage deblurs the inversion results and leads to parameter estimation with greater precision. Notably, the computation consumption of the TV regularization stage can be ignored compared to the first stage because it is solved using the fast split Bregman iterations. Numerical examples using a well log and the Marmousi II model show that the proposed joint inversion is a reliable method capable of accurately estimating the density parameter as well as P-wave velocity and S-wave velocity, even when the seismic data is noisy with signal-to-noise ratio of 5.

Regular Wave Propagation Out of Noise in Chemical Active Media

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

Alonso, S.; Sendina-Nadal, I.; Perez-Munuzuri, V.

2001-08-13

A pacemaker, regularly emitting chemical waves, is created out of noise when an excitable photosensitive Belousov-Zhabotinsky medium, strictly unable to autonomously initiate autowaves, is forced with a spatiotemporal patterned random illumination. These experimental observations are also reproduced numerically by using a set of reaction-diffusion equations for an activator-inhibitor model, and further analytically interpreted in terms of genuine coupling effects arising from parametric fluctuations. Within the same framework we also address situations of noise-sustained propagation in subexcitable media.

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship.

PubMed

Yan, Zai You; Hung, Kin Chew; Zheng, Hui

2003-05-01

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.

Generation of long subharmonic internal waves by surface waves

NASA Astrophysics Data System (ADS)

Tahvildari, Navid; Kaihatu, James M.; Saric, William S.

2016-10-01

A new set of Boussinesq equations is derived to study the nonlinear interactions between long waves in a two-layer fluid. The fluid layers are assumed to be homogeneous, inviscid, incompressible, and immiscible. Based on the Boussinesq equations, an analytical model is developed using a second-order perturbation theory and applied to examine the transient evolution of a resonant triad composed of a surface wave and two oblique subharmonic internal waves. Wave damping due to weak viscosity in both layers is considered. The Boussinesq equations and the analytical model are verified. In contrast to previous studies which focus on short internal waves, we examine long waves and investigate some previously unexplored characteristics of this class of triad interaction. In viscous fluids, surface wave amplitudes must be larger than a threshold to overcome viscous damping and trigger internal waves. The dependency of this critical amplitude as well as the growth and damping rates of internal waves on important parameters in a two-fluid system, namely the directional angle of the internal waves, depth, density, and viscosity ratio of the fluid layers, and surface wave amplitude and frequency is investigated.

Conformal Infinity.

PubMed

Frauendiener, Jörg

2000-01-01

The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related with almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved out of physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation and how it lends itself very naturally to solve radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection.

Conformal Infinity.

PubMed

Frauendiener, Jörg

2004-01-01

The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related to almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved from physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation, and how it lends itself very naturally to the solution of radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection.

No regularity singularities exist at points of general relativistic shock wave interaction between shocks from different characteristic families.

PubMed

Reintjes, Moritz; Temple, Blake

2015-05-08

We give a constructive proof that coordinate transformations exist which raise the regularity of the gravitational metric tensor from C 0,1 to C 1,1 in a neighbourhood of points of shock wave collision in general relativity. The proof applies to collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. Our result here implies that spacetime is locally inertial and corrects an error in our earlier Proc. R. Soc. A publication, which led us to the false conclusion that such coordinate transformations, which smooth the metric to C 1,1 , cannot exist. Thus, our result implies that regularity singularities (a type of mild singularity introduced in our Proc. R. Soc. A paper) do not exist at points of interacting shock waves from different families in spherically symmetric spacetimes. Our result generalizes Israel's celebrated 1966 paper to the case of such shock wave interactions but our proof strategy differs fundamentally from that used by Israel and is an extension of the strategy outlined in our original Proc. R. Soc. A publication. Whether regularity singularities exist in more complicated shock wave solutions of the Einstein-Euler equations remains open.

No regularity singularities exist at points of general relativistic shock wave interaction between shocks from different characteristic families

PubMed Central

Reintjes, Moritz; Temple, Blake

2015-01-01

We give a constructive proof that coordinate transformations exist which raise the regularity of the gravitational metric tensor from C0,1 to C1,1 in a neighbourhood of points of shock wave collision in general relativity. The proof applies to collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. Our result here implies that spacetime is locally inertial and corrects an error in our earlier Proc. R. Soc. A publication, which led us to the false conclusion that such coordinate transformations, which smooth the metric to C1,1, cannot exist. Thus, our result implies that regularity singularities (a type of mild singularity introduced in our Proc. R. Soc. A paper) do not exist at points of interacting shock waves from different families in spherically symmetric spacetimes. Our result generalizes Israel's celebrated 1966 paper to the case of such shock wave interactions but our proof strategy differs fundamentally from that used by Israel and is an extension of the strategy outlined in our original Proc. R. Soc. A publication. Whether regularity singularities exist in more complicated shock wave solutions of the Einstein–Euler equations remains open. PMID:27547092

Gravitational self-force on generic bound geodesics in Kerr spacetime

NASA Astrophysics Data System (ADS)

van de Meent, Maarten

2018-05-01

In this work we present the first calculation of the gravitational self-force on generic bound geodesics in Kerr spacetime to first order in the mass ratio. That is, the local correction to equations of motion for a compact object orbiting a larger rotating black hole due to its own impact on the gravitational field. This includes both dissipative and conservative effects. Our method builds on and extends earlier methods for calculating the gravitational self-force on equatorial orbits. In particular we reconstruct the local metric perturbation in the outgoing radiation gauge from the Weyl scalar ψ4 , which in turn is obtained by solving the Teukolsky equation using semianalytical frequency domain methods. The gravitational self-force is subsequently obtained using (spherical) l -mode regularization. We test our implementation by comparing the large l -behavior against the analytically known regularization parameters. In addition we validate our results by comparing the long-term average changes to the energy, angular momentum, and Carter constant to changes to these constants of motion inferred from the gravitational wave flux to infinity and down the horizon.

On the modified intermediate long-wave equation

NASA Astrophysics Data System (ADS)

Naumkin, Pavel I.; Sánchez-Suárez, Isahi

2018-03-01

We consider the modified intermediate long-wave equation ut-∂xu3+1ϑux+VP∫R12ϑcoth(π(y-x)2ϑ)uyy(t,y)dy=0. We develop the factorization technique to study the large time asymptotics of solutions.

Scalar field coupling to Einstein tensor in regular black hole spacetime

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wu, Chen

2018-02-01

In this paper, we study the perturbation property of a scalar field coupling to Einstein's tensor in the background of the regular black hole spacetimes. Our calculations show that the the coupling constant η imprints in the wave equation of a scalar perturbation. We calculated the quasinormal modes of scalar field coupling to Einstein's tensor in the regular black hole spacetimes by the 3rd order WKB method.

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

PubMed

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

2017-06-01

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

Regularization of Grad’s 13 -Moment-Equations in Kinetic Gas Theory

DTIC Science & Technology

2011-01-01

variant of the moment method has been proposed by Eu (1980) and is used, e.g., in Myong (2001). Recently, a maximum- entropy 10-moment system has been used...small amplitude linear waves, the R13 system is linearly stable in time for all modes and wave lengths. The instability of the Burnett system indicates...Boltzmann equation. Related to the problem of global hyperbolicity is the questions of the existence of an entropy law for the R13 system . In the linear

Inverse random source scattering for the Helmholtz equation in inhomogeneous media

NASA Astrophysics Data System (ADS)

Li, Ming; Chen, Chuchu; Li, Peijun

2018-01-01

This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

A note on specific variability of long surface gravity waves and drag coefficient in coastal upwelling zone

NASA Astrophysics Data System (ADS)

Krzyścin, Janusz

1990-01-01

In this paper we solve analytically wave kinematic equations and the wave energy transport equation, for basic long surface gravity wave in the coastal upwelling zone. Using Gent and Taylor's (1978) parameterization of drag coefficient (which includes interaction between long surface waves and the air flow) we find variability of this coefficient due to wave amplification and refraction caused by specific surface water current in the region. The drag coefficient grows towards the shore. The growth is faster for stronger current. When the angle between waves and the current is less than 90° the growth is mainly connected with the waves steepness, but when the angle is larger, it is caused by relative growth of the wave phase velocity.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

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

NASA Astrophysics Data System (ADS)

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

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

Mathematical problems arising in interfacial electrohydrodynamics

NASA Astrophysics Data System (ADS)

Tseluiko, Dmitri

In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, the effect of normal electric fields on films lying above, or hanging from, horizontal substrates is considered. Systematic asymptotic expansions are used to derive fully nonlinear long wave model equations for the scaled interface motion and corresponding flow fields. For the case of an inclined plane, higher order terms are need to be retained to regularize the problem in the sense that the long wave approximation remains valid for long times. For the case of a horizontal plane the fully nonlinear evolution equation which is derived at the leading order, is asymptotically correct and no regularization procedure is required. In both physical situations, the effect of the electric field is to introduce a non-local term which arises from the potential region above the liquid film, and enters through the electric Maxwell stresses at the interface. This term is always linearly destabilizing and produces growth rates proportional to the cubic power of the wavenumber - surface tension is included and provides a short wavelength cut-off, that is, all sufficiently short waves are linearly stable. For the case of film flow down an inclined plane, the fully nonlinear equation can produce singular solutions (for certain parameter values) after a finite time, even in the absence of an electric field. This difficulty is avoided at smaller amplitudes where the weakly nonlinear evolution is governed by an extension of the Kuramoto-Sivashinsky (KS) equation. Global existence and uniqueness results are proved, and refined estimates of the radius of the absorbing ball in L2 are obtained in terms of the parameters of the equations for a generalized class of modified KS equations. The established estimates are compared with numerical solutions of the equations which in turn suggest an optimal upper bound for the radius of the absorbing ball. A scaling argument is used to explain this, and a general conjecture is made based on extensive computations. We also carry out a complete study of the nonlinear behavior of competing physical mechanisms: long wave instability above a critical Reynolds number, short wave damping due to surface tension and intermediate growth due to the electric field. Through a combination of analysis and extensive numerical experiments, we elucidate parameter regimes that support non-uniform travelling waves, time-periodic travelling waves and complex nonlinear dynamics including chaotic interfacial oscillations. It is established that a sufficiently high electric field will drive the system to chaotic oscillations, even when the Reynolds number is smaller than the critical value below which the non-electrified problem is linearly stable. A particular case of this is Stokes flow, which is known to be stable for this class of problems (an analogous statement holds for horizontally supported films also). Our theoretical results indicate that such highly stable flows can be rendered unstable by using electric fields. This opens the way for possible heat and mass transfer applications which can benefit significantly from interfacial oscillations and interfacial turbulence. For the case of a horizontal plane, a weakly nonlinear theory is not possible due to the absence of the shear flow generated by the gravitational force along the plate when the latter is inclined. We study the fully nonlinear equation, which in this case is asymptotically correct and is obtained at the leading order. The model equation describes both overlying and hanging films - in the former case gravity is stabilizing while in the latter it is destabilizing. The numerical and theoretical analysis of the fully nonlinear evolution is complicated by the fact that the coefficients of the highest order terms (surface tension in this instance) are nonlinear. We implement a fully implicit two level numerical scheme and perform numerical experiments. We also prove global boundedness of positive periodic smooth solutions, using an appropriate energy functional. This global boundedness result is seen in all our numerical results. Through a combination of analysis and extensive numerical experiments we present evidence for global existence of positive smooth solutions. This means, in turn, that the film does not touch the wall in finite time but asymptotically at infinite time. Numerical solutions are presented to support such phenomena.

Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion

PubMed Central

Grimshaw, Roger; Stepanyants, Yury; Alias, Azwani

2016-01-01

It is well known that the Ostrovsky equation with normal dispersion does not support steady solitary waves. An initial Korteweg–de Vries solitary wave decays adiabatically through the radiation of long waves and is eventually replaced by an envelope solitary wave whose carrier wave and envelope move with different velocities (phase and group velocities correspondingly). Here, we examine the same initial condition for the Ostrovsky equation with anomalous dispersion, when the wave frequency increases with wavenumber in the limit of very short waves. The essential difference is that now there exists a steady solitary wave solution (Ostrovsky soliton), which in the small-amplitude limit can be described asymptotically through the solitary wave solution of a nonlinear Schrödinger equation, based at that wavenumber where the phase and group velocities coincide. Long-time numerical simulations show that the emergence of this steady envelope solitary wave is a very robust feature. The initial Korteweg–de Vries solitary wave transforms rapidly to this envelope solitary wave in a seemingly non-adiabatic manner. The amplitude of the Ostrovsky soliton strongly correlates with the initial Korteweg–de Vries solitary wave. PMID:26997887

Effects of Magnetic field on Peristalsis transport of a Carreau Fluid in a tapered asymmetric channel

NASA Astrophysics Data System (ADS)

Prakash, J.; Balaji, N.; Siva, E. P.; Kothandapani, M.; Govindarajan, A.

2018-04-01

The paper is concerned with effects of a uniform applied magnetic field on a Carreau fluid flow in a tapered asymmetric channel with peristalsis. The channel non-uniform & asymmetry are formed by choosing the peristaltic wave train on the tapered walls to have different amplitude and phase (ϕ). The governing equations of the Carreau model in two - dimensional peristaltic flow phenomena are constructed under assumptions of long wave length and low Reynolds number approximations. The simplified non - linear governing equations are solved by regular perturbation method. The expressions for pressure rise, frictional force, velocity and stream function are determined and the effects of different parameters like non-dimensional amplitudes walls (a and b), non - uniform parameter (m), Hartmann number (M), phase difference (ϕ),power law index (n) and Weissenberg numbers (We) on the flow characteristics are discussed. It is viewed that the rheological parameter for large (We), the curves of the pressure rise are not linear but it behaves like a Newtonian fluid for very small Weissenberg number.

Nonlocal symmetries, solitary waves and cnoidal periodic waves of the (2+1)-dimensional breaking soliton equation

NASA Astrophysics Data System (ADS)

Zou, Li; Tian, Shou-Fu; Feng, Lian-Li

2017-12-01

In this paper, we consider the (2+1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.

Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Pitton, G.

2018-02-01

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

Analysis of Real Ship Rolling Dynamics under Wave Excitement Force Composed of Sums of Cosine Functions

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

Zhang, Y. S.; Cai, F.; Xu, W. M.

2011-09-28

The ship motion equation with a cosine wave excitement force describes the slip moments in regular waves. A new kind of wave excitement force model, with the form as sums of cosine functions was proposed to describe ship rolling in irregular waves. Ship rolling time series were obtained by solving the ship motion equation with the fourth-order-Runger-Kutta method. These rolling time series were synthetically analyzed with methods of phase-space track, power spectrum, primary component analysis, and the largest Lyapunove exponent. Simulation results show that ship rolling presents some chaotic characteristic when the wave excitement force was applied by sums ofmore » cosine functions. The result well explains the course of ship rolling's chaotic mechanism and is useful for ship hydrodynamic study.« less

Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance.

PubMed

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

2014-09-01

The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics.

Wave propagation problem for a micropolar elastic waveguide

NASA Astrophysics Data System (ADS)

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

2018-04-01

A propagation problem for coupled harmonic waves of translational displacements and microrotations along the axis of a long cylindrical waveguide is discussed at present study. Microrotations modeling is carried out within the linear micropolar elasticity frameworks. The mathematical model of the linear (or even nonlinear) micropolar elasticity is also expanded to a field theory model by variational least action integral and the least action principle. The governing coupled vector differential equations of the linear micropolar elasticity are given. The translational displacements and microrotations in the harmonic coupled wave are decomposed into potential and vortex parts. Calibrating equations providing simplification of the equations for the wave potentials are proposed. The coupled differential equations are then reduced to uncoupled ones and finally to the Helmholtz wave equations. The wave equations solutions for the translational and microrotational waves potentials are obtained for a high-frequency range.

Multiple branches of travelling waves for the Gross–Pitaevskii equation

NASA Astrophysics Data System (ADS)

Chiron, David; Scheid, Claire

2018-06-01

Explicit solitary waves are known to exist for the Kadomtsev–Petviashvili-I (KP-I) equation in dimension 2. We first address numerically the question of their Morse index. The results confirm that the lump solitary wave has Morse index one and that the other explicit solutions correspond to excited states. We then turn to the 2D Gross–Pitaevskii (GP) equation, which in some long wave regime converges to the KP-I equation. Numerical simulations have already shown that a branch of travelling waves of GP converges to a ground state of KP-I, expected to be the lump. In this work, we perform numerical simulations showing that other explicit solitary waves solutions to the KP-I equation give rise to new branches of travelling waves of GP corresponding to excited states.

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Small data global solutions for the Camassa–Choi equations

NASA Astrophysics Data System (ADS)

Harrop-Griffiths, Benjamin; Marzuola, Jeremy L.

2018-05-01

We consider solutions to the Cauchy problem for an internal-wave model derived by Camassa–Choi (1996 J. Fluid Mech. 313 83–103). This model is a natural generalization of the Benjamin–Ono and intermediate long wave equations for weak transverse effects as in the case of the Kadomtsev–Petviashvili equations for the Korteweg-de Vries equation. For that reason they are often referred to as the KP-ILW or the KP–Benjamin–Ono equations regarding finite or infinite depth respectively. We prove the existence and long-time dynamics of global solutions from small, smooth, spatially localized initial data on . The techniques applied here involve testing by wave packet techniques developed by Ifrim and Tataru in (2015 Nonlinearity 28 2661–75 2016 Bull. Soc. Math. France 144 369–94).

On multi-graded-index soliton solutions for the Boussinesq-Burgers equations in optical communications

NASA Astrophysics Data System (ADS)

Abdel-Gawad, H. I.; Tantawy, M.

2017-02-01

Very recently, multi-solitary long waves for the homogeneous Boussinesq-Burgers equations (BBEs) were studied. Here its found that the time dependent coefficients (BBEs), shows multi-graded-index solitons waves, which are graded refractive index profile and can offer a new route for high-power lasers and transmission. They should increase data rates in low-cost telecommunications systems. Further, that (BBEs) show long periodic solitons waves in communications and television antennas.

Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

NASA Technical Reports Server (NTRS)

Cockrell, C. R.

1989-01-01

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.

Simple, explicitly time-dependent, and regular solutions of the linearized vacuum Einstein equations in Bondi-Sachs coordinates

NASA Astrophysics Data System (ADS)

Mädler, Thomas

2013-05-01

Perturbations of the linearized vacuum Einstein equations in the Bondi-Sachs formulation of general relativity can be derived from a single master function with spin weight two, which is related to the Weyl scalar Ψ0, and which is determined by a simple wave equation. By utilizing a standard spin representation of tensors on a sphere and two different approaches to solve the master equation, we are able to determine two simple and explicitly time-dependent solutions. Both solutions, of which one is asymptotically flat, comply with the regularity conditions at the vertex of the null cone. For the asymptotically flat solution we calculate the corresponding linearized perturbations, describing all multipoles of spin-2 waves that propagate on a Minkowskian background spacetime. We also analyze the asymptotic behavior of this solution at null infinity using a Penrose compactification and calculate the Weyl scalar Ψ4. Because of its simplicity, the asymptotically flat solution presented here is ideally suited for test bed calculations in the Bondi-Sachs formulation of numerical relativity. It may be considered as a sibling of the Bergmann-Sachs or Teukolsky-Rinne solutions, on spacelike hypersurfaces, for a metric adapted to null hypersurfaces.

Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.

PubMed

Whitfield, A J; Johnson, E R

2015-05-01

The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation.

PubMed

Liu, Wei; Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

PubMed Central

Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota’s bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides. PMID:29432495

Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2017-12-01

In this paper, the generalized variable-coefficient forced Kadomtsev-Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell’s polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient.

Experimental study on the bed shear stress under breaking waves

NASA Astrophysics Data System (ADS)

Hao, Si-yu; Xia, Yun-feng; Xu, Hua

2017-06-01

The object of present study is to investigate the bed shear stress on a slope under regular breaking waves by a novel instrument named Micro-Electro-Mechanical System (MEMS) flexible hot-film shear stress sensor. The sensors were calibrated before application, and then a wave flume experiment was conducted to study the bed shear stress for the case of regular waves spilling and plunging on a 1:15 smooth PVC slope. The experiment shows that the sensor is feasible for the measurement of the bed shear stress under breaking waves. For regular incident waves, the bed shear stress is mainly periodic in both outside and inside the breaking point. The fluctuations of the bed shear stress increase significantly after waves breaking due to the turbulence and vortexes generated by breaking waves. For plunging breaker, the extreme value of the mean maximum bed shear stress appears after the plunging point, and the more violent the wave breaks, the more dramatic increase of the maximum bed shear stress will occur. For spilling breaker, the increase of the maximum bed shear stress along the slope is gradual compared with the plunging breaker. At last, an empirical equation about the relationship between the maximum bed shear stress and the surf similarity parameter is given, which can be used to estimate the maximum bed shear stress under breaking waves in practice.

KP Equation in a Three-Dimensional Unmagnetized Warm Dusty Plasma with Variable Dust Charge

NASA Astrophysics Data System (ADS)

El-Shorbagy, Kh. H.; Mahassen, Hania; El-Bendary, Atef Ahmed

2017-12-01

In this work, we investigate the propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in an unmagnetized warm dusty plasma consisting of electrons, ions, and charged dust particles. The grain charge fluctuation is incorporated through the current balance equation. Using the perturbation method, a Kadomtsev-Petviashvili (KP) equation is obtained. It has been shown that the charge fluctuation would modify the wave structures, and the waves in such systems are unstable due to high-order long wave perturbations.

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

On the transition towards slow manifold in shallow-water and 3D Euler equations in a rotating frame

NASA Technical Reports Server (NTRS)

Mahalov, A.

1994-01-01

The long-time, asymptotic state of rotating homogeneous shallow-water equations is investigated. Our analysis is based on long-time averaged rotating shallow-water equations describing interactions of large-scale, horizontal, two-dimensional motions with surface inertial-gravity waves field for a shallow, uniformly rotating fluid layer. These equations are obtained in two steps: first by introducing a Poincare/Kelvin linear propagator directly into classical shallow-water equations, then by averaging. The averaged equations describe interaction of wave fields with large-scale motions on time scales long compared to the time scale 1/f(sub o) introduced by rotation (f(sub o)/2-angular velocity of background rotation). The present analysis is similar to the one presented by Waleffe (1991) for 3D Euler equations in a rotating frame. However, since three-wave interactions in rotating shallow-water equations are forbidden, the final equations describing the asymptotic state are simplified considerably. Special emphasis is given to a new conservation law found in the asymptotic state and decoupling of the dynamics of the divergence free part of the velocity field. The possible rising of a decoupled dynamics in the asymptotic state is also investigated for homogeneous turbulence subjected to a background rotation. In our analysis we use long-time expansion, where the velocity field is decomposed into the 'slow manifold' part (the manifold which is unaffected by the linear 'rapid' effects of rotation or the inertial waves) and a formal 3D disturbance. We derive the physical space version of the long-time averaged equations and consider an invariant, basis-free derivation. This formulation can be used to generalize Waleffe's (1991) helical decomposition to viscous inhomogeneous flows (e.g. problems in cylindrical geometry with no-slip boundary conditions on the cylinder surface and homogeneous in the vertical direction).

A far-field non-reflecting boundary condition for two-dimensional wake flows

NASA Technical Reports Server (NTRS)

Danowitz, Jeffrey S.; Abarbanel, Saul A.; Turkel, Eli

1995-01-01

Far-field boundary conditions for external flow problems have been developed based upon long-wave perturbations of linearized flow equations about a steady state far field solution. The boundary improves convergence to steady state in single-grid temporal integration schemes using both regular-time-stepping and local-time-stepping. The far-field boundary may be near the trailing edge of the body which significantly reduces the number of grid points, and therefore the computational time, in the numerical calculation. In addition the solution produced is smoother in the far-field than when using extrapolation conditions. The boundary condition maintains the convergence rate to steady state in schemes utilizing multigrid acceleration.

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

NASA Astrophysics Data System (ADS)

Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

2018-04-01

Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

NASA Astrophysics Data System (ADS)

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

2013-12-01

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.

Dispersive estimates for massive Dirac operators in dimension two

NASA Astrophysics Data System (ADS)

Erdoğan, M. Burak; Green, William R.; Toprak, Ebru

2018-05-01

We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the t-1 decay rate holds in the L1 →L∞ setting if the threshold energies are regular. We also show these bounds hold in the presence of s-wave resonances at the threshold. We further show that, if the threshold energies are regular then a faster decay rate of t-1(log ⁡ t) - 2 is attained for large t, at the cost of logarithmic spatial weights. The free Dirac equation does not satisfy this bound due to the s-wave resonances at the threshold energies.

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

PubMed

Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N

2013-07-01

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Electromagnetic or other directed energy pulse launcher

DOEpatents

Ziolkowski, Richard W.

1990-01-01

The physical realization of new solutions of wave propagation equations, such as Maxwell's equations and the scaler wave equation, produces localized pulses of wave energy such as electromagnetic or acoustic energy which propagate over long distances without divergence. The pulses are produced by driving each element of an array of radiating sources with a particular drive function so that the resultant localized packet of energy closely approximates the exact solutions and behaves the same.

Comparison of the Effect of Horizontal Vibrations on Interfacial Waves in a Two-Layer System of Inviscid Liquids to Effective Gravity Inversion

NASA Astrophysics Data System (ADS)

Pimenova, Anastasiya V.; Goldobin, Denis S.; Lyubimova, Tatyana P.

2018-02-01

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.

Evolution of nonlinear waves in a blood-filled artery with an aneurysm

NASA Astrophysics Data System (ADS)

Nikolova, E. V.; Jordanov, I. P.; Dimitrova, Z. I.; Vitanov, N. K.

2017-10-01

We discuss propagation of traveling waves in a blood-filled hyper-elastic artery with a local dilatation (an aneurysm). The processes in the injured artery are modeled by an equation of the motion of the arterial wall and by equations of the motion of the fluid (the blood). Taking into account the specific arterial geometry and applying the reductive perturbation method in long-wave approximation we reduce the model equations to a version of the perturbed Korteweg-de Vries kind equation with variable coefficients. Exact traveling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is numerically simulated and discussed from the point of view of arterial disease mechanics.

Stability of planar traveling waves in a Keller-Segel equation on an infinite strip domain

NASA Astrophysics Data System (ADS)

Chae, Myeongju; Choi, Kyudong; Kang, Kyungkeun; Lee, Jihoon

2018-07-01

We consider a simplified model of tumor angiogenesis, described by a Keller-Segel equation on the two dimensional domain (x , y) ∈ R ×Sλ where Sλ is the circle of perimeter λ. It is known that the system allows planar traveling wave solutions of an invading type. In case that λ is sufficiently small, we establish the nonlinear stability of traveling wave solutions in the absence of chemical diffusion if the initial perturbation is sufficiently small in some weighted Sobolev space. When chemical diffusion is present, it can be shown that the system is linearly stable. Lastly, we prove that any solution with our front condition eventually becomes planar under certain regularity conditions.

Long Wave Runup in Asymmetric Bays and in Fjords With Two Separate Heads

NASA Astrophysics Data System (ADS)

Raz, Amir; Nicolsky, Dmitry; Rybkin, Alexei; Pelinovsky, Efim

2018-03-01

Modeling of tsunamis in glacial fjords prompts us to evaluate applicability of the cross-sectionally averaged nonlinear shallow water equations to model propagation and runup of long waves in asymmetrical bays and also in fjords with two heads. We utilize the Tuck-Hwang transformation, initially introduced for the plane beaches and currently generalized for bays with arbitrary cross section, to transform the nonlinear governing equations into a linear equation. The solution of the linearized equation describing the runup at the shore line is computed by taking into account the incident wave at the toe of the last sloping segment. We verify our predictions against direct numerical simulation of the 2-D shallow water equations and show that our solution is valid both for bays with an asymmetric L-shaped cross section, and for fjords with two heads—bays with a W-shaped cross section.

Semiclassical Wheeler-DeWitt equation: Solutions for long-wavelength fields

NASA Astrophysics Data System (ADS)

Salopek, D. S.; Stewart, J. M.; Parry, J.

1993-07-01

In the long-wavelength approximation, a general set of semiclassical wave functionals is given for gravity and matter interacting in 3+1 dimensions. In the long-wavelength theory, one neglects second-order spatial gradients in the energy constraint. These solutions satisfy the Hamilton-Jacobi equation, the momentum constraint, and the equation of continuity. It is essential to introduce inhomogeneities to discuss the role of time. The time hypersurface is chosen to be a homogeneous field in the wave functional. It is shown how to introduce tracer particles through a dust field χ into the dynamical system. The formalism can be used to describe stochastic inflation.

The excitation of spiral density waves through turbulent fluctuations in accretion discs - I. WKBJ theory

NASA Astrophysics Data System (ADS)

Heinemann, T.; Papaloizou, J. C. B.

2009-07-01

We study and elucidate the mechanism of spiral density wave excitation in a differentially rotating flow with turbulence which could result from the magneto-rotational instability. We formulate a set of wave equations with sources that are only non-zero in the presence of turbulent fluctuations. We solve these in a shearing box domain, subject to the boundary conditions of periodicity in shearing coordinates, using a WKBJ method. It is found that, for a particular azimuthal wavelength, the wave excitation occurs through a sequence of regularly spaced swings during which the wave changes from leading to trailing form. This is a generic process that is expected to occur in shearing discs with turbulence. Trailing waves of equal amplitude propagating in opposite directions are produced, both of which produce an outward angular momentum flux that we give expressions for as functions of the disc parameters and azimuthal wavelength. By solving the wave amplitude equations numerically, we justify the WKBJ approach for a Keplerian rotation law for all parameter regimes of interest. In order to quantify the wave excitation completely, the important wave source terms need to be specified. Assuming conditions of weak non-linearity, these can be identified and are associated with a quantity related to the potential vorticity, being the only survivors in the linear regime. Under the additional assumption that the source has a flat power spectrum at long azimuthal wavelengths, the optimal azimuthal wavelength produced is found to be determined solely by the WKBJ response and is estimated to be 2πH, with H being the nominal disc scaleheight. In a following paper by Heinemann & Papaloizou, we perform direct three-dimensional simulations and compare results manifesting the wave excitation process and its source with the assumptions made and the theory developed here in detail, finding excellent agreement.

New exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in multi-temperature electron plasmas

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu; Zeng, Zhi-Fang

2017-10-01

In this paper, we aim to introduce a new form of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation for the long waves of small amplitude with slow dependence on the transverse coordinate. By using the Hirota's bilinear form and the extended homoclinic test approach, new exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are presented. Moreover, the properties and characteristics for these new exact periodic solitary-wave solutions are discussed with some figures.

A nonlinear wave equation in nonadiabatic flame propagation

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

Booty, M.R.; Matalon, M.; Matkowsky, B.J.

1988-06-01

The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time.

Laboratory and field investigations of wave attenuation by live marsh vegetation

USDA-ARS?s Scientific Manuscript database

Wave attenuation by live marsh vegetation was investigated experimentally in this study. Laboratory experiments were conducted in a 20.6 m long, 0.69 m wide and 1.22 m deep wave flume under regular and random waves. The vegetation species used are Spartina alterniflora and Juncus roemerianus, which ...

Alfven waves associated with long cylindrical satellites

NASA Technical Reports Server (NTRS)

Venkataraman, N. S.; Gustafson, W. A.

1973-01-01

The Alfven wave excited by a long cylindrical satellite moving with a constant velocity at an angle relative to a uniform magnetic field has been calculated. Assuming a plasma with infinite conductivity, the linearized momentum equation and Maxwell's equations are applied to a cylindrical satellite carrying a variable current. The induced magnetic field is determined, and it is shown that the Alfven disturbance zone is of limited extent, depending on the satellite shape. The wave drag coefficient is calculated and shown to be small compared to the induction drag coefficient at all altitudes considered.

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special non-deteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of 'non-reflecting kernels,' nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The non-deteriorating algorithm, which is the core of the new ABCs is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals, and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimension spaces, It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the non-modified scheme. In the paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABCs' algorithm.

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

NASA Astrophysics Data System (ADS)

Ryaben'kii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.

2001-12-01

We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special nondeteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of “nonreflecting kernels” nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The nondeteriorating algorithm, which is the core of the new ABCs, is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimensional spaces. It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the unmodified scheme. In this paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABC algorithm.

Internally electrodynamic particle model: Its experimental basis and its predictions

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

Zheng-Johansson, J. X., E-mail: jxzj@iofpr.or

2010-03-15

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts: (a) electric charges present with all material particles, (b) an accelerated charge generates electromagnetic waves according to Maxwell's equations and Planck energy equation, and (c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schroedinger equation, mass, Einstein mass-energy relation, Newton's law of gravity,more » single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A conditioned solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.« less

Internally electrodynamic particle model: Its experimental basis and its predictions

NASA Astrophysics Data System (ADS)

Zheng-Johansson, J. X.

2010-03-01

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts: (a) electric charges present with all material particles, (b) an accelerated charge generates electromagnetic waves according to Maxwell’s equations and Planck energy equation, and (c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schrödinger equation, mass, Einstein mass-energy relation, Newton’s law of gravity, single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A conditioned solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.

Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving Source

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Turchaninov, V. I.; Tsynkov, S. V.

1999-01-01

We propose a family of algorithms for solving numerically a Cauchy problem for the three-dimensional wave equation. The sources that drive the equation (i.e., the right-hand side) are compactly supported in space for any given time; they, however, may actually move in space with a subsonic speed. The solution is calculated inside a finite domain (e.g., sphere) that also moves with a subsonic speed and always contains the support of the right-hand side. The algorithms employ a standard consistent and stable explicit finite-difference scheme for the wave equation. They allow one to calculate tile solution for arbitrarily long time intervals without error accumulation and with the fixed non-growing amount of tile CPU time and memory required for advancing one time step. The algorithms are inherently three-dimensional; they rely on the presence of lacunae in the solutions of the wave equation in oddly dimensional spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.

Spatiotemporal optical dark X solitary waves.

PubMed

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

2016-12-01

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

Ince's limits for confluent and double-confluent Heun equations

NASA Astrophysics Data System (ADS)

Bonorino Figueiredo, B. D.

2005-11-01

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable z, while the other is given by a series of modified Bessel functions and converges for ∣z∣>∣z0∣, where z0 denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when z0 tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schrödinger equation for inverse fourth- and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.

A model of recovering the parameters of fast nonlocal heat transport in magnetic fusion plasmas

NASA Astrophysics Data System (ADS)

Kukushkin, A. B.; Kulichenko, A. A.; Sdvizhenskii, P. A.; Sokolov, A. V.; Voloshinov, V. V.

2017-12-01

A model is elaborated for interpreting the initial stage of the fast nonlocal transport events, which exhibit immediate response, in the diffusion time scale, of the spatial profile of electron temperature to its local perturbation, while the net heat flux is directed opposite to ordinary diffusion (i.e. along the temperature gradient). We solve the inverse problem of recovering the kernel of the integral equation, which describes nonlocal (superdiffusive) transport of energy due to emission and absorption of electromagnetic (EM) waves with long free path and strong reflection from the vacuum vessel’s wall. To allow for the errors of experimental data, we use the method based on the regularized (in the framework of an ill-posed problem, using the parametric models) approximation of available experimental data. The model is applied to interpreting the data from stellarator LHD and tokamak TFTR. The EM wave transport is considered here in the single-group approximation, however the limitations of the physics model enable us to identify the spectral range of the EM waves which might be responsible for the observed phenomenon.

Weakly decaying solutions of nonlinear Schrödinger equation in the plane

NASA Astrophysics Data System (ADS)

Villarroel, Javier; Prada, Julia; Estévez, Pilar G.

2017-12-01

We show that the nonlinear Schrödinger equation in 2  +  1 dimensions possesses a class of regular and rationally decaying solutions associated to interacting solitons. The interesting dynamics of the associated pulses is studied in detail and related to homothetic Lagrange configurations of certain N- body problems. These solutions correspond to the discrete spectrum of the Lax pair associated operator. A natural characterization of this spectrum is given. We show that a certain subset of solutions correspond to rogue waves, localized along curves in the plane. Other configurations like grey solitons, cnoidal waves and general N- lumps solutions are also described.

On critical behaviour in generalized Kadomtsev-Petviashvili equations

NASA Astrophysics Data System (ADS)

Dubrovin, B.; Grava, T.; Klein, C.

2016-10-01

An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev-Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a special solution to an ordinary differential equation of the Painlevé I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture. The numerical study of the long time behaviour of these examples indicates persistence of dispersive shock waves in solutions to the (subcritical) KP equations, while in the supercritical KP equations a blow-up occurs after the formation of the dispersive shock waves.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

An Analytical Model of Periodic Waves in Shallow Water--Summary.

DTIC Science & Technology

1984-01-01

Petviashvili equation , and is based on a Riemann theta function of genus 2. These bi-periodic waves are direct generalizations of the well-known (simply... Petviashvili (KP; 1970) equation , (ut 6uux + U ) 3uyy -0, (1) is a scaled, dimensionless equation that describes the evolution of long water waves of...Fluid Mech., vol. 92, pp 691-715 Dubrovin, B. A., 1981, Russ. Math. Surveys, vol. 36, pp 11-92 Kadomtsev , B. B. & V. I. Petviashvili , 1970,) Soy. Phys

Convective wave breaking in the KdV equation

NASA Astrophysics Data System (ADS)

Brun, Mats K.; Kalisch, Henrik

2018-03-01

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

Lump Solitons in Surface Tension Dominated Flows

NASA Astrophysics Data System (ADS)

Milewski, Paul; Berger, Kurt

1999-11-01

The Kadomtsev-Petviashvilli I equation (KPI) which models small-amplitude, weakly three-dimensional surface-tension dominated long waves is integrable and allows for algebraically decaying lump solitary waves. It is not known (theoretically or numerically) whether the full free-surface Euler equations support such solutions. We consider an intermediate model, the generalised Benney-Luke equation (gBL) which is isotropic (not weakly three-dimensional) and contains KPI as a limit. We show numerically that: 1. gBL supports lump solitary waves; 2. These waves collide elastically and are stable; 3. They are generated by resonant flow over an obstacle.

Modeling unsteady sound refraction by coherent structures in a high-speed jet

NASA Astrophysics Data System (ADS)

Kan, Pinqing; Lewalle, Jacques

2011-11-01

We construct a visual model for the unsteady refraction of sound waves from point sources in a Ma = 0.6 jet. The mass and inviscid momentum equations give an equation governing acoustic fluctuations, including anisotropic propagation, attenuation and sources; differences with Lighthill's equation will be discussed. On this basis, the theory of characteristics gives canonical equations for the acoustic paths from any source into the far field. We model a steady mean flow in the near-jet region including the potential core and the mixing region downstream of its collapse, and model the convection of coherent structures as traveling wave perturbations of this mean flow. For a regular distribution of point sources in this region, we present a visual rendition of fluctuating distortion, lensing and deaf spots from the viewpoint of a far-field observer. Supported in part by AFOSR Grant FA-9550-10-1-0536 and by a Syracuse University Graduate Fellowship.

MSW (Magnetostatic Wave) Variable Time-Delay Techniques.

DTIC Science & Technology

1983-09-01

will be releasable to the general public, including foreign nations. RADC-TR-83-139 has been reviewed and is approved for publication. APPROVED: 4...film carries by itself an infinite set of modes ( exchange effects being ignored). In the absence of ground planes, the secular equation for a single... exchange (3 2 ) * spin waves, which produces regularly spaced narrow-band absorbtions or "notches" in the delay line transmission response. This effect is

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.

2007-01-01

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

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

PubMed

Kataoka; Tsutahara; Negoro

2000-04-03

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

Numerical solution of the generalized, dissipative KdV-RLW-Rosenau equation with a compact method

NASA Astrophysics Data System (ADS)

Apolinar-Fernández, Alejandro; Ramos, J. I.

2018-07-01

The nonlinear dynamics of the one-dimensional, generalized Korteweg-de Vries-regularized-long wave-Rosenau (KdV-RLW-Rosenau) equation with second- and fourth-order dissipative terms subject to initial Gaussian conditions is analyzed numerically by means of three-point, fourth-order accurate, compact finite differences for the discretization of the spatial derivatives and a trapezoidal method for time integration. By means of a Fourier analysis and global integration techniques, it is shown that the signs of both the fourth-order dissipative and the mixed fifth-order derivative terms must be negative. It is also shown that an increase of either the linear drift or the nonlinear convection coefficients results in an increase of the steepness, amplitude and speed of the right-propagating wave, whereas the speed and amplitude of the wave decrease as the power of the nonlinearity is increased, if the amplitude of the initial Gaussian condition is equal to or less than one. It is also shown that the wave amplitude and speed decrease and the curvature of the wave's trajectory increases as the coefficients of the second- and fourth-order dissipative terms are increased, while an increase of the RLW coefficient was found to decrease both the damping and the phase velocity, and generate oscillations behind the wave. For some values of the coefficients of both the fourth-order dissipative and the Rosenau terms, it has been found that localized dispersion shock waves may form in the leading part of the right-propagating wave, and that the formation of a train of solitary waves that result from the breakup of the initial Gaussian conditions only occurs in the absence of both Rosenau's, Kortweg-de Vries's and second- and fourth-order dissipative terms, and for some values of the amplitude and width of the initial condition and the RLW coefficient. It is also shown that negative values of the KdV term result in steeper, larger amplitude and faster waves and a train of oscillations behind the wave, whereas positive values of that coefficient may result in negative phase and group velocities, no wave breakup and oscillations ahead of the right-propagating wave.

Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

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

Sardar, Sankirtan; Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com; Das, K. P.

A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KPmore » and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.« less

Numerical studies of the KP line-solitons

NASA Astrophysics Data System (ADS)

Chakravarty, S.; McDowell, T.; Osborne, M.

2017-03-01

The Kadomtsev-Petviashvili (KP) equation admits a class of solitary wave solutions localized along distinct rays in the xy-plane, called the line-solitons, which describe the interaction of shallow water waves on a flat surface. These wave interactions have been observed on long, flat beaches, as well as have been recreated in laboratory experiments. In this paper, the line-solitons are investigated via direct numerical simulations of the KP equation, and the interactions of the evolved solitary wave patterns are studied. The objective is to obtain greater insight into solitary wave interactions in shallow water and to determine the extent the KP equation is a good model in describing these nonlinear interactions.

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

NASA Astrophysics Data System (ADS)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

Assessment of First- and Second-Order Wave-Excitation Load Models for Cylindrical Substructures: Preprint

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

Pereyra, Brandon; Wendt, Fabian; Robertson, Amy

2017-03-09

The hydrodynamic loads on an offshore wind turbine's support structure present unique engineering challenges for offshore wind. Two typical approaches used for modeling these hydrodynamic loads are potential flow (PF) and strip theory (ST), the latter via Morison's equation. This study examines the first- and second-order wave-excitation surge forces on a fixed cylinder in regular waves computed by the PF and ST approaches to (1) verify their numerical implementations in HydroDyn and (2) understand when the ST approach breaks down. The numerical implementation of PF and ST in HydroDyn, a hydrodynamic time-domain solver implemented as a module in the FASTmore » wind turbine engineering tool, was verified by showing the consistency in the first- and second-order force output between the two methods across a range of wave frequencies. ST is known to be invalid at high frequencies, and this study investigates where the ST solution diverges from the PF solution. Regular waves across a range of frequencies were run in HydroDyn for a monopile substructure. As expected, the solutions for the first-order (linear) wave-excitation loads resulting from these regular waves are similar for PF and ST when the diameter of the cylinder is small compared to the length of the waves (generally when the diameter-to-wavelength ratio is less than 0.2). The same finding applies to the solutions for second-order wave-excitation loads, but for much smaller diameter-to-wavelength ratios (based on wavelengths of first-order waves).« less

Assessment of First- and Second-Order Wave-Excitation Load Models for Cylindrical Substructures

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

Pereyra, Brandon; Wendt, Fabian; Robertson, Amy

2016-07-01

The hydrodynamic loads on an offshore wind turbine's support structure present unique engineering challenges for offshore wind. Two typical approaches used for modeling these hydrodynamic loads are potential flow (PF) and strip theory (ST), the latter via Morison's equation. This study examines the first- and second-order wave-excitation surge forces on a fixed cylinder in regular waves computed by the PF and ST approaches to (1) verify their numerical implementations in HydroDyn and (2) understand when the ST approach breaks down. The numerical implementation of PF and ST in HydroDyn, a hydrodynamic time-domain solver implemented as a module in the FASTmore » wind turbine engineering tool, was verified by showing the consistency in the first- and second-order force output between the two methods across a range of wave frequencies. ST is known to be invalid at high frequencies, and this study investigates where the ST solution diverges from the PF solution. Regular waves across a range of frequencies were run in HydroDyn for a monopile substructure. As expected, the solutions for the first-order (linear) wave-excitation loads resulting from these regular waves are similar for PF and ST when the diameter of the cylinder is small compared to the length of the waves (generally when the diameter-to-wavelength ratio is less than 0.2). The same finding applies to the solutions for second-order wave-excitation loads, but for much smaller diameter-to-wavelength ratios (based on wavelengths of first-order waves).« less

Small signal analysis of four-wave mixing in InAs/GaAs quantum-dot semiconductor optical amplifiers

NASA Astrophysics Data System (ADS)

Ma, Shaozhen; Chen, Zhe; Dutta, Niloy K.

2009-02-01

A model to study four-wave mixing (FWM) wavelength conversion in InAs-GaAs quantum-dot semiconductor optical amplifier is proposed. Rate equations involving two QD states are solved to simulate the carrier density modulation in the system, results show that the existence of QD excited state contributes to the ultra fast recover time for single pulse response by serving as a carrier reservoir for the QD ground state, its speed limitations are also studied. Nondegenerate four-wave mixing process with small intensity modulation probe signal injected is simulated using this model, a set of coupled wave equations describing the evolution of all frequency components in the active region of QD-SOA are derived and solved numerically. Results show that better FWM conversion efficiency can be obtained compared with the regular bulk SOA, and the four-wave mixing bandwidth can exceed 1.5 THz when the detuning between pump and probe lights is 0.5 nm.

Long waves in parallel flow in Hele-Shaw cells

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

Zeybek, M.; Yortsos, Y.C.

1991-09-09

The evolution of fluid interfaces in parallel flow in Hele-Shaw cells is studied theoretically and experimentally in the limit of large capillary number. It is shown that such interfaces support wave motion, the amplitude of which for long waves is governed by a set of Korteweg--de Vries and Airy equations. Experiments conducted in a long Hele-Shaw cell validate the theory in the symmetric case.

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

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Curtis, Christopher W.

2011-05-01

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

Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.

2009-09-01

Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.

Efficiency of perfectly matched layers for seismic wave modeling in second-order viscoelastic equations

NASA Astrophysics Data System (ADS)

Ping, Ping; Zhang, Yu; Xu, Yixian; Chu, Risheng

2016-12-01

In order to improve the perfectly matched layer (PML) efficiency in viscoelastic media, we first propose a split multi-axial PML (M-PML) and an unsplit convolutional PML (C-PML) in the second-order viscoelastic wave equations with the displacement as the only unknown. The advantage of these formulations is that it is easy and efficient to revise the existing codes of the second-order spectral element method (SEM) or finite-element method (FEM) with absorbing boundaries in a uniform equation, as well as more economical than the auxiliary differential equations PML. Three models which are easily suffered from late time instabilities are considered to validate our approaches. Through comparison the M-PML with C-PML efficiency of absorption and stability for long time simulation, it can be concluded that: (1) for an isotropic viscoelastic medium with high Poisson's ratio, the C-PML will be a sufficient choice for long time simulation because of its weak reflections and superior stability; (2) unlike the M-PML with high-order damping profile, the M-PML with second-order damping profile loses its stability in long time simulation for an isotropic viscoelastic medium; (3) in an anisotropic viscoelastic medium, the C-PML suffers from instabilities, while the M-PML with second-order damping profile can be a better choice for its superior stability and more acceptable weak reflections than the M-PML with high-order damping profile. The comparative analysis of the developed methods offers meaningful significance for long time seismic wave modeling in second-order viscoelastic wave equations.

Nonlinear optimization method of ship floating condition calculation in wave based on vector

NASA Astrophysics Data System (ADS)

Ding, Ning; Yu, Jian-xing

2014-08-01

Ship floating condition in regular waves is calculated. New equations controlling any ship's floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship's displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.

Validation and Comparison of 2D and 3D Codes for Nearshore Motion of Long Waves Using Benchmark Problems

NASA Astrophysics Data System (ADS)

Velioǧlu, Deniz; Cevdet Yalçıner, Ahmet; Zaytsev, Andrey

2016-04-01

Tsunamis are huge waves with long wave periods and wave lengths that can cause great devastation and loss of life when they strike a coast. The interest in experimental and numerical modeling of tsunami propagation and inundation increased considerably after the 2011 Great East Japan earthquake. In this study, two numerical codes, FLOW 3D and NAMI DANCE, that analyze tsunami propagation and inundation patterns are considered. Flow 3D simulates linear and nonlinear propagating surface waves as well as long waves by solving three-dimensional Navier-Stokes (3D-NS) equations. NAMI DANCE uses finite difference computational method to solve 2D depth-averaged linear and nonlinear forms of shallow water equations (NSWE) in long wave problems, specifically tsunamis. In order to validate these two codes and analyze the differences between 3D-NS and 2D depth-averaged NSWE equations, two benchmark problems are applied. One benchmark problem investigates the runup of long waves over a complex 3D beach. The experimental setup is a 1:400 scale model of Monai Valley located on the west coast of Okushiri Island, Japan. Other benchmark problem is discussed in 2015 National Tsunami Hazard Mitigation Program (NTHMP) Annual meeting in Portland, USA. It is a field dataset, recording the Japan 2011 tsunami in Hilo Harbor, Hawaii. The computed water surface elevation and velocity data are compared with the measured data. The comparisons showed that both codes are in fairly good agreement with each other and benchmark data. The differences between 3D-NS and 2D depth-averaged NSWE equations are highlighted. All results are presented with discussions and comparisons. Acknowledgements: Partial support by Japan-Turkey Joint Research Project by JICA on earthquakes and tsunamis in Marmara Region (JICA SATREPS - MarDiM Project), 603839 ASTARTE Project of EU, UDAP-C-12-14 project of AFAD Turkey, 108Y227, 113M556 and 213M534 projects of TUBITAK Turkey, RAPSODI (CONCERT_Dis-021) of CONCERT-Japan Joint Call and Istanbul Metropolitan Municipality are all acknowledged.

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

NASA Astrophysics Data System (ADS)

Paldor, N.

2017-12-01

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

Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-12-01

In this study, we presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface. The nonlinear higher order of extended KdV equations for the free surface displacement is generated. We derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory. The wave amplitude potential and the fluid pressure of the extended KdV equation in the form of solitary-wave solutions are deduced. We discussed and analyzed the stability of the obtained solutions and the movement role of the waves by making graphs of the exact solutions.

Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Grelu, Philippe; Mihalache, Dumitru

2017-11-01

This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks—the infinite nonlinear Schrödinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright-dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2  +  1)D nonlinear systems, namely, the Davey-Stewartson equation, the composite (2  +  1)D NLS equation, and the Kadomtsev-Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.

A model for the generation of two-dimensional surf beat

USGS Publications Warehouse

List, Jeffrey H.

1992-01-01

A finite difference model predicting group-forced long waves in the nearshore is constructed with two interacting parts: an incident wave model providing time-varying radiation stress gradients across the nearshore, and a long-wave model which solves the equations of motion for the forcing imposed by the incident waves. Both shallow water group-bound long waves and long waves generated by a time-varying breakpoint are simulated. Model-generated time series are used to calculate the cross correlation between wave groups and long waves through the surf zone. The cross-correlation signal first observed by Tucker (1950) is well predicted. For the first time, this signal is decomposed into the contributions from the two mechanisms of leaky mode forcing. Results show that the cross-correlation signal can be explained by bound long waves which are amplified, though strongly modified, through the surf zone before reflection from the shoreline. The breakpoint-forced long waves are added to the bound long waves at a phase of pi/2 and are a secondary contribution owing to their relatively small size.

A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

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

Goullet, Arnaud; Choi, Wooyoung; Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701

2011-01-15

The spatial evolution of nonlinear long-crested irregular waves characterized by the JONSWAP spectrum is studied numerically using a nonlinear wave model based on a pseudospectral (PS) method and the modified nonlinear Schroedinger (MNLS) equation. In addition, new laboratory experiments with two different spectral bandwidths are carried out and a number of wave probe measurements are made to validate these two wave models. Strongly nonlinear wave groups are observed experimentally and their propagation and interaction are studied in detail. For the comparison with experimental measurements, the two models need to be initialized with care and the initialization procedures are described. Themore » MNLS equation is found to approximate reasonably well for the wave fields with a relatively smaller Benjamin-Feir index, but the phase error increases as the propagation distance increases. The PS model with different orders of nonlinear approximation is solved numerically, and it is shown that the fifth-order model agrees well with our measurements prior to wave breaking for both spectral bandwidths.« less

Rogue periodic waves of the focusing nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Rogue periodic waves of the focusing nonlinear Schrödinger equation.

PubMed

Chen, Jinbing; Pelinovsky, Dmitry E

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Consistent three-equation model for thin films

NASA Astrophysics Data System (ADS)

Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

2017-11-01

Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

Nonlinear coherent structures of Alfvén wave in a collisional plasma

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

Jana, Sayanee; Chakrabarti, Nikhil; Ghosh, Samiran

2016-07-15

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

Fifth-order complex Korteweg-de Vries-type equations

NASA Astrophysics Data System (ADS)

Khanal, Netra; Wu, Jiahong; Yuan, Juan-Ming

2012-05-01

This paper studies spatially periodic complex-valued solutions of the fifth-order Korteweg-de Vries (KdV)-type equations. The aim is at several fundamental issues including the existence, uniqueness and finite-time blowup problems. Special attention is paid to the Kawahara equation, a fifth-order KdV-type equation. When a Burgers dissipation is attached to the Kawahara equation, we establish the existence and uniqueness of the Fourier series solution with the Fourier modes decaying algebraically in terms of the wave numbers. We also examine a special series solution to the Kawahara equation and prove the convergence and global regularity of such solutions associated with a single mode initial data. In addition, finite-time blowup results are discussed for the special series solution of the Kawahara equation.

Stability of Planar Rarefaction Wave to 3D Full Compressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Li, Lin-an; Wang, Teng; Wang, Yi

2018-05-01

We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier-Stokes equations with the heat-conductivities in an infinite long flat nozzle domain {R × T^2} . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x 2 and x 3 and its interactions with the planar rarefaction wave in x 1 direction.

The KP Approximation Under a Weak Coriolis Forcing

NASA Astrophysics Data System (ADS)

Melinand, Benjamin

2018-02-01

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.

Numerical Study of Nonlinear Structures of Locally Excited Marangoni Convection in the Long-Wave Approximation

NASA Astrophysics Data System (ADS)

Wertgeim, Igor I.

2018-02-01

We investigate stationary and non-stationary solutions of nonlinear equations of the long-wave approximation for the Marangoni convection caused by a localized source of heat or a surface active impurity (surfactant) in a thin horizontal layer of a viscous incompressible fluid with a free surface. The distribution of heat or concentration flux is determined by the uniform vertical gradient of temperature or impurity concentration, distorted by the imposition of a slightly inhomogeneous heating or of surfactant, localized in the horizontal plane. The lower boundary of the layer is considered thermally insulated or impermeable, whereas the upper boundary is free and deformable. The equations obtained in the long-wave approximation are formulated in terms of the amplitudes of the temperature distribution or impurity concentration, deformation of the surface, and vorticity. For a simplification of the problem, a sequence of nonlinear equations is obtained, which in the simplest form leads to a nonlinear Schrödinger equation with a localized potential. The basic state of the system, its dependence on the parameters and stability are investigated. For stationary solutions localized in the region of the surface tension inhomogeneity, domains of parameters corresponding to different spatial patterns are delineated.

On the instability of wave-fields with JONSWAP spectra to inhomogeneous disturbances, and the consequent long-time evolution

NASA Astrophysics Data System (ADS)

Ribal, A.; Stiassnie, M.; Babanin, A.; Young, I.

2012-04-01

The instability of two-dimensional wave-fields and its subsequent evolution in time are studied by means of the Alber equation for narrow-banded random surface-waves in deep water subject to inhomogeneous disturbances. A linear partial differential equation (PDE) is obtained after applying an inhomogeneous disturbance to the Alber's equation and based on the solution of this PDE, the instability of the ocean wave surface is studied for a JONSWAP spectrum, which is a realistic ocean spectrum with variable directional spreading and steepness. The steepness of the JONSWAP spectrum depends on γ and α which are the peak-enhancement factor and energy scale of the spectrum respectively and it is found that instability depends on the directional spreading, α and γ. Specifically, if the instability stops due to the directional spreading, increase of the steepness by increasing α or γ can reactivate it. This result is in qualitative agreement with the recent large-scale experiment and new theoretical results. In the instability area of α-γ plane, a long-time evolution has been simulated by integrating Alber's equation numerically and recurrent evolution is obtained which is the stochastic counterpart of the Fermi-Pasta-Ulam recurrence obtained for the cubic Schrödinger equation.

Maintenance of Austral Summertime Upper-Tropospheric Circulation over Tropical South America: The Bolivian High-Nordeste Low System.

NASA Astrophysics Data System (ADS)

Chen, Tsing-Chang; Weng, Shu-Ping; Schubert, Siegfried

1999-07-01

Using the NASA/GEOS reanalysis data for 1980-95, the austral-summer stationary eddies in the tropical-subtropical Southern Hemisphere are examined in two wave regimes: long and short wave (wave 1 and waves 2-6, respectively). The basic structure of the Bolivian high-Nordeste low (BH-NL) system is formed by a short-wave train across South America but modulated by the long-wave regime. The short-wave train exhibits a monsoonlike vertical phase reversal in the midtroposphere and a quarter-wave phase shift relative to the divergent circulation. As inferred from (a) the spatial relationship between the streamfunction and velocity potential and (b) the structure of the divergent circulation, the short-wave train forming the BH-NL system is maintained by South American local heating and remote African heating, while the long-wave regime is maintained by western tropical Pacific heating.The maintenance of the stationary waves in the two wave regimes is further illustrated by a simple diagnostic scheme that includes the velocity-potential maintenance equation (which links velocity potential and diabatic heating) and the streamfunction budget (which is the inverse Laplacian transform of the vorticity equation). Some simple relationships between streamfunction and velocity potential for both wave regimes are established to substantiate the links between diabatic heating and streamfunction; of particular interest is a Sverdrup balance in the short-wave regime. This simplified vorticity equation explains the vertical structure of the short-wave train associated with the BH-NL system and its spatial relationship with the divergent circulation.Based upon the diagnostic analysis of its maintenance a simple forced barotropic model is adopted to simulate the BH-NL system with idealized forcings, which imitates the real 200-mb divergence centers over South America, Africa, and the tropical Pacific. Numerical simulations demonstrate that the formation of the BH-NL system is affected not only by the African remote forcing, but also by the tropical Pacific forcing.

Rogue waves and large deviations in deep sea.

PubMed

Dematteis, Giovanni; Grafke, Tobias; Vanden-Eijnden, Eric

2018-01-30

The appearance of rogue waves in deep sea is investigated by using the modified nonlinear Schrödinger (MNLS) equation in one spatial dimension with random initial conditions that are assumed to be normally distributed, with a spectrum approximating realistic conditions of a unidirectional sea state. It is shown that one can use the incomplete information contained in this spectrum as prior and supplement this information with the MNLS dynamics to reliably estimate the probability distribution of the sea surface elevation far in the tail at later times. Our results indicate that rogue waves occur when the system hits unlikely pockets of wave configurations that trigger large disturbances of the surface height. The rogue wave precursors in these pockets are wave patterns of regular height, but with a very specific shape that is identified explicitly, thereby allowing for early detection. The method proposed here combines Monte Carlo sampling with tools from large deviations theory that reduce the calculation of the most likely rogue wave precursors to an optimization problem that can be solved efficiently. This approach is transferable to other problems in which the system's governing equations contain random initial conditions and/or parameters.

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

PubMed

Yu, Fajun

2017-02-01

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

Dissipation-preserving spectral element method for damped seismic wave equations

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai; Wang, Yushun

2017-12-01

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

Self-dual form of Ruijsenaars-Schneider models and ILW equation with discrete Laplacian

NASA Astrophysics Data System (ADS)

Zabrodin, A.; Zotov, A.

2018-02-01

We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable) glN Ruijsenaars-Schneider model. It is based on the first order equations in N + M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars-Schneider model. In the elliptic case it holds M = N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero-Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars-Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero-Moser models arise from ordinary intermediate long wave and Benjamin-Ono equations.

Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: nonspherical Schwarzschild waves and singularities at null infinity

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Hennig, Jörg

2018-03-01

We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Frauendiener and Hennig (2017 Class. Quantum Grav. 34 045005), to the case of general, nonsymmetric solutions. A key element of our approach is the modern standard representation of spacelike infinity as a cylinder. With a decomposition into spherical harmonics, we reduce the four-dimensional wave equation to a family of two-dimensional equations. These equations can be used to study the behaviour at the cylinder, where the solutions turn out to have, in general, logarithmic singularities at infinitely many orders. We derive regularity conditions that may be imposed on the initial data, in order to avoid the first singular terms. We then demonstrate that the fully pseudospectral time evolution scheme can be applied to this problem leading to a highly accurate numerical reconstruction of the nonsymmetric solutions. We are particularly interested in the behaviour of the solutions at future null infinity, and we numerically show that the singularities spread to null infinity from the critical set, where the cylinder approaches null infinity. The observed numerical behaviour is consistent with similar logarithmic singularities found analytically on the critical set. Finally, we demonstrate that even solutions with singularities at low orders can be obtained with high accuracy by virtue of a coordinate transformation that converts solutions with logarithmic singularities into smooth solutions.

Rogue waves in the multicomponent Mel'nikov system and multicomponent Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Sun, Baonan; Lian, Zhan

2018-02-01

By virtue of the bilinear method and the KP hierarchy reduction technique, exact explicit rational solutions of the multicomponent Mel'nikov equation and the multicomponent Schrödinger-Boussinesq equation are constructed, which contain multicomponent short waves and single-component long wave. For the multicomponent Mel'nikov equation, the fundamental rational solutions possess two different behaviours: lump and rogue wave. It is shown that the fundamental (simplest) rogue waves are line localised waves which arise from the constant background with a line profile and then disappear into the constant background again. The fundamental line rogue waves can be classified into three: bright, intermediate and dark line rogue waves. Two subclasses of non-fundamental rogue waves, i.e., multirogue waves and higher-order rogue waves are discussed. The multirogue waves describe interaction of several fundamental line rogue waves, in which interesting wave patterns appear in the intermediate time. Higher-order rogue waves exhibit dynamic behaviours that the wave structures start from lump and then retreat back to it. Moreover, by taking the parameter constraints further, general higher-order rogue wave solutions for the multicomponent Schrödinger-Boussinesq system are generated.

Do the freak waves exist in soliton gas?

NASA Astrophysics Data System (ADS)

Shurgalina, Ekaterina; Pelinovsky, Efim

2016-04-01

The possibility of short-lived anomalous large waves (rogue waves) in soliton gas in the frameworks of integrable models like the Korteweg - de Vries - type equations is studied. It is shown that the dynamics of heteropolar soliton gas differs sufficiently from the dynamics of unipolar soliton fields. In particular, in the wave fields consisting of solitons with different polarities the freak wave appearance is possible. It is shown numerically in [Shurgalina and Pelinovsky, 2015]. Freak waves in the framework of the modified Korteweg-de Vries equation have been studied previously in the case of narrowband initial conditions [Grimshaw et al, 2005, 2010; Talipova, 2011]. In this case, the mechanism of freak wave generation was modulation instability of modulated quasi-sinusoidal wave packets. At the same time the modulation instability of modulated cnoidal waves was studied in the mathematical work [Driscoll & O'Neil, 1976]. Since a sequence of solitary waves can be a special case of cnoidal wave, the modulation instability can be a possible mechanism of freak wave appearance in a soliton gas. Thus, we expect that rogue wave phenomenon in soliton gas appears in nonlinear integrable models admitting an existence of modulation instability of periodic waves (like cnoidal waves). References: 1. Shurgalina E.G., Pelinovsky E.N. Dynamics of irregular wave ensembles in the coastal zone, Nizhny Novgorod State Technical University n.a. R.E. Alekseev. - Nizhny Novgorod, 2015, 179 pp. 2. Grimshaw R., Pelinovsky E., Talipova T., Sergeeva A. Rogue internal waves in the ocean: long wave model. European Physical Journal Special Topics, 2010, 185, 195 - 208. 3. Grimshaw R., Pelinovsky E., Talipova T., Ruderman M. Erdelyi R. Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg-de Vries equation. Studied Applied Mathematics, 2005, 114 (2), 189. 4. Talipova T.G. Mechanisms of internal freak waves, Fundamental and Applied Hydrophysics, 2011, 4(4), 58-70. 5. Driscoll F., O'Neil T.M. Modulational instability of cnoidal wave solutions of the modified Korteweg-de Vries equation. Journal of Mathematical Physics, 1976, 17 (7), 1196-1200.

Drift-wave turbulence and zonal flow generation.

PubMed

Balescu, R

2003-10-01

Drift-wave turbulence in a plasma is analyzed on the basis of the wave Liouville equation, describing the evolution of the distribution function of wave packets (quasiparticles) characterized by position x and wave vector k. A closed kinetic equation is derived for the ensemble-averaged part of this function by the methods of nonequilibrium statistical mechanics. It has the form of a non-Markovian advection-diffusion equation describing coupled diffusion processes in x and k spaces. General forms of the diffusion coefficients are obtained in terms of Lagrangian velocity correlations. The latter are calculated in the decorrelation trajectory approximation, a method recently developed for an accurate measure of the important trapping phenomena of particles in the rugged electrostatic potential. The analysis of individual decorrelation trajectories provides an illustration of the fragmentation of drift-wave structures in the radial direction and the generation of long-wavelength structures in the poloidal direction that are identified as zonal flows.

Regularized Dual Averaging Image Reconstruction for Full-Wave Ultrasound Computed Tomography.

PubMed

Matthews, Thomas P; Wang, Kun; Li, Cuiping; Duric, Neb; Anastasio, Mark A

2017-05-01

Ultrasound computed tomography (USCT) holds great promise for breast cancer screening. Waveform inversion-based image reconstruction methods account for higher order diffraction effects and can produce high-resolution USCT images, but are computationally demanding. Recently, a source encoding technique has been combined with stochastic gradient descent (SGD) to greatly reduce image reconstruction times. However, this method bundles the stochastic data fidelity term with the deterministic regularization term. This limitation can be overcome by replacing SGD with a structured optimization method, such as the regularized dual averaging method, that exploits knowledge of the composition of the cost function. In this paper, the dual averaging method is combined with source encoding techniques to improve the effectiveness of regularization while maintaining the reduced reconstruction times afforded by source encoding. It is demonstrated that each iteration can be decomposed into a gradient descent step based on the data fidelity term and a proximal update step corresponding to the regularization term. Furthermore, the regularization term is never explicitly differentiated, allowing nonsmooth regularization penalties to be naturally incorporated. The wave equation is solved by the use of a time-domain method. The effectiveness of this approach is demonstrated through computer simulation and experimental studies. The results suggest that the dual averaging method can produce images with less noise and comparable resolution to those obtained by the use of SGD.

Diffusion of strongly magnetized cosmic ray particles in a turbulent medium

NASA Technical Reports Server (NTRS)

Ptuskin, V. S.

1985-01-01

Cosmic ray (CR) propagation in a turbulent medium is usually considered in the diffusion approximation. Here, the diffusion equation is obtained for strongly magnetized particles in the general form. The influence of a large-scale random magnetic field on CR propagation in interstellar medium is discussed. Cosmic rays are assumed to propagate in a medium with a regular field H and an ensemble of random MHD waves. The energy density of waves on scales smaller than the free path 1 of CR particles is small. The collision integral of the general form which describes interaction between relativistic particles and waves in the quasilinear approximation is used.

Structure-preserving spectral element method in attenuating seismic wave modeling

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai

2016-04-01

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

Nonideal Rayleigh–Taylor mixing

PubMed Central

Lim, Hyunkyung; Iwerks, Justin; Glimm, James; Sharp, David H.

2010-01-01

Rayleigh–Taylor mixing is a classical hydrodynamic instability that occurs when a light fluid pushes against a heavy fluid. The two main sources of nonideal behavior in Rayleigh–Taylor (RT) mixing are regularizations (physical and numerical), which produce deviations from a pure Euler equation, scale invariant formulation, and nonideal (i.e., experimental) initial conditions. The Kolmogorov theory of turbulence predicts stirring at all length scales for the Euler fluid equations without regularization. We interpret mathematical theories of existence and nonuniqueness in this context, and we provide numerical evidence for dependence of the RT mixing rate on nonideal regularizations; in other words, indeterminacy when modeled by Euler equations. Operationally, indeterminacy shows up as nonunique solutions for RT mixing, parametrized by Schmidt and Prandtl numbers, in the large Reynolds number (Euler equation) limit. Verification and validation evidence is presented for the large eddy simulation algorithm used here. Mesh convergence depends on breaking the nonuniqueness with explicit use of the laminar Schmidt and Prandtl numbers and their turbulent counterparts, defined in terms of subgrid scale models. The dependence of the mixing rate on the Schmidt and Prandtl numbers and other physical parameters will be illustrated. We demonstrate numerically the influence of initial conditions on the mixing rate. Both the dominant short wavelength initial conditions and long wavelength perturbations are observed to play a role. By examination of two classes of experiments, we observe the absence of a single universal explanation, with long and short wavelength initial conditions, and the various physical and numerical regularizations contributing in different proportions in these two different contexts. PMID:20615983

Eulerian Simulation of Acoustic Waves Over Long Range in Realistic Environments

NASA Astrophysics Data System (ADS)

Chitta, Subhashini; Steinhoff, John

2015-11-01

In this paper, we describe a new method for computation of long-range acoustics. The approach is a hybrid of near and far-field methods, and is unique in its Eulerian treatment of the far-field propagation. The near-field generated by any existing method to project an acoustic solution onto a spherical surface that surrounds a source. The acoustic field on this source surface is then extended to an arbitrarily large distance in an inhomogeneous far-field. This would normally require an Eulerian solution of the wave equation. However, conventional Eulerian methods have prohibitive grid requirements. This problem is overcome by using a new method, ``Wave Confinement'' (WC) that propagates wave-identifying phase fronts as nonlinear solitary waves that live on grid indefinitely. This involves modification of wave equation by the addition of a nonlinear term without changing the basic conservation properties of the equation. These solitary waves can then be used to ``carry'' the essential integrals of the acoustic wave. For example, arrival time, centroid position and other properties that are invariant as the wave passes a grid point. Because of this property the grid can be made as coarse as necessary, consistent with overall accuracy to resolve atmospheric/ground variations. This work is being funded by the U.S. Army under a Small Business Innovation Research (SBIR) program (contract number: # W911W6-12-C-0036). The authors would like to thank Dr. Frank Caradonna and Dr. Ben W. Sim for this support.

Dynamics of Whistler-mode Waves Below LHR Frequency: Application for the Equatorial Noise

NASA Astrophysics Data System (ADS)

Balikhin, M. A.; Shklyar, D. R.

2017-12-01

Plasma waves that are regularly observed in the vicinity of geomagnetic equator since 1970's are often referred to as "equatorial noise" or "equatorial magnetosonic" emission. Currently, it is accepted that these waves can have significant effects on both the processes of loss and acceleration of energetic electrons within the radiation belts. A model to explain the observed features of the equatorial noise is presented. It is assumed that the loss-cone instability of supra-thermal ions is the reason for their generation. It is argued that as these waves propagate their growth/damping rate changes and, therefore the integral wave amplification is more important to explain observed spectral features than the local growth rate. The qualitative correspondence of Cluster observations with dynamical spectra arising from the model is shown.

On the Asymptotic Regimes and the Strongly Stratified Limit of Rotating Boussinesq Equations

NASA Technical Reports Server (NTRS)

Babin, A.; Mahalov, A.; Nicolaenko, B.; Zhou, Y.

1997-01-01

Asymptotic regimes of geophysical dynamics are described for different Burger number limits. Rotating Boussinesq equations are analyzed in the asymptotic limit, of strong stratification in the Burger number of order one situation as well as in the asymptotic regime of strong stratification and weak rotation. It is shown that in both regimes horizontally averaged buoyancy variable is an adiabatic invariant for the full Boussinesq system. Spectral phase shift corrections to the buoyancy time scale associated with vertical shearing of this invariant are deduced. Statistical dephasing effects induced by turbulent processes on inertial-gravity waves are evidenced. The 'split' of the energy transfer of the vortical and the wave components is established in the Craya-Herring cyclic basis. As the Burger number increases from zero to infinity, we demonstrate gradual unfreezing of energy cascades for ageostrophic dynamics. The energy spectrum and the anisotropic spectral eddy viscosity are deduced with an explicit dependence on the anisotropic rotation/stratification time scale which depends on the vertical aspect ratio parameter. Intermediate asymptotic regime corresponding to strong stratification and weak rotation is analyzed where the effects of weak rotation are accounted for by an asymptotic expansion with full control (saturation) of vertical shearing. The regularizing effect of weak rotation differs from regularizations based on vertical viscosity. Two scalar prognostic equations for ageostrophic components (divergent velocity potential and geostrophic departure ) are obtained.

PHYSICS OF OUR DAYS: Nonlinear long waves on water and solitons

NASA Astrophysics Data System (ADS)

Zeytounian, R. Kh

1995-12-01

The water wave problem has been pivotal in the history of nonlinear wave theory. This problem is one of the most interesting and successful applications of nonlinear hydrodynamics. Waves on the free surface of a body of water (perfect liquid) have always been a fascinating subject, for they represent a familiar yet complex phenomenon, easy to observe but very difficult to describe! The archetypical model equations of Kordeweg and de Vries and of Boussinesq, for example, were originally derived as approximations for water waves, and research into the problem has been sustained vigorously up to the present day. In the present paper, the derivation of the model equations is given in depth and rational use is made of asymptotic methods. Indeed, it is important to understand that in some cases the derivation of these approximate equations is intuitive and heuristic. In fact, it is not clear how to insert the model equation under consideration into a hierarchy of rational approximations, which in turn result from the exact formulation of the selected water wave problem.

Lagrangian averaging, nonlinear waves, and shock regularization

NASA Astrophysics Data System (ADS)

Bhat, Harish S.

In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in both material and spatial frames. Writing the resulting equations of motion requires certain Lie-algebraic calculations that we carry out in detail for expository purposes. Next, we extend the derivation of the Lagrangian averaged Euler (LAE-alpha) equations to the case of barotropic compressible flows. The derivation in this thesis involves averaging over a tube of trajectories etaepsilon centered around a given Lagrangian flow eta. With this tube framework, the LAE-alpha equations are derived by following a simple procedure: start with a given action, expand via Taylor series in terms of small-scale fluid fluctuations xi, truncate, average, and then model those terms that are nonlinear functions of xi. We then analyze a one-dimensional subcase of the general models derived above. We prove the existence of a large family of traveling wave solutions. Computing the dispersion relation for this model, we find it is nonlinear, implying that the equation is dispersive. We carry out numerical experiments that show that the model possesses smooth, bounded solutions that display interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a nonlinear smoothing term that we have added to the inviscid Burgers equation. We show the existence of a large family of traveling front solutions. We analyze the initial-value problem and prove well-posedness for a certain class of initial data. We prove that in the zero-alpha limit, without any standard viscosity, solutions of the PDE converge strongly to weak solutions of the inviscid Burgers equation. We provide numerical evidence that this limit satisfies an entropy inequality for the inviscid Burgers equation. We demonstrate a Hamiltonian structure for the PDE.

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

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

Ruban, V. P., E-mail: ruban@itp.ac.ru

2015-05-15

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.

PubMed

Deng, Yongbo; Korvink, Jan G

2016-05-01

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

PubMed Central

Korvink, Jan G.

2016-01-01

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable. PMID:27279766

Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves

NASA Technical Reports Server (NTRS)

Fibich, G.; Ilan, B.; Tsynkov, S.

2002-01-01

The critical nonlinear Schrodinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L(sub 2) norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e.. collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the 'parent' equation, may nonetheless exist and remain regular everywhere, in particular for those initial conditions (input powers) that lead to blowup in the NLS. In the current study, we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem). Linear damping is introduced in much the same way as done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NHS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular. whereas the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than that for the NLS is accounted for by precisely those mechanisms, that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering.

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

Krasnobaeva, L. A., E-mail: kla1983@mail.ru; Siberian State Medical University Moscowski Trakt 2, Tomsk, 634050; Shapovalov, A. V.

Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on dynamics local conformational perturbations (kink) propagating along the DNA molecule is investigated. Such waves have an important role in the regulation of important biological processes in living systems at the molecular level. As a dynamic model of DNA was used a modified sine-Gordon equation, simulating the rotational oscillations of bases in one of the chains DNA. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the frameworkmore » of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker– Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum. Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine–Gordon model. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker–Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum.« less

Rogue wave modes for a derivative nonlinear Schrödinger model.

PubMed

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

2014-03-01

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

Effect of small floating disks on the propagation of gravity waves

NASA Astrophysics Data System (ADS)

De Santi, F.; Olla, P.

2017-04-01

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

Hybrid soliton solutions in the (2+1)-dimensional nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Chen, Meidan; Li, Biao

2017-11-01

Rational solutions and hybrid solutions from N-solitons are obtained by using the bilinear method and a long wave limit method. Line rogue waves and lumps in the (2+1)-dimensional nonlinear Schrödinger (NLS) equation are derived from two-solitons. Then from three-solitons, hybrid solutions between kink soliton with breathers, periodic line waves and lumps are derived. Interestingly, after the collision, the breathers are kept invariant, but the amplitudes of the periodic line waves and lumps change greatly. For the four-solitons, the solutions describe as breathers with breathers, line rogue waves or lumps. After the collision, breathers and lumps are kept invariant, but the line rogue wave has a great change.

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures.

PubMed

Khusnutdinova, Karima R; Samsonov, Alexander M; Zakharov, Alexey S

2009-05-01

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

Long-range intercellular Ca2+ wave patterns

NASA Astrophysics Data System (ADS)

Tabi, C. B.; Maïna, I.; Mohamadou, A.; Ekobena, H. P. F.; Kofané, T. C.

2015-10-01

Modulational instability is utilized to investigate intercellular Ca2+ wave propagation in an array of diffusively coupled cells. Cells are supposed to be connected via paracrine signaling, where long-range effects, due to the presence of extracellular messengers, are included. The multiple-scale expansion is used to show that the whole dynamics of Ca2+ waves, from the endoplasmic reticulum to the cytosol, can be reduced to a single differential-difference nonlinear equation whose solutions are assumed to be plane waves. Their linear stability analysis is studied, with emphasis on the impact of long-range coupling, via the range parameter s. It is shown that s, as well as the number of interacting cells, importantly modifies the features of modulational instability, as small values of s imply a strong coupling, and increasing its value rather reduces the problem to a first-neighbor one. Our theoretical findings are numerically tested, as the generic equations are fully integrated, leading to the emergence of nonlinear patterns of Ca2+ waves. Strong long-range coupling is pictured by extended trains of breather-like structures whose frequency decreases with increasing s. We also show numerically that the number of interacting cells plays on the spatio-temporal formation of Ca2+ patterns, whilst the quasi-perfect intercellular communication depends on the paracrine coupling parameter.

Linear and nonlinear propagation of water wave groups

NASA Technical Reports Server (NTRS)

Pierson, W. J., Jr.; Donelan, M. A.; Hui, W. H.

1992-01-01

Results are presented from a study of the evolution of waveforms with known analytical group shapes, in the form of both transient wave groups and the cloidal (cn) and dnoidal (dn) wave trains as derived from the nonlinear Schroedinger equation. The waveforms were generated in a long wind-wave tank of the Canada Centre for Inland Waters. It was found that the low-amplitude transients behaved as predicted by the linear theory and that the cn and dn wave trains of moderate steepness behaved almost as predicted by the nonlinear Schroedinger equation. Some of the results did not fit into any of the available theories for waves on water, but they provide important insight on how actual groups of waves propagate and on higher-order effects for a transient waveform.

Bound vector solitons and soliton complexes for the coupled nonlinear Schrödinger equations.

PubMed

Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Wen-Jun; Liu, Ying

2009-12-01

Dynamic features describing the collisions of the bound vector solitons and soliton complexes are investigated for the coupled nonlinear Schrödinger (CNLS) equations, which model the propagation of the multimode soliton pulses under some physical situations in nonlinear fiber optics. Equations of such type have also been seen in water waves and plasmas. By the appropriate choices of the arbitrary parameters for the multisoliton solutions derived through the Hirota bilinear method, the periodic structures along the propagation are classified according to the relative relations of the real wave numbers. Furthermore, parameters are shown to control the intensity distributions and interaction patterns for the bound vector solitons and soliton complexes. Transformations of the soliton types (shape changing with intensity redistribution) during the collisions of those stationary structures with the regular one soliton are discussed, in which a class of inelastic properties is involved. Discussions could be expected to be helpful in interpreting such structures in the multimode nonlinear fiber optics and equally applied to other systems governed by the CNLS equations, e.g., the plasma physics and Bose-Einstein condensates.

Description of waves in inhomogeneous domains using Heun's equation

NASA Astrophysics Data System (ADS)

Bednarik, M.; Cervenka, M.

2018-04-01

There are a number of model equations describing electromagnetic, acoustic or quantum waves in inhomogeneous domains and some of them are of the same type from the mathematical point of view. This isomorphism enables us to use a unified approach to solving the corresponding equations. In this paper, the inhomogeneity is represented by a trigonometric spatial distribution of a parameter determining the properties of an inhomogeneous domain. From the point of view of modeling, this trigonometric parameter function can be smoothly connected to neighboring constant-parameter regions. For this type of distribution, exact local solutions of the model equations are represented by the local Heun functions. As the interval for which the solution is sought includes two regular singular points. For this reason, a method is proposed which resolves this problem only based on the local Heun functions. Further, the transfer matrix for the considered inhomogeneous domain is determined by means of the proposed method. As an example of the applicability of the presented solutions the transmission coefficient is calculated for the locally periodic structure which is given by an array of asymmetric barriers.

Canonical structures for dispersive waves in shallow water

NASA Astrophysics Data System (ADS)

Neyzi, Fahrünisa; Nutku, Yavuz

1987-07-01

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

Quantum transport with long-range steps on Watts-Strogatz networks

NASA Astrophysics Data System (ADS)

Wang, Yan; Xu, Xin-Jian

2016-07-01

We study transport dynamics of quantum systems with long-range steps on the Watts-Strogatz network (WSN) which is generated by rewiring links of the regular ring. First, we probe physical systems modeled by the discrete nonlinear schrödinger (DNLS) equation. Using the localized initial condition, we compute the time-averaged occupation probability of the initial site, which is related to the nonlinearity, the long-range steps and rewiring links. Self-trapping transitions occur at large (small) nonlinear parameters for coupling ɛ=-1 (1), as long-range interactions are intensified. The structure disorder induced by random rewiring, however, has dual effects for ɛ=-1 and inhibits the self-trapping behavior for ɛ=1. Second, we investigate continuous-time quantum walks (CTQW) on the regular ring ruled by the discrete linear schrödinger (DLS) equation. It is found that only the presence of the long-range steps does not affect the efficiency of the coherent exciton transport, while only the allowance of random rewiring enhances the partial localization. If both factors are considered simultaneously, localization is greatly strengthened, and the transport becomes worse.

Multiple attenuation to reflection seismic data using Radon filter and Wave Equation Multiple Rejection (WEMR) method

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

Erlangga, Mokhammad Puput

Separation between signal and noise, incoherent or coherent, is important in seismic data processing. Although we have processed the seismic data, the coherent noise is still mixing with the primary signal. Multiple reflections are a kind of coherent noise. In this research, we processed seismic data to attenuate multiple reflections in the both synthetic and real seismic data of Mentawai. There are several methods to attenuate multiple reflection, one of them is Radon filter method that discriminates between primary reflection and multiple reflection in the τ-p domain based on move out difference between primary reflection and multiple reflection. However, inmore » case where the move out difference is too small, the Radon filter method is not enough to attenuate the multiple reflections. The Radon filter also produces the artifacts on the gathers data. Except the Radon filter method, we also use the Wave Equation Multiple Elimination (WEMR) method to attenuate the long period multiple reflection. The WEMR method can attenuate the long period multiple reflection based on wave equation inversion. Refer to the inversion of wave equation and the magnitude of the seismic wave amplitude that observed on the free surface, we get the water bottom reflectivity which is used to eliminate the multiple reflections. The WEMR method does not depend on the move out difference to attenuate the long period multiple reflection. Therefore, the WEMR method can be applied to the seismic data which has small move out difference as the Mentawai seismic data. The small move out difference on the Mentawai seismic data is caused by the restrictiveness of far offset, which is only 705 meter. We compared the real free multiple stacking data after processing with Radon filter and WEMR process. The conclusion is the WEMR method can more attenuate the long period multiple reflection than the Radon filter method on the real (Mentawai) seismic data.« less

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

NASA Astrophysics Data System (ADS)

Deconinck, Bernard; Upsal, Jeremy

2018-07-01

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

A depth-averaged 2-D shallow water model for breaking and non-breaking long waves affected by rigid vegetation

USDA-ARS?s Scientific Manuscript database

This paper presents a depth-averaged two-dimensional shallow water model for simulating long waves in vegetated water bodies under breaking and non-breaking conditions. The effects of rigid vegetation are modelled in the form of drag and inertia forces as sink terms in the momentum equations. The dr...

Higher-Order Hamiltonian Model for Unidirectional Water Waves

NASA Astrophysics Data System (ADS)

Bona, J. L.; Carvajal, X.; Panthee, M.; Scialom, M.

2018-04-01

Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of these more complex equations is that their solutions corresponding to physically relevant initial perturbations of the rest state may be accurate on a much longer timescale. The initial value problem for the class of equations that emerges from our derivation is then considered. A local well-posedness theory is straightforwardly established by a contraction mapping argument. A subclass of these equations possess a special Hamiltonian structure that implies the local theory can be continued indefinitely.

Numerical modeling of Gaussian beam propagation and diffraction in inhomogeneous media based on the complex eikonal equation

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Hui

2018-05-01

Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss-Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.

Propagation of large-amplitude waves on dielectric liquid sheets in a tangential electric field: exact solutions in three-dimensional geometry.

PubMed

Zubarev, Nikolay M; Zubareva, Olga V

2010-10-01

Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.

A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics

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

Shao, Yan-Lin, E-mail: yanlin.shao@dnvgl.com; Faltinsen, Odd M.

2014-10-01

We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods,more » e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.« less

Analytical solution of reaction-diffusion equations for calcium wave propagation in a starburst amacrine cell.

PubMed

Poznanski, R R

2010-09-01

A reaction-diffusion model is presented to encapsulate calcium-induced calcium release (CICR) as a potential mechanism for somatofugal bias of dendritic calcium movement in starburst amacrine cells. Calcium dynamics involves a simple calcium extrusion (pump) and a buffering mechanism of calcium binding proteins homogeneously distributed over the plasma membrane of the endoplasmic reticulum within starburst amacrine cells. The system of reaction-diffusion equations in the excess buffer (or low calcium concentration) approximation are reformulated as a nonlinear Volterra integral equation which is solved analytically via a regular perturbation series expansion in response to calcium feedback from a continuously and uniformly distributed calcium sources. Calculation of luminal calcium diffusion in the absence of buffering enables a wave to travel at distances of 120 μm from the soma to distal tips of a starburst amacrine cell dendrite in 100 msec, yet in the presence of discretely distributed calcium-binding proteins it is unknown whether the propagating calcium wave-front in the somatofugal direction is further impeded by endogenous buffers. If so, this would indicate CICR to be an unlikely mechanism of retinal direction selectivity in starburst amacrine cells.

General high-order breathers and rogue waves in the (3 + 1) -dimensional KP-Boussinesq equation

NASA Astrophysics Data System (ADS)

Sun, Baonan; Wazwaz, Abdul-Majid

2018-11-01

In this work, we investigate the (3 + 1) -dimensional KP-Boussinesq equation, which can be used to describe the nonlinear dynamic behavior in scientific and engineering applications. We derive general high-order soliton solutions by using the Hirota's bilinear method combined with the perturbation expansion technique. We also obtain periodic solutions comprising of high-order breathers, periodic line waves, and mixed solutions consisting of breathers and periodic line waves upon selecting particular parameter constraints of the obtained soliton solutions. Furthermore, smooth rational solutions are generated by taking a long wave limit of the soliton solutions. These smooth rational solutions include high-order rogue waves, high-order lumps, and hybrid solutions consisting of lumps and line rogue waves. To better understand the dynamical behaviors of these solutions, we discuss some illustrative graphical analyses. It is expected that our results can enrich the dynamical behavior of the (3 + 1) -dimensional nonlinear evolution equations of other forms.

Hydroelectromechanical modelling of a piezoelectric wave energy converter

NASA Astrophysics Data System (ADS)

Renzi, E.

2016-11-01

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

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

PubMed

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

PubMed Central

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y. C.

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591

The cosmic-ray shock structure problem for relativistic shocks

NASA Technical Reports Server (NTRS)

Webb, G. M.

1985-01-01

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

A shallow water model for the propagation of tsunami via Lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Zergani, Sara; Aziz, Z. A.; Viswanathan, K. K.

2015-01-01

An efficient implementation of the lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g. tsunami), based on the nonlinear shallow water (NSW) wave equation is presented. The LBM is an alternative numerical procedure for the description of incompressible hydrodynamics and has the potential to serve as an efficient solver for incompressible flows in complex geometries. This work proposes the NSW equations for the irrotational surface waves in the case of complex bottom elevation. In recent time, equation involving shallow water is the current norm in modelling tsunami operations which include the propagation zone estimation. Several test-cases are presented to verify our model. Some implications to tsunami wave modelling are also discussed. Numerical results are found to be in excellent agreement with theory.

Spin waves in rings of classical magnetic dipoles

NASA Astrophysics Data System (ADS)

Schmidt, Heinz-Jürgen; Schröder, Christian; Luban, Marshall

2017-03-01

We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting cases that can be analyzed in detail. One case is that of spin waves as infinitesimal excitations from the system’s ground state, where the dispersion relation can be determined analytically. The frequencies of these infinitesimal spin waves are compared with the peaks of the Fourier transform of the thermal expectation value of the autocorrelation function calculated by Monte Carlo simulations. In the special case of vanishing wave number an exact solution of the equations of motion is possible describing synchronized oscillations with finite amplitudes. Finally, the limiting case of a dipole chain with N\\longrightarrow ∞ is investigated and completely solved.

A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

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

Haut, T. S.; Babb, T.; Martinsson, P. G.

2015-06-16

Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existingmore » methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.« less

An Experiment on Two-Dimensional Interaction of Solitary Waves in Shallow Water System

NASA Astrophysics Data System (ADS)

Tsuji, Hidekazu; Yufu, Kei; Marubayashi, Kenji

2012-11-01

The dynamics of solitary waves in horizontally two-dimensional region is not yet well understood. Recently two-dimensional soliton interaction of Kadmotsetv-Petviashvili (KP) equation which describes the weakly nonlinear long wave in shallow water system has been theoretically studied (e.g. Kodama (2010)). It is clarified that the ``resonant'' interaction which forms Y-shaped triad can be described by exact solution. Li et al. (2011) experimentally studied the reflection of solitary wave at the wall and verified the theory of KP equation. To investigate more general interaction process, an experiment in wave tank using two wave makers which are controlled independently is carried out. The wave tank is 4 m in length and 3.6 m in width. The depth of the water is about 8cm. The wavemakers, which are piston-type and have board about 1.5 m in length, can produce orderly solitary wave which amplitude is 1.0-3.5 cm. We observe newly generated solitary wave due to interaction of original solitary waves which have different amplitude and/or propagation direction. The results are compared with the aforementioned theory of KP equation.

Synchronism of nonlinear internal waves in a three-layer fluid

NASA Astrophysics Data System (ADS)

Talipova, Tatiana; Kurkina, Oxana; Terletska, Katerina; Rouvinskaya, Ekaterina

2017-04-01

In a three layer fluid with arbitrary layer widths and densities the existence of long internal solitons and breathers is proven theoretically and numerically, see for example (Pelinovsky et al., 2007; Lamb et al., 2007). The existence of breather-like waves of the intermediate length is also shown in numerical simulations (Terletska et al., 2016). For such waves conditions of synchronism are valid when a breather of the first mode and a soliton of the second mode move together with the same speed and form an asymmetric solitary wave of the second mode. The process of strong interaction of long nonlinear internal waves in the framework of three-layer Camassa-Choi model demonstrates the same effect (Jo&Choi, 2014; Barros, 2016). We analyze possible synchronism conditions for steady-state internal waves in a three-layer fluid analytically the framework of the Gardner equation, which is valid for long weakly nonlinear internal waves. The equations for synchronism conditions are derived and considered in terms of wave amplitudes, layer widths and density jumps. The configurations of three-layer fluid are found for which such a synchronism is possible. References: Barros R. Large amplitude internal waves in three-layer flows. The forth international conference "Nonlinear Waves - Theory and Applications", MS7, Beijing, China, June 25 - 28, 2016 Pelinovsky E., Polukhina O., Slunyaev A., Talipova T. Internal solitary waves // Chapter 4 in the book "Solitary Waves in Fluids". WIT Press. Southampton, Boston. 2007. P. 85 - 110. K. Terletska., K. T. Jung, T. Talipova, V. Maderich, I. Brovchenko and R. Grimshaw Internal breather-like wave generation by the second mode solitary wave interaction with a step// Physics of Fluids, 2016, accepted

Diffraction of a shock wave by a compression corner; regular and single Mach reflection

NASA Technical Reports Server (NTRS)

Vijayashankar, V. S.; Kutler, P.; Anderson, D.

1976-01-01

The two dimensional, time dependent Euler equations which govern the flow field resulting from the injection of a planar shock with a compression corner are solved with initial conditions that result in either regular reflection or single Mach reflection of the incident planar shock. The Euler equations which are hyperbolic are transformed to include the self similarity of the problem. A normalization procedure is employed to align the reflected shock and the Mach stem as computational boundaries to implement the shock fitting procedure. A special floating fitting scheme is developed in conjunction with the method of characteristics to fit the slip surface. The reflected shock, the Mach stem, and the slip surface are all treated as harp discontinuities, thus, resulting in a more accurate description of the inviscid flow field. The resulting numerical solutions are compared with available experimental data and existing first-order, shock-capturing numerical solutions.

Nonlinear wave runup in long bays and firths: Samoa 2009 and Tohoku 2011 tsunamis

NASA Astrophysics Data System (ADS)

Didenkulova, I.; Pelinovsky, E.

2012-04-01

Last catastrophic tsunami events in Samoa on 29 September 2009 and in Japan on 11 March 2011 demonstrated that tsunami may experience abnormal amplification in long bays and firths and result in an unexpectedly high wave runup. The capital city Pago Pago, which is located at the toe of a narrow 4-km-long bay and represents the most characteristic example of a long and narrow bay, was considerably damaged during Samoa 2009 tsunami (destroyed infrastructures, boats and shipping containers carried inland into commercial areas, etc.) The runup height there reached 8 m over an inundation of 538 m at its toe, while the tsunami wave height measured by the tide-gauge at the entrance of the bay was at most 3 m. The same situation was observed during catastrophic Tohoku tsunami in Japan, which coast contains numerous long bays and firths, which experienced the highest wave runup and the strongest amplification. Such examples are villages: Ofunato, Ryori Bay, where the wave runup reached 30 m high, and Onagawa, where the wave amplified up to 17 m. Here we study the nonlinear dynamics of tsunami waves in an inclined U-shaped bay. Nonlinear shallow water equations can in this case be written in 1D form and solved analytically with the use of the hodograph transformation. This approach generalizes the well-known Carrier-Greenspan transformation for long wave runup on a plane beach. In the case of an inclined U-shaped bay it leads to the associated generalized wave equation for symmetrical wave in fractal space. In the special case of the channel of parabolic cross-section it is a spherical symmetrical linear wave equation. As a result, the solution of the Cauchy problem can be expressed in terms of elementary functions and has a simple form (with respect to analysis) for any kind of initial conditions. Wave regimes associated with various localized initial conditions, corresponding to problems of evolution and runup of tsunami, are considered and analyzed. Special attention is paid to the wave breaking criterion. Theoretical estimates of tsunami runup are applied to cases of 2009 Samoa and 2011 Tohoku tsunamis. The data of tide-gauges or computed tide-gauges are used to calculate wave runup for two approximations of the bottom topography: a plane beach and for a narrow bay. It is shown that theory of 1D runup on a plane beach underestimate the tsunami runup height and the influence of the narrow bay geometry should be taken into account. The differences in estimated shoreline velocity, travel time and wave breaking regime, calculated in the framework of these two approximations are also discussed. It is concluded that the wave runup in narrow bays should by calculated by the corresponding formulas, which should be taken into account by TEWS.

Internal Wave-Convection-Mean Flow Interactions

NASA Astrophysics Data System (ADS)

Lecoanet, D.; Couston, L. A.; Favier, B.; Le Bars, M.

2017-12-01

We present a series of simulations of Boussinesq fluid with a nonlinear equation of state which in thermal equilibrium is convective in the bottom part of the domain, but stably stratified in the upper part of the domain. The stably stratified region supports internal gravity waves, which are excited by the convection. The convection can significantly affected by the stably stratified region. Furthermore, the waves in the stable region can interact nonlinearly to drive coherent mean flows which exhibit regular oscillations, similar to the QBO in the Earth's atmosphere. We will describe the dependence of the mean flow oscillations on the properties of the convection which generate the internal waves. This provides a novel framework for understanding mean flow oscillations in the Earth's atmosphere, as well as the atmospheres of giant planets.

One-dimensional optical wave turbulence: Experiment and theory

NASA Astrophysics Data System (ADS)

Laurie, Jason; Bortolozzo, Umberto; Nazarenko, Sergey; Residori, Stefania

2012-05-01

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Falling films on flexible inclines

NASA Astrophysics Data System (ADS)

Matar, O. K.; Craster, R. V.; Kumar, S.

2007-11-01

The nonlinear stability and dynamic behavior of falling fluid films is studied for flow over a flexible substrate. We use asymptotic methods to deduce governing equations valid in various limits. Long-wave theory is used to derive Benney-like coupled equations for the film thickness and substrate deflection. Weakly nonlinear equations are then derived from these equations that, in the limit of large wall damping and/or large wall tension, reduce to the Kuramoto-Sivashinsky equation. These models break down when inertia becomes more significant, so we also use a long-wave approximation in conjunction with integral theory to derive three strongly coupled nonlinear evolution equations for the film thickness, substrate deflection, and film volumetric flow rate valid at higher Reynolds numbers. These equations, accounting for inertia, capillary, viscous, wall tension, and damping effects, are solved over a wide range of parameters. Our results suggest that decreasing wall damping and/or wall tension can promote the development of chaos in the weakly nonlinear regime and lead to severe substrate deformations in the strongly nonlinear regime; these can give rise to situations in which the free surface and underlying substrate come into contact in finite time.

Modeling of Wave Spectrum and Wave Breaking Statistics Based on Balance Equation

NASA Astrophysics Data System (ADS)

Irisov, V.

2012-12-01

Surface roughness and foam coverage are the parameters determining microwave emissivity of sea surface in a wide range of wind. Existing empirical wave spectra are not associated with wave breaking statistics although physically they are closely related. We propose a model of sea surface based on the balance of three terms: wind input, dissipation, and nonlinear wave-wave interaction. It provides an insight on wave generation, interaction, and dissipation - very important parameters for understanding of wave development under changing oceanic and atmospheric conditions. The wind input term is the best known among all three. For our analysis we assume a wind input term as it was proposed by Plant [1982] and consider modification necessary to do to account for proper interaction of long fast waves with wind. For long gravity waves (longer than 15-30 cm) the dissipation term can be related to the wave breaking with whitecaps, as it was shown by Kudryavtsev et al. [2003], so we assume the cubic dependence of dissipation term on wind. It implies certain limitations on the spectrum shape. The most difficult is to estimate the term describing nonlinear wave-wave interaction. Hasselmann [1962] and Zakharov [1999] developed theory of 4-wave interaction, but the resulting equation requires at least 3-fold integration over wavenumbers at each time step of integration of balance equation, which makes it difficult for direct numerical modeling. It is desirable to use an approximation of wave-wave interaction term, which preserves wave action, energy, and momentum, and can be easily estimated during time integration of balance equation. Zakharov and Pushkarev [1999] proposed the diffusion approximation of the wave interaction term and showed that it can be used for estimate of wave spectrum. We believe their assumption that wave-wave interaction is the dominant factor in forming the wave spectrum does not agree with the observations made by Hwang and Sletten [2008]. Finally we consider modifications of the model equation, which can be done to describe gravity-capillary and capillary waves. An obvious correction is to add viscous dissipation. A little less obvious is a transition from 4-wave to 3-wave interaction. The model allows one to include easily generation of parasitic capillary waves as it was proposed by Kudryavtsev et al. [2003]. A modification of dissipation term can explain an "overshoot" phenomenon observed in JONSWAP spectrum. These examples demonstrate that the proposed model is quite flexible and can be used to account for various physical phenomena. The resulting balance equation is easy to integrate using a personal computer and necessity of its numerical solution is paid by the model flexibility and better physical background compared with empirical spectra. References Hasselmann, K., J. Fluid Mech., 12, pp.481-500, 1962. Hwang, P., and M. Sletten, J. Geophys. Res., 113, doi:10.1029/2007JC004277, 2008. Kudryavtsev, V., et al., J. Geophys. Res., 108 (C3), doi:10.1029/2001JC001003, 2003. Plant, W. J., J. Geophys. Res., vol. 87, pp. 1961-1967, 1982. Zakharov, V., and A. Pushkarev, Nonlinear Processes in Geophysics, 6, pp.1-10, 1999. Zakharov, V., Eur. J. Mech. B/Fluids, 18, pp.327-344, 1999.

Study of a Novel Oscillating Surge Wave Energy Converter: Preprint

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

Tom, Nathan M; Choiniere, Michael; Thiagarajan, Krish P.

This study investigates the performance of an oscillating surge wave energy converter (OSWEC) that utilizes adjustable geometry as a means of controlling the hydrodynamic coefficients, a concept originally proposed by [1]. The body of the device consists of a bottom-hinged solid rectangular frame with five horizontal flaps spanning the interior of the frame. The flaps can rotate independently about their center of rotation within the frame like a large window shutter. Changing the orientation of the flaps alters the hydrodynamic coefficients and natural frequency of the device as well as the ability to shed or absorb structural loads accordingly. Thismore » ability may allow the device to operate in a wider range of sea states than other current wave energy converter designs. This paper presents and compares the results of numerical simulations and experimental testing of the OSWEC's response to regular waves with all five of the horizontal fin configurations sharing the same orientation of 0 degrees (fully closed interior) and 90 degrees (fully open). The numerical simulations were performed using WAMIT, which calculates hydrodynamic coefficients using a boundary element method code to solve the linear potential flow problem, and WEC-Sim, a MATLAB-based tool that simulates multibody devices in the time domain by solving the governing equations of motion. A 1:14 scale model of the device was built for experimental evaluation in an 8-m-long, 1-m wide wave tank, which supports a water depth of 0.7 m. The OSWEC motion in different wave conditions was measured with displacement sensors while nonlinear wave-structure interaction effects like slamming and overtopping were captured using a high-speed camera and used to understand differences between the simulation and experiments.« less

A Numerical Investigation of the Burnett Equations Based on the Second Law

NASA Technical Reports Server (NTRS)

Comeaux, Keith A.; Chapman, Dean R.; MacCormack, Robert W.; Edwards, Thomas A. (Technical Monitor)

1995-01-01

The Burnett equations have been shown to potentially violate the second law of thermodynamics. The objective of this investigation is to correlate the numerical problems experienced by the Burnett equations to the negative production of entropy. The equations have had a long history of numerical instability to small wavelength disturbances. Recently, Zhong corrected the instability problem and made solutions attainable for one dimensional shock waves and hypersonic blunt bodies. Difficulties still exist when attempting to solve hypersonic flat plate boundary layers and blunt body wake flows, however. Numerical experiments will include one-dimensional shock waves, quasi-one dimensional nozzles, and expanding Prandlt-Meyer flows and specifically examine the entropy production for these cases.

Oscillatory instability of a self-rewetting film driven by thermal modulation

NASA Astrophysics Data System (ADS)

Batson, William; Agnon, Yehuda; Oron, Alex

2016-11-01

Here we consider the self-rewetting fluids (SRWFs) that exhibit a well-defined minimum surface tension with respect to temperature, in contrast to those where surface tension decreases linearly. Utilization of SRWFs has grown significantly in the past decade, due to observations that heat transfer is enhanced in applications such as film boiling and pulsating heat pipes. With similar applications in mind, we investigate the dynamics of a thin SRWF film which is subjected to a temperature modulation in the bounding gas. A model is developed within the framework of the long-wave approximation, and a time-averaged thermocapillary driving force for destabilization is uncovered for SRWFs that results from the nonlinear surface tension. Linear analysis of the nonlinear PDE for the film thickness is used to determine the critical conditions at which this driving force destabilizes the film, and, numerical integration of this evolution equation reveals that linearly unstable perturbations saturate to regular periodic solutions (when the modulational frequency is set properly). Properties of these flows such as bifurcation and long-domain flows, where multiple unstable linear modes interact, will also be discussed.

Shock formation in the dispersionless Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Eggers, J.

2016-04-01

The dispersionless Kadomtsev-Petviashvili (dKP) equation {{≤ft({{u}t}+u{{u}x}\\right)}x}={{u}yy} is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation numerically we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation {{u}t}+u{{u}x}=0 . We show numerically that the solutions to the transformed equation stays regular for longer times than the solution of the dKP equation. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape region in the (x, y) plane, where the solution of the dKP equation exists in a weak sense only, and a shock front develops. A local expansion reveals the universal scaling structure of the shock, which after a suitable change of coordinates corresponds to a generic cusp catastrophe. We provide a heuristic derivation of the shock front position near the critical point for the solution of the dKP equation, and study the solution of the dKP equation when a small amount of dissipation is added. Using multiple-scale analysis, we show that in the limit of small dissipation and near the critical point of the dKP solution, the solution of the dissipative dKP equation converges to a Pearcey integral. We test and illustrate our results by detailed comparisons with numerical simulations of both the regularized equation, the dKP equation, and the asymptotic description given in terms of the Pearcey integral.

Hydroelastic analysis of ice shelves under long wave excitation

NASA Astrophysics Data System (ADS)

Papathanasiou, T. K.; Karperaki, A. E.; Theotokoglou, E. E.; Belibassakis, K. A.

2015-05-01

The transient hydroelastic response of an ice shelf under long wave excitation is analysed by means of the finite element method. The simple model, presented in this work, is used for the simulation of the generated kinematic and stress fields in an ice shelf, when the latter interacts with a tsunami wave. The ice shelf, being of large length compared to its thickness, is modelled as an elastic Euler-Bernoulli beam, constrained at the grounding line. The hydrodynamic field is represented by the linearised shallow water equations. The numerical solution is based on the development of a special hydroelastic finite element for the system of governing of equations. Motivated by the 2011 Sulzberger Ice Shelf (SIS) calving event and its correlation with the Honshu Tsunami, the SIS stable configuration is studied. The extreme values of the bending moment distribution in both space and time are examined. Finally, the location of these extrema is investigated for different values of ice shelf thickness and tsunami wave length.

Hydroelastic analysis of ice shelves under long wave excitation

NASA Astrophysics Data System (ADS)

Papathanasiou, T. K.; Karperaki, A. E.; Theotokoglou, E. E.; Belibassakis, K. A.

2015-08-01

The transient hydroelastic response of an ice shelf under long wave excitation is analysed by means of the finite element method. The simple model, presented in this work, is used for the simulation of the generated kinematic and stress fields in an ice shelf, when the latter interacts with a tsunami wave. The ice shelf, being of large length compared to its thickness, is modelled as an elastic Euler-Bernoulli beam, constrained at the grounding line. The hydrodynamic field is represented by the linearised shallow water equations. The numerical solution is based on the development of a special hydroelastic finite element for the system of governing of equations. Motivated by the 2011 Sulzberger Ice Shelf (SIS) calving event and its correlation with the Honshu Tsunami, the SIS stable configuration is studied. The extreme values of the bending moment distribution in both space and time are examined. Finally, the location of these extrema is investigated for different values of ice shelf thickness and tsunami wave length.

Generalized intermediate long-wave hierarchy in zero-curvature representation with noncommutative spectral parameter

NASA Astrophysics Data System (ADS)

Degasperis, A.; Lebedev, D.; Olshanetsky, M.; Pakuliak, S.; Perelomov, A.; Santini, P. M.

1992-11-01

The simplest generalization of the intermediate long-wave hierarchy (ILW) is considered to show how to extend the Zakharov-Shabat dressing method to nonlocal, i.e., integro-partial differential, equations. The purpose is to give a procedure of constructing the zero-curvature representation of this class of equations. This result obtains by combining the Drinfeld-Sokolov formalism together with the introduction of an operator-valued spectral parameter, namely, a spectral parameter that does not commute with the space variable x. This extension provides a connection between the ILWk hierarchy and the Saveliev-Vershik continuum graded Lie algebras. In the case of ILW2 the Fairlie-Zachos sinh-algebra was found.

Chaotic scattering in an open vase-shaped cavity: Topological, numerical, and experimental results

NASA Astrophysics Data System (ADS)

Novick, Jaison Allen

We present a study of trajectories in a two-dimensional, open, vase-shaped cavity in the absence of forces The classical trajectories freely propagate between elastic collisions. Bound trajectories, regular scattering trajectories, and chaotic scattering trajectories are present in the vase. Most importantly, we find that classical trajectories passing through the vase's mouth escape without return. In our simulations, we propagate bursts of trajectories from point sources located along the vase walls. We record the time for escaping trajectories to pass through the vase's neck. Constructing a plot of escape time versus the initial launch angle for the chaotic trajectories reveals a vastly complicated recursive structure or a fractal. This fractal structure can be understood by a suitable coordinate transform. Reducing the dynamics to two dimensions reveals that the chaotic dynamics are organized by a homoclinic tangle, which is formed by the union of infinitely long, intersecting stable and unstable manifolds. This study is broken down into three major components. We first present a topological theory that extracts the essential topological information from a finite subset of the tangle and encodes this information in a set of symbolic dynamical equations. These equations can be used to predict a topologically forced minimal subset of the recursive structure seen in numerically computed escape time plots. We present three applications of the theory and compare these predictions to our simulations. The second component is a presentation of an experiment in which the vase was constructed from Teflon walls using an ultrasound transducer as a point source. We compare the escaping signal to a classical simulation and find agreement between the two. Finally, we present an approximate solution to the time independent Schrodinger Equation for escaping waves. We choose a set of points at which to evaluate the wave function and interpolate trajectories connecting the source point to each "detector point". We then construct the wave function directly from these classical trajectories using the two-dimensional WKB approximation. The wave function is Fourier Transformed using a Fast Fourier Transform algorithm resulting in a spectrum in which each peak corresponds to an interpolated trajectory. Our predictions are based on an imagined experiment that uses microwave propagation within an electromagnetic waveguide. Such an experiment exploits the fact that under suitable conditions both Maxwell's Equations and the Schrodinger Equation can be reduced to the Helmholtz Equation. Therefore, our predictions, while compared to the electromagnetic experiment, contain information about the quantum system. Identifying peaks in the transmission spectrum with chaotic trajectories will allow for an additional experimental verification of the intermediate recursive structure. Finally, we summarize our results and discuss possible extensions of this project.

Vortical and acoustical mode coupling inside a porous tube with uniform wall suction.

PubMed

Jankowskia, T A; Majdalani, J

2005-06-01

This paper considers the oscillatory motion of gases inside a long porous tube of the closed-open type. In particular, the focus is placed on describing an analytical solution for the internal acoustico-vortical coupling that arises in the presence of appreciable wall suction. This unsteady field is driven by longitudinal oscillatory waves that are triggered by small unavoidable fluctuations in the wall suction speed. Under the assumption of small amplitude oscillations, the time-dependent governing equations are linearized through a regular perturbation of the dependent variables. Further application of the Helmholtz vector decomposition theorem enables us to discriminate between acoustical and vortical equations. After solving the wave equation for the acoustical contribution, the boundary-driven vortical field is considered. The method of matched-asymptotic expansions is then used to obtain a closed-form solution for the unsteady momentum equation developing from flow decomposition. An exact series expansion is also derived and shown to coincide with the numerical solution for the problem. The numerically verified end results suggest that the asymptotic scheme is capable of providing a sufficiently accurate solution. This is due to the error associated with the matched-asymptotic expansion being smaller than the error introduced in the Navier-Stokes linearization. A basis for comparison is established by examining the evolution of the oscillatory field in both space and time. The corresponding boundary-layer behavior is also characterized over a range of oscillation frequencies and wall suction velocities. In general, the current solution is found to exhibit features that are consistent with the laminar theory of periodic flows. By comparison to the Sexl profile in nonporous tubes, the critically damped solution obtained here exhibits a slightly smaller overshoot and depth of penetration. These features may be attributed to the suction effect that tends to attract the shear layers closer the wall.

An outline of cellular automaton universe via cosmological KdV equation

NASA Astrophysics Data System (ADS)

Christianto, V.; Smarandache, F.; Umniyati, Y.

2018-03-01

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. Then we advance further this KdV equation by virtue of Cellular Automaton method to solve the PDEs. We submit wholeheartedly Robert Kuruczs hypothesis that Big Bang should be replaced with a finite cellular automaton universe with no expansion [4][5]. Nonetheless, we are fully aware that our model is far from being complete, but it appears the proposed cellular automaton model of the Universe is very close in spirit to what Konrad Zuse envisaged long time ago. It is our hope that the new proposed method can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Global smooth solutions of 3-D null-form wave equations in exterior domains with Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Jun, Li; Huicheng, Yin

2018-05-01

The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions. Concretely speaking, when the surface of a 3-D compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition, we prove that the smooth small data solution exists globally provided that the Neumann boundary condition on the exterior domain is given. One of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself. As an application of the main result, the global stability to 3-D static compressible Chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude.

Modulational stability of periodic solutions of the Kuramoto-Sivaskinsky equation

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.; Papanicolaou, George C.; Smyrlis, Yiorgos S.

1993-01-01

We study the long-wave, modulational, stability of steady periodic solutions of the Kuramoto-Sivashinsky equation. The analysis is fully nonlinear at first, and can in principle be carried out to all orders in the small parameter, which is the ratio of the spatial period to a characteristic length of the envelope perturbations. In the linearized regime, we recover a high-order version of the results of Frisch, She, and Thual, which shows that the periodic waves are much more stable than previously expected.

Mechanical balance laws for fully nonlinear and weakly dispersive water waves

NASA Astrophysics Data System (ADS)

Kalisch, Henrik; Khorsand, Zahra; Mitsotakis, Dimitrios

2016-10-01

The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is known to describe accurately the wave motion at the surface of an incompressible inviscid fluid in the case when the fluid flow is irrotational and two-dimensional. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected. In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, the conservation equations are satisfied exactly by the solutions of the Serre-Green-Naghdi system. The case of variable bathymetry is more complicated, with mass and momentum conservation satisfied exactly, and energy conservation satisfied only in a global sense. In all cases, the quantities found here reduce correctly to the corresponding counterparts in both the Boussinesq and the shallow-water scaling. One consequence of the present analysis is that the energy loss appearing in the shallow-water theory of undular bores is fully compensated by the emergence of oscillations behind the bore front. The situation is analyzed numerically by approximating solutions of the Serre-Green-Naghdi equations using a finite-element discretization coupled with an adaptive Runge-Kutta time integration scheme, and it is found that the energy is indeed conserved nearly to machine precision. As a second application, the shoaling of solitary waves on a plane beach is analyzed. It appears that the Serre-Green-Naghdi equations are capable of predicting both the shape of the free surface and the evolution of kinetic and potential energy with good accuracy in the early stages of shoaling.

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.

Nonlinear Wave Propagation.

DTIC Science & Technology

1981-11-25

dimensional KdV ( Kadomtsev - Petviashvili ) equation [56). Furthermore it has been found that these newly found decaying mode solutions and usual soliton...Ablowitz and R. Haberman, Phys. Rev. Lett. 35, 1185, 1975. 26. S.V. !anakov, "On the Solutions of the Kadomtsev - Petviashvili equation ; Proc. of Symposium...accomplished relates to fluid mechanics, nonlinear optics, multidimensional solitons, Painlev e equations , long time asymptotic solu- tions, new

A semi-analytical method for near-trapped mode and fictitious frequencies of multiple scattering by an array of elliptical cylinders in water waves

NASA Astrophysics Data System (ADS)

Chen, Jeng-Tzong; Lee, Jia-Wei

2013-09-01

In this paper, we focus on the water wave scattering by an array of four elliptical cylinders. The null-field boundary integral equation method (BIEM) is used in conjunction with degenerate kernels and eigenfunctions expansion. The closed-form fundamental solution is expressed in terms of the degenerate kernel containing the Mathieu and the modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. To avoid using the addition theorem to translate the Mathieu functions, the present approach can solve the water wave problem containing multiple elliptical cylinders in a semi-analytical manner by introducing the adaptive observer system. Regarding water wave problems, the phenomena of numerical instability of fictitious frequencies may appear when the BIEM/boundary element method (BEM) is used. Besides, the near-trapped mode for an array of four identical elliptical cylinders is observed in a special layout. Both physical (near-trapped mode) and mathematical (fictitious frequency) resonances simultaneously appear in the present paper for a water wave problem by an array of four identical elliptical cylinders. Two regularization techniques, the combined Helmholtz interior integral equation formulation (CHIEF) method and the Burton and Miller approach, are adopted to alleviate the numerical resonance due to fictitious frequency.

Nuclear Poincaré cycle synchronizes with the incident de Broglie wave to predict regularity in neutron resonance energies

NASA Astrophysics Data System (ADS)

Ohkubo, Makio

2016-06-01

In observed neutron resonances, long believed to be a form of quantum chaos, regular family structures are found in the s-wave resonances of many even-even nuclei in the tens keV to MeV region [M.Ohkubo, Phys. Rev. C 87, 014608(2013)]. Resonance reactions take place when the incident de Broglie wave synchronizes with the Poincaré cycle of the compound nucleus, which is composed of several normal modes with periods that are time quantized by inverse Fermi energy. Based on the breathing model of the compound nucleus, neutron resonance energies in family structures are written by simple arithmetic expressions using Sn and small integers. Family structures in observed resonances of 40Ca+n and 37Cl+n are described as simple cases. A model for time quantization is discussed.

Generation of long waves in a fluid flowing over a localized topography at a periodically varying velocity

NASA Astrophysics Data System (ADS)

Ohsugi, Yasuo; Funakoshi, Mitsuaki

2000-05-01

The generation of long waves in a fluid flowing over a localized topography is examined numerically using the forced KdV equation under the assumption that the velocity U of the fluid far from the topography is close to the phase speed of a linear long wave and varies periodically with period T. For T within a few regions, we observe the 1: n entrainment of the wave motion near the topography to period T, in which n upstream-advancing waves are generated in period T. These regions extend and shift to larger T as the average value or amplitude of the variation of U increases. Furthermore, when the entrainment occurs, the spatial region where time-periodic evolution is almost attained extends toward both upstream and downstream directions with increasing time.

Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films

NASA Technical Reports Server (NTRS)

Krishnamoorthy, S.; Ramaswamy, B.; Joo, S. W.

1995-01-01

A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary Lagrangian Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.

Zonal flow evolution and overstability in accretion discs

NASA Astrophysics Data System (ADS)

Vanon, R.; Ogilvie, G. I.

2017-04-01

This work presents a linear analytical calculation on the stability and evolution of a compressible, viscous self-gravitating (SG) Keplerian disc with both horizontal thermal diffusion and a constant cooling time-scale when an axisymmetric structure is present and freely evolving. The calculation makes use of the shearing sheet model and is carried out for a range of cooling times. Although the solutions to the inviscid problem with no cooling or diffusion are well known, it is non-trivial to predict the effect caused by the introduction of cooling and of small diffusivities; this work focuses on perturbations of intermediate wavelengths, therefore representing an extension to the classical stability analysis on thermal and viscous instabilities. For density wave modes, the analysis can be simplified by means of a regular perturbation analysis; considering both shear and thermal diffusivities, the system is found to be overstable for intermediate and long wavelengths for values of the Toomre parameter Q ≲ 2; a non-SG instability is also detected for wavelengths ≳18H, where H is the disc scale-height, as long as γ ≲ 1.305. The regular perturbation analysis does not, however, hold for the entropy and potential vorticity slow modes as their ideal growth rates are degenerate. To understand their evolution, equations for the axisymmetric structure's amplitudes in these two quantities are analytically derived and their instability regions obtained. The instability appears boosted by increasing the value of the adiabatic index and of the Prandtl number, while it is quenched by efficient cooling.

Role of short-range correlation in facilitation of wave propagation in a long-range ladder chain

NASA Astrophysics Data System (ADS)

Farzadian, O.; Niry, M. D.

2018-09-01

We extend a new method for generating a random chain, which has a kind of short-range correlation induced by a repeated sequence while retaining long-range correlation. Three distinct methods are considered to study the localization-delocalization transition of mechanical waves in one-dimensional disordered media with simultaneous existence of short and long-range correlation. First, a transfer-matrix method was used to calculate numerically the localization length of a wave in a binary chain. We found that the existence of short-range correlation in a long-range correlated chain can increase the localization length at the resonance frequency Ωc. Then, we carried out an analytical study of the delocalization properties of the waves in correlated disordered media around Ωc. Finally, we apply a dynamical method based on the direct numerical simulation of the wave equation to study the propagation of waves in the correlated chain. Imposing short-range correlation on the long-range background will lead the propagation to super-diffusive transport. The results obtained with all three methods are in agreement with each other.

Contribution of non-resonant wave-wave interactions in the dynamics of long-crested sea wave fields

NASA Astrophysics Data System (ADS)

Benoit, Michel

2017-04-01

Gravity waves fields at the surface of the oceans evolve under the combined effects of several physical mechanisms, of which nonlinear wave-wave interactions play a dominant role. These interactions transfer energy between components within the energy spectrum and allow in particular to explain the shape of the distribution of wave energy according to the frequencies and directions of propagation. In the oceanic domain (deep water conditions), dominant interactions are third-order resonant interactions, between quadruplets (or quartets) of wave components, and the evolution of the wave spectrum is governed by a kinetic equation, established by Hasselmann (1962) and Zakharov (1968). The kinetic equation has a number of interesting properties, including the existence of self-similar solutions and cascades to small and large wavelengths of waves, which can be studied in the framework of the wave (or weak) turbulence theory (e.g. Badulin et al., 2005). With the aim to obtain more complete and precise modelling of sea states dynamics, we investigate here the possibility and consequences of taking into account the non-resonant interactions -quasi-resonant in practice- among 4 waves. A mathematical formalism has recently been proposed to account for these non-resonant interactions in a statistical framework by Annenkov & Shrira (2006) (Generalized Kinetic Equation, GKE) and Gramstad & Stiassnie (2013) (Phase Averaged Equation, PAE). In order to isolate the non-resonant contributions, we limit ourselves here to monodirectional (i.e. long-crested) wave trains, since in this case the 4-wave resonant interactions vanish. The (stochastic) modelling approaches proposed by Annenkov & Shrira (2006) and Gramstad & Stiassnie (2013) are compared to phase-resolving (deterministic) simulations based on a fully nonlinear potential approach (using a high-order spectral method, HOS). We study and compare the evolution dynamics of the wave spectrum at different time scales (i.e. over durations ranging from a few wave periods to 1000 periods), with the aim of highlighting the capabilities and limitations of the GKE-PAE models. Different situations are considered by varying the relative water depth, the initial steepness of the wave field, and the shape of the initial wave spectrum, including arbitrary forms. References: Annenkov S.Y., Shrira V.I. (2006) Role of non-resonant interactions in the evolution of nonlinear random water wave fields. J. Fluid Mech., 561, 181-207. Badulin S.I., Pushkarev A.N., Resio D., Zakharov V.E. (2005) Self-similarity of wind-driven seas. Nonlin. Proc. Geophys., 12, 891-946. Gramstad O., Stiassnie M. (2013) Phase-averaged equation for water waves. J. Fluid Mech., 718, 280- 303. Hasselmann K. (1962) On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech., 12, 481-500. Zakharov V.E. (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. App. Mech. Tech. Phys., 9(2), 190-194.

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.

PubMed

Kanna, T; Sakkaravarthi, K; Tamilselvan, K

2013-12-01

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.

Quantum effects on compressional Alfven waves in compensated semiconductors

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

Amin, M. R.

2015-03-15

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

Rogue waves in a water tank: Experiments and modeling

NASA Astrophysics Data System (ADS)

Lechuga, Antonio

2013-04-01

Recently many rogue waves have been reported as the main cause of ship incidents on the sea. One of the main characteristics of rogue waves is its elusiveness: they present unexpectedly and disappear in the same wave. Some authors (Zakharov and al.2010) are attempting to find the probability of their appearances apart from studyingthe mechanism of the formation. As an effort on this topic we tried the generation of rogue waves in a water wave tank using a symmetric spectrum(Akhmediev et al. 2011) as input on the wave maker. The produced waves were clearly rogue waves with a rate (maximum wave height/ Significant wave height) of 2.33 and a kurtosis of 4.77 (Janssen 2003, Onorato 2006). These results were already presented (Lechuga 2012). Similar waves (in pattern aspect, but without being extreme waves) were described as crossing waves in a water tank(Shemer and Lichter1988). To go on further the next step has been to apply a theoretical model to the envelope of these waves. After some considerations the best model has been an analogue of the Ginzburg-Landau equation. This apparently amazing result is easily explained: We know that the Ginzburg-Landau model is related to some regular structures on the surface of a liquid and also in plasmas, electric and magnetic fields and other media. Another important characteristic of the model is that their solutions are invariants with respectto the translation group. The main aim of this presentation is to extract conclusions of the model and the comparison with the measured waves in the water tank.The nonlinear structure of waves and their regularity make suitable the use of the Ginzburg-Landau model to the envelope of generated waves in the tank,so giving us a powerful tool to cope with the results of our experiment.

Regularized Transformation-Optics Cloaking for the Helmholtz Equation: From Partial Cloak to Full Cloak

NASA Astrophysics Data System (ADS)

Li, Jingzhi; Liu, Hongyu; Rondi, Luca; Uhlmann, Gunther

2015-04-01

We develop a very general theory on the regularized approximate invisibility cloaking for the wave scattering governed by the Helmholtz equation in any space dimensions via the approach of transformation optics. There are four major ingredients in our proposed theory: (1) The non-singular cloaking medium is obtained by the push-forwarding construction through a transformation that blows up a subset in the virtual space, where is an asymptotic regularization parameter. will degenerate to K 0 as , and in our theory K 0 could be any convex compact set in , or any set whose boundary consists of Lipschitz hypersurfaces, or a finite combination of those sets. (2) A general lossy layer with the material parameters satisfying certain compatibility integral conditions is employed right between the cloaked and cloaking regions. (3) The contents being cloaked could also be extremely general, possibly including, at the same time, generic mediums and, sound-soft, sound-hard and impedance-type obstacles, as well as some sources or sinks. (4) In order to achieve a cloaking device of compact size, particularly for the case when is not "uniformly small", an assembly-by-components, the (ABC) geometry is developed for both the virtual and physical spaces and the blow-up construction is based on concatenating different components. Within the proposed framework, we show that the scattered wave field corresponding to a cloaking problem will converge to u 0 as , with u 0 being the scattered wave field corresponding to a sound-hard K 0. The convergence result is used to theoretically justify the approximate full and partial invisibility cloaks, depending on the geometry of K 0. On the other hand, the convergence results are conducted in a much more general setting than what is needed for the invisibility cloaking, so they are of significant mathematical interest for their own sake. As for applications, we construct three types of full and partial cloaks. Some numerical experiments are also conducted to illustrate our theoretical results.

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

PubMed

Kanagawa, Tetsuya

2015-05-01

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

Lump and rogue waves for the variable-coefficient Kadomtsev-Petviashvili equation in a fluid

NASA Astrophysics Data System (ADS)

Jia, Xiao-Yue; Tian, Bo; Du, Zhong; Sun, Yan; Liu, Lei

2018-04-01

Under investigation in this paper is the variable-coefficient Kadomtsev-Petviashvili equation, which describes the long waves with small amplitude and slow dependence on the transverse coordinate in a single-layer shallow fluid. Employing the bilinear form and symbolic computation, we obtain the lump, mixed lump-stripe soliton and mixed rogue wave-stripe soliton solutions. Discussions indicate that the variable coefficients are related to both the lump soliton’s velocity and amplitude. Mixed lump-stripe soliton solutions display two different properties, fusion and fission. Mixed rogue wave-stripe soliton solutions show that a rogue wave arises from one of the stripe solitons and disappears into the other. When the time approaches 0, rogue wave’s energy reaches the maximum. Interactions between a lump soliton and one-stripe soliton, and between a rogue wave and a pair of stripe solitons, are shown graphically.

A modified and stable version of a perfectly matched layer technique for the 3-d second order wave equation in time domain with an application to aeroacoustics

PubMed Central

Kaltenbacher, Barbara; Kaltenbacher, Manfred; Sim, Imbo

2013-01-01

We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems. PMID:23888085

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane.

PubMed

Liu, T Y; Chiu, T L; Clarkson, P A; Chow, K W

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane

NASA Astrophysics Data System (ADS)

Liu, T. Y.; Chiu, T. L.; Clarkson, P. A.; Chow, K. W.

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

Numerical modeling of surface wave development under the action of wind

NASA Astrophysics Data System (ADS)

Chalikov, Dmitry

2018-06-01

The numerical modeling of two-dimensional surface wave development under the action of wind is performed. The model is based on three-dimensional equations of potential motion with a free surface written in a surface-following nonorthogonal curvilinear coordinate system in which depth is counted from a moving surface. A three-dimensional Poisson equation for the velocity potential is solved iteratively. A Fourier transform method, a second-order accuracy approximation of vertical derivatives on a stretched vertical grid and fourth-order Runge-Kutta time stepping are used. Both the input energy to waves and dissipation of wave energy are calculated on the basis of earlier developed and validated algorithms. A one-processor version of the model for PC allows us to simulate an evolution of the wave field with thousands of degrees of freedom over thousands of wave periods. A long-time evolution of a two-dimensional wave structure is illustrated by the spectra of wave surface and the input and output of energy.

Amplitude variations during SIDs in 10.2 and 13.6 kHz waves propagating long distances in the subionospheric waveguide - Theoretical interpretation

NASA Astrophysics Data System (ADS)

Charcosset, G.; Tixier, M.

1981-12-01

During sudden ionospheric disturbances (SIDs), vertical electric field amplitude variations of waves emitted at 10.2 and 13.6 kHz in Norway and Liberia and observed in France were found to result in a regular decrease at the former wavelength and more complex behavior at the latter, where amplitude behavior depends on the importance of the SID. A theoretical interpretation employing a waveguide mode hypothesis of long distance wave propagation is presented, in which it is assumed that the D-region ionization enhancement produced by the solar X-ray flux during SID can be represented by a decrease of the waveguide height in which the shape of the density profile remains unchanged.

Multifluxon dynamics in driven Josephson junctions

NASA Astrophysics Data System (ADS)

Lawrence, Albert; Kim, Nung Soo; McDaniel, James; Jack, Michael

1985-06-01

The dynamics of fluxons in a long Josephson junction driven by time-varying nonuniform bias currents are described by a generalization of the sine-Gordon equation. This equation has solitary wave solutions which correspond to current vortices or quantized packets of magnetic flux in the junction. As with the sine-Gordon equation, multifluxon solutions may be demonstrated for the long Josephson junction. Our numerical calculations show that several fluxons may be launched or annihilated at the end of a junction. We also show multiple steady state conditions which correspond to one or more flux quanta trapped in the junction.

Renormalization group procedure for potential -g/r2

NASA Astrophysics Data System (ADS)

Dawid, S. M.; Gonsior, R.; Kwapisz, J.; Serafin, K.; Tobolski, M.; Głazek, S. D.

2018-02-01

Schrödinger equation with potential - g /r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r = 0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Mechanical Balance Laws for Boussinesq Models of Surface Water Waves

NASA Astrophysics Data System (ADS)

Ali, Alfatih; Kalisch, Henrik

2012-06-01

Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features conservation of mass, momentum and energy for smooth solutions, mechanical balance equations are not widely used in Boussinesq scaling, and it appears that the expressions for many of these quantities are not known. This work presents a systematic derivation of mass, momentum and energy densities and fluxes associated with a general family of Boussinesq systems. The derivation is based on a reconstruction of the velocity field and the pressure in the fluid column below the free surface, and the derivation of differential balance equations which are of the same asymptotic validity as the evolution equations. It is shown that all these mechanical quantities can be expressed in terms of the principal dependent variables of the Boussinesq system: the surface excursion η and the horizontal velocity w at a given level in the fluid.

The Effect of Orifice Eccentricity on Instability of Liquid Jets

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Dolatabadi, Ali

2011-11-01

The hydrodynamic instability of inviscid jets issuing from elliptic orifices is studied. A linear stability analysis is presented for liquid jets that includes the effect of the surrounding gas and an explicit dispersion equation is derived for waves on an infinite uniform jet column. Elliptic configuration has two extreme cases; round jet when ratio of minor to major axis is unity and plane sheet when this ratio approaches zero. Dispersion equation of elliptic jet is approximated for large and small aspect ratios considering asymptotic of the dispersion equation. In case of aspect ratio equal to one, the dispersion equation is analogous to one of the circular jets derived by Yang. In case of aspect ratio approaches zero, the behavior of waves is qualitatively similar to that of long waves on a two dimensional liquid jets and the varicose and sinuous modes are predicted. The growth rate of initial disturbances for various azimuthal modes has been presented in a wide range of disturbances. PhD Candidate.

Reorientational versus Kerr dark and gray solitary waves using modulation theory.

PubMed

Assanto, Gaetano; Marchant, T R; Minzoni, Antonmaria A; Smyth, Noel F

2011-12-01

We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schrödinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations, which have no exact solitary wave solution. We find that the evolution of dark and gray NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive radiation, in contrast to the evolution of bright NLS solitons and bright nematicons. Moreover, the steady nematicon profile is nonmonotonic due to the long-range nonlocality associated with the perturbation of the optic axis. Excellent agreement is obtained with numerical solutions of both the defocusing NLS and nematicon equations. The comparisons for the nematicon solutions raise a number of subtle issues relating to the definition and measurement of the width of a dark or gray nematicon.

Ince-Strutt stability charts for ship parametric roll resonance in irregular waves

NASA Astrophysics Data System (ADS)

Zhang, Xiao; Yang, He-zhen; Xiao, Fei; Xu, Pei-ji

2017-08-01

Ince-Strutt stability chart of ship parametric roll resonance in irregular waves is conducted and utilized for the exploration of the parametric roll resonance in irregular waves. Ship parametric roll resonance will lead to large amplitude roll motion and even wreck. Firstly, the equation describing the parametric roll resonance in irregular waves is derived according to Grim's effective theory and the corresponding Ince-Strutt stability charts are obtained. Secondly, the differences of stability charts for the parametric roll resonance in irregular and regular waves are compared. Thirdly, wave phases and peak periods are taken into consideration to obtain a more realistic sea condition. The influence of random wave phases should be taken into consideration when the analyzed points are located near the instability boundary. Stability charts for different wave peak periods are various. Stability charts are helpful for the parameter determination in design stage to better adapt to sailing condition. Last, ship variables are analyzed according to stability charts by a statistical approach. The increase of the metacentric height will help improve ship stability.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Evidence for self-refraction in a convergence zone: NPE (Nonlinear progressive wave equation) model results

NASA Technical Reports Server (NTRS)

Mcdonald, B. Edward; Plante, Daniel R.

1989-01-01

The nonlinear progressive wave equation (NPE) model was developed by the Naval Ocean Research and Development Activity during 1982 to 1987 to study nonlinear effects in long range oceanic propagation of finite amplitude acoustic waves, including weak shocks. The NPE model was applied to propagation of a generic shock wave (initial condition provided by Sandia Division 1533) in a few illustrative environments. The following consequences of nonlinearity are seen by comparing linear and nonlinear NPE results: (1) a decrease in shock strength versus range (a well-known result of entropy increases at the shock front); (2) an increase in the convergence zone range; and (3) a vertical meandering of the energy path about the corresponding linear ray path. Items (2) and (3) are manifestations of self-refraction.

Parametric resonant triad interactions in a free shear layer

NASA Technical Reports Server (NTRS)

Mallier, R.; Maslowe, S. A.

1993-01-01

We investigate the weakly nonlinear evolution of a triad of nearly-neutral modes superimposed on a mixing layer with velocity profile u bar equals Um + tanh y. The perturbation consists of a plane wave and a pair of oblique waves each inclined at approximately 60 degrees to the mean flow direction. Because the evolution occurs on a relatively fast time scale, the critical layer dynamics dominate the process and the amplitude evolution of the oblique waves is governed by an integro-differential equation. The long-time solution of this equation predicts very rapid (exponential of an exponential) amplification and we discuss the pertinence of this result to vortex pairing phenomena in mixing layers.

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

PubMed

Shukla, P K

2004-04-01

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

The interaction between a propagating coastal vortex and topographic waves

NASA Astrophysics Data System (ADS)

Parry, Simon Wyn

This thesis investigates the motion of a point vortex near coastal topography in a rotating frame of reference at constant latitude (f-plane) in the linear and weakly nonlinear limits. Topography is considered in the form of an infinitely long escarpment running parallel to a wall. The vortex motion and topographic waves are governed by the conservation of quasi-geostrophic potential vorticity in shallow water, from which a nonlinear system of equations is derived. First the linear limit is studied for three cases; a weak vortex on- and off-shelf and a weak vortex close to the wall. For the first two cases it is shown that to leading order the vortex motion is stationary and a solution for the topographic waves at the escarpment can be found in terms of Fourier integrals. For a weak vortex close to a wall, the leading order solution is a steadily propagating vortex with a topographic wavetrain at the step. Numerical results for the higher order interactions are also presented and explained in terms of conservation of momentum in the along-shore direction. For the second case a resonant interaction between the vortex and the waves occurs when the vortex speed is equal to the maximum group velocity of the waves and the linear response becomes unbounded at large times. Thus it becomes necessary to examine the weakly nonlinear near-resonant case. Using a long wave approximation a nonlinear evolution equation for the interface separating the two regions of differing relative potential vorticity is derived and has similar form to the BDA (Benjamin, Davies, Acrivos 1967) equation. Results for the leading order steadily propagating vortex and for the vortex-wave feedback problem are calculated numerically using spectral multi-step Adams methods.

A Computational Study of Shear Layer Receptivity

NASA Astrophysics Data System (ADS)

Barone, Matthew; Lele, Sanjiva

2002-11-01

The receptivity of two-dimensional, compressible shear layers to local and external excitation sources is examined using a computational approach. The family of base flows considered consists of a laminar supersonic stream separated from nearly quiescent fluid by a thin, rigid splitter plate with a rounded trailing edge. The linearized Euler and linearized Navier-Stokes equations are solved numerically in the frequency domain. The flow solver is based on a high order finite difference scheme, coupled with an overset mesh technique developed for computational aeroacoustics applications. Solutions are obtained for acoustic plane wave forcing near the most unstable shear layer frequency, and are compared to the existing low frequency theory. An adjoint formulation to the present problem is developed, and adjoint equation calculations are performed using the same numerical methods as for the regular equation sets. Solutions to the adjoint equations are used to shed light on the mechanisms which control the receptivity of finite-width compressible shear layers.

A rule-based phase control methodology for a slider-crank wave energy converter power take-off system

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

Sang, Yuanrui; Karayaka, H. Bora; Yan, Yanjun

The slider crank is a proven mechanical linkage system with a long history of successful applications, and the slider-crank ocean wave energy converter (WEC) is a type of WEC that converts linear motion into rotation. This paper presents a control algorithm for a slider-crank WEC. In this study, a time-domain hydrodynamic analysis is adopted, and an AC synchronous machine is used in the power take-off system to achieve relatively high system performance. Also, a rule-based phase control strategy is applied to maximize energy extraction, making the system suitable for not only regular sinusoidal waves but also irregular waves. Simulations aremore » carried out under regular sinusoidal wave and synthetically produced irregular wave conditions; performance validations are also presented with high-precision, real ocean wave surface elevation data. The influences of significant wave height, and peak period upon energy extraction of the system are studied. Energy extraction results using the proposed method are compared to those of the passive loading and complex conjugate control strategies; results show that the level of energy extraction is between those of the passive loading and complex conjugate control strategies, and the suboptimal nature of this control strategy is verified.« less

An improved understanding of the natural resonances of moonpools contained within floating rigid-bodies: Theory and application to oscillating water column devices

DOE PAGES

Bull, Diana L.

2015-09-23

The fundamental interactions between waves, a floating rigid-body, and a moonpool that is selectively open to atmosphere or enclosed to purposefully induce pressure fluctuations are investigated. The moonpool hydrodynamic characteristics and the hydrodynamic coupling to the rigid-body are derived implicitly through reciprocity relations on an array of field points. By modeling the free surface of the moonpool in this manner, an explicit hydrodynamic coupling term is included in the equations of motion. This coupling results in the migration of the moonpool's natural resonance frequency from the piston frequency to a new frequency when enclosed in a floating rigid-body. Two geometriesmore » that highlight distinct aspects of marine vessels and oscillating water column (OWC) renewable energy devices are analyzed to reveal the coupled natural resonance migration. The power performance of these two OWCs in regular waves is also investigated. The air chamber is enclosed and a three-dimensional, linear, frequency domain performance model that links the rigid-body to the moonpool through a linear resistive control strategy is detailed. Furthermore, an analytic expression for the optimal linear resistive control values in regular waves is presented.« less

An improved understanding of the natural resonances of moonpools contained within floating rigid-bodies: Theory and application to oscillating water column devices

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

Bull, Diana L.

The fundamental interactions between waves, a floating rigid-body, and a moonpool that is selectively open to atmosphere or enclosed to purposefully induce pressure fluctuations are investigated. The moonpool hydrodynamic characteristics and the hydrodynamic coupling to the rigid-body are derived implicitly through reciprocity relations on an array of field points. By modeling the free surface of the moonpool in this manner, an explicit hydrodynamic coupling term is included in the equations of motion. This coupling results in the migration of the moonpool's natural resonance frequency from the piston frequency to a new frequency when enclosed in a floating rigid-body. Two geometriesmore » that highlight distinct aspects of marine vessels and oscillating water column (OWC) renewable energy devices are analyzed to reveal the coupled natural resonance migration. The power performance of these two OWCs in regular waves is also investigated. The air chamber is enclosed and a three-dimensional, linear, frequency domain performance model that links the rigid-body to the moonpool through a linear resistive control strategy is detailed. Furthermore, an analytic expression for the optimal linear resistive control values in regular waves is presented.« less

Regularity estimates up to the boundary for elliptic systems of difference equations

NASA Technical Reports Server (NTRS)

Strikwerda, J. C.; Wade, B. A.; Bube, K. P.

1986-01-01

Regularity estimates up to the boundary for solutions of elliptic systems of finite difference equations were proved. The regularity estimates, obtained for boundary fitted coordinate systems on domains with smooth boundary, involve discrete Sobolev norms and are proved using pseudo-difference operators to treat systems with variable coefficients. The elliptic systems of difference equations and the boundary conditions which are considered are very general in form. The regularity of a regular elliptic system of difference equations was proved equivalent to the nonexistence of eigensolutions. The regularity estimates obtained are analogous to those in the theory of elliptic systems of partial differential equations, and to the results of Gustafsson, Kreiss, and Sundstrom (1972) and others for hyperbolic difference equations.

Spectral evolution of weakly nonlinear random waves: kinetic description vs direct numerical simulations

NASA Astrophysics Data System (ADS)

Annenkov, Sergei; Shrira, Victor

2016-04-01

We study numerically the long-term evolution of water wave spectra without wind forcing, using three different models, aiming at understanding the role of different sets of assumptions. The first model is the classical Hasselmann kinetic equation (KE). We employ the WRT code kindly provided by G. van Vledder. Two other models are new. As the second model, we use the generalised kinetic equation (gKE), derived without the assumption of quasi-stationarity. Thus, unlike the KE, the gKE is valid in the cases when a wave spectrum is changing rapidly (e.g. at the initial stage of evolution of a narrow spectrum). However, the gKE employs the same statistical closure as the KE. The third model is based on the Zakharov integrodifferential equation for water waves and does not depend on any statistical assumptions. Since the Zakharov equation plays the role of the primitive equation of the theory of wave turbulence, we refer to this model as direct numerical simulation of spectral evolution (DNS-ZE). For initial conditions, we choose two narrow-banded spectra with the same frequency distribution (a JONSWAP spectrum with high peakedness γ = 6) and different degrees of directionality. These spectra are from the set of observations collected in a directional wave tank by Onorato et al (2009). Spectrum A is very narrow in angle (corresponding to N = 840 in the cosN directional model). Spectrum B is initially wider in angle (corresponds to N = 24). Short-term evolution of both spectra (O(102) wave periods) has been studied numerically by Xiao et al (2013) using two other approaches (broad-band modified nonlinear Schrödinger equation and direct numerical simulation based on the high-order spectral method). We use these results to verify the initial stage of our DNS-ZE simulations. However, the advantage of the DNS-ZE method is that it allows to study long-term spectral evolution (up to O(104) periods), which was previously possible only with the KE. In the short-term evolution, we find a good agreement between our DNS-ZE results and simulations by Xiao et al (2013), both for the evolution of frequency spectra and for the directional spreading. In the long term, all three approaches demonstrate very close evolution of integral characteristics of spectra, approaching for large time the theoretical asymptotes of the self-similar stage of evolution. However, the detailed comparison of the spectral evolution shows certain notable differences. Both kinetic equations give virtually identical evolution of spectrum B, but in the case of initially nearly one-dimensional spectrum A the KE overestimates the amplitude of the spectral peak. Meanwhile, the DNS-ZE results show considerably wider spectra with less pronounced peak. There is a striking difference for the rate of spectral broadening, which is much larger for the gKE and especially for the KE, than for the DNS-ZE. We show that the rates of change of the spectra obtained with the DNS-ZE are proportional to the fourth power of nonlinearity, corresponding to the dynamical timescale of evolution, rather than the statistical timescale of both kinetic equations.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method

NASA Astrophysics Data System (ADS)

Volokitin, V.; Liniov, A.; Meyerov, I.; Hartmann, M.; Ivanchenko, M.; Hänggi, P.; Denisov, S.

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dim H =N ≲300 , while the direct long-time numerical integration of the master equation becomes increasingly problematic for N ≳400 , especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η1,η2,...,ηn} , one could propagate a quantum trajectory (with ηi's as norm thresholds) in a numerically exact way. By using a scalable N -particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N =2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method.

PubMed

Volokitin, V; Liniov, A; Meyerov, I; Hartmann, M; Ivanchenko, M; Hänggi, P; Denisov, S

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dimH=N≲300, while the direct long-time numerical integration of the master equation becomes increasingly problematic for N≳400, especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η_{1},η_{2},...,η_{n}}, one could propagate a quantum trajectory (with η_{i}'s as norm thresholds) in a numerically exact way. By using a scalable N-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N=2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

NASA Astrophysics Data System (ADS)

Dutykh, Denys; Hoefer, Mark; Mitsotakis, Dimitrios

2018-04-01

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order 4.

Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order

NASA Astrophysics Data System (ADS)

Reinert, P.; Krebs, H.; Epelbaum, E.

2018-05-01

We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion exchange contributions which i) maintains the long-range part of the interaction, ii) is implemented in momentum space and iii) can be straightforwardly applied to regularize many-body forces and current operators. We discuss in detail the two-nucleon contact interactions at fourth order and demonstrate that three terms out of fifteen used in previous calculations can be eliminated via suitably chosen unitary transformations. The removal of the redundant contact terms results in a drastic simplification of the fits to scattering data and leads to interactions which are much softer ( i.e., more perturbative) than our recent semilocal coordinate-space regularized potentials. Using the pion-nucleon low-energy constants from matching pion-nucleon Roy-Steiner equations to chiral perturbation theory, we perform a comprehensive analysis of nucleon-nucleon scattering and the deuteron properties up to fifth chiral order and study the impact of the leading F-wave two-nucleon contact interactions which appear at sixth order. The resulting chiral potentials at fifth order lead to an outstanding description of the proton-proton and neutron-proton scattering data from the self-consistent Granada-2013 database below the pion production threshold, which is significantly better than for any other chiral potential. For the first time, the chiral potentials match in precision and even outperform the available high-precision phenomenological potentials, while the number of adjustable parameters is, at the same time, reduced by about ˜ 40%. Last but not least, we perform a detailed error analysis and, in particular, quantify for the first time the statistical uncertainties of the fourth- and the considered sixth-order contact interactions.

The Ostrovsky-Vakhnenko equation by a Riemann-Hilbert approach

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry

2015-01-01

We present an inverse scattering transform (IST) approach for the (differentiated) Ostrovsky-Vakhnenko equation This equation can also be viewed as the short wave model for the Degasperis-Procesi (sDP) equation. Our IST approach is based on an associated Riemann-Hilbert problem, which allows us to give a representation for the classical (smooth) solution, to get the principal term of its long time asymptotics, and also to describe loop soliton solutions. Dedicated to Johannes Sjöstrand with gratitude and admiration.

Long-Time Behavior and Critical Limit of Subcritical SQG Equations in Scale-Invariant Sobolev Spaces

NASA Astrophysics Data System (ADS)

Coti Zelati, Michele

2018-02-01

We consider the subcritical SQG equation in its natural scale-invariant Sobolev space and prove the existence of a global attractor of optimal regularity. The proof is based on a new energy estimate in Sobolev spaces to bootstrap the regularity to the optimal level, derived by means of nonlinear lower bounds on the fractional Laplacian. This estimate appears to be new in the literature and allows a sharp use of the subcritical nature of the L^∞ bounds for this problem. As a by-product, we obtain attractors for weak solutions as well. Moreover, we study the critical limit of the attractors and prove their stability and upper semicontinuity with respect to the strength of the diffusion.

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.

Generalized spheroidal wave equation and limiting cases

NASA Astrophysics Data System (ADS)

Figueiredo, B. D. Bonorino

2007-01-01

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the complex plane but present series coefficients proportional to each other. These solutions for the GSWE afford solutions to a double-confluent Heun equation by a taking-limit process due to Leaver. [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. Another procedure, called Whittaker-Ince limit [B. D. Figueiredo, J. Math. Phys. 46, 113503 (2005)], provides solutions in series of powers and Bessel functions for two other equations with a different type of singularity at infinity. In addition, new solutions are obtained for the Whittaker-Hill and Mathieu equations [F. M. Arscott, Proc. R. Soc. Edinburg A67, 265 (1967)] by considering these as special cases of both the confluent and double-confluent Heun equations. In particular, we find that each of the Lindemann-Stieltjes solutions for the Mathieu equation [E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press (1945)] is associated with two expansions in series of Bessel functions. We also discuss a set of solutions in series of hypergeometric and confluent hypergeometric functions for the GSWE and use their Leaver limits to obtain infinite-series solutions for the Schrödinger equation with an asymmetric double-Morse potential. Finally, the possibility of extending the solutions of the GSWE to the general Heun equation is briefly discussed.

On long-time instabilities in staggered finite difference simulations of the seismic acoustic wave equations on discontinuous grids

NASA Astrophysics Data System (ADS)

Gao, Longfei; Ketcheson, David; Keyes, David

2018-02-01

We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

Exhaustive Classification of the Invariant Solutions for a Specific Nonlinear Model Describing Near Planar and Marginally Long-Wave Unstable Interfaces for Phase Transition

NASA Astrophysics Data System (ADS)

Ahangari, Fatemeh

2018-05-01

Problems of thermodynamic phase transition originate inherently in solidification, combustion and various other significant fields. If the transition region among two locally stable phases is adequately narrow, the dynamics can be modeled by an interface motion. This paper is devoted to exhaustive analysis of the invariant solutions for a modified Kuramoto-Sivashinsky equation in two spatial and one temporal dimensions is presented. This nonlinear partial differential equation asymptotically characterizes near planar interfaces, which are marginally long-wave unstable. For this purpose, by applying the classical symmetry method for this model the classical symmetry operators are attained. Moreover, the structure of the Lie algebra of symmetries is discussed and the optimal system of subalgebras, which yields the preliminary classification of group invariant solutions is constructed. Mainly, the Lie invariants corresponding to the infinitesimal symmetry generators as well as associated similarity reduced equations are also pointed out. Furthermore, the nonclassical symmetries of this nonlinear PDE are also comprehensively investigated.

The aerodynamics of propellers and rotors using an acoustic formulation in the time domain

NASA Technical Reports Server (NTRS)

Long, L. N.

1983-01-01

The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.

Scattering theory for the radial H˙1/2-critical wave equation with a cubic convolution

NASA Astrophysics Data System (ADS)

Miao, Changxing; Zhang, Junyong; Zheng, Jiqiang

2015-12-01

In this paper, we study the global well-posedness and scattering for the wave equation with a cubic convolution ∂t2u - Δu = ± (| x | - 3 *| u | 2) u in dimensions d ≥ 4. We prove that if the radial solution u with life-span I obeys (u ,ut) ∈ Lt∞ (I H˙x 1 / 2 (Rd) × H˙x-1/2 (Rd)), then u is global and scatters. By the strategy derived from concentration compactness, we show that the proof of the global well-posedness and scattering is reduced to disprove the existence of two scenarios: soliton-like solution and high to low frequency cascade. Making use of the No-waste Duhamel formula and double Duhamel trick, we deduce that these two scenarios enjoy the additional regularity by the bootstrap argument of [7]. This together with virial analysis implies the energy of such two scenarios is zero and so we get a contradiction.

On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds

NASA Astrophysics Data System (ADS)

Lupo, Umberto

2018-04-01

The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth "on each side" of the initial value hypersurface. A uniqueness result in Sobolev regularity H^{1/2+ɛ }_{loc} is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.

Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation With Small Viscosity

NASA Astrophysics Data System (ADS)

Beck, Margaret; Wayne, C. Eugene

2009-01-01

The large-time behavior of solutions to the Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted L^2 space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this metastable manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave.

Mathematical investigation of tsunami-like long waves interaction with submerge dike of different thickness

NASA Astrophysics Data System (ADS)

Zhiltsov, Konstantin; Kostyushin, Kirill; Kagenov, Anuar; Tyryshkin, Ilya

2017-11-01

This paper presents a mathematical investigation of the interaction of a long tsunami-type wave with a submerge dike. The calculations were performed by using the freeware package OpenFOAM. Unsteady two-dimensional Navier-Stokes equations were used for mathematical modeling of incompressible two-phase medium. The Volume of Fluid (VOF) method is used to capture the free surface of a liquid. The effects caused by long wave of defined amplitude motion through a submerged dike of varying thickness were discussed in detail. Numerical results show that after wave passing through the barrier, multiple vortex structures were formed behind. Intensity of vortex depended on the size of the barrier. The effectiveness of the submerge barrier was estimated by evaluating the wave reflection and transmission coefficients using the energy integral method. Then, the curves of the dependences of the reflection and transmission coefficients were obtained for the interaction of waves with the dike. Finally, it was confirmed that the energy of the wave could be reduced by more than 50% when it passed through the barrier.

Long-time asymptotic analysis of the Korteweg-de Vries equation via the dbar steepest descent method: the soliton region

NASA Astrophysics Data System (ADS)

Giavedoni, Pietro

2017-03-01

We address the problem of long-time asymptotics for the solutions of the Korteweg-de Vries equation under low regularity assumptions. We consider decaying initial data admitting only a finite number of moments. For the so-called ‘soliton region’, an improved asymptotic estimate is provided, in comparison with the one in Grunert and Teschl (2009 Math. Phys. Anal. Geom. 12 287-324). Our analysis is based on the dbar steepest descent method proposed by Miller and McLaughlin. Dedicated to Dora, Paolo and Sanja, with deep gratitude for their love and support.

Huygens triviality of the time-independent Schrödinger equation. Applications to atomic and high energy physics

NASA Astrophysics Data System (ADS)

Kholodenko, Arkady L.; Kauffman, Louis H.

2018-03-01

Huygens triviality - a concept invented by Jacques Hadamard - describes an equivalence class connecting those 2nd order partial differential equations which are transformable into the wave equation. In this work it is demonstrated, that the Schrödinger equation with the time-independent Hamiltonian belongs to such an equivalence class. The wave equation is the equation for which Huygens' principle (HP) holds. The HP was a subject of confusion in both physics and mathematics literature for a long time. Not surprisingly, the role of this principle was obscured from the beginnings of quantum mechanics causing some theoretical and experimental misunderstandings. The purpose of this work is to bring the full clarity into this topic. By doing so, we obtained a large amount of new results related to uses of Lie sphere geometry, of twistors, of Dupin cyclides, of null electromagnetic fields, of AdS-CFT correspondence, of Penrose limits, of geometric algebra, etc. in physical problems ranging from the atomic to high energy physics and cosmology.

Modelling of squall with the generalised kinetic equation

NASA Astrophysics Data System (ADS)

Annenkov, Sergei; Shrira, Victor

2014-05-01

We study the long-term evolution of random wind waves using the new generalised kinetic equation (GKE). The GKE derivation [1] does not assume the quasi-stationarity of a random wave field. In contrast with the Hasselmann kinetic equation, the GKE can describe fast spectral changes occurring when a wave field is driven out of a quasi-equilibrium state by a fast increase or decrease of wind, or by other factors. In these cases, a random wave field evolves on the dynamic timescale typical of coherent wave processes, rather than on the kinetic timescale predicted by the conventional statistical theory. Besides that, the generalised theory allows to trace the evolution of higher statistical moments of the field, notably the kurtosis, which is important for assessing the risk of freak waves and other applications. A new efficient and highly parallelised algorithm for the numerical simulation of the generalised kinetic equation is presented and discussed. Unlike in the case of the Hasselmann equation, the algorithm takes into account all (resonant and non-resonant) nonlinear wave interactions, but only approximately resonant interactions contribute to the spectral evolution. However, counter-intuitively, all interactions contribute to the kurtosis. Without forcing or dissipation, the algorithm is shown to conserve the relevant integrals. We show that under steady wind forcing the wave field evolution predicted by the GKE is close to the predictions of the conventional statistical theory, which is applicable in this case. In particular, we demonstrate the known long-term asymptotics for the evolution of the spectrum. When the wind forcing is not steady (in the simplest case, an instant increase or decrease of wind occurs), the generalised theory is the only way to study the spectral evolution, apart from the direct numerical simulation. The focus of the work is a detailed analysis of the fast evolution after an instant change of forcing, and of the subsequent transition to the new quasi-stationary state of a wave field. It is shown that both increase and decrease of wind lead to a significant transient increase of the dynamic kurtosis, although these changes remain small compared to the changes of the other component of the kurtosis, which is due to bound harmonics. A special consideration is given to the case of the squall, i.e. an instant and large (by a factor of 2-4) increase of wind, which lasts for O(102) characteristic wave periods. We show that fast adjustment processes lead to the formation of a transient spectrum, which has a considerably narrower peak than the spectra developed under a steady forcing. These transient spectra differ qualitatively from those predicted by the Hasselmann kinetic equation under the squall with the same parameters. 1. S.Annenkov, V.Shrira (2006) Role of non-resonant interactions in evolution of nonlinear random water wave fields, J. Fluid Mech. 561, 181-207.

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

Kim, K.; Petersson, N. A.; Rodgers, A.

Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examplesmore » and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.« less

Quasi-static evolution of coronal magnetic fields

NASA Technical Reports Server (NTRS)

Longcope, D. W.; Sudan, R. N.

1992-01-01

A formalism is developed to describe the purely quasi-static part of the evolution of a coronal loop driven by its footpoints. This is accomplished under assumptions of a long, thin loop. The quasi-static equations reveal the possibility for sudden 'loss of equilibrium' at which time the system evolves dynamically rather than quasi-statically. Such quasi-static crises produce high-frequency Alfven waves and, in conjunction with Alfven wave dissipation models, form a viable coronal heating mechanism. Furthermore, an approximate solution to the quasi-static equations by perturbation method verifies the development of small-scale spatial current structure.

Exact traveling soliton solutions for the generalized Benjamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Boudoue Hubert, Malwe; Kudryashov, Nikolai A.; Justin, Mibaile; Abbagari, Souleymanou; Betchewe, Gambo; Doka, Serge Y.

2018-03-01

In this paper, we investigate the generalized Benjamin-Bona-Mahony equation which better describes long waves with arbitrary power-law nonlinearity. As a result, we obtain exact travelling wave soliton solutions, such as anti-kink soliton solution, bright soliton solution, dark soliton solution and periodic solution. These solutions have many free parameters such that they may be used to simulate many experimental situations. The main contribution, in this work, is to not apply the computer codes for construction of exact solutions and not consider the integration constants as zero, because they give all variants for solutions.

Dynamical relationship between wind speed magnitude and meridional temperature contrast: Application to an interannual oscillation in Venusian middle atmosphere GCM

NASA Astrophysics Data System (ADS)

Yamamoto, Masaru; Takahashi, Masaaki

2018-03-01

We derive simple dynamical relationships between wind speed magnitude and meridional temperature contrast. The relationship explains scatter plot distributions of time series of three variables (maximum zonal wind speed UMAX, meridional wind speed VMAX, and equator-pole temperature contrast dTMAX), which are obtained from a Venus general circulation model with equatorial Kelvin-wave forcing. Along with VMAX and dTMAX, UMAX likely increases with the phase velocity and amplitude of a forced wave. In the scatter diagram of UMAX versus dTMAX, points are plotted along a linear equation obtained from a thermal-wind relationship in the cloud layer. In the scatter diagram of VMAX versus UMAX, the apparent slope is somewhat steep in the high UMAX regime, compared with the low UMAX regime. The scatter plot distributions are qualitatively consistent with a quadratic equation obtained from a diagnostic equation of the stream function above the cloud top. The plotted points in the scatter diagrams form a linear cluster for weak wave forcing, whereas they form a small cluster for strong wave forcing. An interannual oscillation of the general circulation forming the linear cluster in the scatter diagram is apparent in the experiment of weak 5.5-day wave forcing. Although a pair of equatorial Kelvin and high-latitude Rossby waves with a same period (Kelvin-Rossby wave) produces equatorward heat and momentum fluxes in the region below 60 km, the equatorial wave does not contribute to the long-period oscillation. The interannual fluctuation of the high-latitude jet core leading to the time variation of UMAX is produced by growth and decay of a polar mixed Rossby-gravity wave with a 14-day period.

Evaluating crude oil chemical dispersion efficacy in a flow-through wave tank under regular non-breaking wave and breaking wave conditions.

PubMed

Li, Zhengkai; Lee, Kenneth; King, Thomas; Boufadel, Michel C; Venosa, Albert D

2009-05-01

Testing dispersant effectiveness under conditions similar to that of the open environment is required for improvements in operational procedures and the formulation of regulatory guidelines. To this end, a novel wave tank facility was fabricated to study the dispersion of crude oil under regular non-breaking and irregular breaking wave conditions. This wave tank facility was designed for operation in a flow-through mode to simulate both wave- and current-driven hydrodynamic conditions. We report here an evaluation of the effectiveness of chemical dispersants (Corexit EC9500A and SPC 1000) on two crude oils (Medium South American [MESA] and Alaska North Slope [ANS]) under two different wave conditions (regular non-breaking and plunging breaking waves) in this wave tank. The dispersant effectiveness was assessed by measuring the water column oil concentration and dispersed oil droplet size distribution. In the absence of dispersants, nearly 8-19% of the test crude oils were dispersed and diluted under regular wave and breaking wave conditions. In the presence of dispersants, about 21-36% of the crude oils were dispersed and diluted under regular waves, and 42-62% under breaking waves. Consistently, physical dispersion under regular waves produced large oil droplets (volumetric mean diameter or VMD > or = 300 microm), whereas chemical dispersion under breaking waves created small droplets (VMD < or = 50 microm). The data can provide useful information for developing better operational guidelines for dispersant use and improved predictive models on dispersant effectiveness in the field.

Numerical and Experimental Study on the Effect of Coral Reef and Beach Vegetation on Reduction of Long Wave Run-Up

NASA Astrophysics Data System (ADS)

Mohandie, R. K.; Teng, M. H.

2009-12-01

Numerical and experimental studies were carried out to examine the mitigating capabilities of coral reefs and vegetations on tsunami and storm surge inundation. For long waves propagating over variable depth such as that over a reef, the nonlinear and dispersive Boussinesq equations were applied. For run-up onto dry land where the nonlinear effect dominates, the nonlinear and nondispersive shallow water equations were used. Long waves with various amplitudes and wavelengths propagating over coral reefs of different length and height were investigated to quantify under which conditions a coral reef may be effective in reducing the wave impact. It was observed that a reef can make a long wave separate into several smaller waves and it can also cause wave breaking resulting in energy dissipation. Our data suggest that both wave separation and breaking induced by coral reefs are effective at mitigating long wave run-up, with the latter being noticeably more effective than the former. As expected, it was observed that the higher the coral reef height, the more the reduction in wave run-up especially when the reef height is greater than 50% of the water depth. For reefs to be effective as a barrier for long waves such as tsunamis and storm surges, it was found that the reefs must be sufficiently long in the wave propagation direction, for example, with its length to be at least of the same magnitude as the wavelength or longer. In this study, it was shown that an effective reef can reduce the long wave run-up by as much as 25% and 50% by wave separation and wave breaking, respectively. Three types of vegetation, namely, grass, shrub and coconut trees, were modeled and tested in a wave tank against various initial wave amplitude and beach slopes in the Hydraulics Lab at the University of Hawaii (UH) to examine each particular type’s effectiveness in reducing wave run-up and to determine its roughness coefficient for wave run-up through numerical simulation and experimental measurement. These roughness coefficients were shown to be higher than the traditional Manning’s coefficient values for vegetation in channel flows. Also, the coefficients were shown to be a function of the ratio of the initial wave amplitude over the vegetation height and are relatively independent of the beach slope. The vegetation spacing and tree diameters in the lab models were selected based on the typical spacing and tree diameter observed in the field through a reduced scale. All three types of vegetation were found to be effective in reducing wave run-up especially on mildly sloped beaches with a reduction rate ranging from 20% to more than 50%. A numerical simulation that incorporated the effects of coral reef and the combined vegetation types showed that on a 5 degree slope the reduction in run-up was 61% as compared to an unprotected scenario. A larger scale experimental study on coconut and bushes in the NSF-funded tsunami basin at the OSU also showed these vegetations are effective at reducing wave run-up. These results can be helpful in achieving a better understanding of the role that coral reefs and vegetation play in tsunami and storm surge mitigation.

3D superwide-angle one-way propagator and its application in seismic modeling and imaging

NASA Astrophysics Data System (ADS)

Jia, Xiaofeng; Jiang, Yunong; Wu, Ru-Shan

2018-07-01

Traditional one-way wave-equation based propagators have been widely used in past decades. Comparing to two-way propagators, one-way methods have higher efficiency and lower memory demands. These two features are especially important in solving large-scale 3D problems. However, regular one-way propagators cannot simulate waves that propagate in large angles within 90° because of their inherent wide angle limitation. Traditional one-way can only propagate along the determined direction (e.g., z-direction), so simulation of turning waves is beyond the ability of one-way methods. We develop 3D superwide-angle one-way propagator to overcome angle limitation and to simulate turning waves with superwide-angle propagation angle (>90°) for modeling and imaging complex geological structures. Wavefields propagating along vertical and horizontal directions are combined using typical stacking scheme. A weight function related to the propagation angle is used for combining and updating wavefields in each propagating step. In the implementation, we use graphics processing units (GPU) to accelerate the process. Typical workflow is designed to exploit the advantages of GPU architecture. Numerical examples show that the method achieves higher accuracy in modeling and imaging steep structures than regular one-way propagators. Actually, superwide-angle one-way propagator can be applied based on any one-way method to improve the effects of seismic modeling and imaging.

Quantum electron levels in the field of a charged black hole

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

Dokuchaev, V. I.; Eroshenko, Yu. N., E-mail: eroshenko@ms2.inr.ac.ru

2015-12-15

Stationary solutions of the Dirac equation in the metric of the charged Reissner–Nordstrom black hole are found. In the case of an extremal black hole, the normalization integral of the wave functions is finite, and the regular stationary solution is physically self-consistent. The presence of quantum electron levels under the Cauchy horizon can have an impact on the final stage of the Hawking evaporation of the black hole, as well as on the particle scattering in the field of the black hole.

Rogue wave generation by inelastic quasi-soliton collisions in optical fibres

NASA Astrophysics Data System (ADS)

Eberhard, M.; Savojardo, A.; Maruta, A.; Römer, R. A.

2017-11-01

We demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schr\\"{o}dinger equation with third-order dispersion. This conceptually novel generation mechanism is based on inelastic collisions of quasi-solitons and is well described by a resonant-like scattering behaviour for the energy transfer in pair-wise quasi-soliton collisions. Our results demonstrate a threshold for rogue wave emergence and the existence of a period of reduced amplitudes - a "calm before the storm" - preceding the arrival of a rogue wave event. Comparing with ultra-long time window simulations of $3.865\\times 10^{6}$ps we observe the statistics of rogue waves in optical fibres with an unprecedented level of detail and accuracy, unambiguously establishing the long-ranged character of the rogue wave power-distribution function over seven orders of magnitude.

Distributional and regularized radiation fields of non-uniformly moving straight dislocations, and elastodynamic Tamm problem

NASA Astrophysics Data System (ADS)

Lazar, Markus; Pellegrini, Yves-Patrick

2016-11-01

This work introduces original explicit solutions for the elastic fields radiated by non-uniformly moving, straight, screw or edge dislocations in an isotropic medium, in the form of time-integral representations in which acceleration-dependent contributions are explicitly separated out. These solutions are obtained by applying an isotropic regularization procedure to distributional expressions of the elastodynamic fields built on the Green tensor of the Navier equation. The obtained regularized field expressions are singularity-free, and depend on the dislocation density rather than on the plastic eigenstrain. They cover non-uniform motion at arbitrary speeds, including faster-than-wave ones. A numerical method of computation is discussed, that rests on discretizing motion along an arbitrary path in the plane transverse to the dislocation, into a succession of time intervals of constant velocity vector over which time-integrated contributions can be obtained in closed form. As a simple illustration, it is applied to the elastodynamic equivalent of the Tamm problem, where fields induced by a dislocation accelerated from rest beyond the longitudinal wave speed, and thereafter put to rest again, are computed. As expected, the proposed expressions produce Mach cones, the dynamic build-up and decay of which is illustrated by means of full-field calculations.

Global-in-time solutions for the isothermal Matovich-Pearson equations

NASA Astrophysics Data System (ADS)

Feireisl, Eduard; Laurençot, Philippe; Mikelić, Andro

2011-01-01

In this paper we study the Matovich-Pearson equations describing the process of glass fibre drawing. These equations may be viewed as a 1D-reduction of the incompressible Navier-Stokes equations including free boundary, valid for the drawing of a long and thin glass fibre. We concentrate on the isothermal case without surface tension. Then the Matovich-Pearson equations represent a nonlinearly coupled system of an elliptic equation for the axial velocity and a hyperbolic transport equation for the fluid cross-sectional area. We first prove existence of a local solution, and, after constructing appropriate barrier functions, we deduce that the fluid radius is always strictly positive and that the local solution remains in the same regularity class. This estimate leads to the global existence and uniqueness result for this important system of equations.

Numerical study on the instabilities in H2-air rotating detonation engines

NASA Astrophysics Data System (ADS)

Liu, Yan; Zhou, Weijiang; Yang, Yunjun; Liu, Zhou; Wang, Jianping

2018-04-01

Numerical simulations of rotating detonation engines (RDEs) are performed using two-dimensional Euler equations and a detailed chemistry model of H2-air. Two propagation modes, the one-wave mode and the two-wave mode, are observed in the RDEs. The instabilities of the RDEs are studied and analyzed specifically. A low frequency instability and a high frequency instability are found from the pressure-time trace measured at a fixed location and the average density-time trace of the RDEs. For the low frequency instability, the pressure peak of the pressure-time trace oscillates with a low frequency while the average density is stable. The deviation between the measurement location and the location of the detonation wave results in the low frequency instability. For the high frequency instability, the average density of the RDEs oscillates regularly with a single frequency while the pressure oscillates irregularly with several frequencies. The oscillation of the detonation wave height results in the high frequency instability. Furthermore, the low frequency instability and the high frequency instability both occur in the one-wave and two-wave mode RDEs.

Nonlinear dynamics of electromagnetic turbulence in a nonuniform magnetized plasma

NASA Astrophysics Data System (ADS)

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

1998-03-01

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

Two different kinds of rogue waves in weakly crossing sea states

NASA Astrophysics Data System (ADS)

Ruban, V. P.

2009-06-01

Formation of giant waves in sea states with two spectral maxima centered at close wave vectors k0±Δk/2 in the Fourier plane is numerically simulated using the fully nonlinear model for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Depending on an angle θ between the vectors k0 and Δk , which determines a typical orientation of interference stripes in the physical plane, rogue waves arise having different spatial structure. If θ≲arctan(1/2) , then typical giant waves are relatively long fragments of essentially two-dimensional (2D) ridges, separated by wide valleys and consisting of alternating oblique crests and troughs. At nearly perpendicular k0 and Δk , the interference minima develop to coherent structures similar to the dark solitons of the nonlinear Schrodinger equation, and a 2D freak wave looks much as a piece of a one-dimensional freak wave bounded in the transversal direction by two such dark solitons.

Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Athanassoulis, Agissilaos

2018-03-01

We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

NASA Astrophysics Data System (ADS)

Boué, Laurent; Dasgupta, Ratul; Laurie, Jason; L'Vov, Victor; Nazarenko, Sergey; Procaccia, Itamar

2011-08-01

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett.JTPLA20021-364010.1134/S002136401008014X 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Twisted gravitational waves

NASA Astrophysics Data System (ADS)

Bini, Donato; Chicone, Carmen; Mashhoon, Bahram

2018-03-01

In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in GR have been studied theoretically for a long time and many exact vacuum solutions of the gravitational field equations are known that represent plane gravitational waves. These have parallel rays and uniform wave fronts. It turns out, however, that GR also admits exact solutions representing gravitational waves propagating along a fixed direction that are nonplanar. The wave front is then nonuniform and the bundle of rays is twisted. We find a class of solutions representing nonplanar unidirectional gravitational waves and study some of the properties of these twisted waves.

The breakdown of the weakly-nonlinear regime for kinetic instabilities

NASA Astrophysics Data System (ADS)

Sanz-Orozco, David; Berk, Herbert; Wang, Ge

2017-10-01

The evolution of marginally-unstable waves that interact resonantly with populations of energetic particles is governed by a well-known cubic integro-differential equation for the mode amplitude. One of the outcomes predicted by the equation is the so-called ``explosive'' regime, where the amplitude grows indefinitely, eventually taking the equation outside of its domain of validity. Beyond this point, only full Vlasov simulations will accurately describe the evolution of the mode amplitude. In this work, we study the breakdown of the cubic equation in detail. We find that, while the cubic equation is still valid, the distribution function of the energetic particles locally flattens or ``folds'' in phase space. This feature is unexpected in view of the assumptions of the theory that are given in. We also derive fifth-order terms in the wave equation, which not only give us a more accurate description of the marginally-unstable modes, but they also allow us to predict the breakdown of the cubic equation. Our findings allow us to better understand the transition between weakly-nonlinear modes and the long-term chirping modes that ultimately emerge.

Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

NASA Astrophysics Data System (ADS)

Hu, Jun; Hadid, Hamda Ben; Henry, Daniel; Mojtabi, Abdelkader

Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka, G, Pr, L, ) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (0), and oscillatory for =0 remains so for >0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability.

Alfvén wave interactions in the solar wind

NASA Astrophysics Data System (ADS)

Webb, G. M.; McKenzie, J. F.; Hu, Q.; le Roux, J. A.; Zank, G. P.

2012-11-01

Alfvén wave mixing (interaction) equations used in locally incompressible turbulence transport equations in the solar wind are analyzed from the perspective of linear wave theory. The connection between the wave mixing equations and non-WKB Alfven wave driven wind theories are delineated. We discuss the physical wave energy equation and the canonical wave energy equation for non-WKB Alfven waves and the WKB limit. Variational principles and conservation laws for the linear wave mixing equations for the Heinemann and Olbert non-WKB wind model are obtained. The connection with wave mixing equations used in locally incompressible turbulence transport in the solar wind are discussed.

Optimization of one-way wave equations.

USGS Publications Warehouse

Lee, M.W.; Suh, S.Y.

1985-01-01

The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors

Strong motion from surface waves in deep sedimentary basins

USGS Publications Warehouse

Joyner, W.B.

2000-01-01

It is widely recognized that long-period surface waves generated by conversion of body waves at the boundaries of deep sedimentary basins make an important contribution to strong ground motion. The factors controlling the amplitude of such motion, however, are not widely understood. A study of pseudovelocity response spectra of strong-motion records from the Los Angeles Basin shows that late-arriving surface waves with group velocities of about 1 km/sec dominate the ground motion for periods of 3 sec and longer. The rate of amplitude decay for these waves is less than for the body waves and depends significantly on period, with smaller decay for longer periods. The amplitude can be modeled by the equation log y = f(M, RE) + c + bRB where y is the pseudovelocity response, f(M, RE) is an attenuation relation based on a general strong-motion data set, M is moment magnitude, RE is the distance from the source to the edge of the basin, RB is the distance from the edge of the basin to the recording site, and b and c are parameters fit to the data. The equation gives values larger by as much as a factor of 3 than given by the attenuation relationships based on general strong-motion data sets for the same source-site distance. It is clear that surface waves need to be taken into account in the design of long-period structures in deep sedimentary basins. The ground-motion levels specified by the earthquake provisions of current building codes, in California at least, accommodate the long-period ground motions from basin-edge-generated surface waves for periods of 5 sec and less and earthquakes with moment magnitudes of 7.5 or less located more than 20 km outside the basin. There may be problems at longer periods and for earthquakes located closer to the basin edge. The results of this study suggest that anelastic attenuation may need to be included in attempts to model long-period motion in deep sedimentary basins. To obtain better data on surface waves in the future, operators of strong-motion networks should take special care for the faithful recording of the long-period components of ground motion. It will also be necessary to insure that at least some selected recorders, once triggered, continue to operate for a time sufficient for the surface waves to traverse the basin. With velocities of about 1 km/sec, that time will be as long as 100 sec for a basin the size of the Los Angeles Basin.

Stochastic dynamic modeling of regular and slow earthquakes

NASA Astrophysics Data System (ADS)

Aso, N.; Ando, R.; Ide, S.

2017-12-01

Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal diffusion appears much slower than the particle velocity of each molecule. The concept of stochastic triggering originates in the Brownian walk model [Ide, 2008], and the present study introduces the stochastic dynamics into dynamic simulations. The stochastic dynamic model has the potential to explain both regular and slow earthquakes more realistically.

Numerical Study of Mixed Convective Peristaltic Flow through Vertical Tube with Heat Generation for Moderate Reynolds and Wave Numbers

NASA Astrophysics Data System (ADS)

Javed, Tariq; Ahmed, B.; Sajid, M.

2018-04-01

The current study focuses on the numerical investigation of the mixed convective peristaltic mechanism through a vertical tube for non-zero Reynolds and wave number. In the set of constitutional equations, energy equation contains the term representing heat generation parameter. The problem is formulated by dropping the assumption of lubrication theory that turns the model mathematically into a system of the nonlinear partial differential equations. The results of the long wavelength in a creeping flow are deduced from the present analysis. Thus, the current study explores the neglected features of peristaltic heat flow in the mixed convective model by considering moderate values of Reynolds and wave numbers. The finite element based on Galerkin’s weighted residual scheme is applied to solve the governing equations. The computed solution is presented in the form of contours of streamlines and isothermal lines, velocity and temperature profiles for variation of different involved parameters. The investigation shows that the strength of circulation for stream function increases by increasing the wave number and Reynolds number. Symmetric isotherms are reported for small values of time-mean flow. Linear behavior of pressure is noticed by vanishing inertial forces while the increase in pressure is observed by amplifying the Reynolds number.

Perfectly invisible PT -symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry

NASA Astrophysics Data System (ADS)

Guilarte, Juan Mateos; Plyushchay, Mikhail S.

2017-12-01

We investigate a special class of the PT -symmetric quantum models being perfectly invisible zero-gap systems with a unique bound state at the very edge of continuous spectrum of scattering states. The family includes the PT -regularized two particle Calogero systems (conformal quantum mechanics models of de Alfaro-Fubini-Furlan) and their rational extensions whose potentials satisfy equations of the KdV hierarchy and exhibit, particularly, a behaviour typical for extreme waves. We show that the two simplest Hamiltonians from the Calogero subfamily determine the fluctuation spectra around the PT -regularized kinks arising as traveling waves in the field-theoretical Liouville and SU(3) conformal Toda systems. Peculiar properties of the quantum systems are reflected in the associated exotic nonlinear supersymmetry in the unbroken or partially broken phases. The conventional N=2 supersymmetry is extended here to the N=4 nonlinear supersymmetry that involves two bosonic generators composed from Lax-Novikov integrals of the subsystems, one of which is the central charge of the superalgebra. Jordan states are shown to play an essential role in the construction.

Global Simulation of Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, George V.; Gallagher, D. L.; Kozyra, J. U.

2007-01-01

It is very well known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (RB) electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. The consequence is that accurate modeling of EMIC waves and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping, wave propagation, and particles. Such a self-consistent model is being progressively developed by Khazanov et al. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density along with the ray tracing equations. We will discuss the recent progress in understanding EMIC waves formation mechanisms in the inner magnetosphere. This problem remains unsettled in spite of many years of experimental and theoretical studies. Modern satellite observations by CRRES, Polar and Cluster still do not reveal the whole picture experimentally since they do not stay long enough in the generation region to give a full account of all the spatio-temporal structure of EMIC waves. The complete self-consistent theory taking into account all factors significant for EMIC waves generation remains to be developed. Several mechanisms are discussed with respect to formation of EMIC waves, among them are nonlinear modification of the ionospheric reflection by precipitating energetic protons, modulation of ion-cyclotron instability by long-period (Pc3/4) pulsations, reflection of waves from layers of heavy-ion gyroresonances, and nonlinearities of wave generation process. We show that each of these mechanisms have their attractive features and explains certain part experimental data but any of them, if taken alone, meets some difficulties when compared to observations. We conclude that development of a refined nonlinear theory and further correlated analysis of modern satellite and ground-based data is needed to solve this very intriguing problem.

Global Simulation of Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K.; Gallagher, D. L.; Kozyra, J. U.

2007-01-01

It is well known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (RB) electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. The consequence is that accurate modeling of EMIC waves and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping, wave propagation, and particles. Such a self-consistent model is being progressively developed by Khazanov et al. [2002 - 2007]. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density along with the ray tracing equations. We will discuss the recent progress in understanding EMIC waves formation mechanisms in the inner magnetosphere. This problem remains unsettled in spite of many years of experimental and theoretical studies. Modern satellite observations by CRRES, Polar and Cluster still do not reveal the whole picture experimentally since they do not stay long enough in the generation region to give a full account of all the spatio-temporal structure of EMIC waves. The complete self-consistent theory taking into account all factors significant for EMIC waves generation remains to be developed. Several mechanisms are discussed with respect to formation of EMIC waves, among them are nonlinear modification of the ionospheric reflection by precipitating energetic protons, modulation of ion-cyclotron instability by long-period (Pc3/4) pulsations, reflection of waves from layers of heavy-ion gyroresonances, and nonlinearities of wave generation process. We show that each of these mechanisms have their attractive features and explains certain part experimental data but any of them, if taken alone, meets some difficulties when compared to observations. We conclude that development of a refined nonlinear theory and further correlated analysis of modern satellite and ground-based data is needed to solve this very intriguing problem.

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

NASA Astrophysics Data System (ADS)

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

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

An Analytical Model of Periodic Waves in Shallow Water,

DTIC Science & Technology

1984-07-01

the KP equation , "f’ + 6f +x + 3 f 0 (1.8) "’ S(t o x yy describes their evolution if they are weakly two-dimensional ( Kadomtsev & Petviashvili ...directions. Both short-crested and long-crested waves are available from the model. Every wave pattern is an exact solution of the Kadomtsev - Petviashvili ...vol. 9, pp 65-66 Kadomtsev , B. B. & V. I. Petviashvili , 1970, Soy. Phys. Doklady, vol. 15, pp 539-541 Korteweg, D. J. & G. de~ries, 1895, Phil Mag

Theoretical Investigation of Dual Tuning of Solitonic Processes in Multiferroic Structures

NASA Astrophysics Data System (ADS)

Cherkasskii, M. A.; Nikitin, A. A.; Ustinov, A. B.; Stashkevich, A.; Kalinikos, B. A.

2016-11-01

. The solitonic wave processes in a multiferroic structure based on ferroelectric and ferrite layers are studied. The influence of external electric and magnetic fields on frequency and wave-number ranges, where bright and dark solitons can exist, are analysed. The investigation was carried out with the nonlinear Schrodinger equation. Results show that an increase of the electric field shifts the boundary between bright and dark solitons to long-wave region. An increase in magnetic field results in the opposite effect.

The Effects of Internal Waves on Acoustic Normal Modes.

DTIC Science & Technology

1984-12-01

amplitudes derived by suppressing azimuthal acoustic fluctuations are still valid as long as each range function is interpreted as a sum over all the...thatp HTp HTv + CvS(!!)(..)(25 The hydrodynamic equations appropriate to an ocean are Du p b + p(fxuL) + Vp - = V-A + F (2.6a) Do + pv.u 0(2.6b) pT Ln+ V... interpreted their scattering coefficients as representing contributions from the internal wave field with hori- zontal wave numbers equal to the

High-order rogue waves of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liu, Wei

2017-10-01

High-order rogue wave solutions of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin-Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

Rogue Wave Modes for the Long Wave-Short Wave Resonance and the Derivative Nonlinear Schrödinger Models

NASA Astrophysics Data System (ADS)

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

2014-11-01

Rogue waves are unexpectedly large displacements of the water surface and will obviously pose threat to maritime activities. Recently, the formation of rogue waves is correlated with the onset of modulation instabilities of plane waves of the system. The long wave-short wave resonance and the derivative nonlinear Schrödinger models are considered. They are relevant in a two-layer fluid and a fourth order perturbation expansion of free surface waves respectively. Analytical solutions of rogue wave modes for the two models are derived by the Hirota bilinear method. Properties and amplitudes of these rogue wave modes are investigated. Conditions for modulation instability of the plane waves are shown to be precisely the requirements for the occurrence of rogue waves. In contrast with the nonlinear Schrödinger equation, rogue wave modes for the derivative nonlinear Schrödinger model exist even if the dispersion and cubic nonlinearity are of the opposite signs, provided that a sufficiently strong self-steepening nonlinearity is present. Extensions to the coupled case (multiple waveguides) will be discussed. This work is partially supported by the Research Grants Council General Research Fund Contract HKU 711713E.

Non-perturbational surface-wave inversion: A Dix-type relation for surface waves

USGS Publications Warehouse

Haney, Matt; Tsai, Victor C.

2015-01-01

We extend the approach underlying the well-known Dix equation in reflection seismology to surface waves. Within the context of surface wave inversion, the Dix-type relation we derive for surface waves allows accurate depth profiles of shear-wave velocity to be constructed directly from phase velocity data, in contrast to perturbational methods. The depth profiles can subsequently be used as an initial model for nonlinear inversion. We provide examples of the Dix-type relation for under-parameterized and over-parameterized cases. In the under-parameterized case, we use the theory to estimate crustal thickness, crustal shear-wave velocity, and mantle shear-wave velocity across the Western U.S. from phase velocity maps measured at 8-, 20-, and 40-s periods. By adopting a thin-layer formalism and an over-parameterized model, we show how a regularized inversion based on the Dix-type relation yields smooth depth profiles of shear-wave velocity. In the process, we quantitatively demonstrate the depth sensitivity of surface-wave phase velocity as a function of frequency and the accuracy of the Dix-type relation. We apply the over-parameterized approach to a near-surface data set within the frequency band from 5 to 40 Hz and find overall agreement between the inverted model and the result of full nonlinear inversion.

Lipschitz regularity results for nonlinear strictly elliptic equations and applications

NASA Astrophysics Data System (ADS)

Ley, Olivier; Nguyen, Vinh Duc

2017-10-01

Most of Lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic growth power in gradient, one usually uses weak Bernstein-type arguments which require regularity and/or convex-type assumptions on the gradient nonlinearity. In this article, we obtain new Lipschitz regularity results for a large class of nonlinear strictly elliptic equations with possibly arbitrary growth power of the Hamiltonian with respect to the gradient variable using some ideas coming from Ishii-Lions' method. We use these bounds to solve an ergodic problem and to study the regularity and the large time behavior of the solution of the evolution equation.

Metachronal wave analysis for non-Newtonian fluid under thermophoresis and Brownian motion effects

NASA Astrophysics Data System (ADS)

Shaheen, A.; Nadeem, S.

This paper analyse the mathematical model of ciliary motion in an annulus. The effect of convective heat transfer and nanoparticle are taken into account. The governing equations of Jeffrey six-constant fluid along with heat and nanoparticle are modelled and then simplified by using long wavelength and low Reynolds number assumptions. The reduced equations are solved with the help of homotopy perturbation method. The obtained expressions for the velocity, temperature and nanoparticles concentration profiles are plotted and the impact of various physical parameters are investigated for different peristaltic waves. Streamlines has also been plotted at the last part of the paper.

On a solution of the nonlinear differential equation for transonic flow past a wave-shaped wall

NASA Technical Reports Server (NTRS)

Kaplan, Carl

1952-01-01

The Prandtl-Busemann small-perturbation method is utilized to obtain the flow of a compressible fluid past an infinitely long wave-shaped wall. When the essential assumption for transonic flow (that all Mach numbers in the region of flow are nearly unity) is introduced, the expression for the velocity potential takes the form of a power series in the transonic similarity parameter. On the basis of this form of the solution, an attempt is made to solve the nonlinear differential equation for transonic flow past the wavy wall. The analysis utilized exhibits clearly the difficulties inherent in nonlinear-flow problems.

Discrete spacetime, quantum walks, and relativistic wave equations

NASA Astrophysics Data System (ADS)

Mlodinow, Leonard; Brun, Todd A.

2018-04-01

It has been observed that quantum walks on regular lattices can give rise to wave equations for relativistic particles in the continuum limit. In this paper, we define the three-dimensional discrete-time walk as a product of three coined one-dimensional walks. The factor corresponding to each one-dimensional walk involves two projection operators that act on an internal coin space; each projector is associated with either the "forward" or "backward" direction in that physical dimension. We show that the simple requirement that there is no preferred axis or direction along an axis—that is, that the walk be symmetric under parity transformations and steps along different axes of the cubic lattice be uncorrelated—leads, in the case of the simplest solution, to the requirement that the continuum limit of the walk is fully Lorentz-invariant. We show further that, in the case of a massive particle, this symmetry requirement necessitates the use of a four-dimensional internal space (as in the Dirac equation). The "coin flip" operation is generated by the parity transformation on the internal coin space, while the differences of the projection operators associated with each dimension must all anticommute. Finally, we discuss the leading correction to the continuum limit, and the possibility of distinguishing through experiment between the discrete random walk and the continuum-based Dirac equation as a description of fermion dynamics.

A theory of self-organized zonal flow with fine radial structure in tokamak

NASA Astrophysics Data System (ADS)

Zhang, Y. Z.; Liu, Z. Y.; Xie, T.; Mahajan, S. M.; Liu, J.

2017-12-01

The (low frequency) zonal flow-ion temperature gradient (ITG) wave system, constructed on Braginskii's fluid model in tokamak, is shown to be a reaction-diffusion-advection system; it is derived by making use of a multiple spatiotemporal scale technique and two-dimensional (2D) ballooning theory. For real regular group velocities of ITG waves, two distinct temporal processes, sharing a very similar meso-scale radial structure, are identified in the nonlinear self-organized stage. The stationary and quasi-stationary structures reflect a particular feature of the poloidal group velocity. The equation set posed to be an initial value problem is numerically solved for JET low mode parameters; the results are presented in several figures and two movies that show the spatiotemporal evolutions as well as the spectrum analysis—frequency-wave number spectrum, auto power spectrum, and Lissajous diagram. This approach reveals that the zonal flow in tokamak is a local traveling wave. For the quasi-stationary process, the cycle of ITG wave energy is composed of two consecutive phases in distinct spatiotemporal structures: a pair of Cavitons growing and breathing slowly without long range propagation, followed by a sudden decay into many Instantons that carry negative wave energy rapidly into infinity. A spotlight onto the motion of Instantons for a given radial position reproduces a Blob-Hole temporal structure; the occurrence as well as the rapid decay of Caviton into Instantons is triggered by zero-crossing of radial group velocity. A sample of the radial profile of zonal flow contributed from 31 nonlinearly coupled rational surfaces near plasma edge is found to be very similar to that observed in the JET Ohmic phase [J. C. Hillesheim et al., Phys. Rev. Lett. 116, 165002 (2016)]. The theory predicts an interior asymmetric dipole structure associated with the zonal flow that is driven by the gradients of ITG turbulence intensity.

Simulating three dimensional wave run-up over breakwaters covered by antifer units

NASA Astrophysics Data System (ADS)

Najafi-Jilani, A.; Niri, M. Zakiri; Naderi, Nader

2014-06-01

The paper presents the numerical analysis of wave run-up over rubble-mound breakwaters covered by antifer units using a technique integrating Computer-Aided Design (CAD) and Computational Fluid Dynamics (CFD) software. Direct application of Navier-Stokes equations within armour blocks, is used to provide a more reliable approach to simulate wave run-up over breakwaters. A well-tested Reynolds-averaged Navier-Stokes (RANS) Volume of Fluid (VOF) code (Flow-3D) was adopted for CFD computations. The computed results were compared with experimental data to check the validity of the model. Numerical results showed that the direct three dimensional (3D) simulation method can deliver accurate results for wave run-up over rubble mound breakwaters. The results showed that the placement pattern of antifer units had a great impact on values of wave run-up so that by changing the placement pattern from regular to double pyramid can reduce the wave run-up by approximately 30%. Analysis was done to investigate the influences of surface roughness, energy dissipation in the pores of the armour layer and reduced wave run-up due to inflow into the armour and stone layer.

Generic effective source for scalar self-force calculations

NASA Astrophysics Data System (ADS)

Wardell, Barry; Vega, Ian; Thornburg, Jonathan; Diener, Peter

2012-05-01

A leading approach to the modeling of extreme mass ratio inspirals involves the treatment of the smaller mass as a point particle and the computation of a regularized self-force acting on that particle. In turn, this computation requires knowledge of the regularized retarded field generated by the particle. A direct calculation of this regularized field may be achieved by replacing the point particle with an effective source and solving directly a wave equation for the regularized field. This has the advantage that all quantities are finite and require no further regularization. In this work, we present a method for computing an effective source which is finite and continuous everywhere, and which is valid for a scalar point particle in arbitrary geodesic motion in an arbitrary background spacetime. We explain in detail various technical and practical considerations that underlie its use in several numerical self-force calculations. We consider as examples the cases of a particle in a circular orbit about Schwarzschild and Kerr black holes, and also the case of a particle following a generic timelike geodesic about a highly spinning Kerr black hole. We provide numerical C code for computing an effective source for various orbital configurations about Schwarzschild and Kerr black holes.

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680

[The evaluation of the thermal environment of man (author's transl)].

PubMed

Sönning, W; Jendritzky, G

1979-10-01

Many problems in bioclimatology require an accurate knowledge of the variations of all meteorological parameters which influence the thermal environment of man (i.g. short- and long-wave radiation, air temperature, wind velocity and air humidity). In addition to that a method for determining this thermal environment by a biometeorological index has to consider thermophysiologically relevant factors so as activity level and thermal resistance of the clothing. By means of the comfort equation (Fanger, 1970) it is possible, for any activity level and clothing to calculate all combinations of meteorological parameters, which will create optimal thermal comfort. The parametrization of the fluxes of short- and long-wave radiation permits to applicate this equation to outdoor conditions (Jendritzky, Sönning and Swantes, 1977). Examples for calculating some given conditions (i.g. street in the city, cross-country kinesitherapy, special land-use areas within a city) are demonstrated.

Quaternion Regularization of the Equations of the Perturbed Spatial Restricted Three-Body Problem: I

NASA Astrophysics Data System (ADS)

Chelnokov, Yu. N.

2017-11-01

We develop a quaternion method for regularizing the differential equations of the perturbed spatial restricted three-body problem by using the Kustaanheimo-Stiefel variables, which is methodologically closely related to the quaternion method for regularizing the differential equations of perturbed spatial two-body problem, which was proposed by the author of the present paper. A survey of papers related to the regularization of the differential equations of the two- and threebody problems is given. The original Newtonian equations of perturbed spatial restricted three-body problem are considered, and the problem of their regularization is posed; the energy relations and the differential equations describing the variations in the energies of the system in the perturbed spatial restricted three-body problem are given, as well as the first integrals of the differential equations of the unperturbed spatial restricted circular three-body problem (Jacobi integrals); the equations of perturbed spatial restricted three-body problem written in terms of rotating coordinate systems whose angular motion is described by the rotation quaternions (Euler (Rodrigues-Hamilton) parameters) are considered; and the differential equations for angular momenta in the restricted three-body problem are given. Local regular quaternion differential equations of perturbed spatial restricted three-body problem in the Kustaanheimo-Stiefel variables, i.e., equations regular in a neighborhood of the first and second body of finite mass, are obtained. The equations are systems of nonlinear nonstationary eleventhorder differential equations. These equations employ, as additional dependent variables, the energy characteristics of motion of the body under study (a body of a negligibly small mass) and the time whose derivative with respect to a new independent variable is equal to the distance from the body of negligibly small mass to the first or second body of finite mass. The equations obtained in the paper permit developing regular methods for determining solutions, in analytical or numerical form, of problems difficult for classicalmethods, such as the motion of a body of negligibly small mass in a neighborhood of the other two bodies of finite masses.

Numerical Simulation of Floating Bodies in Extreme Free Surface Waves

NASA Astrophysics Data System (ADS)

Hu, Zheng Zheng; Causon, Derek; Mingham, Clive; Qiang, Ling

2010-05-01

A task of the EPSRC funded research project 'Extreme Wave loading on Offshore Wave Energy Devices: a Hierarchical Team Approach' is to investigate the survivability of two wave energy converter (WEC) devices Pelamis and the Manchester Bobber using different CFD approaches. Both devices float on the water surface, generating the electricity from the motion of the waves. In this paper, we describe developments of the AMAZON-SC 3D numerical wave tank (NWT) to study extreme wave loading of a fixed or floating (in Heave motion) structure. The extreme wave formulation as an inlet condition is due to Dalzell (1999) and Ning et. al. (2009) in which a first or second-order Stokes focused wave can be prescribed. The AMAZON-SC 3D code (see e.g. Hu et al. (2009)) uses a cell centred finite volume method of the Godunov-type for the space discretization of the Euler and Navier Stokes equations. The computational domain includes both air and water regions with the air/water boundary captured as a discontinuity in the density field thereby admitting the break up and recombination of the free surface. Temporal discretisation uses the artificial compressibility method and a dual time stepping strategy to maintain a divergence free velocity field. Cartesian cut cells are used to provide a fully boundary-fitted gridding capability on an regular background Cartesian grid. Solid objects are cut out of the background mesh leaving a set of irregularly shaped cells fitted to the boundary. The advantages of the cut cell approach have been outlined previously by Causon et al. (2000, 2001) including its flexibility for dealing with complex geometries whether stationary or in relative motion. The field grid does not need to be recomputed globally or even locally for moving body cases; all that is necessary is to update the local cut cell data at the body contour for as long as the motion continues. The handing of numerical wave paddles and device motion in a NWT is therefore straightforward and efficient. Firstly, extreme design wave conditions are generated in an empty NWT and compared with physical experiments as a precursor to calculations to investigate the survivability of the Bobber device operating in a challenging wave climate. Secondly, we consider a bench-mark test case involving in a first order regular wave maker acting on a fixed cylinder and Pelamis. Finally, a floating Bobber has been simulated under extreme wave conditions. These results will be reported at the meeting. Causon D.M., Ingram D.M., Mingham C.G., Yang G. Pearson R.V. (2000). Calculation of shallow water flows using a Cartesian cut cell approach. Advances in Water resources, 23: 545-562. Causon D.M., Ingram D.M., Mingham C.G. (2000). A Cartesian cut cell method for shallow water flows with moving boundaries. Advances in Water resources, 24: 899-911. Dalzell J.F. 1999 A note on finite depth second-order wave-wave interactions. Appl. Ocean Res. 21, 105-111. Ning D.Z., Zang J., Liu S.X. Eatock Taylor R. Teng B. & Taylor P.H. 2009 Free surface and wave kinematics for nonlinear focused wave groups. J. Ocean Engineering. Accepted. Hu Z.Z., Causon D.M., Mingham C.M. and Qian L.(2009). Numerical wave tank study of a wave energy converter in heave. Proceedlings 19th ISOPE conference, Osaka, Japan Qian L., Causon D.M. & Mingham C.G., Ingram D.M. 2006 A free-surface capturing method for two fluid flows with moving bodies. Proc. Roy. Soc. London, Vol. A 462 21-42.

Bäcklund transformations for the Boussinesq equation and merging solitons

NASA Astrophysics Data System (ADS)

Rasin, Alexander G.; Schiff, Jeremy

2017-08-01

The Bäcklund transformation (BT) for the ‘good’ Boussinesq equation and its superposition principles are presented and applied. Unlike other standard integrable equations, the Boussinesq equation does not have a strictly algebraic superposition principle for 2 BTs, but it does for 3. We present this and discuss associated lattice systems. Applying the BT to the trivial solution generates both standard solitons and what we call ‘merging solitons’—solutions in which two solitary waves (with related speeds) merge into a single one. We use the superposition principles to generate a variety of interesting solutions, including superpositions of a merging soliton with 1 or 2 regular solitons, and solutions that develop a singularity in finite time which then disappears at a later finite time. We prove a Wronskian formula for the solutions obtained by applying a general sequence of BTs on the trivial solution. Finally, we obtain the standard conserved quantities of the Boussinesq equation from the BT, and show how the hierarchy of local symmetries follows in a simple manner from the superposition principle for 3 BTs.

Gravity-Capillary Lumps

NASA Astrophysics Data System (ADS)

Akylas, Triantaphyllos R.; Kim, Boguk

2004-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Global Regularity for Several Incompressible Fluid Models with Partial Dissipation

NASA Astrophysics Data System (ADS)

Wu, Jiahong; Xu, Xiaojing; Ye, Zhuan

2017-09-01

This paper examines the global regularity problem on several 2D incompressible fluid models with partial dissipation. They are the surface quasi-geostrophic (SQG) equation, the 2D Euler equation and the 2D Boussinesq equations. These are well-known models in fluid mechanics and geophysics. The fundamental issue of whether or not they are globally well-posed has attracted enormous attention. The corresponding models with partial dissipation may arise in physical circumstances when the dissipation varies in different directions. We show that the SQG equation with either horizontal or vertical dissipation always has global solutions. This is in sharp contrast with the inviscid SQG equation for which the global regularity problem remains outstandingly open. Although the 2D Euler is globally well-posed for sufficiently smooth data, the associated equations with partial dissipation no longer conserve the vorticity and the global regularity is not trivial. We are able to prove the global regularity for two partially dissipated Euler equations. Several global bounds are also obtained for a partially dissipated Boussinesq system.

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.

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

PubMed Central

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

2013-01-01

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

Pile-Driving Pressure and Particle Velocity at the Seabed: Quantifying Effects on Crustaceans and Groundfish.

PubMed

Miller, James H; Potty, Gopu R; Kim, Hui-Kwan

2016-01-01

We modeled the effects of pile driving on crustaceans, groundfish, and other animals near the seafloor. Three different waves were investigated, including the compressional wave, shear wave, and interface wave. A finite element (FE) technique was employed in and around the pile, whereas a parabolic equation (PE) code was used to predict propagation at long ranges from the pile. Pressure, particle displacement, and particle velocity are presented as a function of range at the seafloor for a shallow-water environment near Rhode Island. We discuss the potential effects on animals near the seafloor.

Experimental Study of Internal Waves and Vortices Past 2d Obstacles In A Continuously Stratified Fluid

NASA Astrophysics Data System (ADS)

Mitkin, V.

Experimental investigations of fine and macroscopic structures of density and veloc- ity disturbances generated by a towing cylinder or a vertical strip in a linearly strati- fied liquid are carried out in a rectangular tank. A density gradient field is visualised by different Schlieren methods (direct shadow, 'slit-knife', 'slit-thread', 'natural rain- bow') characterised by a high spatial resolution. Profiles of fluid velocity are visu- alised by density markers U wakes past a vertically descending sugar crystal or an ascending gas bubble. In a fluid at rest the density marker acts as a vertical linear source of internal oscillations, which allows us to measure buoyancy frequency over all depth by the Schlieren instrument directly or by a conductivity probe in a particular point. Sensitive methods reveal a set of high gradient interfaces inside and outside the downstream wake besides well-known large-scale elements: upstream disturbances, attached internal waves and vortices. High gradient interfaces bound compact vor- tices. Vortices moving with respect to environment emit their own systems of internal waves randomising a regular pattern of attached antisymmetric internal waves. But after a rather long time a wave recurrence occurs and a regular but symmetric struc- ture of the longest waves (similar to the pattern of initial attached internal waves) is observed again. Results of studying of the influence of obstacles shape on phase struc- ture and amplitudes of attached internal waves field, vortex formation, their structure and characteristics are presented.

Value of Excess Pressure Integral for Predicting 15-Year All-Cause and Cardiovascular Mortalities in End-Stage Renal Disease Patients.

PubMed

Huang, Jui-Tzu; Cheng, Hao-Min; Yu, Wen-Chung; Lin, Yao-Ping; Sung, Shih-Hsien; Wang, Jiun-Jr; Wu, Chung-Li; Chen, Chen-Huan

2017-11-29

The excess pressure integral (XSPI), derived from analysis of the arterial pressure curve, may be a significant predictor of cardiovascular events in high-risk patients. We comprehensively investigated the prognostic value of XSPI for predicting long-term mortality in end-stage renal disease patients undergoing regular hemodialysis. A total of 267 uremic patients (50.2% female; mean age 54.2±14.9 years) receiving regular hemodialysis for more than 6 months were enrolled. Cardiovascular parameters were obtained by echocardiography and applanation tonometry. Calibrated carotid arterial pressure waveforms were analyzed according to the wave-transmission and reservoir-wave theories. Multivariable Cox proportional hazard models were constructed to account for age, sex, diabetes mellitus, albumin, body mass index, and hemodialysis treatment adequacy. Incremental utility of the parameters to risk stratification was assessed by net reclassification improvement. During a median follow-up of 15.3 years, 124 deaths (46.4%) incurred. Baseline XSPI was significantly predictive of all-cause (hazard ratio per 1 SD 1.4, 95% confidence interval 1.15-1.70, P =0.0006) and cardiovascular mortalities (1.47, 1.18-1.84, P =0.0006) after accounting for the covariates. The addition of XSPI to the base prognostic model significantly improved prediction of both all-cause mortality (net reclassification improvement=0.1549, P =0.0012) and cardiovascular mortality (net reclassification improvement=0.1535, P =0.0033). XSPI was superior to carotid-pulse wave velocity, forward and backward wave amplitudes, and left ventricular ejection fraction in consideration of overall independent and incremental prognostics values. In end-stage renal disease patients undergoing regular hemodialysis, XSPI was significantly predictive of long-term mortality and demonstrated an incremental value to conventional prognostic factors. © 2017 The Authors. Published on behalf of the American Heart Association, Inc., by Wiley.

The theory of transient radiation of a charged particle in a waveguide with an anisotropic magnetodielectric filling

NASA Astrophysics Data System (ADS)

Gevorkyan, E. A.

2015-08-01

We have considered transient radiation of a charged particle that moves at a constant velocity perpendicularly to the axis of a regular waveguide filled with an anisotropic magnetodielectric medium. Wave equations and analytical expressions for transverse electric (TE) and transverse magnetic (TM) fields in the waveguide have been found. Energies of transient radiation of the particle moving in a rectangular waveguide have been determined. We have obtained conditions of occurrence, the frequency, and the energy of Vavilov-Cherenkov radiation.

FIBER OPTICS: Ray invariants and wave equations for transverse modes in three-dimensional graded-index waveguides

NASA Astrophysics Data System (ADS)

Voevodin, V. G.; Morozov, A. N.; Stepanov, V. E.

1992-09-01

A theory of the second ray invariant is proposed using the theory of plane Frenet curves. Its existence requires that the coordinate dependence of the refractive index in the waveguide cross section should satisfy the regularity condition: curves of equal refractive index differ only by an amount which can be obtained using an isotropic scaling transformation. The theoretical conclusions are illustrated using the example of waveguides having the generalized refractive index distribution n ( r ) = n [ (x/ a) + (y/ b)q].

Reconstruction Of The Permittivity Profile Of A Stratified Dielectric Layer

NASA Astrophysics Data System (ADS)

Vogelzang, E.; Ferwerda, H. A.; Yevick, D.

1985-03-01

A numerical procedure is given for the reconstruction of the permittivity profile of a dielectric slab on a perfect conductor. Profiles not supporting guided modes are reconstructed from the complex reflection amplitude for TE-polarized, monochromatic plane waves incident from different directions using the Marchenko theory. The contribution of guided modes is incorporated in the reconstruction procedure through the Gelfand-Levitan equations. An advantage of our approach is that a unique solution for the permittivity profile is obtained without the use of complicated regularization techniques. Some illustrative numerical examples are presented.

Spontaneous long-range calcium waves in developing butterfly wings.

PubMed

Ohno, Yoshikazu; Otaki, Joji M

2015-03-25

Butterfly wing color patterns emerge as the result of a regular arrangement of scales produced by epithelial scale cells at the pupal stage. These color patterns and scale arrangements are coordinated throughout the wing. However, the mechanism by which the development of scale cells is controlled across the entire wing remains elusive. In the present study, we used pupal wings of the blue pansy butterfly, Junonia orithya, which has distinct eyespots, to examine the possible involvement of Ca(2+) waves in wing development. Here, we demonstrate that the developing pupal wing tissue of the blue pansy butterfly displayed spontaneous low-frequency Ca(2+) waves in vivo that propagated slowly over long distances. Some waves appeared to be released from the immediate peripheries of the prospective eyespot and discal spot, though it was often difficult to identify the specific origins of these waves. Physical damage, which is known to induce ectopic eyespots, led to the radiation of Ca(2+) waves from the immediate periphery of the damaged site. Thapsigargin, which is a specific inhibitor of Ca(2+)-ATPases in the endoplasmic reticulum, induced an acute increase in cytoplasmic Ca(2+) levels and halted the spontaneous Ca(2+) waves. Additionally, thapsigargin-treated wings showed incomplete scale development as well as other scale and color pattern abnormalities. We identified a novel form of Ca(2+) waves, spontaneous low-frequency slow waves, which travel over exceptionally long distances. Our results suggest that spontaneous Ca(2+) waves play a critical role in the coordinated development of scale arrangements and possibly in color pattern formation in butterflies.

Seismic gradiometry using ambient seismic noise in an anisotropic Earth

NASA Astrophysics Data System (ADS)

de Ridder, S. A. L.; Curtis, A.

2017-05-01

We introduce a wavefield gradiometry technique to estimate both isotropic and anisotropic local medium characteristics from short recordings of seismic signals by inverting a wave equation. The method exploits the information in the spatial gradients of a seismic wavefield that are calculated using dense deployments of seismic arrays. The application of the method uses the surface wave energy in the ambient seismic field. To estimate isotropic and anisotropic medium properties we invert an elliptically anisotropic wave equation. The spatial derivatives of the recorded wavefield are evaluated by calculating finite differences over nearby recordings, which introduces a systematic anisotropic error. A two-step approach corrects this error: finite difference stencils are first calibrated, then the output of the wave-equation inversion is corrected using the linearized impulse response to the inverted velocity anomaly. We test the procedure on ambient seismic noise recorded in a large and dense ocean bottom cable array installed over Ekofisk field. The estimated azimuthal anisotropy forms a circular geometry around the production-induced subsidence bowl. This conforms with results from studies employing controlled sources, and with interferometry correlating long records of seismic noise. Yet in this example, the results were obtained using only a few minutes of ambient seismic noise.

Formation of Large-Amplitude Wave Groups in an Experimental Model Basin

DTIC Science & Technology

2008-08-01

varying parameters, including amplitude, frequency, and signal duration. Superposition of thes finite regular waves produced repeatable wave groups at a...19 Regular Waves 20 Irregular Waves 21 Senix Wave Gages 21 GLRP 23 Instrumentation Calibration and Uncertainty 26 Senix Ultrasonic Wave Gages... signal output from sine wave superposition, two sine waves combined: x] + x2 (top) and x3 + x4 (middle), all four waves (x, + x2 + x, + xA

An efficient algorithm for the generalized Foldy-Lax formulation

NASA Astrophysics Data System (ADS)

Huang, Kai; Li, Peijun; Zhao, Hongkai

2013-02-01

Consider the scattering of a time-harmonic plane wave incident on a two-scale heterogeneous medium, which consists of scatterers that are much smaller than the wavelength and extended scatterers that are comparable to the wavelength. In this work we treat those small scatterers as isotropic point scatterers and use a generalized Foldy-Lax formulation to model wave propagation and capture multiple scattering among point scatterers and extended scatterers. Our formulation is given as a coupled system, which combines the original Foldy-Lax formulation for the point scatterers and the regular boundary integral equation for the extended obstacle scatterers. The existence and uniqueness of the solution for the formulation is established in terms of physical parameters such as the scattering coefficient and the separation distances. Computationally, an efficient physically motivated Gauss-Seidel iterative method is proposed to solve the coupled system, where only a linear system of algebraic equations for point scatterers or a boundary integral equation for a single extended obstacle scatterer is required to solve at each step of iteration. The convergence of the iterative method is also characterized in terms of physical parameters. Numerical tests for the far-field patterns of scattered fields arising from uniformly or randomly distributed point scatterers and single or multiple extended obstacle scatterers are presented.

On the initial value problem for the wave equation in Friedmann-Robertson-Walker space-times.

PubMed

Abbasi, Bilal; Craig, Walter

2014-09-08

The propagator W ( t 0 , t 1 )( g , h ) for the wave equation in a given space-time takes initial data ( g ( x ), h ( x )) on a Cauchy surface {( t , x ) :  t = t 0 } and evaluates the solution ( u ( t 1 , x ),∂ t u ( t 1 , x )) at other times t 1 . The Friedmann-Robertson-Walker space-times are defined for t 0 , t 1 >0, whereas for t 0 →0, there is a metric singularity. There is a spherical means representation for the general solution of the wave equation with the Friedmann-Robertson-Walker background metric in the three spatial dimensional cases of curvature K =0 and K =-1 given by S. Klainerman and P. Sarnak. We derive from the expression of their representation three results about the wave propagator for the Cauchy problem in these space-times. First, we give an elementary proof of the sharp rate of time decay of solutions with compactly supported data. Second, we observe that the sharp Huygens principle is not satisfied by solutions, unlike in the case of three-dimensional Minkowski space-time (the usual Huygens principle of finite propagation speed is satisfied, of course). Third, we show that for 0< t 0 < t the limit, [Formula: see text] exists, it is independent of h ( x ), and for all reasonable initial data g ( x ), it gives rise to a well-defined solution for all t >0 emanating from the space-time singularity at t =0. Under reflection t →- t , the Friedmann-Robertson-Walker metric gives a space-time metric for t <0 with a singular future at t =0, and the same solution formulae hold. We thus have constructed solutions u ( t , x ) of the wave equation in Friedmann-Robertson-Walker space-times which exist for all [Formula: see text] and [Formula: see text], where in conformally regularized coordinates, these solutions are continuous through the singularity t =0 of space-time, taking on specified data u (0,⋅)= g (⋅) at the singular time.

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

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Statistical properties of nonlinear one-dimensional wave fields

NASA Astrophysics Data System (ADS)

Chalikov, D.

2005-06-01

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

The evolution of hyperboloidal data with the dual foliation formalism: mathematical analysis and wave equation tests

NASA Astrophysics Data System (ADS)

Hilditch, David; Harms, Enno; Bugner, Marcus; Rüter, Hannes; Brügmann, Bernd

2018-03-01

A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed at infinity. The main idea is to apply the ‘dual foliation’ formalism in combination with hyperboloidal coordinates and the generalized harmonic gauge formulation. The strength of the present approach is that, following the ideas of Zenginoğlu, a hyperboloidal layer can be naturally attached to a central region using standard coordinates of numerical relativity applications. Employing a generalization of the standard hyperboloidal slices, developed by Calabrese et al, we find that all formally singular terms take a trivial limit as we head to null-infinity. A byproduct is a numerical approach for hyperboloidal evolution of nonlinear wave equations violating the null-condition. The height-function method, used often for fixed background spacetimes, is generalized in such a way that the slices can be dynamically ‘waggled’ to maintain the desired outgoing coordinate lightspeed precisely. This is achieved by dynamically solving the eikonal equation. As a first numerical test of the new approach we solve the 3D flat space scalar wave equation. The simulations, performed with the pseudospectral bamps code, show that outgoing waves are cleanly absorbed at null-infinity and that errors converge away rapidly as resolution is increased.

Computing many-body wave functions with guaranteed precision: the first-order Møller-Plesset wave function for the ground state of helium atom.

PubMed

Bischoff, Florian A; Harrison, Robert J; Valeev, Edward F

2012-09-14

We present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectral-element multiresolution representation for the two-electron wave function. Because of the exponential storage complexity of the spectral-element representation with the number of dimensions, a brute-force computation of two-electron (six-dimensional) wave functions with high precision was not practical. To overcome the key storage bottlenecks we utilized (1) a low-rank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly correlated R12-type terms in the wave function to regularize the Coulomb electron-electron singularities of the Hamiltonian. All operations necessary to solve the Schrödinger equation were expressed so that the reconstruction of the full-rank form of the wave function is never necessary. Numerical performance of the method was highlighted by computing the first-order Møller-Plesset wave function of a helium atom. The computed second-order Møller-Plesset energy is precise to ~2 microhartrees, which is at the precision limit of the existing general atomic-orbital-based approaches. Our approach does not assume special geometric symmetries, hence application to molecules is straightforward.

The FLAME-slab method for electromagnetic wave scattering in aperiodic slabs

NASA Astrophysics Data System (ADS)

Mansha, Shampy; Tsukerman, Igor; Chong, Y. D.

2017-12-01

The proposed numerical method, "FLAME-slab," solves electromagnetic wave scattering problems for aperiodic slab structures by exploiting short-range regularities in these structures. The computational procedure involves special difference schemes with high accuracy even on coarse grids. These schemes are based on Trefftz approximations, utilizing functions that locally satisfy the governing differential equations, as is done in the Flexible Local Approximation Method (FLAME). Radiation boundary conditions are implemented via Fourier expansions in the air surrounding the slab. When applied to ensembles of slab structures with identical short-range features, such as amorphous or quasicrystalline lattices, the method is significantly more efficient, both in runtime and in memory consumption, than traditional approaches. This efficiency is due to the fact that the Trefftz functions need to be computed only once for the whole ensemble.

Piecewise silence in discrete cosmological models

NASA Astrophysics Data System (ADS)

Clifton, Timothy; Gregoris, Daniele; Rosquist, Kjell

2014-05-01

We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to consider the evolution of a number of geometrically distinguished surfaces that exist within each of them. We find that the evolution equations for the reflection symmetric surfaces can be written as a simple set of Friedmann-like equations, with source terms that behave like a set of interacting effective fluids. We then show that gravitational waves are effectively trapped within small chambers for all time, and are not free to propagate throughout the space-time. Each chamber therefore evolves as if it were in isolation from the rest of the universe. We call this phenomenon ‘piecewise silence’.

The staircase method: integrals for periodic reductions of integrable lattice equations

NASA Astrophysics Data System (ADS)

van der Kamp, Peter H.; Quispel, G. R. W.

2010-11-01

We show, in full generality, that the staircase method (Papageorgiou et al 1990 Phys. Lett. A 147 106-14, Quispel et al 1991 Physica A 173 243-66) provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the quotient-difference (QD)-algorithm and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r, then one can introduce q <= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular {\\ Z}^2 lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.

Investigating and understanding fouling in a planar setup using ultrasonic methods.

PubMed

Wallhäusser, E; Hussein, M A; Becker, T

2012-09-01

Fouling is an unwanted deposit on heat transfer surfaces and occurs regularly in foodstuff heat exchangers. Fouling causes high costs because cleaning of heat exchangers has to be carried out and cleaning success cannot easily be monitored. Thus, used cleaning cycles in foodstuff industry are usually too long leading to high costs. In this paper, a setup is described with which it is possible, first, to produce dairy protein fouling similar to the one found in industrial heat exchangers and, second, to detect the presence and absence of such fouling using an ultrasonic based measuring method. The developed setup resembles a planar heat exchanger in which fouling can be made and cleaned reproducible. Fouling presence, absence, and cleaning progress can be monitored by using an ultrasonic detection unit. The setup is described theoretically based on electrical and mechanical lumped circuits to derive the wave equation and the transfer function to perform a sensitivity analysis. Sensitivity analysis was done to determine influencing quantities and showed that fouling is measurable. Also, first experimental results are compared with results from sensitivity analysis.

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

NASA Astrophysics Data System (ADS)

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

2008-05-01

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

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.

Regularity of the 3D Navier-Stokes equations with viewpoint of 2D flow

NASA Astrophysics Data System (ADS)

Bae, Hyeong-Ohk

2018-04-01

The regularity of 2D Navier-Stokes flow is well known. In this article we study the relationship of 3D and 2D flow, and the regularity of the 3D Naiver-Stokes equations with viewpoint of 2D equations. We consider the problem in the Cartesian and in the cylindrical coordinates.

Lutetia: an example of prediction of polyhedra in shapes of small cosmic bodies

NASA Astrophysics Data System (ADS)

Kochemasov, G. G.

2011-10-01

The following prediction based on rules of the wave planetology [1-12] was published before the Rosetta spacecraft imaged asteroid Lutetia [13]. "A 100 km long flattened asteroid 21-Lutetia will be imaged by the "Ros etta' s pacecraft in July 2010. Knowing that heavenly bodies are effectively structurized by warping inertia -gravity waves one might expect that Lutetia will not be an exclusion out of a row of bodies subjected to an action of these waves [1-9]. The elliptical keplerian orbits with periodically changing bodies 'accelerations imply inertia -gravity forces applied to any body notwithstanding its size, mass, density, chemical composition, and physical state. These forces produce inertia-gravity waves having in rotating bodied standing character and four direct ions of propagation (orthogonal and diagonal). Interfering these waves produce in bodies three (five) kinds of tectonic blocks: uprising s trongly and moderately (++, +), subsiding deeply and moderately (--, -), and neutral (0) where + and - are compensated. Lengths and amplitudes of warping waves form the harmonic sequence. The fundamental wave1 (long 2πR) ma kes ubiquitous tectonic dichotomy (two antipodean segments or hemispheres: one risen, another fallen). In small bodies this structurization is expressed in their convexo-concave shape: one hemisphere is bulged, another one pressed in. Bulging hemisphere is extended, pressed in hemisphere contracted. This wave shaping tends to transform a globular body into a tetrahedron - the ess entially dichotomous s imp les t Plato's figure. In this polyhedron always there is an oppos ition of extension (a face) to contraction (a vertex). The firs t overtone wave2 (long πR) ma kes tectonic s ectors , als o ris en and fallen, and regularly disposed on (and in) a globe. This regularity is expressed in an octahedron form. The octahedron (diamond) or its parts are often observed in shapes of small bodies with small gravities. Larger bodies with rather strong gravity tend to smooth polyhedron vertices and edges but a polyhedron structurization is always present inside their globes a nd is shown in their tectonics, geomorphology and geophysical fields. The shorter warping waves are also present but because of their comparatively small lengths and amplitudes they are not so important in distorting globes. The presented main harmonic row is complicated by superimposed individual waves lengths of which are inversely proportional to orbital frequencies: higher frequency - smaller wave, and, vice versa, lower frequency - larger wave. In the main asteroid belt the fundamental wave of the ma in s equence and the individual wave (a ls o long 2π R) a re in the s tron gest 1:1 resonance what prohibits an accretion of a real planet because of prevailing debris scattering. Thus, the Lutetia shape can support the main point of the wave planetology - "orbits make s tructures ." [13]. Below are some examples of cosmic polyhedra belonging to small bodies of various classes (asteroids, satellites, comets), s izes and compos itions . Thus , the prediction of Lutetia' s hape (s trengthened by the later Tempel's images ) was bas ed on rathe r representative observations.

A modified symplectic PRK scheme for seismic wave modeling

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Ma, Jian

2017-02-01

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

Spectral-Element Simulations of Wave Propagation in Porous Media: Finite-Frequency Sensitivity Kernels Based Upon Adjoint Methods

NASA Astrophysics Data System (ADS)

Morency, C.; Tromp, J.

2008-12-01

The mathematical formulation of wave propagation in porous media developed by Biot is based upon the principle of virtual work, ignoring processes at the microscopic level, and does not explicitly incorporate gradients in porosity. Based on recent studies focusing on averaging techniques, we derive the macroscopic porous medium equations from the microscale, with a particular emphasis on the effects of gradients in porosity. In doing so, we are able to naturally determine two key terms in the momentum equations and constitutive relationships, directly translating the coupling between the solid and fluid phases, namely a drag force and an interfacial strain tensor. In both terms, gradients in porosity arise. One remarkable result is that when we rewrite this set of equations in terms of the well known Biot variables us, w), terms involving gradients in porosity are naturally accommodated by gradients involving w, the fluid motion relative to the solid, and Biot's formulation is recovered, i.e., it remains valid in the presence of porosity gradients We have developed a numerical implementation of the Biot equations for two-dimensional problems based upon the spectral-element method (SEM) in the time domain. The SEM is a high-order variational method, which has the advantage of accommodating complex geometries like a finite-element method, while keeping the exponential convergence rate of (pseudo)spectral methods. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well-suited to simulations on parallel computers. Effects associated with physical dispersion & attenuation and frequency-dependent viscous resistance are addressed by using a memory variable approach. Various benchmarks involving poroelastic wave propagation in the high- and low-frequency regimes, and acoustic-poroelastic and poroelastic-poroelastic discontinuities have been successfully performed. We present finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present finite-frequency kernels for seismic phases in porous media (e.g., fast P, slow P, and S). These kernels illustrate the sensitivity of seismic observables to structural parameters and form the basis of tomographic inversions. Finally, we show an application of this imaging technique related to the detection of buried landmines and unexploded ordnance (UXO) in porous environments.

Tsunamis generated by long and thin granular landslides in a large flume

NASA Astrophysics Data System (ADS)

Miller, Garrett S.; Andy Take, W.; Mulligan, Ryan P.; McDougall, Scott

2017-01-01

In this experimental study, granular material is released down slope to investigate landslide-generated waves. Starting with a known volume and initial position of the landslide source, detailed data are obtained on the velocity and thickness of the granular flow, the shape and location of the submarine landslide deposit, the amplitude and shape of the near-field wave, the far-field wave evolution, and the wave runup elevation on a smooth impermeable slope. The experiments are performed on a 6.7 m long 30° slope on which gravity accelerates the landslides into a 2.1 m wide and 33.0 m long wave flume that terminates with a 27° runup ramp. For a fixed landslide volume of 0.34 m3, tests are conducted in a range of still water depths from 0.05 to 0.50 m. Observations from high-speed cameras and measurements from wave probes indicate that the granular landslide moves as a long and thin train of material, and that only a portion of the landslide (termed the "effective mass") is engaged in activating the leading wave. The wave behavior is highly dependent on the water depth relative to the size of the landslide. In deeper water, the near-field wave behaves as a stable solitary-like wave, while in shallower water, the wave behaves as a breaking dissipative bore. Overall, the physical model observations are in good agreement with the results of existing empirical equations when the effective mass is used to predict the maximum near-field wave amplitude, the far-field amplitude, and the runup of tsunamis generated by granular landslides.

Long-wave equivalent viscoelastic solids for porous rocks saturated by two-phase fluids

NASA Astrophysics Data System (ADS)

Santos, J. E.; Savioli, G. B.

2018-04-01

Seismic waves traveling across fluid-saturated poroelastic materials with mesoscopic-scale heterogeneities induce fluid flow and Biot's slow waves generating energy loss and velocity dispersion. Using Biot's equations of motion to model these type of heterogeneities would require extremely fine meshes. We propose a numerical upscaling procedure to determine the complex and frequency dependent P-wave and shear moduli of an effective viscoelastic medium long-wave equivalent to a poroelastic solid saturated by a two-phase fluid. The two-phase fluid is defined in terms of capillary pressure and relative permeability flow functions. The P-wave and shear effective moduli are determined using harmonic compressibility and shear experiments applied on representative samples of the bulk material. Each experiment is associated with a boundary value problem that is solved using the finite element method. Since a poroelastic solid saturated by a two-phase fluid supports the existence of two slow waves, this upscaling procedure allows to analyze their effect on the mesoscopic-loss mechanism in hydrocarbon reservoir formations. Numerical results show that a two-phase Biot medium model predicts higher attenuation than classic Biot models.

“Kerrr” black hole: The lord of the string

NASA Astrophysics Data System (ADS)

Smailagic, Anais; Spallucci, Euro

2010-04-01

Kerrr in the title is not a typo. The third “r” stands for regular, in the sense of pathology-free rotating black hole. We exhibit a long search-for, exact, Kerr-like, solution of the Einstein equations with novel features: (i) no curvature ring singularity; (ii) no “anti-gravity” universe with causality violating time-like closed world-lines; (iii) no “super-luminal” matter disk. The ring singularity is replaced by a classical, circular, rotating string with Planck tension representing the inner engine driving the rotation of all the surrounding matter. The resulting geometry is regular and smoothly interpolates among inner Minkowski space, borderline de Sitter and outer Kerr universe. The key ingredient to cure all unphysical features of the ordinary Kerr black hole is the choice of a “non-commutative geometry inspired” matter source as the input for the Einstein equations, in analogy with spherically symmetric black holes described in earlier works.

Regularization of the Perturbed Spatial Restricted Three-Body Problem by L-Transformations

NASA Astrophysics Data System (ADS)

Poleshchikov, S. M.

2018-03-01

Equations of motion for the perturbed circular restricted three-body problem have been regularized in canonical variables in a moving coordinate system. Two different L-matrices of the fourth order are used in the regularization. Conditions for generalized symplecticity of the constructed transform have been checked. In the unperturbed case, the regular equations have a polynomial structure. The regular equations have been numerically integrated using the Runge-Kutta-Fehlberg method. The results of numerical experiments are given for the Earth-Moon system parameters taking into account the perturbation of the Sun for different L-matrices.

On the Vertical Structure of Seasonal, Interannual and Intraseasonal Flows

DTIC Science & Technology

1992-12-01

regions. Extensive use is made of a primitive equation (PE) model, as a diagnostic tool, to explore the extent to which tropical heating might influence ...vertical modes, while Wiin-Nielsen (1971a and b) studied the time 2 behaviour of long waves for various vertical structures. More recent investigations...nonlinear three-leve PE model, are used to determine the influence of tropical heating on extratropica wave response. In Chapter 4, the interannual changes

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

Field, Scott E.; Hesthaven, Jan S.; Lau, Stephen R.

In the context of metric perturbation theory for nonspinning black holes, extreme mass ratio binary systems are described by distributionally forced master wave equations. Numerical solution of a master wave equation as an initial boundary value problem requires initial data. However, because the correct initial data for generic-orbit systems is unknown, specification of trivial initial data is a common choice, despite being inconsistent and resulting in a solution which is initially discontinuous in time. As is well known, this choice leads to a burst of junk radiation which eventually propagates off the computational domain. We observe another potential consequence ofmore » trivial initial data: development of a persistent spurious solution, here referred to as the Jost junk solution, which contaminates the physical solution for long times. This work studies the influence of both types of junk on metric perturbations, waveforms, and self-force measurements, and it demonstrates that smooth modified source terms mollify the Jost solution and reduce junk radiation. Our concluding section discusses the applicability of these observations to other numerical schemes and techniques used to solve distributionally forced master wave equations.« less

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

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Manafian, Jalil

2018-03-01

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

S-Wave Normal Mode Propagation in Aluminum Cylinders

USGS Publications Warehouse

Lee, Myung W.; Waite, William F.

2010-01-01

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

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

PubMed

Mazzotti, M; Marzani, A; Bartoli, I

2014-01-01

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

Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Zhang, Kai

2018-06-01

In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we derive the pointwise C α, C 1,α and C 2,α regularity. As byproducts, we also prove the A-B-P maximum principle, Harnack inequality, uniqueness and solvability of the equations.

Solitary waves, rogue waves and homoclinic breather waves for a (2 + 1)-dimensional generalized Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Dong, Min-Jie; Tian, Shou-Fu; Yan, Xue-Wei; Zou, Li; Li, Jin

2017-10-01

We study a (2 + 1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation, which characterizes the formation of patterns in liquid drops. By using Bell’s polynomials, an effective way is employed to succinctly construct the bilinear form of the gKP equation. Based on the resulting bilinear equation, we derive its solitary waves, rogue waves and homoclinic breather waves, respectively. Our results can help enrich the dynamical behavior of the KP-type equations.

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

NASA Astrophysics Data System (ADS)

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

2010-07-01

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

Compressed modes for variational problems in mathematical physics and compactly supported multiresolution basis for the Laplace operator

NASA Astrophysics Data System (ADS)

Ozolins, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2014-03-01

We will describe a general formalism for obtaining spatially localized (``sparse'') solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger's equation in quantum mechanics. Sparsity is achieved by adding an L1 regularization term to the variational principle, which is shown to yield solutions with compact support (``compressed modes''). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. In addition, we introduce an L1 regularized variational framework for developing a spatially localized basis, compressed plane waves (CPWs), that spans the eigenspace of a differential operator, for instance, the Laplace operator. Our approach generalizes the concept of plane waves to an orthogonal real-space basis with multiresolution capabilities. Supported by NSF Award DMR-1106024 (VO), DOE Contract No. DE-FG02-05ER25710 (RC) and ONR Grant No. N00014-11-1-719 (SO).

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Physiological breakdown of Jeffrey six constant nanofluid flow in an endoscope with nonuniform wall

NASA Astrophysics Data System (ADS)

Nadeem, S.; Shaheen, A.; Hussain, S.

2015-12-01

This paper analyse the endoscopic effects of peristaltic nanofluid flow of Jeffrey six-constant fluid model in the presence of magnetohydrodynamics flow. The current problem is modeled in the cylindrical coordinate system and exact solutions are managed (where possible) under low Reynolds number and long wave length approximation. The influence of emerging parameters on temperature and velocity profile are discussed graphically. The velocity equation is solved analytically by utilizing the homotopy perturbation technique strongly, while the exact solutions are computed from temperature equation. The obtained expressions for velocity , concentration and temperature is sketched during graphs and the collision of assorted parameters is evaluate for transform peristaltic waves. The solution depend on thermophoresis number Nt, local nanoparticles Grashof number Gr, and Brownian motion number Nb. The obtained expressions for the velocity, temperature, and nanoparticles concentration profiles are plotted and the impact of various physical parameters are investigated for different peristaltic waves.

A Parallel, Multi-Scale Watershed-Hydrologic-Inundation Model with Adaptively Switching Mesh for Capturing Flooding and Lake Dynamics

NASA Astrophysics Data System (ADS)

Ji, X.; Shen, C.

2017-12-01

Flood inundation presents substantial societal hazards and also changes biogeochemistry for systems like the Amazon. It is often expensive to simulate high-resolution flood inundation and propagation in a long-term watershed-scale model. Due to the Courant-Friedrichs-Lewy (CFL) restriction, high resolution and large local flow velocity both demand prohibitively small time steps even for parallel codes. Here we develop a parallel surface-subsurface process-based model enhanced by multi-resolution meshes that are adaptively switched on or off. The high-resolution overland flow meshes are enabled only when the flood wave invades to floodplains. This model applies semi-implicit, semi-Lagrangian (SISL) scheme in solving dynamic wave equations, and with the assistant of the multi-mesh method, it also adaptively chooses the dynamic wave equation only in the area of deep inundation. Therefore, the model achieves a balance between accuracy and computational cost.

Multiple scattering and stop band characteristics of flexural waves on a thin plate with circular holes

NASA Astrophysics Data System (ADS)

Wang, Zuowei; Biwa, Shiro

2018-03-01

A numerical procedure is proposed for the multiple scattering analysis of flexural waves on a thin plate with circular holes based on the Kirchhoff plate theory. The numerical procedure utilizes the wave function expansion of the exciting as well as scattered fields, and the boundary conditions at the periphery of holes are incorporated as the relations between the expansion coefficients of exciting and scattered fields. A set of linear algebraic equations with respect to the wave expansion coefficients of the exciting field alone is established by the numerical collocation method. To demonstrate the applicability of the procedure, the stop band characteristics of flexural waves are analyzed for different arrangements and concentrations of circular holes on a steel plate. The energy transmission spectra of flexural waves are shown to capture the detailed features of the stop band formation of regular and random arrangements of holes. The increase of the concentration of holes is found to shift the dips of the energy transmission spectra toward higher frequencies as well as deepen them. The hexagonal hole arrangement can form a much broader stop band than the square hole arrangement for flexural wave transmission. It is also demonstrated that random arrangements of holes make the transmission spectrum more complicated.

Rotation-induced nonlinear wavepackets in internal waves

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

Whitfield, A. J., E-mail: ashley.whitfield.12@ucl.ac.uk; Johnson, E. R., E-mail: e.johnson@ucl.ac.uk

2014-05-15

The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets.more » It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.« less

Partial differential equation-based localization of a monopole source from a circular array.

PubMed

Ando, Shigeru; Nara, Takaaki; Levy, Tsukassa

2013-10-01

Wave source localization from a sensor array has long been the most active research topics in both theory and application. In this paper, an explicit and time-domain inversion method for the direction and distance of a monopole source from a circular array is proposed. The approach is based on a mathematical technique, the weighted integral method, for signal/source parameter estimation. It begins with an exact form of the source-constraint partial differential equation that describes the unilateral propagation of wide-band waves from a single source, and leads to exact algebraic equations that include circular Fourier coefficients (phase mode measurements) as their coefficients. From them, nearly closed-form, single-shot and multishot algorithms are obtained that is suitable for use with band-pass/differential filter banks. Numerical evaluation and several experimental results obtained using a 16-element circular microphone array are presented to verify the validity of the proposed method.

A numerical study of the 3-periodic wave solutions to KdV-type equations

NASA Astrophysics Data System (ADS)

Zhang, Yingnan; Hu, Xingbiao; Sun, Jianqing

2018-02-01

In this paper, by using the direct method of calculating periodic wave solutions proposed by Akira Nakamura, we present a numerical process to calculate the 3-periodic wave solutions to several KdV-type equations: the Korteweg-de Vries equation, the Sawada-Koterra equation, the Boussinesq equation, the Ito equation, the Hietarinta equation and the (2 + 1)-dimensional Kadomtsev-Petviashvili equation. Some detailed numerical examples are given to show the existence of the three-periodic wave solutions numerically.

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

DOE PAGES

Larios, Adam; Petersen, Mark R.; Titi, Edriss S.; ...

2017-04-29

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formationmore » in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.« less

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

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

Larios, Adam; Petersen, Mark R.; Titi, Edriss S.

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formationmore » in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.« less

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

PubMed

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

Wave friction factor rediscovered

NASA Astrophysics Data System (ADS)

Le Roux, J. P.

2012-02-01

The wave friction factor is commonly expressed as a function of the horizontal water particle semi-excursion ( A wb) at the top of the boundary layer. A wb, in turn, is normally derived from linear wave theory by {{U_{{wb}}/T_{{w}}}}{{2π }} , where U wb is the maximum water particle velocity measured at the top of the boundary layer and T w is the wave period. However, it is shown here that A wb determined in this way deviates drastically from its real value under both linear and non-linear waves. Three equations for smooth, transitional and rough boundary conditions, respectively, are proposed to solve this problem, all three being a function of U wb, T w, and δ, the thickness of the boundary layer. Because these variables can be determined theoretically for any bottom slope and water depth using the deepwater wave conditions, there is no need to physically measure them. Although differing substantially from many modern attempts to define the wave friction factor, the results coincide with equations proposed in the 1960s for either smooth or rough boundary conditions. The findings also confirm that the long-held notion of circular water particle motion down to the bottom in deepwater conditions is erroneous, the motion in fact being circular at the surface and elliptical at depth in both deep and shallow water conditions, with only horizontal motion at the top of the boundary layer. The new equations are incorporated in an updated version (WAVECALC II) of the Excel program published earlier in this journal by Le Roux et al. Geo-Mar Lett 30(5): 549-560, (2010).

Nonlinear acoustic wave equations with fractional loss operators.

PubMed

Prieur, Fabrice; Holm, Sverre

2011-09-01

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.

Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems

NASA Astrophysics Data System (ADS)

Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.

2015-10-01

In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of variables applied to the Helmholtz, Laplace, or Schrödinger equation leads to a multiparameter eigenvalue problem (MEP); important cases include Mathieu's system, Lamé's system, and a system of spheroidal wave functions. Although multiparameter approaches are exploited occasionally to solve such equations numerically, MEPs remain less well known, and the variety of available numerical methods is not wide. The classical approach of discretizing the equations using standard finite differences leads to algebraic MEPs with large matrices, which are difficult to solve efficiently. The aim of this paper is to change this perspective. We show that by combining spectral collocation methods and new efficient numerical methods for algebraic MEPs it is possible to solve such problems both very efficiently and accurately. We improve on several previous results available in the literature, and also present a MATLAB toolbox for solving a wide range of problems.

Computational Study of Chaotic and Ordered Solutions of the Kuramoto-Sivashinsky Equation

NASA Technical Reports Server (NTRS)

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1996-01-01

We report the results of extensive numerical experiments on the Kuramoto-Sivashinsky equation in the strongly chaotic regime as the viscosity parameter is decreased and increasingly more linearly unstable modes enter the dynamics. General initial conditions are used and evolving states do not assume odd-parity. A large number of numerical experiments are employed in order to obtain quantitative characteristics of the dynamics. We report on different routes to chaos and provide numerical evidence and construction of strange attractors with self-similar characteristics. As the 'viscosity' parameter decreases the dynamics becomes increasingly more complicated and chaotic. In particular it is found that regular behavior in the form of steady state or steady state traveling waves is supported amidst the time-dependent and irregular motions. We show that multimodal steady states emerge and are supported on decreasing windows in parameter space. In addition we invoke a self-similarity property of the equation, to show that these profiles are obtainable from global fixed point attractors of the Kuramoto-Sivashinsky equation at much larger values of the viscosity.

Experimental investigation of linear and nonlinear wave systems: A quantum chaos approach

NASA Astrophysics Data System (ADS)

Neicu, Toni

2002-09-01

An experimental and numerical study of linear and nonlinear wave systems using methods and ideas developed from quantum chaos is presented. We exploit the analogy of the wave equation for the flexural modes of a thin clover-shaped acoustic plate to the stationary solutions of the Schrodinger wave equation for a quantum clover-shaped billiard, a generic system that has regular and chaotic regions in its phase space. We observed periodic orbits in the spectral properties of the acoustic plate, the first such definitive acoustic experiment. We also solved numerically the linear wave equation of the acoustic plate for the first few hundred eigenmodes. The Fourier transform of the eigenvalues show peaks corresponding to the principal periodic orbits of the classical billiard. The signatures of the periodic orbits in the spectra were unambiguously verified by deforming one edge of the plate and observing that only the peaks corresponding to the orbits that hit this edge changed. The statistical measures of the eigenvalues are intermediate between universal forms for completely integrable and chaotic systems. The density distribution of the eigenfunctions agrees with the Porter-Thomas formula of chaotic systems. The viscosity dependence and effects of nonlinearity on the Faraday surface wave patterns in a stadium geometry were also investigated. The ray dynamics inside the stadium, a paradigm of quantum chaos, is completely chaotic. The majority of the observed patterns of the orbits resemble three eigenstates of the stadium: the bouncing ball, longitudinal, and bowtie patterns. We observed many disordered patterns that increase with the viscosity. The experimental results were analyzed using recent theoretical work that explains the suppression of certain modes. The theory also predicts that the perimeter dissipation is too strong for whispering gallery modes, which contradicts our observations of these modes for a fluid with low viscosity. Novel vortex patterns were observed in a strongly nonlinear, dissipative granular system of vertically vibrated rods. Above a critical packing fraction, moving domains of nearly vertical rods were seen to coexist with horizontal rods. The vertical domains coarsen to form several large vortices, which were driven by the anisotropy and inclination of the rods.

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.

Characterization of Regular Wave, Irregular Wave, and Large-Amplitude Wave Group Kinematics in an Experimental Basin

DTIC Science & Technology

2011-02-01

seakeeping was the transient wave technique, developed analytically by Davis and Zarnick (1964). At the David Taylor Model Basin, Davis and Zarnick, and...Gersten and Johnson (1969) applied the transient wave technique to regular wave model experiments for heave and pitch, at zero forward speed. These...tests demonstrated a potential reduction by an order of magnitude of the total necessary testing time. The transient wave technique was also applied to

Finite Difference Modeling of Wave Progpagation in Acoustic TiltedTI Media

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

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

2005-03-21

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

True amplitude wave equation migration arising from true amplitude one-way wave equations

NASA Astrophysics Data System (ADS)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition to these newly defined wavefields in heterogeneous media leads to the Kirchhoff inversion formula for common-shot data when the one-way wavefields are replaced by their ray theoretic approximations. This extension enhances the original WEM method. The objective of that technique was a reflector map, only. The underlying theory did not address amplitude issues. Computer output obtained using numerically generated data confirms the accuracy of this inversion method. However, there are practical limitations. The observed data must be a solution of the wave equation. Therefore, the data over the entire survey area must be collected from a single common-shot experiment. Multi-experiment data, such as common-offset data, cannot be used with this method as currently formulated. Research on extending the method is ongoing at this time.

3D numerical simulation of the long range propagation of acoustical shock waves through a heterogeneous and moving medium

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

Luquet, David; Marchiano, Régis; Coulouvrat, François, E-mail: francois.coulouvrat@upmc.fr

2015-10-28

Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength,more » the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D aspect, the code was massively parallelized using the single program, multiple data paradigm with the Message Passing Interfaces (MPI) for distributed memory architectures. This allows us to handle problems in the order of a thousand billion mesh points in the four dimensions (3 dimensions of space plus time). The validity of the method has been thoroughly evaluated on many cases with known solutions: linear piston, scattering of plane wave by a heterogeneous sphere, propagation in a waveguide with a shear flow, scattering by a finite amplitude vortex and nonlinear propagation in a thermoviscous medium. This validation process allows for a detailed assessment of the advantages and limitations of the method. Finally, applications to atmospheric propagation of shock waves will be presented.« less

3D numerical simulation of the long range propagation of acoustical shock waves through a heterogeneous and moving medium

NASA Astrophysics Data System (ADS)

Luquet, David; Marchiano, Régis; Coulouvrat, François

2015-10-01

Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D aspect, the code was massively parallelized using the single program, multiple data paradigm with the Message Passing Interfaces (MPI) for distributed memory architectures. This allows us to handle problems in the order of a thousand billion mesh points in the four dimensions (3 dimensions of space plus time). The validity of the method has been thoroughly evaluated on many cases with known solutions: linear piston, scattering of plane wave by a heterogeneous sphere, propagation in a waveguide with a shear flow, scattering by a finite amplitude vortex and nonlinear propagation in a thermoviscous medium. This validation process allows for a detailed assessment of the advantages and limitations of the method. Finally, applications to atmospheric propagation of shock waves will be presented.

Contraction of high eccentricity satellite orbits using uniformly regular KS canonical elements with oblate diurnally varying atmosphere.

NASA Astrophysics Data System (ADS)

Raj, Xavier James

2016-07-01

Accurate orbit prediction of an artificial satellite under the influence of air drag is one of the most difficult and untraceable problem in orbital dynamics. The orbital decay of these satellites is mainly controlled by the atmospheric drag effects. The effects of the atmosphere are difficult to determine, since the atmospheric density undergoes large fluctuations. The classical Newtonian equations of motion, which is non linear is not suitable for long-term integration. Many transformations have emerged in the literature to stabilize the equations of motion either to reduce the accumulation of local numerical errors or allowing the use of large integration step sizes, or both in the transformed space. One such transformation is known as KS transformation by Kustaanheimo and Stiefel, who regularized the nonlinear Kepler equations of motion and reduced it into linear differential equations of a harmonic oscillator of constant frequency. The method of KS total energy element equations has been found to be a very powerful method for obtaining numerical as well as analytical solution with respect to any type of perturbing forces, as the equations are less sensitive to round off and truncation errors. The uniformly regular KS canonical equations are a particular canonical form of the KS differential equations, where all the ten KS Canonical elements αi and βi are constant for unperturbed motion. These equations permit the uniform formulation of the basic laws of elliptic, parabolic and hyperbolic motion. Using these equations, developed analytical solution for short term orbit predictions with respect to Earth's zonal harmonic terms J2, J3, J4. Further, these equations were utilized to include the canonical forces and analytical theories with air drag were developed for low eccentricity orbits (e < 0.2) with different atmospheric models. Using uniformly regular KS canonical elements developed analytical theory for high eccentricity (e > 0.2) orbits by assuming the atmosphere to be oblate only. In this paper a new non-singular analytical theory is developed for the motion of high eccentricity satellite orbits with oblate diurnally varying atmosphere in terms of the uniformly regular KS canonical elements. The analytical solutions are generated up to fourth-order terms using a new independent variable and c (a small parameter dependent on the flattening of the atmosphere). Due to symmetry, only two of the nine equations need to be solved analytically to compute the state vector and change in energy at the end of each revolution. The theory is developed on the assumption that density is constant on the surfaces of spheroids of fixed ellipticity ɛ (equal to the Earth's ellipticity, 0.00335) whose axes coincide with the Earth's axis. Numerical experimentation with the analytical solution for a wide range of perigee height, eccentricity, and orbital inclination has been carried out up to 100 revolutions. Comparisons are made with numerically integrated values and found that they match quite well. Effectiveness of the present analytical solutions will be demonstrated by comparing the results with other analytical solutions in the literature.

The soliton transform and a possible application to nonlinear Alfven waves in space

NASA Technical Reports Server (NTRS)

Hada, T.; Hamilton, R. L.; Kennel, C. F.

1993-01-01

The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.

Typology of nonlinear activity waves in a layered neural continuum.

PubMed

Koch, Paul; Leisman, Gerry

2006-04-01

Neural tissue, a medium containing electro-chemical energy, can amplify small increments in cellular activity. The growing disturbance, measured as the fraction of active cells, manifests as propagating waves. In a layered geometry with a time delay in synaptic signals between the layers, the delay is instrumental in determining the amplified wavelengths. The growth of the waves is limited by the finite number of neural cells in a given region of the continuum. As wave growth saturates, the resulting activity patterns in space and time show a variety of forms, ranging from regular monochromatic waves to highly irregular mixtures of different spatial frequencies. The type of wave configuration is determined by a number of parameters, including alertness and synaptic conditioning as well as delay. For all cases studied, using numerical solution of the nonlinear Wilson-Cowan (1973) equations, there is an interval in delay in which the wave mixing occurs. As delay increases through this interval, during a series of consecutive waves propagating through a continuum region, the activity within that region changes from a single-frequency to a multiple-frequency pattern and back again. The diverse spatio-temporal patterns give a more concrete form to several metaphors advanced over the years to attempt an explanation of cognitive phenomena: Activity waves embody the "holographic memory" (Pribram, 1991); wave mixing provides a plausible cause of the competition called "neural Darwinism" (Edelman, 1988); finally the consecutive generation of growing neural waves can explain the discontinuousness of "psychological time" (Stroud, 1955).

Theory of energy and power flow of plasmonic waves on single-walled carbon nanotubes

NASA Astrophysics Data System (ADS)

Moradi, Afshin

2017-10-01

The energy theorem of electrodynamics is extended so as to apply to the plasmonic waves on single-walled carbon nanotubes which propagate parallel to the axial direction of the system and are periodic waves in the azimuthal direction. Electronic excitations on the nanotube surface are modeled by an infinitesimally thin layer of free-electron gas which is described by means of the linearized hydrodynamic theory. General expressions of energy and power flow associated with surface waves are obtained by solving Maxwell and hydrodynamic equations with appropriate boundary conditions. Numerical results for the transverse magnetic mode show that energy, power flow, and energy transport velocity of the plasmonic waves strongly depend on the nanotube radius in the long-wavelength region.

Steady-state turbulence with a narrow inertial range

NASA Technical Reports Server (NTRS)

Weatherall, J. C.; Nicholson, D. R.; Goldman, M. V.

1983-01-01

Coupled two-dimensional wave equations are solved on a computer to model Langmuir wave turbulence excited by a weak electron beam. The model includes wave growth due to beam-plasma interaction, and dissipation by Landau damping. The inertial range is limited to a relatively small number of modes such as could occur when the ratio of masses between the negative and positive ions is larger than in a hydrogen plasma, or when there is damping in long wavelength Langmuir waves. A steady state is found consisting of quasistable, collapsed wave packets. The effects of different beam parameters and the assumed narrow inertial range are considered. The results may be relevant to plasma turbulence observed in connection with type III solar bursts.

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

NASA Astrophysics Data System (ADS)

Kourakis, Ioannis; Sultana, Sharmin; Verheest, Frank

2012-04-01

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

Acoustic plane wave diffraction from a truncated semi-infinite cone in axial irradiation

NASA Astrophysics Data System (ADS)

Kuryliak, Dozyslav; Lysechko, Victor

2017-11-01

The diffraction problem of the plane acoustic wave on the semi-infinite truncated soft and rigid cones in the case of axial incidence is solved. The problem is formulated as a boundary-value problem in terms of Helmholtz equation, with Dirichlet and Neumann boundary conditions, for scattered velocity potential. The incident field is taken to be the total field of semi-infinite cone, the expression of which is obtained by solving the auxiliary diffraction problem by the use of Kontorovich-Lebedev integral transformation. The diffracted field is sought via the expansion in series of the eigenfunctions for subdomains of the Helmholtz equation taking into account the edge condition. The corresponding diffraction problem is reduced to infinite system of linear algebraic equations (ISLAE) making use of mode matching technique and orthogonality properties of the Legendre functions. The method of analytical regularization is applied in order to extract the singular part in ISLAE, invert it exactly and reduce the problem to ISLAE of the second kind, which is readily amenable to calculation. The numerical solution of this system relies on the reduction method; and its accuracy depends on the truncation order. The case of degeneration of the truncated semi-infinite cone into an aperture in infinite plane is considered. Characteristic features of diffracted field in near and far fields as functions of cone's parameters are examined.

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

DTIC Science & Technology

2009-07-01

are described in this chapter. These details are required to compute interference. WC can be used to generate constant arrival time ( Eikonal phase...complicated using Eikonal schemes. Some recent developments in Eikonal methods [2] can treat multiple arrival times but, these methods require extra

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

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

PubMed

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

2014-01-01

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

An approach to rogue waves through the cnoidal equation

NASA Astrophysics Data System (ADS)

Lechuga, Antonio

2014-05-01

Lately it has been realized the importance of rogue waves in some events happening in open seas. Extreme waves and extreme weather could explain some accidents, but not all of them. Every now and then inflicted damages on ships only can be reported to be caused by anomalous and elusive waves, such as rogue waves. That's one of the reason why they continue attracting considerable interest among researchers. In the frame of the Nonlinear Schrödinger equation(NLS), Witham(1974) and Dingemans and Otta (2001)gave asymptotic solutions in moving coordinates that transformed the NLS equation in a ordinary differential equation that is the Duffing or cnoidal wave equation. Applying the Zakharov equation, Stiassnie and Shemer(2004) and Shemer(2010)got also a similar equation. It's well known that this ordinary equation can be solved in elliptic functions. The main aim of this presentation is to sort out the domains of the solutions of this equation, that, of course, are linked to the corresponding solutions of the partial differential equations(PDEs). That being, Lechuga(2007),a simple way to look for anomalous waves as it's the case with some "chaotic" solutions of the Duffing equation.

Theoretical Studies of Alfven Waves and Energetic Particle Physics in Fusion Plasmas

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

Chen, Liu

This report summarizes major theoretical findings in the linear as well as nonlinear physics of Alfvén waves and energetic particles in magnetically confined fusion plasmas. On the linear physics, a variational formulation, based on the separation of singular and regular spatial scales, for drift-Alfvén instabilities excited by energetic particles is established. This variational formulation is then applied to derive the general fishbone-like dispersion relations corresponding to the various Alfvén eigenmodes and energetic-particle modes. It is further employed to explore in depth the low-frequency Alfvén eigenmodes and demonstrate the non-perturbative nature of the energetic particles. On the nonlinear physics, new novelmore » findings are obtained on both the nonlinear wave-wave interactions and nonlinear wave-energetic particle interactions. It is demonstrated that both the energetic particles and the fine radial mode structures could qualitatively affect the nonlinear evolution of Alfvén eigenmodes. Meanwhile, a theoretical approach based on the Dyson equation is developed to treat self-consistently the nonlinear interactions between Alfvén waves and energetic particles, and is then applied to explain simulation results of energetic-particle modes. Relevant list of journal publications on the above findings is also included.« less

Kinetic-scale fluctuations resolved with the Fast Plasma Investigation on NASA's Magnetospheric Multiscale mission.

NASA Astrophysics Data System (ADS)

Gershman, D. J.; Figueroa-Vinas, A.; Dorelli, J.; Goldstein, M. L.; Shuster, J. R.; Avanov, L. A.; Boardsen, S. A.; Stawarz, J. E.; Schwartz, S. J.; Schiff, C.; Lavraud, B.; Saito, Y.; Paterson, W. R.; Giles, B. L.; Pollock, C. J.; Strangeway, R. J.; Russell, C. T.; Torbert, R. B.; Moore, T. E.; Burch, J. L.

2017-12-01

Measurements from the Fast Plasma Investigation (FPI) on NASA's Magnetospheric Multiscale (MMS) mission have enabled unprecedented analyses of kinetic-scale plasma physics. FPI regularly provides estimates of current density and pressure gradients of sufficient accuracy to evaluate the relative contribution of terms in plasma equations of motion. In addition, high-resolution three-dimensional velocity distribution functions of both ions and electrons provide new insights into kinetic-scale processes. As an example, for a monochromatic kinetic Alfven wave (KAW) we find non-zero, but out-of-phase parallel current density and electric field fluctuations, providing direct confirmation of the conservative energy exchange between the wave field and particles. In addition, we use fluctuations in current density and magnetic field to calculate the perpendicular and parallel wavelengths of the KAW. Furthermore, examination of the electron velocity distribution inside the KAW reveals a population of electrons non-linearly trapped in the kinetic-scale magnetic mirror formed between successive wave peaks. These electrons not only contribute to the wave's parallel electric field but also account for over half of the density fluctuations within the wave, supplying an unexpected mechanism for maintaining quasi-neutrality in a KAW. Finally, we demonstrate that the employed wave vector determination technique is also applicable to broadband fluctuations found in Earth's turbulent magnetosheath.

Synchronization of Long Ocean Waves by Coastal Relief on the Southeast Shelf of Sakhalin Island

NASA Astrophysics Data System (ADS)

Kovalev, Dmitry P.; Kovalev, Peter D.

2017-12-01

The phenomenon of synchronization (trapping) of coming waves by the resonant water area in a coastal zone of the sea found from the observed data is considered in the paper. Edge waves with the period of about 10.7 minutes are visually observed in sea level fluctuations near the village of Okhotskoye and the cape Ostri on the southeast coast of Sakhalin Island. These waves are synchronized with the resonance water area. It becomes apparent from the unlimited increase of a phase between the bottom stations installed at distance of about 7.5km. In relation to the phenomenon found, the problem of weak and periodic impact on regular self-oscillatory system — Van der Paul’s oscillator — is considered. Good compliance between theoretical model and data of experiments is obtained.

Improvment of short cut numerical method for determination of periods of free oscillations for basins with irregular geometry and bathymetry

NASA Astrophysics Data System (ADS)

Chernov, Anton; Kurkin, Andrey; Pelinovsky, Efim; Yalciner, Ahmet; Zaytsev, Andrey

2010-05-01

A short cut numerical method for evaluation of the modes of free oscillations of the basins which have irregular geometry and bathymetry was presented in the paper (Yalciner A.C., Pelinovsky E., 2007). In the method, a single wave is inputted to the basin as an initial impulse. The respective agitation in the basin is computed by using the numerical method solving the nonlinear form of long wave equations. The time histories of water surface fluctuations at different locations due to propagation of the waves in relation to the initial impulse are stored and analyzed by the fast Fourier transform technique (FFT) and energy spectrum curves for each location are obtained. The frequencies of each mode of free oscillations are determined from the peaks of the spectrum curves. Some main features were added for this method and will be discussed here: 1. Instead of small number of gauges which were manually installed in the studied area the information from numerical simulation now is recorded on the regular net of the «simulation» gauges which was place everywhere on the sea surface in the depth deeper than "coast" level with the fixed presetted distance between gauges. The spectral analysis of wave records was produced by Welch periodorgam method instead of simple FFT so it's possible to get spectral power estimation for wave process and determine confidence interval for spectra peaks. 2. After the power spectral estimation procedure the common peak of studied seiche can be found and mean spectral amplitudes for this peak were calculated numerically by a Simpson integration method for all gauges in the basin and the mean spectral amplitudes spatial distribution map can be ploted. The spatial distribution helps to study structure of seiche and determine effected dangerous areas. 3. Nested grid module in the NAMI-DANCE - nonlinear shallow water equations calculation software package was developed. This is very important feature for complicated different scale (ocean - sea - bay - harbor) phenomenons studying. The new developed software was tested for Mediterranian, Sea of Okhotsk and South China sea regions. This software can be usefull in local tsunami mapping and tsunami propagation in the coastal zone. References: Yalciner A.C., Pelinovsky E. A short cut numerical method for determination of periods of free oscillations for basins with irregular geometry and bathymetry // Ocean engineering. V. 34. 2007. С. 747 - 757

Bulk Nonlinear Elastic Strain Waves in a Bilayer Coaxial Cylindrical Rod

NASA Astrophysics Data System (ADS)

Gula, I. A.; Samsonov, A. M.

2017-12-01

The problem of the propagation of long nonlinear elastic strain waves in a bilayer coaxial cylindrical rod with an ideal contact between the layers has been considered. Expressions for transverse displacements through longitudinal displacements have been derived. The former satisfies free boundary conditions and continuity conditions for displacements and stresses at the interlayer interface with the desired accuracy. It has been shown how these expressions generalize the well-known plane-section and Love hypotheses for an isotropic homogeneous rod. An equation for the propagation of a nonlinearly elastic strain longitudinal wave has been derived, and its particular solution in the form of a solitary traveling wave has been studied.

Study on longitudinal dispersion relation in one-dimensional relativistic plasma: Linear theory and Vlasov simulation

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

Zhang, H.; Wu, S. Z.; Zhou, C. T.

2013-09-15

The dispersion relation of one-dimensional longitudinal plasma waves in relativistic homogeneous plasmas is investigated with both linear theory and Vlasov simulation in this paper. From the Vlasov-Poisson equations, the linear dispersion relation is derived for the proper one-dimensional Jüttner distribution. Numerically obtained linear dispersion relation as well as an approximate formula for plasma wave frequency in the long wavelength limit is given. The dispersion of longitudinal wave is also simulated with a relativistic Vlasov code. The real and imaginary parts of dispersion relation are well studied by varying wave number and plasma temperature. Simulation results are in agreement with establishedmore » linear theory.« less

Fate of the open-shell singlet ground state in the experimentally accessible acenes: A quantum Monte Carlo study

NASA Astrophysics Data System (ADS)

Dupuy, Nicolas; Casula, Michele

2018-04-01

By means of the Jastrow correlated antisymmetrized geminal power (JAGP) wave function and quantum Monte Carlo (QMC) methods, we study the ground state properties of the oligoacene series, up to the nonacene. The JAGP is the accurate variational realization of the resonating-valence-bond (RVB) ansatz proposed by Pauling and Wheland to describe aromatic compounds. We show that the long-ranged RVB correlations built in the acenes' ground state are detrimental for the occurrence of open-shell diradical or polyradical instabilities, previously found by lower-level theories. We substantiate our outcome by a direct comparison with another wave function, tailored to be an open-shell singlet (OSS) for long-enough acenes. By comparing on the same footing the RVB and OSS wave functions, both optimized at a variational QMC level and further projected by the lattice regularized diffusion Monte Carlo method, we prove that the RVB wave function has always a lower variational energy and better nodes than the OSS, for all molecular species considered in this work. The entangled multi-reference RVB state acts against the electron edge localization implied by the OSS wave function and weakens the diradical tendency for higher oligoacenes. These properties are reflected by several descriptors, including wave function parameters, bond length alternation, aromatic indices, and spin-spin correlation functions. In this context, we propose a new aromatic index estimator suitable for geminal wave functions. For the largest acenes taken into account, the long-range decay of the charge-charge correlation functions is compatible with a quasi-metallic behavior.

Properties of regular polygons of coupled microring resonators.

PubMed

Chremmos, Ioannis; Uzunoglu, Nikolaos

2007-11-01

The resonant properties of a closed and symmetric cyclic array of N coupled microring resonators (coupled-microring resonator regular N-gon) are for the first time determined analytically by applying the transfer matrix approach and Floquet theorem for periodic propagation in cylindrically symmetric structures. By solving the corresponding eigenvalue problem with the field amplitudes in the rings as eigenvectors, it is shown that, for even or odd N, this photonic molecule possesses 1 + N/2 or 1+N resonant frequencies, respectively. The condition for resonances is found to be identical to the familiar dispersion equation of the infinite coupled-microring resonator waveguide with a discrete wave vector. This result reveals the so far latent connection between the two optical structures and is based on the fact that, for a regular polygon, the field transfer matrix over two successive rings is independent of the polygon vertex angle. The properties of the resonant modes are discussed in detail using the illustration of Brillouin band diagrams. Finally, the practical application of a channel-dropping filter based on polygons with an even number of rings is also analyzed.

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

NASA Astrophysics Data System (ADS)

Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

2018-06-01

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

On the regularity criterion of weak solutions for the 3D MHD equations

NASA Astrophysics Data System (ADS)

Gala, Sadek; Ragusa, Maria Alessandra

2017-12-01

The paper deals with the 3D incompressible MHD equations and aims at improving a regularity criterion in terms of the horizontal gradient of velocity and magnetic field. It is proved that the weak solution ( u, b) becomes regular provided that ( \

Statistical properties and correlation functions for drift waves

NASA Technical Reports Server (NTRS)

Horton, W.

1986-01-01

The dissipative one-field drift wave equation is solved using the pseudospectral method to generate steady-state fluctuations. The fluctuations are analyzed in terms of space-time correlation functions and modal probability distributions. Nearly Gaussian statistics and exponential decay of the two-time correlation functions occur in the presence of electron dissipation, while in the absence of electron dissipation long-lived vortical structures occur. Formulas from renormalized, Markovianized statistical turbulence theory are given in a local approximation to interpret the dissipative turbulence.

Nonlinear amplification of coherent waves in media with soliton-type refractive index pattern.

PubMed

Bugaychuk, S; Conte, R

2012-08-01

We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity (including a local and a nonlocal nonlinear responses) and the relaxation is considered. A stable localized spatial structure in the form of a "dark" dissipative soliton is formed in the cavity in the steady state. The envelope of the intensity pattern, as well as of the dynamical grating amplitude, takes the shape of a tanh function. The obtained complex Ginzburg-Landau equation describes the dynamics of this envelope; at the same time, the evolution of this spatial structure changes the parameters of the output waves. New effects are predicted in this system due to the transformation of the dissipative soliton which takes place during the interaction of a pulse with a continuous wave, such as retention of the pulse shape during the transmission of impulses in a long nonlinear cavity, and giant amplification of a seed pulse, which takes energy due to redistribution of the pump continuous energy into the signal.

Long waves in parallel flow in Hele-Shaw cells

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

Zeybek, M.; Yortsos, Y.C.

During the past several years the flow of immiscible flow in Hele-Shaw cells and porous media has been investigated extensively. Of particular interest to most studies has been frontal displacement, specifically viscous fingering instabilities and finger growth. The practical ramifications regarding oil recovery, as well as many other industrial processes in porous media, have served as the primary driving force for most of these investigations. By contrast, little attention has been paid to the motion of lateral fluid interface, which are parallel to the main flow direction. Parallel flow is an often encountered, although much overlooked regime. The evolution ofmore » fluid interfaces in parallel flow in Hele-Shaw cells is studied both theoretically and experimentally in the large capillary number limit. It is shown that such interfaces support wave motion, the amplitude of which for long waves is governed by the KdV equation. Experiments are conducted in a long Hele-Shaw cell that validate the theory in the symmetric case. 35 refs., 16 figs.« less

Symmetry Reductions and Group-Invariant Radial Solutions to the n-Dimensional Wave Equation

NASA Astrophysics Data System (ADS)

Feng, Wei; Zhao, Songlin

2018-01-01

In this paper, we derive explicit group-invariant radial solutions to a class of wave equation via symmetry group method. The optimal systems of one-dimensional subalgebras for the corresponding radial wave equation are presented in terms of the known point symmetries. The reductions of the radial wave equation into second-order ordinary differential equations (ODEs) with respect to each symmetry in the optimal systems are shown. Then we solve the corresponding reduced ODEs explicitly in order to write out the group-invariant radial solutions for the wave equation. Finally, several analytical behaviours and smoothness of the resulting solutions are discussed.

Nonlinear rovibrational polarization response of water vapor to ultrashort long-wave infrared pulses

NASA Astrophysics Data System (ADS)

Schuh, K.; Rosenow, P.; Kolesik, M.; Wright, E. M.; Koch, S. W.; Moloney, J. V.

2017-10-01

We study the rovibrational polarization response of water vapor using a fully correlated optical Bloch equation approach employing data from the HITRAN database. For a 10 -μ m long-wave infrared pulse the resulting linear response is negative, with a negative nonlinear response at intermediate intensities and a positive value at higher intensities. For a model atmosphere comprised of the electronic response of argon combined with the rovibrational response of water vapor this leads to a weakened positive nonlinear response at intermediate intensities. Propagation simulations using a simplified noncorrelated approach show the resultant reduction in the peak filament intensity sustained during filamentation due to the presence of the water vapor.

Derivation of Nonlinear Wave Equation for Flexural Motions of AN Elastic Beam Travelling in AN Air-Filled Tube

NASA Astrophysics Data System (ADS)

Sugimoto, N.; Kugo, K.; Watanabe, Y.

2002-07-01

Asymptotic analysis is carried out to derive a nonlinear wave equation for flexural motions of an elastic beam of circular cross-section travelling along the centre-axis of an air-filled, circular tube placed coaxially. Both the beam and tube are assumed to be long enough for end-effects to be ignored and the aerodynamic loading on the lateral surface of the beam is considered. Assuming a compressible inviscid fluid, the velocity potential of the air is sought systematically in the form of power series in terms of the ratios of the tube radius to a wavelength and of a typical deflection to the radius. Evaluating the pressure force acting on the lateral surface of the beam, the aerodynamic loading including the effects of finite deflection as well as of air's compressibility and axial curvature of the beam are obtained. Although the nonlinearity arises from the kinematical condition on the beam surface, it may be attributed to the presence of the tube wall. With the aerodynamic loading thus obtained, a nonlinear wave equation is derived, whereas linear theory is assumed for the flexural motions of the beam. Some discussions are given on the results.

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.

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

NASA Astrophysics Data System (ADS)

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

2004-05-01

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

Hydrodynamics of Turning Flocks.

PubMed

Yang, Xingbo; Marchetti, M Cristina

2015-12-18

We present a hydrodynamic model of flocking that generalizes the familiar Toner-Tu equations to incorporate turning inertia of well-polarized flocks. The continuum equations controlled by only two dimensionless parameters, orientational inertia and alignment strength, are derived by coarse-graining the inertial spin model recently proposed by Cavagna et al. The interplay between orientational inertia and bend elasticity of the flock yields anisotropic spin waves that mediate the propagation of turning information throughout the flock. The coupling between spin-current density to the local vorticity field through a nonlinear friction gives rise to a hydrodynamic mode with angular-dependent propagation speed at long wavelengths. This mode becomes unstable as a result of the growth of bend and splay deformations augmented by the spin wave, signaling the transition to complex spatiotemporal patterns of continuously turning and swirling flocks.

Efficient three-dimensional resist profile-driven source mask optimization optical proximity correction based on Abbe-principal component analysis and Sylvester equation

NASA Astrophysics Data System (ADS)

Lin, Pei-Chun; Yu, Chun-Chang; Chen, Charlie Chung-Ping

2015-01-01

As one of the critical stages of a very large scale integration fabrication process, postexposure bake (PEB) plays a crucial role in determining the final three-dimensional (3-D) profiles and lessening the standing wave effects. However, the full 3-D chemically amplified resist simulation is not widely adopted during the postlayout optimization due to the long run-time and huge memory usage. An efficient simulation method is proposed to simulate the PEB while considering standing wave effects and resolution enhancement techniques, such as source mask optimization and subresolution assist features based on the Sylvester equation and Abbe-principal component analysis method. Simulation results show that our algorithm is 20× faster than the conventional Gaussian convolution method.

Laboratory tests of short intense envelope solitons

NASA Astrophysics Data System (ADS)

Slunyaev, A.; Clauss, G. F.; Klein, M.; Onorato, M.

2012-04-01

Stability of short intense nonlinear wave groups propagating over deep water is tested in laboratory runs which are performed in the facility of the Technical University of Berlin. The strongly nonlinear simulation of quasi-steady nonlinear wave groups within the framework of the Euler equations is used to generate the surface elevation time series at a border of the water tank. Besides, the exact analytic solution of the nonlinear Schrodinger equation is used for this purpose. The time series is then transformed to a wave maker signal with use of a designed transfer algorithm. Wave group propagation along the tank was recorded by 4 distant gauges and by an array of 6 densely situated gauges. This setup allows to consider the wave evolution from 10 to 85 m from the wave maker, and to obtain the wave envelope shape directly from the instrumental data. In the experiments wave groups were characterized by the steepness values up to kAcr < 0.32 and kAtr < 0.24, where k is the mean wavenumber, Acr is the crest amplitude, and Atr is the trough amplitude; and the maximum local wave slope was up to 0.34. Wave breaking phenomenon was not observed in the experiments. Different mean wave numbers and wave groups of different intensities were considered. In some cases the wave groups exhibit noticeable radiation in the course of propagation, though the groups are not dispersed fully. The effect of finite water depth is found to be significant on the wave group stability. Intense wave groups have shorter time of adjustment, what in some sense may help them to manifest their individuality clearer. The experimental tests confirm recent numerical simulations of fully nonlinear equations, where very steep stable single and interacting nonlinear wave groups were reported [1-3]. The quasi-stationary wave groups observed in numerical and laboratory experiments are strongly nonlinear analogues of the nonlinear Schrodinger envelope solitons. The results emphasize the importance of long-living nonlinear wave groups in dynamics of intense sea waves. [1] V.E. Zakharov, A.I. Dyachenko, A.O. Prokofiev, Eur. J. Mech. B / Fluids 25, 677 (2006). [2] A.I. Dyachenko, V.E. Zakharov, JETP Lett. 88, 307 (2008). [3] A.V. Slunyaev, JETP 109, 676 (2009).

Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation

NASA Technical Reports Server (NTRS)

Spangler, Steven R.

1990-01-01

A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.

Wave energy trapping and localization in a plate with a delamination

NASA Astrophysics Data System (ADS)

Glushkov, Evgeny; Glushkova, Natalia; Golub, Mikhail V.; Moll, Jochen; Fritzen, Claus-Peter

2012-12-01

The research aims at an experimental approval of the trapping mode effect theoretically predicted for an elastic plate-like structure with a horizontal crack. The effect is featured by a sharp capture of incident wave energy at certain resonance frequencies with its localization between the crack and plate surfaces in the form of energy vortices yielding long-enduring standing waves. The trapping modes are eigensolutions of the related diffraction problem associated with nearly real complex points of its discrete frequency spectrum. To detect such resonance motion, a laser vibrometer based system has been employed for the acquisition and appropriate visualization of piezoelectrically actuated out-of-plane surface motion of a two-layer aluminum plate with an artificial strip-like delamination. The measurements at resonance and off-resonance frequencies have revealed a time-harmonic oscillation of good quality above the delamination in the resonance case. It lasts for a long time after the scattered waves have left that area. The measured frequency of the trapped standing-wave oscillation is in a good agreement with that predicted using the integral equation based mathematical model.

Long-wave equivalent viscoelastic solids for porous rocks saturated by two-phase fluids

NASA Astrophysics Data System (ADS)

Santos, J. E.; Savioli, G. B.

2018-07-01

Seismic waves travelling across fluid-saturated poroelastic materials with mesoscopic-scale heterogeneities induce fluid flow and Biot's slow waves generating energy loss and velocity dispersion. Using Biot's equations of motion to model these type of heterogeneities would require extremely fine meshes. We propose a numerical upscaling procedure to determine the complex and frequency-dependent Pwave and shear moduli of an effective viscoelastic medium long-wave equivalent to a poroelastic solid saturated by a two-phase fluid. The two-phase fluid is defined in terms of capillary pressure and relative permeability flow functions. The Pwave and shear effective moduli are determined using harmonic compressibility and shear experiments applied on representative samples of the bulk material. Each experiment is associated with a boundary value problem that is solved using the finite element method. Since a poroelastic solid saturated by a two-phase fluid supports the existence of two slow waves, this upscaling procedure allows to analyse their effect on the mesoscopic loss mechanism in hydrocarbon reservoir formations. Numerical results show that a two-phase Biot medium model predicts higher attenuation than classic Biot models.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

VLF wave injections from the ground

NASA Technical Reports Server (NTRS)

Helliwell, R. A.

1983-01-01

Experiments on wave-particle interactions using VLF whistler-mode waves injected into the magnetosphere from Antartica are described. The injected signals are single-frequency coherent waves whose amplitudes and frequencies may be changed slowly with time, or else two or more coherent wave trains transmitted simultaneously to determine the nature of the response to multifrequency excitation. The waves may be amplified 30 dB or more and may trigger intense emissions having bandwidths that vary from a few to several hundred Hertz. In most cases significant growth and triggering occur only when the driving signal is essentially monochromatic (bandwidth 10 Hz). If two frequencies are transmitted simultaneously the signal at the lower frequency tends to be suppressed by 20 dB or more. These results are interpreted in terms of a feedback interaction between the waves and counter-streaming cyclotron resonant electrons in a region several hundred wavelengths long, centered on the magnetic equator.

Acoustic wave simulation using an overset grid for the global monitoring system

NASA Astrophysics Data System (ADS)

Kushida, N.; Le Bras, R.

2017-12-01

The International Monitoring System of the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) has been monitoring hydro-acoustic and infrasound waves over the globe. Because of the complex natures of the oceans and the atmosphere, computer simulation can play an important role in understanding the observed signals. In this regard, methods which depend on partial differential equations and require minimum modelling, are preferable. So far, to our best knowledge, acoustic wave propagation simulations based on partial differential equations on such a large scale have not been performed (pp 147 - 161 of ref [1], [2]). The main difficulties in building such simulation codes are: (1) considering the inhomogeneity of medium including background flows, (2) high aspect ratio of computational domain, (3) stability during long time integration. To overcome these difficulties, we employ a two-dimensional finite different (FDM) scheme on spherical coordinates with the Yin-Yang overset grid[3] solving the governing equation of acoustic waves introduces by Ostashev et. al.[4]. The comparison with real recording examples in hydro-acoustic will be presented at the conference. [1] Paul C. Etter: Underwater Acoustic Modeling and Simulation, Fourth Edition, CRC Press, 2013. [2] LIAN WANG et. al.: REVIEW OF UNDERWATER ACOUSTIC PROPAGATION MODELS, NPL Report AC 12, 2014. [3] A. Kageyama and T. Sato: "Yin-Yang grid": An overset grid in spherical geometry, Geochem. Geophys. Geosyst., 5, Q09005, 2004. [4] Vladimir E. Ostashev et. al: Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation, Acoustical Society of America. DOI: 10.1121/1.1841531, 2005.

Numerical simulation of electromagnetic wave attenuation in a nonequilibrium chemically reacting hypervelocity flow

NASA Astrophysics Data System (ADS)

Nusca, Michael Joseph, Jr.

The effects of various gasdynamic phenomena on the attenuation of an electromagnetic wave propagating through the nonequilibrium chemically reacting air flow field generated by an aerodynamic body travelling at high velocity is investigated. The nonequilibrium flow field is assumed to consist of seven species including nitric oxide ions and free electrons. The ionization of oxygen and nitrogen atoms is ignored. The aerodynamic body considered is a blunt wedge. The nonequilibrium chemically reacting flow field around this body is numerically simulated using a computer code based on computational fluid dynamics. The computer code solves the Navier-Stokes equations including mass diffusion and heat transfer, using a time-marching, explicit Runge-Kutta scheme. A nonequilibrium air kinetics model consisting of seven species and twenty-eight reactions as well as an equilibrium air model consisting of the same seven species are used. The body surface boundaries are considered as adiabatic or isothermal walls, as well as fully-catalytic and non-catalytic surfaces. Both laminar and turbulent flows are considered; wall generated flow turbulence is simulated using an algebraic mixing length model. An electromagnetic wave is considered as originating from an antenna within the body and is effected by the free electrons in the chemically reacting flow. Analysis of the electromagnetics is performed separately from the fluid dynamic analysis using a series solution of Maxwell's equations valid for the propagation of a long-wavelength plane electromagnetic wave through a thin (i.e., in comparison to wavelength) inhomogeneous plasma layer. The plasma layer is the chemically reacting shock layer around the body. The Navier-Stokes equations are uncoupled from Maxwell's equations. The results of this computational study demonstrate for the first time and in a systematic fashion, the importance of several parameters including equilibrium chemistry, nonequilibrium chemical kinetics, the reaction mechanism, flow viscosity, mass diffusion, and wall boundary conditions on modeling wave attenuation resulting from the interaction of an electromagnetic wave with an aerodynamic plasma. Comparison is made with experimental data.

Bulk solitary waves in elastic solids

NASA Astrophysics Data System (ADS)

Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.

2015-10-01

A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the duct-like polymer shell and proved, that there is no tensile area behind the wave, the bulk soliton propagates on a distance many times longer than its wave length, while both its shape and amplitude remain unchanged. We demonstrated recently how the strain solitons can be used for non-destructive testing (NDT) of laminated composites, used nowadays for various applications, e.g., in microelectronics, aerospace and automotive industries, and bulk strain solitons are among prospective instruments for NDT. Being aimed to propose the bulk strain solitons as an instrument for NDT in solids, we studied numerically the evolution of them in various wave guides with local defects, and shown that the strain soliton undergoes changes in amplitude, phase shift and the shape, that are distinctive and can be estimated. To sum up, now we are able to propose a new NDT technique, based on bulk strain soliton propagation in structural elements.

Wave drift damping acting on multiple circular cylinders (model tests)

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

Kinoshita, Takeshi; Sunahara, Shunji; Bao, W.

1995-12-31

The wave drift damping for the slow drift motion of a four-column platform is experimentally investigated. The estimation of damping force of the slow drift motion of moored floating structures in ocean waves, is one of the most important topics. Bao et al. calculated an interaction of multiple circular cylinders based on the potential flow theory, and showed that the wave drift damping is significantly influenced by the interaction between cylinders. This calculation method assumes that the slow drift motion is approximately replaced by steady current, that is, structures on slow drift motion are supposed to be equivalent to onesmore » in both regular waves and slow current. To validate semi-analytical solutions of Bao et al., experiments were carried out. At first, added resistance due to waves acting on a structure composed of multiple (four) vertical circular cylinders fixed to a slowly moving carriage, was measured in regular waves. Next, the added resistance of the structure moored by linear spring to the slowly moving carriage were measured in regular waves. Furthermore, to validate the assumption that the slow drift motion is replaced by steady current, free decay tests in still water and in regular waves were compared with the simulation of the slow drift motion using the wave drift damping coefficient obtained by the added resistance tests.« less

A regularity condition and temporal asymptotics for chemotaxis-fluid equations

NASA Astrophysics Data System (ADS)

Chae, Myeongju; Kang, Kyungkeun; Lee, Jihoon; Lee, Ki-Ahm

2018-02-01

We consider two dimensional chemotaxis equations coupled to the Navier-Stokes equations. We present a new localized regularity criterion that is localized in a neighborhood at each point. Secondly, we establish temporal decays of the regular solutions under the assumption that the initial mass of biological cell density is sufficiently small. Both results are improvements of previously known results given in Chae et al (2013 Discrete Continuous Dyn. Syst. A 33 2271-97) and Chae et al (2014 Commun. PDE 39 1205-35)

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Yang, H. Q.

1989-01-01

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

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.

Computation of rapidly varied unsteady, free-surface flow

USGS Publications Warehouse

Basco, D.R.

1987-01-01

Many unsteady flows in hydraulics occur with relatively large gradients in free surface profiles. The assumption of hydrostatic pressure distribution with depth is no longer valid. These are rapidly-varied unsteady flows (RVF) of classical hydraulics and also encompass short wave propagation of coastal hydraulics. The purpose of this report is to present an introductory review of the Boussinnesq-type differential equations that describe these flows and to discuss methods for their numerical integration. On variable slopes and for large scale (finite-amplitude) disturbances, three independent derivational methods all gave differences in the motion equation for higher order terms. The importance of these higher-order terms for riverine applications must be determined by numerical experiments. Care must be taken in selection of the appropriate finite-difference scheme to minimize truncation error effects and the possibility of diverging (double mode) numerical solutions. It is recommended that practical hydraulics cases be established and tested numerically to demonstrate the order of differences in solution with those obtained from the long wave equations of St. Venant. (USGS)

Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions

NASA Astrophysics Data System (ADS)

Yang, Bo; Chen, Yong

2018-05-01

A study of rogue-wave solutions in the reverse-time nonlocal nonlinear Schrödinger (NLS) and nonlocal Davey-Stewartson (DS) equations is presented. By using Darboux transformation (DT) method, several types of rogue-wave solutions are constructed. Dynamics of these rogue-wave solutions are further explored. It is shown that the (1 + 1)-dimensional fundamental rogue-wave solutions in the reverse-time NLS equation can be globally bounded or have finite-time blowing-ups. It is also shown that the (2 + 1)-dimensional line rogue waves in the reverse-time nonlocal DS equations can be bounded for all space and time or develop singularities in critical time. In addition, the multi- and higher-order rogue waves exhibit richer structures, most of which have no counterparts in the corresponding local nonlinear equations.

Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications

NASA Astrophysics Data System (ADS)

Ali, Asghar; Seadawy, Aly R.; Lu, Dianchen

2018-05-01

The aim of this article is to construct some new traveling wave solutions and investigate localized structures for fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave dynamical equation. The simple equation method (SEM) and the modified simple equation method (MSEM) are applied in this paper to construct the analytical traveling wave solutions of AKNS equation. The different waves solutions are derived by assigning special values to the parameters. The obtained results have their importance in the field of physics and other areas of applied sciences. All the solutions are also graphically represented. The constructed results are often helpful for studying several new localized structures and the waves interaction in the high-dimensional models.

Wiggly tails: A gravitational wave signature of massive fields around black holes

NASA Astrophysics Data System (ADS)

Degollado, Juan Carlos; Herdeiro, Carlos A. R.

2014-09-01

Massive fields can exist in long-lived configurations around black holes. We examine how the gravitational wave signal of a perturbed black hole is affected by such "dirtiness" within linear theory. As a concrete example, we consider the gravitational radiation emitted by the infall of a massive scalar field into a Schwarzschild black hole. Whereas part of the scalar field is absorbed/scattered by the black hole and triggers gravitational wave emission, another part lingers in long-lived quasibound states. Solving numerically the Teukolsky master equation for gravitational perturbations coupled to the massive Klein-Gordon equation, we find a characteristic gravitational wave signal, composed by a quasinormal ringing followed by a late time tail. In contrast to "clean" black holes, however, the late time tail contains small amplitude wiggles with the frequency of the dominating quasibound state. Additionally, an observer dependent beating pattern may also be seen. These features were already observed in fully nonlinear studies; our analysis shows they are present at linear level, and, since it reduces to a 1+1 dimensional numerical problem, allows for cleaner numerical data. Moreover, we discuss the power law of the tail and that it only becomes universal sufficiently far away from the dirty black hole. The wiggly tails, by constrast, are a generic feature that may be used as a smoking gun for the presence of massive fields around black holes, either as a linear cloud or as fully nonlinear hair.

Shock Waves in a Bose-Einstein Condensate

NASA Technical Reports Server (NTRS)

Kulikov, Igor; Zak, Michail

2005-01-01

A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.

Transient response to localized episodic heating in the tropics

NASA Technical Reports Server (NTRS)

Salby, M. L.; Garcia, R. R.

1985-01-01

It is generally recognized that equatorial disturbances in the lower stratosphere are excited by convective latent heat release associated with the Internal Tropical Convergence Zone (ITCZ). Recently, attention has also focused on tropical convection with regard to extratropical teleconnection patterns. Unlike equatorial waves which are trapped about the equator but propagate vertically, the latter extend well out of the tropics but are barotropic. They have been most widely discussed in connection with long-term climatological features. Both types of disturbances have been examined largely from the standpoint of steady monochromatic forcing, in the latter case zero frequency or time-mean heating. However, tropical convection as revealed by recent geostationary satellite imagery is anything but regular, surely not steady. Much of the heating variance is concentrated spatially within three localized convective centers: Indonesia, the Amazon, and the Congo. Convective activity within these regions undergoes an irregular evolution over the span of a couple of days. It involves a rather broad spectrum of spatial and temporal scales. The analysis of cloud brightness over the Eastern Atlantic and Africa suggests a characteristic time scale of 3-4 days and correlations scales in latitude and longitude of approximately 30 deg.

Waiting for 21-Lutetia "Rosetta" images as a final proof of structurizing force of inertia-gravity waves

NASA Astrophysics Data System (ADS)

Kochemasov, Gennady G.

2010-05-01

The 100 km long flattened asteroid 21-Lutetia will be imaged by the "Rosetta' spacecraft in July 2010. Knowing that heavenly bodies are effectively structurized by warping inertia-gravity waves one might expect that Lutetia will not be an exclusion out of a row of bodies subjected to an action of these waves [1-9]. The elliptical keplerian orbits with periodically changing bodies' accelerations imply inertia-gravity forces applied to any body notwithstanding its size, mass, density, chemical composition, and physical state. These forces produce inertia-gravity waves having in rotating bodied standing character and four directions of propagation (orthogonal and diagonal). Interfering these waves produce in bodies three (five) kinds of tectonic blocks: uprising strongly and moderately (++, +), subsiding deeply and moderately (--, -), and neutral (0) where + and - are compensated. Lengths and amplitudes of warping waves form the harmonic sequence. The fundamental wave1 (long 2πR) makes ubiquitous tectonic dichotomy (two antipodean segments or hemispheres: one risen, another fallen). In small bodies this structurization is expressed in their convexo-concave shape: one hemisphere is bulged, another one pressed in. Bulging hemisphere is extended, pressed in hemisphere contracted. This wave shaping tends to transform a globular body into a tetrahedron - the essentially dichotomous simplest Plato's figure. In this polyhedron always there is an opposition of extension (a face) to contraction (a vertex). The first overtone wave2 (long πR) makes tectonic sectors, also risen and fallen, and regularly disposed on (and in) a globe. This regularity is expressed in an octahedron form. The octahedron (diamond) or its parts are often observed in shapes of small bodies with small gravities. Larger bodies with rather strong gravity tend to smooth polyhedron vertices and edges but a polyhedron structurization is always present inside their globes and is shown in their tectonics, geomorphology and geophysical fields. The shorter warping waves are also present but because of their comparatively small lengths and amplitudes they are not so important in distorting globes. The presented main harmonic row is complicated by superimposed individual waves lengths of which are inversely proportional to orbital frequencies: higher frequency - smaller wave, and, vice versa, lower frequency - larger wave. In the main asteroid belt the fundamental wave of the main sequence and the individual wave (also long 2πR) are in the strongest 1:1 resonance what prohibits an accretion of a real planet because of prevailing debris scattering. Thus, the Lutetia shape can support the main point of the wave planetology - «orbits make structures». [1] Kochemasov G.G. (1999) "Diamond" and "dumb-bells"-like shapes of celestial bodies induced by inertia-gravity waves // 30th Vernadsky-Brown microsymposium on comparative planetology, Abstracts, Moscow, Vernadsky Inst., 49-50. [2] -"- (1999) On convexo-concave shape of small celestial bodies // Asteroids, Comets, Meteors. Cornell Univ., July 26-30, 1999, Abstr. # 24.22. [3] -"- (2006) The wave planetology illustrated - I: dichotomy, sectoring // 44th Vernadsky-Brown microsymposium "Topics in Comparative Planetology", Oct. 9-11, 2006, Moscow, Vernadsky Inst., Abstr. m44_39, CD-ROM; [4] -"- (2006) Theorems of the wave planetology imprinted in small bodies // Geophys. Res. Abstracts, Vol. 8, EGU06-A-01098, CD-ROM. [5] -"- (2007) Plato's polyhedra in space // EPSC Abstracts, Vol. 2, EPSC2007-A-00014, 2007. [6] -"-(2007) Wave shaping of small saturnian satellites and wavy granulation of saturnian rings // Geophys. Res. Abstracts, Vol. 9, EGU2007-A-01594, CD-ROM. [7] -"- (2007) Plato's polyhedra as shapes of small satellites in the outer Solar system // New Concepts in Global Tectonics Newsletter, # 44, 43-45. [8] -"- (2008) Plato' polyhedra as shapes of small icy satellites // Geophys. Res. Abstracts, Vol. 10, EGU2008-A-01271, CD-ROM. [9] -"- (2008) A wave geometrization of small heavenly bodies // GRA, Vol. 10, EGU2008-A-01275, CD-ROM.

Propagation of acoustic shock waves between parallel rigid boundaries and into shadow zones

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

Desjouy, C., E-mail: cyril.desjouy@gmail.com; Ollivier, S.; Dragna, D.

2015-10-28

The study of acoustic shock propagation in complex environments is of great interest for urban acoustics, but also for source localization, an underlying problematic in military applications. To give a better understanding of the phenomenon taking place during the propagation of acoustic shocks, laboratory-scale experiments and numerical simulations were performed to study the propagation of weak shock waves between parallel rigid boundaries, and into shadow zones created by corners. In particular, this work focuses on the study of the local interactions taking place between incident, reflected, and diffracted waves according to the geometry in both regular or irregular – alsomore » called Von Neumann – regimes of reflection. In this latter case, an irregular reflection can lead to the formation of a Mach stem that can modify the spatial distribution of the acoustic pressure. Short duration acoustic shock waves were produced by a 20 kilovolts electric spark source and a schlieren optical method was used to visualize the incident shockfront and the reflection/diffraction patterns. Experimental results are compared to numerical simulations based on the high-order finite difference solution of the two dimensional Navier-Stokes equations.« less

Experimental study of a fine structure of 2D wakes and mixing past an obstacle in a continuously stratified fluid

NASA Astrophysics Data System (ADS)

Chashechkin, Yuli. D.; Mitkin, Vladimir V.

2001-10-01

Experimental investigations of fine and macroscopic structures of density and velocity disturbances generated by a towing cylinder or a vertical strip in a linearly stratified liquid are carried out in a rectangular tank. A density gradient field is visualised by different Schlieren methods (direct shadow, 'slit-knife', 'slit-thread', 'natural rainbow') characterised by a high spatial resolution. Profiles of fluid velocity are visualised by density markers — wakes past a vertically descending sugar crystal or an ascending gas bubble. In a fluid at rest, the density marker acts as a vertical linear source of internal oscillations which allows us to measure buoyancy frequency over all depth by the Schlieren instrument directly or by a conductivity probe in a particular point. Sensitive methods reveal a set of high gradient interfaces inside and outside the downstream wake besides well-known large scale elements: upstream disturbances, attached internal waves and vortices. Solitary interfaces located inside the attached internal waves field have no features on their leading and trailing edges. A thickness of interfaces is defined by an appropriate diffusion coefficient and a buoyancy frequency. High gradient interfaces bound compact vortices. Vortices moving with respect to environment emit their own systems of internal waves randomising a regular pattern of attached antisymmetric internal waves. But after a rather long time a wave recurrence occurs and a regular but symmetric structure of the longest waves (similar to the pattern of initial attached internal waves) is observed again. High gradient interfaces and lines of their intersections act as collectors of a dye coming from a compact source or from a coloured liquid volume inside the tank and separate coloured and clear areas.

Quantum square-well with logarithmic central spike

NASA Astrophysics Data System (ADS)

Znojil, Miloslav; Semorádová, Iveta

2018-01-01

Singular repulsive barrier V (x) = -gln(|x|) inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction ℒeff(x) = -gln[ψ∗(x)ψ(x)] in nonlinear Schrödinger equation. In the linearized case, Rayleigh-Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small g or after an amendment of the unperturbed Hamiltonian. At any spike strength g, the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables x = expy which interchanges the roles of the asymptotic and central boundary conditions.

Children's Color Perception in Relation to Habitat and Skin Color.

ERIC Educational Resources Information Center

Gaines, Rosslyn; Powell, Gloria J.

1981-01-01

Developmental color perception of 278 four- and eight-year-old Black and White children in three societies was examined in relation to the theories that proximity to the equator and that fundus pigmentation (as measured by skin color) reduce shortwave (blue-green) in comparison to long-wave perception. (Author/MP)

Evaluating a linearized Euler equations model for strong turbulence effects on sound propagation.

PubMed

Ehrhardt, Loïc; Cheinet, Sylvain; Juvé, Daniel; Blanc-Benon, Philippe

2013-04-01

Sound propagation outdoors is strongly affected by atmospheric turbulence. Under strongly perturbed conditions or long propagation paths, the sound fluctuations reach their asymptotic behavior, e.g., the intensity variance progressively saturates. The present study evaluates the ability of a numerical propagation model based on the finite-difference time-domain solving of the linearized Euler equations in quantitatively reproducing the wave statistics under strong and saturated intensity fluctuations. It is the continuation of a previous study where weak intensity fluctuations were considered. The numerical propagation model is presented and tested with two-dimensional harmonic sound propagation over long paths and strong atmospheric perturbations. The results are compared to quantitative theoretical or numerical predictions available on the wave statistics, including the log-amplitude variance and the probability density functions of the complex acoustic pressure. The match is excellent for the evaluated source frequencies and all sound fluctuations strengths. Hence, this model captures these many aspects of strong atmospheric turbulence effects on sound propagation. Finally, the model results for the intensity probability density function are compared with a standard fit by a generalized gamma function.

The detectability of high frequency energy at teleseismic and regional distances, 1. Studies of radiation from high-explosive and nuclear cratering events, 2

NASA Astrophysics Data System (ADS)

der, Z. A.; Blandford, R. R.

1981-03-01

A survey of the literature on short period seismic studies showed that seismic waves of high frequency in the 3-10 Hz range can be observed regularly at both regional and teleseismic distances. These observations show that the low Q values proposed for the long period seismic waves cannot be valid in the short period band. The data indicate that, in the mantle, Q increases with frequency and may be as much as five times higher at 5-10 Hz than in the long period band. Even with the most conservative assumptions, the level of high frequency amplitudes in the teleseismic P waves exceeds that predicted with a constant t*p = 1 sec by a factor of at least 100,000 at and beyond 5 Hz. The apparent Q beta of the lithosphere, which may be largely due to scattering by the small scale inhomogeneities in the crust, also shows an increase with frequency by as much as a factor of four within the 1-10 Hz band. This parameter controls the attenuation and the detectability of seismic waves at regional distances such as Pn, Pg, Su and Lg.

Thinner plantar fascia predicts decreased pain after extracorporeal shock wave therapy.

PubMed

Liang, Huey-Wen; Wang, Tyng-Guey; Chen, Wen-Shiang; Hou, Sheng-Mou

2007-07-01

Increased plantar fascia thickness is common with chronic plantar fasciitis, and reduction of the thickness after extracorporeal shock wave therapy or steroid injection has been reported. We hypothesized a decrease of plantar fascia thickness was associated with pain reduction after extracorporeal shock wave therapy. Fifty-three eligible patients with 78 symptomatic feet were randomly treated with piezoelectric-type extracorporeal shock wave therapy of two intensity levels (0.12 and 0.56 mJ/mm2). Two thousand shock waves for three consecutive sessions were applied at weekly intervals. A visual analog scale for pain, the Foot Function Index, the Short Form-36 Health Survey, and ultrasonographic measurement of plantar fascia thickness were evaluated at baseline and 3 and 6 months after treatment. We analyzed the association between pain level and plantar fascia thickness with generalized estimating equation analysis and adjusted for demographic and treatment-related variables. Patients with thinner plantar fascia experienced less pain after treatment; high-intensity treatment and regular exercise were associated with lower pain level. The overall success rates were 63% and 60% at the 3- and 6-month followups. High- and low-intensity treatments were associated with similar improvements in pain and function. Receiving high-intensity treatment, although associated with less pain at followup, did not provide a higher success rate.

Tectonic granulation of terrestrial planets in connection with their orbital frequencies

NASA Astrophysics Data System (ADS)

Kochemasov, G.

2007-08-01

The comparative wave planetology states that "orbits make structures" [1, 2 & others]. Moving in elliptical keplerian orbits with periodically changing accelerations celestial bodies are subjected to a warping action of inertia-gravity waves. In rotating bodies they acquire a stationary character and go in 4 crossing ortho- and diagonal directions. Interference of these directions produces uplifting (+), subsiding (-) and neutral (0) tectonic blocks size of which depends on lengths of warping waves. The fundamental wave 1 long 2πR produces ubiquitous tectonic dichotomy - an opposition of two segments - one (+), another (-). Well known at Earth, Mars and the Moon it is not so sharp at Venus and just discovered on Mercury (Dr. Ksanfomality's telescopic observations of a huge basin > 2000 km in diameter on unknown portion of Mercury's surface). Asteroids at the farthest end of the terrestrial planets row all show oblong and convexo-concave shape due to warping action of wave 1. The fundamental wave 1 has overtones of which the first long πR produces tectonic sectors - very prominent features. At Earth, for an example, these are continents and secondary oceans (the primary Pacific is a segment - a part of the dichotomous structure). On these common for all planets basic warpings are superimposed individual warpings or tectonic granules. Their sizes are inversely proportional to orbital frequencies: higher frequency - smaller grain and, vice versa, lower frequency - larger grain. Starting from the solar photosphere (it orbits the center of the solar system with frequency 1/1month) one has the following row of tectonic grains sizes (a half of a wavelength): photosphere πR/60, Mercury πR/16, Venus πR/6, Earth πR/4, Mars πR/2, asteroids πR/1. Photosphere grains are famous solar supergranules about 30000 km across (this size was never explained by the solar physics). Mercury's grains are typical small basins occupying 3-4° of a big circle arc. Venus' grains are 12 superstructures or "blobs" (after Herrick & Phillips, 1990) in the equator about 3000 km across. Earth's grains are represented by superstructures of the AR cratons about 5000 km across. At Mars' equator 4 giant ring superstructures are symmetrically placed: Tharsis, Xanthe, Arabia, Cimmeria. At the main asteroid belt a strong resonance 1:1 occurs between lengths of the fundamental wave 1 and the individual wave also wave 1. This could explain "destruction of Phaethon". In reality, in the asteroid zone the strong wave resonance (1:1) probably prevented an "assembly" of a planet and led to known matter deficit. Mars also is comparatively unstable (in 1:1 resonance are the first overtone wave 2 and the individual wave also wave 2): its shape in the equatorial plane is farther from circle than the Earth's one. This new conception of planet "stability" can be numerically expressed as degree of departure from a circle (a stable configuration) of an inscribed figure - polygon made by standing waves. For this a ratio is taken: denominator - a circle area; numerator - an area of inscribed in circle figure whose shape is determined by a number of waves fitted in the circle. The following row of sphericity (stability) is obtained: photosphere, 60-gon, 0.997; Mercury, 16-gon, 0.973; Venus, hexagon, 0.830; Earth, square, 0.637; Mars, rectangle or rhombus, 0.420; asteroids, line, 0 (zero stability)[3]. Earth is unique by its near to "golden section" value, most favorable position determining its basic features including appearance and existence of a steady life. References: [1] Kochemasov G.G. (1992) Concerted wave supergranulation of the solar system bodies // 16th Russian-American microsymposium on planetology, Abstracts, Moscow, Vernadsky Inst. (GEOKHI), 36-37. [2] Kochemasov G.G. (2002) Mars, Earth, Venus: concerted properties of lithospheres and atmospheres connected with regular tectonic granulation of the planets // Vernadsky-Brown microsymposium 36: "Topics in Comparative Planetology", Oct. 14-16, 2002, Moscow, Russia, Abstracts, CD-ROM. [3] Kochemasov G.G. (1994) Three "melons" and four 'watermelons" in the inner Solar system: why all "melons" are in the martian orbit? // 20th Russian-American microsymposium on planetology, Abstr., Moscow, Vernadsky Inst., 44-45.

Boundary control of elliptic solutions to enforce local constraints

NASA Astrophysics Data System (ADS)

Bal, G.; Courdurier, M.

We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded from below by a positive constant in the vicinity of a finite number of prescribed points; (ii) the determinant of gradients of n solutions is bounded from below in the vicinity of a finite number of prescribed points. Such constructions find applications in recent hybrid medical imaging modalities. The methodology is based on starting from a controlled setting in which the constraints are satisfied and continuously modifying the coefficients in the second-order elliptic equation. The boundary condition is evolved by solving an ordinary differential equation (ODE) defined via appropriate optimality conditions. Unique continuations and standard regularity results for elliptic equations are used to show that the ODE admits a solution for sufficiently long times.

Rogue-wave solutions of the Zakharov equation

NASA Astrophysics Data System (ADS)

Rao, Jiguang; Wang, Lihong; Liu, Wei; He, Jingsong

2017-12-01

Using the bilinear transformation method, we derive general rogue-wave solutions of the Zakharov equation. We present these Nth-order rogue-wave solutions explicitly in terms of Nth-order determinants whose matrix elements have simple expressions. We show that the fundamental rogue wave is a line rogue wave with a line profile on the plane ( x, y) arising from a constant background at t ≪ 0 and then gradually tending to the constant background for t ≫ 0. Higher-order rogue waves arising from a constant background and later disappearing into it describe the interaction of several fundamental line rogue waves. We also consider different structures of higher-order rogue waves. We present differences between rogue waves of the Zakharov equation and of the first type of the Davey-Stewartson equation analytically and graphically.

NEAR-EXTREMAL BLACK HOLES AS INITIAL CONDITIONS OF LONG GRB SUPERNOVAE AND PROBES OF THEIR GRAVITATIONAL WAVE EMISSION

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

Van Putten, Maurice H. P. M.

2015-09-01

Long gamma-ray bursts (GRBs) associated with supernovae and short GRBs with extended emission (SGRBEE) from mergers are probably powered by black holes as a common inner engine, as their prompt GRB emission satisfies the same Amati correlation in the E{sub p,i}–E{sub iso} plane. We introduce modified Bardeen equations to identify hyper-accretion driving newly formed black holes in core-collapse supernovae to near-extremal spin as a precursor to prompt GRB emission. Subsequent spin-down is observed in the BATSE catalog of long GRBs. Spin-down provides a natural unification of long durations associated with the lifetime of black hole spin for normal long GRBsmore » and SGRBEEs, given the absence of major fallback matter in mergers. The results point to major emissions unseen in high frequency gravitational waves. A novel matched filtering method is described for LIGO–Virgo and KAGRA broadband probes of nearby core-collapse supernovae at essentially maximal sensitivity.« less

Optimal boundary regularity for a singular Monge-Ampère equation

NASA Astrophysics Data System (ADS)

Jian, Huaiyu; Li, You

2018-06-01

In this paper we study the optimal global regularity for a singular Monge-Ampère type equation which arises from a few geometric problems. We find that the global regularity does not depend on the smoothness of domain, but it does depend on the convexity of the domain. We introduce (a , η) type to describe the convexity. As a result, we show that the more convex is the domain, the better is the regularity of the solution. In particular, the regularity is the best near angular points.

Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

Classification of the Lie and Noether point symmetries for the Wave and the Klein-Gordon equations in pp-wave spacetimes

NASA Astrophysics Data System (ADS)

Paliathanasis, A.; Tsamparlis, M.; Mustafa, M. T.

2018-02-01

A complete classification of the Lie and Noether point symmetries for the Klein-Gordon and the wave equation in pp-wave spacetimes is obtained. The classification analysis is carried out by reducing the problem of the determination of the point symmetries to the problem of existence of conformal killing vectors on the pp-wave spacetimes. Employing the existing results for the isometry classes of the pp-wave spacetimes, the functional form of the potential is determined for which the Klein-Gordon equation admits point symmetries and Noetherian conservation law. Finally the Lie and Noether point symmetries of the wave equation are derived.

Statistics for long irregular wave run-up on a plane beach from direct numerical simulations

NASA Astrophysics Data System (ADS)

Didenkulova, Ira; Senichev, Dmitry; Dutykh, Denys

2017-04-01

Very often for global and transoceanic events, due to the initial wave transformation, refraction, diffraction and multiple reflections from coastal topography and underwater bathymetry, the tsunami approaches the beach as a very long wave train, which can be considered as an irregular wave field. The prediction of possible flooding and properties of the water flow on the coast in this case should be done statistically taking into account the formation of extreme (rogue) tsunami wave on a beach. When it comes to tsunami run-up on a beach, the most used mathematical model is the nonlinear shallow water model. For a beach of constant slope, the nonlinear shallow water equations have rigorous analytical solution, which substantially simplifies the mathematical formulation. In (Didenkulova et al. 2011) we used this solution to study statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. The influence of the wave nonlinearity was approached by considering modifications of probability distribution of the moving shoreline and its horizontal velocity for waves of different amplitudes. It was shown that wave nonlinearity did not affect the probability distribution of the velocity of the moving shoreline, while the vertical displacement of the moving shoreline was affected substantially demonstrating the longer duration of coastal floods with an increase in the wave nonlinearity. However, this analysis did not take into account the actual transformation of irregular wave field offshore to oscillations of the moving shoreline on a slopping beach. In this study we would like to cover this gap by means of extensive numerical simulations. The modeling is performed in the framework of nonlinear shallow water equations, which are solved using a modern shock-capturing finite volume method. Although the shallow water model does not pursue the wave breaking and bore formation in a general sense (including the water surface overturning), it allows shock-wave formation and propagation with the speed given by Rankine-Hugoniot jump conditions, which to some extent approximates wave breaking. The scheme is second order accurate thanks to the UNO2 special reconstruction. It was described and validated in (Dutykh et al. 2011a) and has already been successfully used to simulate wave run-up on random beaches (Dutykh et al. 2011b). For simplicity the incident wave field offshore is taken Gaussian in the present study, however, this distribution can be easily changed in the numerical code. Similar to (Didenkulova et al. 2011), in order to study influence of wave nonlinearity during wave propagation to the coast we consider waves of different amplitudes and the corresponding modifications of statistics of the moving shoreline. We also consider wave fields with a different bandwidth, so that we can see the influence of the bandwidth of the incoming wave field on statistics of wave run-up on a beach. In order to validate the numerical results we use the available experimental data of irregular wave run-up on a beach (Denissenko et al. 2011; 2013). For this in our simulations we use the corresponding bathymetry set-up: the flat part of the flume with a water depth of 3.5 m is matched with the beach of constant slope 1:6. The significant wave heights Hs are chosen according to (Denissenko et al. 2013) and are equal to 0.1m, 0.2m, 0.3m, 0.4m and 0.5m, while the bandwidth is selected as 0.1, 0.4 and 0.8, which allows comparison of the behavior of wide-band and narrow-band wave fields on the beach. The characteristic wave period is 20s, as in (Denissenko et al. 2013) that provides long wave condition. All time records contain several weeks of simulations that provides significant amount of data for extreme value statistics. [1] P. Denissenko, I. Didenkulova, E. Pelinovsky, J. Pearson. Influence of the nonlinearity on statistical characteristics of long wave runup. Nonlinear Processes in Geophysics 18, 967-975 (2011). [2] P. Denissenko, I. Didenkulova, A. Rodin, M. Listak, E. Pelinovsky. Experimental statistics of long wave runup on a plane beach. Journal of Coastal Research 65, 195-200 (2013). [3] I. Didenkulova, E. Pelinovsky, A. Sergeeva. Statistical characteristics of long waves nearshore. Coastal Engineering 58, 94-102 (2011). [4] D. Dutykh, T. Katsaounis, D. Mitsotakis. Finite volume schemes for dispersive wave propagation and runup. J. Comput. Phys. 230 (8), 3035-3061 (2011a). [5] D. Dutykh, C. Labart, D. Mitsotakis. Long wave run-up on random beaches. Phys. Rev. Lett. 107, 184504 (2011b).

Consistent nonlinear deterministic and stochastic evolution equations for deep to shallow water wave shoaling

NASA Astrophysics Data System (ADS)

Vrecica, Teodor; Toledo, Yaron

2015-04-01

One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly oscillating terms, but as the water depth becomes shallow they change to an exponential growth (or decay) behavior. Hence, the formerly used localization technique cannot be justified for the shallow water region. A new formulation is devised for the localization in shallow water, it approximates the nonlinear non-local shoaling coefficient in shallow water and matches it to the one fitting to the intermediate water region. This allows the model behavior to be consistent from deep water to intermediate depths and up to the shallow water regime. Various simulations of the model were performed for the cases of intermediate, and shallow water, overall the model was found to give good results in both shallow and intermediate water depths. The essential difference between the shallow and intermediate nonlinear shoaling physics is explained via the dominating class III Bragg resonances phenomenon. By inspecting the resonance conditions and the nature of the dispersion relation, it is shown that unlike in the intermediate water regime, in shallow water depths the formation of resonant interactions is possible without taking into account bottom components. References Agnon, Y. & Sheremet, A. 1997 Stochastic nonlinear shoaling of directional spectra. J. Fluid Mech. 345, 79-99. Benney, D. J. & Saffman, P. G. 1966 Nonlinear interactions of random waves. Proc. R. Soc. Lond. A 289, 301-321. Bredmose, H., Agnon, Y., Madsen, P.A. & Schaffer, H.A. 2005 Wave transformation models with exact second-order transfer. European J. of Mech. - B/Fluids 24 (6), 659-682. Eldeberky, Y. & Madsen, P. A. 1999 Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves. Coastal Engineering 38, 1-24. Kaihatu, J. M. & Kirby, J. T. 1995 Nonlinear transformation of waves in infinite water depth. Phys. Fluids 8, 175-188. Holloway, G. 1980 Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10, 906-914. Stiassnie, M. & Drimer, N. 2006 Prediction of long forcing waves for harbor agitation studies. J. of waterways, port, coastal and ocean engineering 132(3), 166-171. Toledo, Y. & Agnon, Y. 2012 Stochastic evolution equations with localized nonlinear shoaling coefficients. European J. of Mech. - B/Fluids 34, 13-18.

RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

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

Anton, Luis; MartI, Jose M; Ibanez, Jose M

2010-05-01

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, andmore » can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.« less

Weierstrass traveling wave solutions for dissipative Benjamin, Bona, and Mahony (BBM) equation

NASA Astrophysics Data System (ADS)

Mancas, Stefan C.; Spradlin, Greg; Khanal, Harihar

2013-08-01

In this paper the effect of a small dissipation on waves is included to find exact solutions to the modified Benjamin, Bona, and Mahony (BBM) equation by viscosity. Using Lyapunov functions and dynamical systems theory, we prove that when viscosity is added to the BBM equation, in certain regions there still exist bounded traveling wave solutions in the form of solitary waves, periodic, and elliptic functions. By using the canonical form of Abel equation, the polynomial Appell invariant makes the equation integrable in terms of Weierstrass ℘ functions. We will use a general formalism based on Ince's transformation to write the general solution of dissipative BBM in terms of ℘ functions, from which all the other known solutions can be obtained via simplifying assumptions. Using ODE (ordinary differential equations) analysis we show that the traveling wave speed is a bifurcation parameter that makes transition between different classes of waves.

Alternative stable qP wave equations in TTI media with their applications for reverse time migration

NASA Astrophysics Data System (ADS)

Zhou, Yang; Wang, Huazhong; Liu, Wenqing

2015-10-01

Numerical instabilities may arise if the spatial variation of symmetry axis is handled improperly when implementing P-wave modeling and reverse time migration in heterogeneous tilted transversely isotropic (TTI) media, especially in the cases where fast changes exist in TTI symmetry axis’ directions. Based on the pseudo-acoustic approximation to anisotropic elastic wave equations in Cartesian coordinates, alternative second order qP (quasi-P) wave equations in TTI media are derived in this paper. Compared with conventional stable qP wave equations, the proposed equations written in stress components contain only spatial derivatives of wavefield variables (stress components) and are free from spatial derivatives involving media parameters. These lead to an easy and efficient implementation for stable P-wave modeling and imaging. Numerical experiments demonstrate the stability and computational efficiency of the presented equations in complex TTI media.

A Non-hydrostatic Atmospheric Model for Global High-resolution Simulation

NASA Astrophysics Data System (ADS)

Peng, X.; Li, X.

2017-12-01

A three-dimensional non-hydrostatic atmosphere model, GRAPES_YY, is developed on the spherical Yin-Yang grid system in order to enforce global high-resolution weather simulation or forecasting at the CAMS/CMA. The quasi-uniform grid makes the computation be of high efficiency and free of pole problem. Full representation of the three-dimensional Coriolis force is considered in the governing equations. Under the constraint of third-order boundary interpolation, the model is integrated with the semi-implicit semi-Lagrangian method using the same code on both zones. A static halo region is set to ensure computation of cross-boundary transport and updating Dirichlet-type boundary conditions in the solution process of elliptical equations with the Schwarz method. A series of dynamical test cases, including the solid-body advection, the balanced geostrophic flow, zonal flow over an isolated mountain, development of the Rossby-Haurwitz wave and a baroclinic wave, are carried out, and excellent computational stability and accuracy of the dynamic core has been confirmed. After implementation of the physical processes of long and short-wave radiation, cumulus convection, micro-physical transformation of water substances and the turbulent processes in the planetary boundary layer include surface layer vertical fluxes parameterization, a long-term run of the model is then put forward under an idealized aqua-planet configuration to test the model physics and model ability in both short-term and long-term integrations. In the aqua-planet experiment, the model shows an Earth-like structure of circulation. The time-zonal mean temperature, wind components and humidity illustrate reasonable subtropical zonal westerly jet, meridional three-cell circulation, tropical convection and thermodynamic structures. The specific SST and solar insolation being symmetric about the equator enhance the ITCZ and tropical precipitation, which concentrated in tropical region. Additional analysis and tuning of the model is still going on, and preliminary results have demonstrated the possibility of high-resolution application of the model to global weather prediction and even seasonal climate projection.

Equatorial Magnetohydrodynamic Shallow Water Waves in the Solar Tachocline

NASA Astrophysics Data System (ADS)

Zaqarashvili, Teimuraz

2018-03-01

The influence of a toroidal magnetic field on the dynamics of shallow water waves in the solar tachocline is studied. A sub-adiabatic temperature gradient in the upper overshoot layer of the tachocline causes significant reduction of surface gravity speed, which leads to trapping of the waves near the equator and to an increase of the Rossby wave period up to the timescale of solar cycles. Dispersion relations of all equatorial magnetohydrodynamic (MHD) shallow water waves are obtained in the upper tachocline conditions and solved analytically and numerically. It is found that the toroidal magnetic field splits equatorial Rossby and Rossby-gravity waves into fast and slow modes. For a reasonable value of reduced gravity, global equatorial fast magneto-Rossby waves (with the spatial scale of equatorial extent) have a periodicity of 11 years, matching the timescale of activity cycles. The solutions are confined around the equator between latitudes ±20°–40°, coinciding with sunspot activity belts. Equatorial slow magneto-Rossby waves have a periodicity of 90–100 yr, resembling the observed long-term modulation of cycle strength, i.e., the Gleissberg cycle. Equatorial magneto-Kelvin and slow magneto-Rossby-gravity waves have the periodicity of 1–2 years and may correspond to observed annual and quasi-biennial oscillations. Equatorial fast magneto-Rossby-gravity and magneto-inertia-gravity waves have periods of hundreds of days and might be responsible for observed Rieger-type periodicity. Consequently, the equatorial MHD shallow water waves in the upper overshoot tachocline may capture all timescales of observed variations in solar activity, but detailed analytical and numerical studies are necessary to make a firm conclusion toward the connection of the waves to the solar dynamo.

The evolution of a localized nonlinear wave of the Kelvin-Helmholtz instability with gravity

NASA Astrophysics Data System (ADS)

Orazzo, Annagrazia; Hoepffner, Jérôme

2012-11-01

At the interface between two fluids of different density and in the presence of gravity, there are well known periodic surface waves which can propagate for long distances with little attenuation, as it is for instance the case at the surface of the sea. If wind is present, these waves progressively accumulate energy as they propagate and grow to large sizes—this is the Kelvin-Helmholtz instability. On the other hand, we show in this paper that for a given wind strength, there is potential for the growth of a localized nonlinear wave. This wave can reach a size such that the hydrostatic pressure drop from top to bottom equals the stagnation pressure of the wind. This process for the disruption of the flat interface is localized and nonlinear. We study the properties of this wave using numerical simulations of the Navier-Stokes equations.

Variability of quasi-stationary planetary waves

NASA Technical Reports Server (NTRS)

Krivolutsky, A. A.; Petushkov, N. D.; Tarasenko, D. A.

1989-01-01

The results of the analysis of nonzonal perturbations (m = 1, 2, 3) of the geopotential field at a 30 mb level are presented. A long period modulation of the harmonics' amplitude is discovered. Calculations of eigenfunctions and eigennumbers of the Laplace tidal equation are carried out for a real latitudinal wind profile. The observed first zonal harmonic in different years is caused by the same mode. Thus, the difference in the wave amplitudes could not be accounted for by the difference in stratospheric zonal circulation in different years and should be related to tropospheric processes.

The influence of pore-fluid in the soil on ground vibrations from a tunnel embedded in a layered half-space

NASA Astrophysics Data System (ADS)

Yuan, Zonghao; Cao, Zhigang; Boström, Anders; Cai, Yuanqiang

2018-04-01

A computationally efficient semi-analytical solution for ground-borne vibrations from underground railways is proposed and used to investigate the influence of hydraulic boundary conditions at the scattering surfaces and the moving ground water table on ground vibrations. The arrangement of a dry soil layer with varying thickness resting on a saturated poroelastic half-space, which includes a circular tunnel subject to a harmonic load at the tunnel invert, creates the scenario of a moving water table for research purposes in this paper. The tunnel is modelled as a hollow cylinder, which is made of viscoelastic material and buried in the half-space below the ground water table. The wave field in the dry soil layer consists of up-going and down-going waves while the wave field in the tunnel wall consists of outgoing and regular cylindrical waves. The complete solution for the saturated half-space with a cylindrical hole is composed of down-going plane waves and outgoing cylindrical waves. By adopting traction-free boundary conditions on the ground surface and continuity conditions at the interfaces of the two soil layers and of the tunnel and the surrounding soil, a set of algebraic equations can be obtained and solved in the transformed domain. Numerical results show that the moving ground water table can cause an uncertainty of up to 20 dB for surface vibrations.

Orbital stability of solitary waves for Kundu equation

NASA Astrophysics Data System (ADS)

Zhang, Weiguo; Qin, Yinghao; Zhao, Yan; Guo, Boling

In this paper, we consider the Kundu equation which is not a standard Hamiltonian system. The abstract orbital stability theory proposed by Grillakis et al. (1987, 1990) cannot be applied directly to study orbital stability of solitary waves for this equation. Motivated by the idea of Guo and Wu (1995), we construct three invariants of motion and use detailed spectral analysis to obtain orbital stability of solitary waves for Kundu equation. Since Kundu equation is more complex than the derivative Schrödinger equation, we utilize some techniques to overcome some difficulties in this paper. It should be pointed out that the results obtained in this paper are more general than those obtained by Guo and Wu (1995). We present a sufficient condition under which solitary waves are orbitally stable for 2c+sυ<0, while Guo and Wu (1995) only considered the case 2c+sυ>0. We obtain the results on orbital stability of solitary waves for the derivative Schrödinger equation given by Colin and Ohta (2006) as a corollary in this paper. Furthermore, we obtain orbital stability of solitary waves for Chen-Lee-Lin equation and Gerdjikov-Ivanov equation, respectively.

Validation and Performance Comparison of Numerical Codes for Tsunami Inundation

NASA Astrophysics Data System (ADS)

Velioglu, D.; Kian, R.; Yalciner, A. C.; Zaytsev, A.

2015-12-01

In inundation zones, tsunami motion turns from wave motion to flow of water. Modelling of this phenomenon is a complex problem since there are many parameters affecting the tsunami flow. In this respect, the performance of numerical codes that analyze tsunami inundation patterns becomes important. The computation of water surface elevation is not sufficient for proper analysis of tsunami behaviour in shallow water zones and on land and hence for the development of mitigation strategies. Velocity and velocity patterns are also crucial parameters and have to be computed at the highest accuracy. There are numerous numerical codes to be used for simulating tsunami inundation. In this study, FLOW 3D and NAMI DANCE codes are selected for validation and performance comparison. Flow 3D simulates linear and nonlinear propagating surface waves as well as long waves by solving three-dimensional Navier-Stokes (3D-NS) equations. FLOW 3D is used specificaly for flood problems. NAMI DANCE uses finite difference computational method to solve linear and nonlinear forms of shallow water equations (NSWE) in long wave problems, specifically tsunamis. In this study, these codes are validated and their performances are compared using two benchmark problems which are discussed in 2015 National Tsunami Hazard Mitigation Program (NTHMP) Annual meeting in Portland, USA. One of the problems is an experiment of a single long-period wave propagating up a piecewise linear slope and onto a small-scale model of the town of Seaside, Oregon. Other benchmark problem is an experiment of a single solitary wave propagating up a triangular shaped shelf with an island feature located at the offshore point of the shelf. The computed water surface elevation and velocity data are compared with the measured data. The comparisons showed that both codes are in fairly good agreement with each other and benchmark data. All results are presented with discussions and comparisons. The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement No 603839 (Project ASTARTE - Assessment, Strategy and Risk Reduction for Tsunamis in Europe)

High Order Filter Methods for the Non-ideal Compressible MHD Equations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, Bjoern

2003-01-01

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard divergence cleaning is not required by the present filter approach. For certain non-ideal MHD test cases, divergence free preservation of the magnetic fields has been achieved.

Divergence Free High Order Filter Methods for the Compressible MHD Equations

NASA Technical Reports Server (NTRS)

Yea, H. C.; Sjoegreen, Bjoern

2003-01-01

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard diver- gence cleaning is not required by the present filter approach. For certain MHD test cases, divergence free preservation of the magnetic fields has been achieved.

Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrödinger equation.

PubMed

Wen, Xiao-Yong; Yang, Yunqing; Yan, Zhenya

2015-07-01

In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.

Experimental modelling of wave amplification over irregular bathymetry for investigations of boulder transport by extreme wave events.

NASA Astrophysics Data System (ADS)

O'Boyle, Louise; Whittaker, Trevor; Cox, Ronadh; Elsäßer, Björn

2017-04-01

During the winter of 2013-2014 the west coast of Ireland was exposed to 6 storms over a period of 8 weeks with wind speeds equating to hurricane categories 3 and 4. During this period, the largest significant wave height recorded at the Marine Institute M6 wave buoy, approximately 300km from the site, was 13.6m (on 26th January 2014). However, this may not be the largest sea state of that winter, because the buoy stopped logging on 30th January and therefore failed to capture the full winter period. During the February 12th 2014 "Darwin" storm, the Kinsale Energy Gas Platform off Ireland's south coast measured a wave height of 25 m, which remains the highest wave measured off Ireland's coasts[1]. Following these storms, significant dislocation and transportation of boulders and megagravel was observed on the Aran Islands, Co. Galway at elevations of up to 25m above the high water mark and distances up to 220 m inland including numerous clasts with masses >50t, and at least one megagravel block weighing >500t [2]. Clast movements of this magnitude would not have been predicted from the measured wave heights. This highlights a significant gap in our understanding of the relationships between storms and the coastal environment: how are storm waves amplified and modified by interactions with bathymetry? To gain further understanding of wave amplification, especially over steep and irregular bathymetry, we have designed Froude-scaled wave tank experiments using the 3D coastal wave basin facility at Queen's University Belfast. The basin is 18m long by 16m wide with wave generation by means of a 12m wide bank of 24 top hinged, force feedback, sector carrier wave paddles at one end. The basin is equipped with gravel beaches to dissipate wave energy on the remaining three sides, capable of absorbing up to 99% of the incident wave energy, to prevent unwanted reflections. Representative bathymetry for the Aran Islands is modelled in the basin based on a high resolution nearshore multibeam sonar survey. Water surface elevation is recorded using twin-wire resistance type wave probes along a shore-normal bathymetry transect as the waves shoal. Variations in significant wave height and maximum elevation are presented for both regular and irregular bathymetry and for a number of typical North Atlantic sea states. These results are significant for calibration of numerical wave propagation models over irregular bathymetry and for those seeking to understand the magnitude of nearshore extreme wave events. References [1] Met Éireann, 2014, Winter 2013/2014: Monthly Weather Bulletin, December issue, p. 1-5. http://www.met.ie/climate-ireland/weather-events/winterstorms13_14.pdf. [2] Cox, R. et. al., 2016, Movement of boulders and megagravel by storm waves Vol. 18, EGU2016-10535, 2016 EGU General Assembly 2016

Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach

NASA Astrophysics Data System (ADS)

Camassa, R.; Falqui, G.; Ortenzi, G.

2017-02-01

The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite two-dimensional channel. The Hamiltonian structure of the averaged equations is obtained directly from that of the Euler equations through the process of Hamiltonian reduction. Long-wave asymptotics together with the Boussinesq approximation of neglecting the fluids’ inertia is then applied to reduce the leading order vertically averaged equations to the shallow-water Airy system, albeit in a non-trivial way. The full non-Boussinesq system for the dispersionless limit can then be viewed as a deformation of this well known equation. In a perturbative study of this deformation, a family of approximate constants of the motion are explicitly constructed and used to find local solutions of the evolution equations by means of hodograph-like formulae.

Upstream-advancing waves generated by a current over a sinusoidal bed

NASA Astrophysics Data System (ADS)

Kyotoh, Harumichi; Fukushima, Masaki

1997-07-01

Upstream-advancing waves are observed in open channel flows over a fixed sinusoidal bed with large amplitude, when the Froude number is less than the resonant value, at which stream velocity is equal to the celerity of the wave with wavelength equal to that of the bottom surface. Their wavelength is about 3-6 times as long as the bottom wavelength and the celerity is close to that obtained from potential flow theory. Therefore, the wavelength of upstream-advancing waves is determined by linear stability analyses assuming that they are induced by the Benjamin-Feir-type instability of steady flow. Here, two formulas for the wavelength with different scaling are introduced and compared with experiment. In addition, the mechanisms of upstream-advancing waves are investigated qualitatively using the forced Schrödinger equation.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

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].

Pure quasi-P wave equation and numerical solution in 3D TTI media

NASA Astrophysics Data System (ADS)

Zhang, Jian-Min; He, Bing-Shou; Tang, Huai-Gu

2017-03-01

Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis (VTI media), a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis (TTI media). This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ɛ. The finite difference method is used to solve the equation. In addition, a perfectly matched layer (PML) absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium.

Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior

NASA Astrophysics Data System (ADS)

Barles, Guy; Ley, Olivier; Topp, Erwin

2017-02-01

In this paper, we provide suitable adaptations of the ‘weak version of Bernstein method’ introduced by the first author in 1991, in order to obtain Lipschitz regularity results and Lipschitz estimates for nonlinear integro-differential elliptic and parabolic equations set in the whole space. Our interest is to obtain such Lipschitz results to possibly degenerate equations, or to equations which are indeed ‘uniformly elliptic’ (maybe in the nonlocal sense) but which do not satisfy the usual ‘growth condition’ on the gradient term allowing to use (for example) the Ishii-Lions’ method. We treat the case of a model equation with a superlinear coercivity on the gradient term which has a leading role in the equation. This regularity result together with comparison principle provided for the problem allow to obtain the ergodic large time behavior of the evolution problem in the periodic setting.

An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

NASA Astrophysics Data System (ADS)

Drivas, Theodore D.; Eyink, Gregory L.

2017-12-01

We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity measuring kinetic energy cascade will also vanish for such Euler solutions, unless the same singularity conditions are satisfied. It is shown furthermore that strong limits of solutions of compressible Navier-Stokes equations that are bounded and exhibit anomalous dissipation are weak Euler solutions. These inviscid limit solutions have non-negative anomalous entropy production and kinetic energy dissipation, with both vanishing when solutions are above the critical degree of Besov regularity. Stationary, planar shocks in Euclidean space with an ideal-gas equation of state provide simple examples that satisfy the conditions of our theorems and which demonstrate sharpness of our L 3-based conditions. These conditions involve space-time Besov regularity, but we show that they are satisfied by Euler solutions that possess similar space regularity uniformly in time.

Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves

NASA Astrophysics Data System (ADS)

Tobita, Miwa; Omura, Yoshiharu

2018-03-01

We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.

On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes

ERIC Educational Resources Information Center

Chandran, Pallath

2004-01-01

The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…

High-frequency homogenization for travelling waves in periodic media.

PubMed

Harutyunyan, Davit; Milton, Graeme W; Craster, Richard V

2016-07-01

We consider high-frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schrödinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 1 plus a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 2 . We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless ω 1 = ω 2 and [Formula: see text] where Λ =(λ 1 λ 2 …λ d ) is the periodicity cell of the medium and for any two vectors [Formula: see text] the product a ⊙ b is defined to be the vector ( a 1 b 1 , a 2 b 2 ,…, a d b d ). This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigour as that of Allaire and co-workers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.

A more fundamental approach to the derivation of nonlinear acoustic wave equations with fractional loss operators (L).

PubMed

Prieur, Fabrice; Vilenskiy, Gregory; Holm, Sverre

2012-10-01

A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["Nonlinear acoustic wave equations with fractional loss operators," J. Acoust. Soc. Am. 130(3), 1125-1132 (2011)]. The loss operator of the obtained nonlinear wave equations differs from the previous derivations as well as the dispersion equation, but when approximating for low frequencies the expressions for the frequency dependent attenuation and velocity dispersion remain unchanged.

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

NASA Astrophysics Data System (ADS)

Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang

2017-06-01

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

System engineering study of electrodynamic tether as a spaceborne generator and radiator of electromagnetic waves in the ULF/ELF frequency band

NASA Technical Reports Server (NTRS)

Estes, R. D.; Grossi, M. D.; Lorenzini, E. C.

1986-01-01

The transmission and generation by orbiting tethered satellite systems of information carrying electromagnetic waves in the ULF/ELF frequency band to the Earth at suitably high signal intensities was examined and the system maintaining these intensities in their orbits for long periods of time without excessive onboard power requirements was investigated. The injection quantity power into electromagnetic waves as a function of system parameters such as tether length and orbital height was estimated. The basic equations needed to evaluate alternataing current tethered systems for external energy requirements are presented. The energy equations to tethered systems with various lengths, tether resistances, and radiation resistances, operating at different current values are applied. Radiation resistance as a function of tether length and orbital height is discussed. It is found that ULF/ELF continuously radiating systems could be maintained in orbit with moderate power requirements. The effect of tether length on the power going into electromagnetic waves and whether a single or dual tether system is preferable for the self-driven mode is discussed. It is concluded that the single tether system is preferable over the dual system.

Two-Dimensional Analysis of Cable Stayed Bridge under Wave Loading

NASA Astrophysics Data System (ADS)

Seeram, Madhuri; Manohar, Y.

2018-06-01

In the present study finite element analysis is performed for a modified fan type cable-stayed bridge using ANSYS Mechanical. A cable stayed bridge with two towers and main deck is considered for the present study. Dynamic analysis is performed to evaluate natural frequencies. The obtained natural frequencies and mode shapes of cable stayed bridge are compared to the existing results. Further studies have been conducted for offshore area application by increasing the pylon/tower height depending upon the water depth. Natural frequencies and mode shapes are evaluated for the cable stayed bridge for offshore area application. The results indicate that the natural periods are higher than the existing results due to the effect of increase in mass of the structure and decrease in stiffness of the pylon/tower. The cable stayed bridge is analyzed under various environmental loads such as dead, live, vehicle, seismic and wave loading. Morison equation is considered to evaluate the wave force. The sum of inertia and drag force is taken as the wave force distribution along the fluid interacting height of the pylon. Airy's wave theory is used to assess water particle kinematics, for the wave periods ranging from 5 to 20 s and unit wave height. The maximum wave force among the different regular waves is considered in the wave load case. The support reactions, moments and deflections for offshore area application are highlighted. It is observed that the maximum support reactions and support moments are obtained due to wave and earthquake loading respectively. Hence, it is concluded that the wave and earthquake forces shall be given significance in the design of cable stayed bridge.

Two-Dimensional Analysis of Cable Stayed Bridge under Wave Loading

NASA Astrophysics Data System (ADS)

Seeram, Madhuri; Manohar, Y.

2018-02-01

In the present study finite element analysis is performed for a modified fan type cable-stayed bridge using ANSYS Mechanical. A cable stayed bridge with two towers and main deck is considered for the present study. Dynamic analysis is performed to evaluate natural frequencies. The obtained natural frequencies and mode shapes of cable stayed bridge are compared to the existing results. Further studies have been conducted for offshore area application by increasing the pylon/tower height depending upon the water depth. Natural frequencies and mode shapes are evaluated for the cable stayed bridge for offshore area application. The results indicate that the natural periods are higher than the existing results due to the effect of increase in mass of the structure and decrease in stiffness of the pylon/tower. The cable stayed bridge is analyzed under various environmental loads such as dead, live, vehicle, seismic and wave loading. Morison equation is considered to evaluate the wave force. The sum of inertia and drag force is taken as the wave force distribution along the fluid interacting height of the pylon. Airy's wave theory is used to assess water particle kinematics, for the wave periods ranging from 5 to 20 s and unit wave height. The maximum wave force among the different regular waves is considered in the wave load case. The support reactions, moments and deflections for offshore area application are highlighted. It is observed that the maximum support reactions and support moments are obtained due to wave and earthquake loading respectively. Hence, it is concluded that the wave and earthquake forces shall be given significance in the design of cable stayed bridge.

Multi-hump bright solitons in a Schrödinger-mKdV system

NASA Astrophysics Data System (ADS)

Cisneros-Ake, Luis A.; Parra Prado, Hugo; López Villatoro, Diego Joselito; Carretero-González, R.

2018-03-01

We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg-de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS-mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution.

Formation of vortices in the presence of sheared electron flows in the earth's ionosphere

NASA Astrophysics Data System (ADS)

Farid, T.; Shukla, P. K.; Sakanaka, P. H.; Mirza, A. M.

2000-12-01

It is shown that sheared electron flows can generate long as well as short wavelength (in comparison with the ion gyroradius) electrostatic waves in a nonuniform magnetplasma. For this purpose, we derive dispersion relations by employing two-fluid and hybrid models; in the two-fluid model the dynamics of both the electrons and ions are governed by the hydrodynamic equations and the guiding center fluid drifts, whereas the hybrid model assumes kinetic ions and fluid electrons. Explicit expressions for the growth rates and thresholds are presented. Linearly excited waves attain finite amplitudes and start interacting among themselves. The interaction is governed by the nonlinear equations containing the Jacobian nonlinearities. Stationary solutions of the nonlinear mode coupling equations can be represented in the form of a dipolar vortex and a vortex street. Conditions under which the latter arise are given. Numerical results for the growth rates of linearly excited modes as well as for various types of vortices are displayed for the parameters that are relevant for the F-region of the Earth's ionosphere. It is suggested that the results of the present investigation are useful in understanding the properties of nonthermal electrostatic waves and associated nonlinear vortex structures in the Earth's ionosphere.

Nonparaxial wave beams and packets with general astigmatism

NASA Astrophysics Data System (ADS)

Kiselev, A. P.; Plachenov, A. B.; Chamorro-Posada, P.

2012-04-01

We present exact solutions of the wave equation involving an arbitrary wave form with a phase closely similar to the general astigmatic phase of paraxial wave optics. Special choices of the wave form allow general astigmatic beamlike and pulselike waves with a Gaussian-type unrestricted localization in space and time. These solutions are generalizations of the known Bateman-type waves obtained from the connection existing between beamlike solutions of the paraxial parabolic equation and relatively undistorted wave solutions of the wave equation. As a technical tool, we present a full description of parametrizations of 2×2 symmetric matrices with positive imaginary part, which arise in the theory of Gaussian beams.

A unifying fractional wave equation for compressional and shear waves.

PubMed

Holm, Sverre; Sinkus, Ralph

2010-01-01

This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is a generalized Hooke's law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo [Geophys J. R. Astron. Soc. 13, 529-539 (1967)] and Wismer [J. Acoust. Soc. Am. 120, 3493-3502 (2006)]. In the low omegatau (low-frequency) case, this equation has an attenuation with a power-law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high omegatau (high-frequency) case, it describes attenuation with a power-law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases.

Two-dimensional dispersion of magnetostatic volume spin waves

NASA Astrophysics Data System (ADS)

Buijnsters, Frank J.; van Tilburg, Lennert J. A.; Fasolino, Annalisa; Katsnelson, Mikhail I.

2018-06-01

Owing to the dipolar (magnetostatic) interaction, long-wavelength spin waves in in-plane magnetized films show an unusual dispersion behavior, which can be mathematically described by the model of and and refinements thereof. However, solving the two-dimensional dispersion requires the evaluation of a set of coupled transcendental equations and one has to rely on numerics. In this work, we present a systematic perturbative analysis of the spin wave model. An expansion in the in-plane wavevector allows us to obtain explicit closed-form expressions for the dispersion relation and mode profiles in various asymptotic regimes. Moreover, we derive a very accurate semi-analytical expression for the dispersion relation of the lowest-frequency mode that is straightforward to evaluate.

Nonequilibrium Precondensation of Classical Waves in Two Dimensions Propagating through Atomic Vapors

NASA Astrophysics Data System (ADS)

Šantić, Neven; Fusaro, Adrien; Salem, Sabeur; Garnier, Josselin; Picozzi, Antonio; Kaiser, Robin

2018-02-01

The nonlinear Schrödinger equation, used to describe the dynamics of quantum fluids, is known to be valid not only for massive particles but also for the propagation of light in a nonlinear medium, predicting condensation of classical waves. Here we report on the initial evolution of random waves with Gaussian statistics using atomic vapors as an efficient two dimensional nonlinear medium. Experimental and theoretical analysis of near field images reveal a phenomenon of nonequilibrium precondensation, characterized by a fast relaxation towards a precondensate fraction of up to 75%. Such precondensation is in contrast to complete thermalization to the Rayleigh-Jeans equilibrium distribution, requiring prohibitive long interaction lengths.

ATHENA 3D: A finite element code for ultrasonic wave propagation

NASA Astrophysics Data System (ADS)

Rose, C.; Rupin, F.; Fouquet, T.; Chassignole, B.

2014-04-01

The understanding of wave propagation phenomena requires use of robust numerical models. 3D finite element (FE) models are generally prohibitively time consuming. However, advances in computing processor speed and memory allow them to be more and more competitive. In this context, EDF R&D developed the 3D version of the well-validated FE code ATHENA2D. The code is dedicated to the simulation of wave propagation in all kinds of elastic media and in particular, heterogeneous and anisotropic materials like welds. It is based on solving elastodynamic equations in the calculation zone expressed in terms of stress and particle velocities. The particularity of the code relies on the fact that the discretization of the calculation domain uses a Cartesian regular 3D mesh while the defect of complex geometry can be described using a separate (2D) mesh using the fictitious domains method. This allows combining the rapidity of regular meshes computation with the capability of modelling arbitrary shaped defects. Furthermore, the calculation domain is discretized with a quasi-explicit time evolution scheme. Thereby only local linear systems of small size have to be solved. The final step to reduce the computation time relies on the fact that ATHENA3D has been parallelized and adapted to the use of HPC resources. In this paper, the validation of the 3D FE model is discussed. A cross-validation of ATHENA 3D and CIVA is proposed for several inspection configurations. The performances in terms of calculation time are also presented in the cases of both local computer and computation cluster use.

Long-Term Stability of Core Language Skill in Children with Contrasting Language Skills

ERIC Educational Resources Information Center

Bornstein, Marc H.; Hahn, Chun-Shin; Putnick, Diane L.

2016-01-01

This 4-wave longitudinal study evaluated stability of core language skill in 421 European American and African American children, half of whom were identified as low (n = 201) and half of whom were average-to-high (n = 220) in later language skill. Structural equation modeling supported loadings of multivariate age-appropriate multisource measures…

Pandemics: waves of disease, waves of hate from the Plague of Athens to A.I.D.S.*

PubMed Central

Cohn, Samuel K.

2015-01-01

This article briefly surveys the history of pandemics in the West, contesting long-held assumptions that epidemics sparked hatred and blame of the ‘Other’, and that it was worse when diseases were mysterious as to their causes and cures. The article finds that blame and hate were rarely connected with pandemics in history. In antiquity, epidemics more often brought societies together rather than dividing them as continued to happen with some diseases such as influenza in modernity. On the other hand, some diseases such as cholera were more regularly blamed than others and triggered violence even after their agents and mechanisms of transmission had become well known. PMID:25960572

The Extended Parabolic Equation Method and Implication of Results for Atmospheric Millimeter-Wave and Optical 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 -correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. 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.

Dust acoustic solitary waves in a dusty plasma with two kinds of nonthermal ions at different temperatures

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

Dorranian, Davoud; Sabetkar, Akbar

The nonlinear dust acoustic solitary waves in a dusty plasma with two nonthermal ion species at different temperatures is studied analytically. Using reductive perturbation method, the Kadomtsev-Petviashivili (KP) equation is derived, and the effects of nonthermal coefficient, ions temperature, and ions number density on the amplitude and width of soliton in dusty plasma are investigated. It is shown that the amplitude of solitary wave of KP equation diverges at critical points of plasma parameters. The modified KP equation is also derived, and from there, the soliton like solutions of modified KP equation with finite amplitude is extracted. Results show thatmore » generation of rarefactive or compressive solitary waves strongly depends on the number and temperature of nonthermal ions. Results of KP equation confirm that for different magnitudes of ions temperature (mass) and number density, mostly compressive solitary waves are generated in a dusty plasma. In this case, the amplitude of solitary wave is decreased, while the width of solitary waves is increased. According to the results of modified KP equation for some certain magnitudes of parameters, there is a condition for generation of an evanescent solitary wave in a dusty plasma.« less

Multi-Periodic Waves in Shallow Water

DTIC Science & Technology

1992-09-01

models-the Kadomtsev - Petviashvili (KP) equation . The KP equation describes the evolu- tion of weakly nonlinear, weakly two-dimensional waves on water of...experimentally. The analytical model is a family of periodic solutions of the Kadomtsev -Petviashuili equation . The experiments demonstrate the accuracy... Petviashvili Equation (with Norman Schef- fner & Harvey Segur). Proceedings, Nonlinear Water Waves Workshop, University of Bristol. England, 1991. Resonant

From the paddle to the beach - A Boussinesq shallow water numerical wave tank based on Madsen and Sørensen's equations

NASA Astrophysics Data System (ADS)

Orszaghova, Jana; Borthwick, Alistair G. L.; Taylor, Paul H.

2012-01-01

This article describes a one-dimensional numerical model of a shallow-water flume with an in-built piston paddle moving boundary wavemaker. The model is based on a set of enhanced Boussinesq equations and the nonlinear shallow water equations. Wave breaking is described approximately, by locally switching to the nonlinear shallow water equations when a critical wave steepness is reached. The moving shoreline is calculated as part of the solution. The piston paddle wavemaker operates on a movable grid, which is Lagrangian on the paddle face and Eulerian away from the paddle. The governing equations are, however, evolved on a fixed mapped grid, and the newly calculated solution is transformed back onto the moving grid via a domain mapping technique. Validation test results are compared against analytical solutions, confirming correct discretisation of the governing equations, wave generation via the numerical paddle, and movement of the wet/dry front. Simulations are presented that reproduce laboratory experiments of wave runup on a plane beach and wave overtopping of a laboratory seawall, involving solitary waves and compact wave groups. In practice, the numerical model is suitable for simulating the propagation of weakly dispersive waves and can additionally model any associated inundation, overtopping or inland flooding within the same simulation.

Simple equations guide high-frequency surface-wave investigation techniques

USGS Publications Warehouse

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

2006-01-01

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

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

NASA Astrophysics Data System (ADS)

Wu, Zedong; Liu, Hongwei; Alkhalifah, Tariq

2018-07-01

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

A mega-nourishment creates novel habitat for intertidal macroinvertebrates by enhancing habitat relief of the sandy beach

NASA Astrophysics Data System (ADS)

van Egmond, E. M.; van Bodegom, P. M.; Berg, M. P.; Wijsman, J. W. M.; Leewis, L.; Janssen, G. M.; Aerts, R.

2018-07-01

Globally, sandy beaches are subject to coastal squeeze due to erosion. Soft-sediment strategies, such as sand nourishment, are increasingly applied to mitigate effects of erosion, but have long-term negative impacts on beach flora and fauna. As a more ecologically and sustainable alternative to regular beach nourishments, a mega-nourishment has been constructed along the Dutch coast by depositing 21.5 Mm3 of sand, from which sand is gradually redistributed along the coast by natural physical processes. The 'Sand Motor' mega-nourishment was constructed as a long-term management alternative for coastal protection and is the first large-scale experiment of its kind. We evaluated the development of intertidal macroinvertebrate communities in relation to this mega-nourishment, and compared it to species composition of beaches subject to regular beach or no nourishment. We found that a mega-nourishment resulted initially in a higher macroinvertebrate richness, but a lower macroinvertebrate abundance, compared to regular beach nourishment. As there was no effect of year after nourishment, this finding suggests that colonization and/or local extinction were not limiting macroinvertebrate richness at the mega-nourishment. In addition, a mega-nourishment does not converge to an intertidal macroinvertebrate community similar to those on unnourished beaches within a time scale of four years. Beach areas at the mega-nourishment sheltered from waves harbored a distinct macroinvertebrate community compared to typical wave-exposed sandy beach communities. Thus, a mega-nourishment temporally creates new habitat for intertidal macroinvertebrates by enhancing habitat relief of the sandy beach. We conclude that a mega-nourishment may be a promising coastal defense strategy for sandy shores in terms of the macroinvertebrate community of the intertidal beach.

Marangoni instability in a thin film heated from below: Effect of nonmonotonic dependence of surface tension on temperature

NASA Astrophysics Data System (ADS)

Sarma, Rajkumar; Mondal, Pranab Kumar

2018-04-01

We investigate Marangoni instability in a thin liquid film resting on a substrate of low thermal conductivity and separated from the surrounding gas phase by a deformable free surface. Considering a nonmonotonic variation of surface tension with temperature, here we analytically derive the neutral stability curve for the monotonic and oscillatory modes of instability (for both the long-wave and short-wave perturbations) under the framework of linear stability analysis. For the long-wave instability, we derive a set of amplitude equations using the scaling k ˜(Bi) 1 /2 , where k is the wave number and Bi is the Biot number. Through this investigation, we demonstrate that for such a fluid layer upon heating from below, both monotonic and oscillatory instability can appear for a certain range of the dimensionless parameters, viz., Biot number (Bi ) , Galileo number (Ga ) , and inverse capillary number (Σ ) . Moreover, we unveil, through this study, the influential role of the above-mentioned parameters on the stability of the system and identify the critical values of these parameters above which instability initiates in the liquid layer.

Nonlinear evolution of the first mode supersonic oblique waves in compressible boundary layers. Part 1: Heated/cooled walls

NASA Technical Reports Server (NTRS)

Gajjar, J. S. B.

1993-01-01

The nonlinear stability of an oblique mode propagating in a two-dimensional compressible boundary layer is considered under the long wave-length approximation. The growth rate of the wave is assumed to be small so that the concept of unsteady nonlinear critical layers can be used. It is shown that the spatial/temporal evolution of the mode is governed by a pair of coupled unsteady nonlinear equations for the disturbance vorticity and density. Expressions for the linear growth rate show clearly the effects of wall heating and cooling and in particular how heating destabilizes the boundary layer for these long wavelength inviscid modes at O(1) Mach numbers. A generalized expression for the linear growth rate is obtained and is shown to compare very well for a range of frequencies and wave-angles at moderate Mach numbers with full numerical solutions of the linear stability problem. The numerical solution of the nonlinear unsteady critical layer problem using a novel method based on Fourier decomposition and Chebychev collocation is discussed and some results are presented.

On the three dimensional structure of stratospheric material transport associated with various types of waves

NASA Astrophysics Data System (ADS)

Kinoshita, T.; Sato, K.

2016-12-01

The Transformed Eulerian-Mean (TEM) equations were derived by Andrews and McIntyre (1976, 1978) and have been widely used to examine wave-mean flow interaction in the meridional cross section. According to previous studies, the Brewer-Dobson circulation in the stratosphere is driven by planetary waves, baroclinic waves, and inertia-gravity waves, and that the meridional circulation from the summer hemisphere to the winter hemisphere in the mesosphere is mainly driven by gravity waves (e.g., Garcia and Boville 1994; Plumb and Semeniuk 2003; Watanabe et al. 2008; Okamoto et al. 2011). However, the TEM equations do not provide the three-dimensional view of the transport, so that the three dimensional TEM equations have been formulated (Hoskins et al. 1983, Trenberth 1986, Plumb 1985, 1986, Takaya and Nakamura 1997, 2001, Miyahara 2006, Kinoshita et al. 2010, Noda 2010, Kinoshita and Sato 2013a, b, and Noda 2014). On the other hand, the TEM equations cannot properly treat the lower boundary and unstable waves. The Mass-weighted Isentropic Mean (MIM) equations derived by Iwasaki (1989, 1990) are the equations that overcome those problems and the formulation of three-dimensional MIM equations have been studied. The present study applies the three-dimensional TEM and MIM equations to the ERA-Interim reanalysis data and examines the climatological character of three-dimensional structure of Stratospheric Brewer-Dobson circulation. Next, we will discuss how to treat the flow associated with spatial structure of stationary waves.

The effect of shear stress on solitary waves in arteries.

PubMed

Demiray, H

1997-09-01

In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materials are depicted in graphic forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissue.

Extreme Wave-Induced Oscillation in Paradip Port Under the Resonance Conditions

NASA Astrophysics Data System (ADS)

Kumar, Prashant; Gulshan

2017-12-01

A mathematical model is constructed to analyze the long wave-induced oscillation in Paradip Port, Odisha, India under the resonance conditions to avert any extreme wave hazards. Boundary element method (BEM) with corner contribution is utilized to solve the Helmholtz equation under the partial reflection boundary conditions. Furthermore, convergence analysis is also performed for the boundary element scheme with uniform and non-uniform discretization of the boundary. The numerical scheme is also validated with analytic approximation and existing studies based on harbor resonance. Then, the amplification factor is estimated at six key record stations in the Paradip Port with multidirectional incident waves and resonance modes are also estimated at the boundary of the port. Ocean surface wave field is predicted in the interior of Paradip Port for the different directional incident wave at various resonance modes. Moreover, the safe locations in the port have been identified for loading and unloading of moored ship with different resonance modes and directional incident waves.

Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E. N.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account.

On the exact solutions of high order wave equations of KdV type (I)

NASA Astrophysics Data System (ADS)

Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

2014-12-01

In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-09-01

Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

Irregular Wave Energy Extraction Analysis for a Slider Crank WEC Power Take-Off System

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

Sang, Yuanrui; Karayaka, H. Bora; Yan, Yanjun

2015-09-02

Slider crank Wave Energy Converter (WEC) is a novel energy conversion device. It converts wave energy into electricity at a relatively high efficiency, and it features a simple structure. Past analysis on this WEC has been done under regular sinusoidal wave conditions, and a suboptimal energy could be achieved. This paper presents the analysis of the system under irregular wave conditions; a time-domain hydrodynamics model is adopted and the control methodology is modified to better serve the irregular wave conditions. Results from the simulations show that the performance of the system under irregular wave conditions is different from that undermore » regular sinusoidal wave conditions, but still a reasonable amount of energy can be extracted.« less

Modelling Of Anticipated Damage Ratio On Breakwaters Using Fuzzy Logic

NASA Astrophysics Data System (ADS)

Mercan, D. E.; Yagci, O.; Kabdasli, S.

2003-04-01

In breakwater design the determination of armour unit weight is especially important in terms of the structure's life. In a typical experimental breakwater stability study, different wave series composed of different wave heights; wave period and wave steepness characteristics are applied in order to investigate performance the structure. Using a classical approach, a regression equation is generated for damage ratio as a function of characteristic wave height. The parameters wave period and wave steepness are not considered. In this study, differing from the classical approach using a fuzzy logic, a relationship between damage ratio as a function of mean wave period (T_m), wave steepness (H_s/L_m) and significant wave height (H_s) was further generated. The system's inputs were mean wave period (T_m), wave steepness (H_s/L_m) and significant wave height (H_s). For fuzzification all input variables were divided into three fuzzy subsets, their membership functions were defined using method developed by Mandani (Mandani, 1974) and the rules were written. While for defuzzification the centroid method was used. In order to calibrate and test the generated models an experimental study was conducted. The experiments were performed in a wave flume (24 m long, 1.0 m wide and 1.0 m high) using 20 different irregular wave series (P-M spectrum). Throughout the study, the water depth was 0.6 m and the breakwater cross-sectional slope was 1V/2H. In the armour layer, a type of artificial armour unit known as antifer cubes were used. The results of the established fuzzy logic model and regression equation model was compared with experimental data and it was determined that the established fuzzy logic model gave a more accurate prediction of the damage ratio on this type of breakwater. References Mandani, E.H., "Application of Fuzzy Algorithms for Control of Simple Dynamic Plant", Proc. IEE, vol. 121, no. 12, December 1974.

Wave propagation through an inhomogeneous slab sandwiched by the piezoelectric and the piezomagnetic half spaces.

PubMed

Jiao, Fengyu; Wei, Peijun; Li, Li

2017-01-01

Wave propagation through a gradient slab sandwiched by the piezoelectric and the piezomagnetic half spaces are studied in this paper. First, the secular equations in the transverse isotropic piezoelectric/piezomagnetic half spaces are derived from the general dynamic equation. Then, the state vectors at piezoelectric and piezomagnetic half spaces are related to the amplitudes of various possible waves. The state transfer equation of the functionally graded slab is derived from the equations of motion by the reduction of order, and the transfer matrix of the functionally gradient slab is obtained by solving the state transfer equation with the spatial-varying coefficient. Finally, the continuous interface conditions are used to lead to the resultant algebraic equations. The algebraic equations are solved to obtain the amplitude ratios of various waves which are further used to obtain the energy reflection and transmission coefficients of various waves. The numerical results are shown graphically and are validated by the energy conservation law. Based on the numerical results on the fives of gradient profiles, the influences of the graded slab on the wave propagation are discussed. It is found that the reflection and transmission coefficients are obviously dependent upon the gradient profile. The various surface waves are more sensitive to the gradient profile than the bulk waves. Copyright © 2016 Elsevier B.V. All rights reserved.

The limitation and applicability of Musher-Sturman equation to two dimensional lower hybrid wave collapse

NASA Technical Reports Server (NTRS)

Tam, Sunny W. Y.; Chang, Tom

1995-01-01

The existence of localized regions of intense lower hybrid waves in the auroral ionosphere recently observed by rocket and satellite experiments can be understood by the study of a non-linear two-timescale coupling process. In this Letter, we demonstrate that the leading non-linear term in the standard Musher-Sturman equation vanishes identically in strict two-dimensions (normal to the magnetic field). Instead, the new two-dimensional equation is characterized by a much weaker non-linear term which arises from the ponderomotive force perpendicular to the magnetic field, particularly that due to the ions. The old and new equations are compared by means of time-evolution calculations of wave fields. The results exhibit a remarkable difference in the evolution of the waves as governed by the two equations. Such dissimilar outcomes motivate our investigation of the limitation of Musher-Sturman equation in quasi-two-dimensions. Only within all these limits can Musher-Sturman equation adequately describe the collapse of lower hybrid waves.

Role of Compressibility on Tsunami Propagation

NASA Astrophysics Data System (ADS)

Abdolali, Ali; Kirby, James T.

2017-12-01

In the present paper, we aim to reduce the discrepancies between tsunami arrival times evaluated from tsunami models and real measurements considering the role of ocean compressibility. We perform qualitative studies to reveal the phase speed reduction rate via a modified version of the Mild Slope Equation for Weakly Compressible fluid (MSEWC) proposed by Sammarco et al. (2013). The model is validated against a 3-D computational model. Physical properties of surface gravity waves are studied and compared with those for waves evaluated from an incompressible flow solver over realistic geometry for 2011 Tohoku-oki event, revealing reduction in phase speed.