WKB solution 4×4 for electromagnetic waves in a planar magnetically anisotropic inhomogeneous layer

NASA Astrophysics Data System (ADS)

Moiseeva, Natalya Michailovna; Moiseev, Anton Vladimirovich

2018-04-01

In the paper, an oblique incidence of a plane electromagnetic wave on a planar magnetically anisotropic inhomogeneous layer is considered. We consider the case when all the components of the magnetic permeability tensor are non zero and vary with distance from the interface of media. The WKB method gives a matrix 4 × 4 solution for the projections of the electromagnetic wave fields during its propagation. The dependence of the cross-polarized components on the orientation of the anisotropic medium relative to the plane of incidence of the medium is analyzed.

On Periodic Water Waves with Coriolis Effects and Isobaric Streamlines

NASA Astrophysics Data System (ADS)

Matioc, Anca-Voichita; Matioc, Bogdan-Vasile

2012-10-01

In this paper we prove that solutions of the f-plane approximation for equatorial geophysical deep water waves, which have the property that the pressure is constant along the streamlines and do not possess stagnation points, are Gerstner-type waves. Furthermore, for waves traveling over a flat bed, we prove that there are only laminar flow solutions with these properties.

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

PubMed

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

2017-04-01

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

Gaussian and Airy wave packets of massive particles with orbital angular momentum

NASA Astrophysics Data System (ADS)

Karlovets, Dmitry V.

2015-01-01

While wave-packet solutions for relativistic wave equations are oftentimes thought to be approximate (paraxial), we demonstrate, by employing a null-plane- (light-cone-) variable formalism, that there is a family of such solutions that are exact. A scalar Gaussian wave packet in the transverse plane is generalized so that it acquires a well-defined z component of the orbital angular momentum (OAM), while it may not acquire a typical "doughnut" spatial profile. Such quantum states and beams, in contrast to the Bessel states, may have an azimuthal-angle-dependent probability density and finite uncertainty of the OAM, which is determined by the packet's width. We construct a well-normalized Airy wave packet, which can be interpreted as a one-particle state for a relativistic massive boson, show that its center moves along the same quasiclassical straight path, and, which is more important, spreads with time and distance exactly as a Gaussian wave packet does, in accordance with the uncertainty principle. It is explained that this fact does not contradict the well-known "nonspreading" feature of the Airy beams. While the effective OAM for such states is zero, its uncertainty (or the beam's OAM bandwidth) is found to be finite, and it depends on the packet's parameters. A link between exact solutions for the Klein-Gordon equation in the null-plane-variable formalism and the approximate ones in the usual approach is indicated; generalizations of these states for a boson in the external field of a plane electromagnetic wave are also presented.

Dynamic growth of mixed-mode shear cracks

USGS Publications Warehouse

Andrews, D.J.

1994-01-01

A pure mode II (in-plane) shear crack cannot propagate spontaneously at a speed between the Rayleigh and S-wave speeds, but a three-dimensional (3D) or two-dimensional (2D) mixed-mode shear crack can propagate in this range, being driven by the mode III (antiplane) component. Two different analytic solutions have been proposed for the mode II component in this case. The first is the solution valid for crack speed less than the Rayleigh speed. When applied above the Rayleigh speed, it predicts a negative stress intensity factor, which implies that energy is generated at the crack tip. Burridge proposed a second solution, which is continuous at the crack tip, but has a singularity in slip velocity at the Rayleigh wave. Spontaneous propagation of a mixed-mode rupture has been calculated with a slip-weakening friction law, in which the slip velocity vector is colinear with the total traction vector. Spontaneous trans-Rayleigh rupture speed has been found. The solution depends on the absolute stress level. The solution for the in-plane component appears to be a superposition of smeared-out versions of the two analytic solutions. The proportion of the first solution increases with increasing absolute stress. The amplitude of the negative in-plane traction pulse is less than the absolute final sliding traction, so that total in-plane traction does not reverse. The azimuth of the slip velocity vector varies rapidly between the onset of slip and the arrival of the Rayleigh wave. The variation is larger at smaller absolute stress.

Radiation of sound from unflanged cylindrical ducts

NASA Technical Reports Server (NTRS)

Hartharan, S. L.; Bayliss, A.

1983-01-01

Calculations of sound radiated from unflanged cylindrical ducts are presented. The numerical simulation models the problem of an aero-engine inlet. The time dependent linearized Euler equations are solved from a state of rest until a harmonic solution is attained. A fourth order accurate finite difference scheme is used and solutions are obtained from a fully vectorized Cyber-203 computer program. Cases of both plane waves and spin modes are treated. Spin modes model the sound generated by a turbofan engine. Boundary conditions for both plane waves and spin modes are treated. Solutions obtained are compared with experiments conducted at NASA Langley Research Center.

Dirac electron in a chiral space-time crystal created by counterpropagating circularly polarized plane electromagnetic waves

NASA Astrophysics Data System (ADS)

Borzdov, G. N.

2017-10-01

The family of solutions to the Dirac equation for an electron moving in an electromagnetic lattice with the chiral structure created by counterpropagating circularly polarized plane electromagnetic waves is obtained. At any nonzero quasimomentum, the dispersion equation has two solutions which specify bispinor wave functions describing electron states with different energies and mean values of momentum and spin operators. The inversion of the quasimomentum results in two other linearly independent solutions. These four basic wave functions are uniquely defined by eight complex scalar functions (structural functions), which serve as convenient building blocks of the relations describing the electron properties. These properties are illustrated in graphical form over a wide range of quasimomenta. The superpositions of two basic wave functions describing different spin states and corresponding to (i) the same quasimomentum (unidirectional electron states with the spin precession) and (ii) the two equal-in-magnitude but oppositely directed quasimomenta (bidirectional electron states) are also treated.

A numerical comparison with an exact solution for the transient response of a cylinder immersed in a fluid. [computer simulated underwater tests to determine transient response of a submerged cylindrical shell

NASA Technical Reports Server (NTRS)

Giltrud, M. E.; Lucas, D. S.

1979-01-01

The transient response of an elastic cylindrical shell immersed in an acoustic media that is engulfed by a plane wave is determined numerically. The method applies to the USA-STAGS code which utilizes the finite element method for the structural analysis and the doubly asymptotic approximation for the fluid-structure interaction. The calculations are compared to an exact analysis for two separate loading cases: a plane step wave and an exponentially decaying plane wave.

Asymmetric Rogue Waves, Breather-to-Soliton Conversion, and Nonlinear Wave Interactions in the Hirota-Maxwell-Bloch System

NASA Astrophysics Data System (ADS)

Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan

2016-02-01

We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.

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.

P-wave fault-plane solutions and the generation of surface waves by earthquakes in the western United States

NASA Astrophysics Data System (ADS)

Patton, Howard J.

1985-08-01

Surface waves recorded at regional distances are used to study the source mechanisms of seven earthquakes in the western United States with magnitudes between 4.3 and 5.5. The source mechanisms of events in or on the margins of the Basin and Range show T-axis with an azimuth of N85°W +/- 16° and a plunge of 12° +/- 16°. Of the seven events, four have P-wave solutions that are inconsistent with surface-wave observations. Azimuths of the T-axis obtained from the surface-wave mechanisms and from the P-wave solutions differ by up to 45°. These events have dip-slip or oblique-slip mechanisms, and the source depths for three of the events are 5 km or less. Their source mechanisms and small magnitudes make identification of the P-wave first motion difficult due to poor signal-to-noise ratio of the initial P-wave and close arrivals of pP or sP with significant amplitude. We suggest that mis-identification of the P-wave first motion and distortion of the body-wave ray paths due to non-planar structure were sources of error in determining the nodal planes for these events.

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

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

PubMed

Pérez-Jordá, José M

2016-02-01

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

Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infinite series and variational approaches

NASA Astrophysics Data System (ADS)

Gambino, G.; Tanriver, U.; Guha, P.; Choudhury, A. Ghose; Choudhury, S. Roy

2015-02-01

In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddle equilibrium points of the corresponding traveling-wave equations, as well as ensure simultaneous convergence and continuity of the multi-infinite series solutions for the homoclinic/heteroclinic orbits anchored by these saddle points. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. And finally, variational methods are employed to generate families of both regular and embedded solitary wave solutions for the SPE PDE. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and it is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the assumed ansatz for the trial functions). Thus, a direct error analysis is performed, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that not much is known about solutions of the family of generalized SPE equations considered here, the results obtained are both new and timely.

Gravitational waves in ghost free bimetric gravity

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

Mohseni, Morteza, E-mail: m-mohseni@pnu.ac.ir

2012-11-01

We obtain a set of exact gravitational wave solutions for the ghost free bimetric theory of gravity. With a flat reference metric, the theory admits the vacuum Brinkmann plane wave solution for suitable choices of the coefficients of different terms in the interaction potential. An exact gravitational wave solution corresponding to a massive scalar mode is also admitted for arbitrary choice of the coefficients with the reference metric being proportional to the spacetime metric. The proportionality factor and the speed of the wave are calculated in terms of the parameters of the theory. We also show that a F(R) extensionmore » of the theory admits similar solutions but in general is plagued with ghost instabilities.« less

Ionic wave propagation and collision in an excitable circuit model of microtubules

NASA Astrophysics Data System (ADS)

Guemkam Ghomsi, P.; Tameh Berinyoh, J. T.; Moukam Kakmeni, F. M.

2018-02-01

In this paper, we report the propensity to excitability of the internal structure of cellular microtubules, modelled as a relatively large one-dimensional spatial array of electrical units with nonlinear resistive features. We propose a model mimicking the dynamics of a large set of such intracellular dynamical entities as an excitable medium. We show that the behavior of such lattices can be described by a complex Ginzburg-Landau equation, which admits several wave solutions, including the plane waves paradigm. A stability analysis of the plane waves solutions of our dynamical system is conducted both analytically and numerically. It is observed that perturbed plane waves will always evolve toward promoting the generation of localized periodic waves trains. These modes include both stationary and travelling spatial excitations. They encompass, on one hand, localized structures such as solitary waves embracing bright solitons, dark solitons, and bisolitonic impulses with head-on collisions phenomena, and on the other hand, the appearance of both spatially homogeneous and spatially inhomogeneous stationary patterns. This ability exhibited by our array of proteinic elements to display several states of excitability exposes their stunning biological and physical complexity and is of high relevance in the description of the developmental and informative processes occurring on the subcellular scale.

Ionic wave propagation and collision in an excitable circuit model of microtubules.

PubMed

Guemkam Ghomsi, P; Tameh Berinyoh, J T; Moukam Kakmeni, F M

2018-02-01

In this paper, we report the propensity to excitability of the internal structure of cellular microtubules, modelled as a relatively large one-dimensional spatial array of electrical units with nonlinear resistive features. We propose a model mimicking the dynamics of a large set of such intracellular dynamical entities as an excitable medium. We show that the behavior of such lattices can be described by a complex Ginzburg-Landau equation, which admits several wave solutions, including the plane waves paradigm. A stability analysis of the plane waves solutions of our dynamical system is conducted both analytically and numerically. It is observed that perturbed plane waves will always evolve toward promoting the generation of localized periodic waves trains. These modes include both stationary and travelling spatial excitations. They encompass, on one hand, localized structures such as solitary waves embracing bright solitons, dark solitons, and bisolitonic impulses with head-on collisions phenomena, and on the other hand, the appearance of both spatially homogeneous and spatially inhomogeneous stationary patterns. This ability exhibited by our array of proteinic elements to display several states of excitability exposes their stunning biological and physical complexity and is of high relevance in the description of the developmental and informative processes occurring on the subcellular scale.

Effects of the horizontal component of the Earth's rotation on wave propagation on an f-plane

NASA Astrophysics Data System (ADS)

Beckmann, Aike; Diebels, Stefan

Scaling arguments are used to show that effects due to the horizontal component of the Coriolis force should be taken into account as a first correction to the traditional hydrostatic theory, before frequency dispersion due to vertical acceleration and nonlinearity are included. It is shown analytically that wave propagation of the f--plane becomes anisotropic and that amphidromic systems do not exist in their usual definition. Another important consequence is the existence of free wave solutions at subinertial frequencies.

Benchmark solution for vibrations from a moving point source in a tunnel embedded in a half-space

NASA Astrophysics Data System (ADS)

Yuan, Zonghao; Boström, Anders; Cai, Yuanqiang

2017-01-01

A closed-form semi-analytical solution for the vibrations due to a moving point load in a tunnel embedded in a half-space is given in this paper. The tunnel is modelled as an elastic hollow cylinder and the ground surrounding the tunnel as a linear viscoelastic material. The total wave field in the half-space with a cylindrical hole is represented by outgoing cylindrical waves and down-going plane waves. To apply the boundary conditions on the ground surface and at the tunnel-soil interface, the transformation properties between the plane and cylindrical wave functions are employed. The proposed solution can predict the ground vibration from an underground railway tunnel of circular cross-section with a reasonable computational effort and can serve as a benchmark solution for other computational methods. Numerical results for the ground vibrations on the free surface due to a moving constant load and a moving harmonic load applied at the tunnel invert are presented for different load velocities and excitation frequencies. It is found that Rayleigh waves play an important role in the ground vibrations from a shallow tunnel.

Time-Harmonic Gaussian Beams: Exact Solutions of the Helmhotz Equation in Free Space

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2017-12-01

An exact solution of the Helmholtz equation u xx + u yy + u zz + k 2 u = 0 is presented, which describes propagation of monochromatic waves in the free space. The solution has the form of a superposition of plane waves with a specific weight function dependent on a certain free parameter a. If ka→∞, the solution is localized in the Gaussian manner in a vicinity of a certain straight line and asymptotically coincides with the famous approximate solution known as the fundamental mode of a paraxial Gaussian beam. The asymptotics of the aforementioned exact solution does not include a backward wave.

Focusing of noncircular self-similar shock waves.

PubMed

Betelu, S I; Aronson, D G

2001-08-13

We study the focusing of noncircular shock waves in a perfect gas. We construct an explicit self-similar solution by combining three convergent plane waves with regular shock reflections between them. We then show, with a numerical Riemann solver, that there are initial conditions with smooth shocks whose intermediate asymptotic stage is described by the exact solution. Unlike the focusing of circular shocks, our self-similar shocks have bounded energy density.

X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

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

Balyan, M. K., E-mail: mbalyan@ysu.am

The two-wave dynamical diffraction in the Laue geometry has been theoretically considered for a plane X-ray wave in a crystal with a third-order nonlinear response to the external field. An analytical solution to the problem stated is found for certain diffraction conditions. A nonlinear pendulum effect is analyzed. The nonlinear extinction length is found to depend on the incident-wave intensity. A pendulum effect of a new type is revealed: the intensities of the transmitted and diffracted waves periodically depend on the incidentwave intensity at a fixed crystal thickness. The rocking curves and Borrmann nonlinear effect are numerically calculated.

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.

Penrose limits of Abelian and non-Abelian T-duals of AdS 5 × S 5 and their field theory duals

NASA Astrophysics Data System (ADS)

Itsios, Georgios; Nastase, Horatiu; Núñez, Carlos; Sfetsos, Konstantinos; Zacarías, Salomón

2018-01-01

We consider the backgrounds obtained by Abelian and non-Abelian T-duality applied on AdS 5 × S 5. We study geodesics, calculate Penrose limits and find the associated plane-wave geometries. We quantise the weakly coupled type-IIA string theory on these backgrounds. We study the BMN sector, finding operators that wrap the original quiver CFT. For the non-Abelian plane wave, we find a `flow' in the frequencies. We report some progress to understand this, in terms of deconstruction of a higher dimensional field theory. We explore a relation with the plane-wave limit of the Janus solution, which we also provide.

Infinite hierarchy of nonlinear Schrödinger equations and their solutions.

PubMed

Ankiewicz, A; Kedziora, D J; Chowdury, A; Bandelow, U; Akhmediev, N

2016-01-01

We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even- order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

Nonlinear waves of a nonlocal modified KdV equation in the atmospheric and oceanic dynamical system

NASA Astrophysics Data System (ADS)

Tang, Xiao-yan; Liang, Zu-feng; Hao, Xia-zhi

2018-07-01

A new general nonlocal modified KdV equation is derived from the nonlinear inviscid dissipative and equivalent barotropic vorticity equation in a β-plane. The nonlocal property is manifested in the shifted parity and delayed time reversal symmetries. Exact solutions of the nonlocal modified KdV equation are obtained including periodic waves, kink waves, solitary waves, kink- and/or anti-kink-cnoidal periodic wave interaction solutions, which can be utilized to describe various two-place and time-delayed correlated events. As an illustration, a special approximate solution is applied to theoretically capture the salient features of two correlated dipole blocking events in atmospheric dynamical systems.

Analytical Time-Domain Solution of Plane Wave Propagation Across a Viscoelastic Rock Joint

NASA Astrophysics Data System (ADS)

Zou, Yang; Li, Jianchun; Laloui, Lyesse; Zhao, Jian

2017-10-01

The effects of viscoelastic filled rock joints on wave propagation are of great significance in rock engineering. The solutions in time domain for plane longitudinal ( P-) and transverse ( S-) waves propagation across a viscoelastic rock joint are derived based on Maxwell and Kelvin models which are, respectively, applied to describe the viscoelastic deformational behaviour of the rock joint and incorporated into the displacement discontinuity model (DDM). The proposed solutions are verified by comparing with the previous studies on harmonic waves, which are simulated by sinusoidal incident P- and S-waves. Comparison between the predicted transmitted waves and the experimental data for P-wave propagation across a joint filled with clay is conducted. The Maxwell is found to be more appropriate to describe the filled joint. The parametric studies show that wave propagation is affected by many factors, such as the stiffness and the viscosity of joints, the incident angle and the duration of incident waves. Furthermore, the dependences of the transmission and reflection coefficients on the specific joint stiffness and viscosity are different for the joints with Maxwell and Kelvin behaviours. The alternation of the reflected and transmitted waveforms is discussed, and the application scope of this study is demonstrated by an illustration of the effects of the joint thickness. The solutions are also extended for multiple parallel joints with the virtual wave source method and the time-domain recursive method. For an incident wave with arbitrary waveform, it is convenient to adopt the present approach to directly calculate wave propagation across a viscoelastic rock joint without additional mathematical methods such as the Fourier and inverse Fourier transforms.

A Model for Measured Traveling Waves at End-Diastole in Human Heart Wall by Ultrasonic Imaging Method

NASA Astrophysics Data System (ADS)

Bekki, Naoaki; Shintani, Seine A.; Ishiwata, Shin'ichi; Kanai, Hiroshi

2016-04-01

We observe traveling waves, measured by the ultrasonic noninvasive imaging method, in a longitudinal beam direction from the apex to the base side on the interventricular septum (IVS) during the period from the end-diastole to the beginning of systole for a healthy human heart wall. We present a possible phenomenological model to explain part of one-dimensional cardiac behaviors for the observed traveling waves around the time of R-wave of echocardiography (ECG) in the human heart. Although the observed two-dimensional patterns of traveling waves are extremely complex and no one knows yet the exact solutions for the traveling homoclinic plane wave in the one-dimensional complex Ginzburg-Landau equation (CGLE), we numerically find that part of the one-dimensional homoclinic dynamics of the phase and amplitude patterns in the observed traveling waves is similar to that of the numerical homoclinic plane-wave solutions in the CGLE with periodic boundary condition in a certain parameter space. It is suggested that part of the cardiac dynamics of the traveling waves on the IVS can be qualitatively described by the CGLE model as a paradigm for understanding biophysical nonlinear phenomena.

Resonant Triad in Boundary-Layer Stability. Part 2; Composite Solution and Comparison with Observations

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

Here, numerical results are computed from an asymptotic near-resonance triad analysis. The analysis considers a resonant triad of instability waves consisting of a plane fundamental wave and a pair of symmetrical oblique subharmonic waves. The relevant scaling ensures that nonlinearity is confined to a distinct critical layer. The analysis is first used to form a composite solution that accounts for both the flow divergence and nonlinear effects. It is shown that the backreaction on the plane Tollmien Schlichting (TS) fundamental wave, although fully accounted for, is of little significance. The observed enhancement at the fundamental frequency disturbance is not in the plane TS wave, but is caused by nonlinearly generated waves at the fundamental frequency that result from nonlinear interactions in the critical layer. The saturation of the oblique waves is caused by their self-interaction. The nonlinear phase-locking phenomenon, the location of resonance with respect to the neutral stability curve, low frequency effects, detuning in the streamwise wave numbers, and nonlinear distortion of the mode shapes are discussed. Nonlinearity modifies the initially two dimensional Blasius profile into a fuller one with spanwise periodicity. The interactions at a wide range of unstable spanwise wave numbers are considered, and the existence of a preferred spanwise wave number is explained by means of the vorticity distribution in the critical layer. Besides presenting novel features of the phenomena and explaining the delicate mechanisms of the interactions, the results of the theory are in excellent agreement with experimental and numerical observations for all stages of the development and for various input parameters.

Impedance of strip-traveling waves on an elastic half space - Asymptotic solution

NASA Technical Reports Server (NTRS)

Crandall, S. H.; Nigam, A. K.

1973-01-01

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.

Scattering by multiple cylinders located on both sides of an interface

NASA Astrophysics Data System (ADS)

Lee, Siu-Chun

2018-07-01

The solution for scattering by multiple parallel infinite cylinders located in adjacent half spaces with dissimilar refractive index is presented in this paper. The incident radiation is an arbitrarily polarized plane wave propagating in the upper half space in the plane perpendicular to the axis of the cylinders. The formulation of the electromagnetic field vectors utilized Hertz potentials that are expressed in terms of an expansion of cylindrical wave functions. It accounts for the near-field multiple scattering, Fresnel effect at the interface, and interaction between cylinders in both half spaces. Analytical formulas are derived for the electromagnetic field and Poynting vector in the far-field. The present solution provides the theoretical framework for deducing the solutions for scattering by cylinders located on either side of an interface irradiated by a propagating or an evanescent incident wave. Deduction of these solutions from the present formulation is demonstrated. Numerical results are presented to illustrate the frustration of total internal reflection and scattering of light beyond the critical angle by nanocylinders located in either or both half spaces.

Determination of the effective transverse coherence of the neutron wave packet as employed in reflectivity investigations of condensed-matter structures. II. Analysis of elastic scattering using energy-gated wave packets with an application to neutron reflection from ruled gratings

NASA Astrophysics Data System (ADS)

Berk, N. F.

2014-03-01

We present a general approach to analyzing elastic scattering for those situations where the incident beam is prepared as an incoherent ensemble of wave packets of a given arbitrary shape. Although wave packets, in general, are not stationary solutions of the Schrödinger equation, the analysis of elastic scattering data treats the scattering as a stationary-state problem. We thus must gate the wave packet, coherently distorting its shape in a manner consistent with the elastic condition. The resulting gated scattering amplitudes (e.g., reflection coefficients) thus are weighted coherent sums of the constituent plane-wave scattering amplitudes, with the weights determined by the shape of the incident wave packet as "filtered" by energy gating. We develop the gating formalism in general and apply it to the problem of neutron scattering from ruled gratings described by Majkrzak et al. in a companion paper. The required exact solution of the associated problem of plane-wave reflection from gratings also is derived.

An Arctic Ice/Ocean Coupled Model with Wave Interactions

DTIC Science & Technology

2013-09-30

motion in the presence of currents and waves. In the wave attenuation experiments, between 35 and 80 ‘ice floes’ (0.99 m diameter wooden disks) were...moored with springs to the tank floor and plane waves were sent down, with an array of wave probes to measure the reflected and transmitted waves...waves propagating in the MIZ as opposed to the acoustic wave solution shown. This outcome offers significant new capabilities for tracking fully

Trapped waves on the mid-latitude β-plane

NASA Astrophysics Data System (ADS)

Paldor, Nathan; Sigalov, Andrey

2008-08-01

A new type of approximate solutions of the Linearized Shallow Water Equations (LSWE) on the mid-latitude β-plane, zonally propagating trapped waves with Airy-like latitude-dependent amplitude, is constructed in this work, for sufficiently small radius of deformation. In contrast to harmonic Poincare and Rossby waves, these newly found trapped waves vanish fast in the positive half-axis, and their zonal phase speed is larger than that of the corresponding harmonic waves for sufficiently large meridional domains. Our analysis implies that due to the smaller radius of deformation in the ocean compared with that in the atmosphere, the trapped waves are relevant to observations in the ocean whereas harmonic waves typify atmospheric observations. The increase in the zonal phase speed of trapped Rossby waves compared with that of harmonic ones is consistent with recent observations that showed that Sea Surface Height features propagated westwards faster than the phase speed of harmonic Rossby waves.

Scaling of plane-wave functions in statistically optimized near-field acoustic holography.

PubMed

Hald, Jørgen

2014-11-01

Statistically Optimized Near-field Acoustic Holography (SONAH) is a Patch Holography method, meaning that it can be applied in cases where the measurement area covers only part of the source surface. The method performs projections directly in the spatial domain, avoiding the use of spatial discrete Fourier transforms and the associated errors. First, an inverse problem is solved using regularization. For each calculation point a multiplication must then be performed with two transfer vectors--one to get the sound pressure and the other to get the particle velocity. Considering SONAH based on sound pressure measurements, existing derivations consider only pressure reconstruction when setting up the inverse problem, so the evanescent wave amplification associated with the calculation of particle velocity is not taken into account in the regularized solution of the inverse problem. The present paper introduces a scaling of the applied plane wave functions that takes the amplification into account, and it is shown that the previously published virtual source-plane retraction has almost the same effect. The effectiveness of the different solutions is verified through a set of simulated measurements.

Alfvén simple waves

NASA Astrophysics Data System (ADS)

Webb, G. M.; Zank, G. P.; Burrows, R. H.; Ratkiewicz, R. E.

2011-02-01

Multi-dimensional Alfvén simple waves in magnetohydrodynamics (MHD) are investigated using Boillat's formalism. For simple wave solutions, all physical variables (the gas density, pressure, fluid velocity, entropy, and magnetic field induction in the MHD case) depend on a single phase function ϕ, which is a function of the space and time variables. The simple wave ansatz requires that the wave normal and the normal speed of the wave front depend only on the phase function ϕ. This leads to an implicit equation for the phase function and a generalization of the concept of a plane wave. We obtain examples of Alfvén simple waves, based on the right eigenvector solutions for the Alfvén mode. The Alfvén mode solutions have six integrals, namely that the entropy, density, magnetic pressure, and the group velocity (the sum of the Alfvén and fluid velocity) are constant throughout the wave. The eigenequations require that the rate of change of the magnetic induction B with ϕ throughout the wave is perpendicular to both the wave normal n and B. Methods to construct simple wave solutions based on specifying either a solution ansatz for n(ϕ) or B(ϕ) are developed.

Alfven Simple Waves

NASA Astrophysics Data System (ADS)

Webb, G. M.; Zank, G. P.; Burrows, R.

2009-12-01

Multi-dimensional Alfvén simple waves in magnetohydrodynamics (MHD) are investigated using Boillat's formalism. For simple wave solutions, all physical variables (the gas density, pressure, fluid velocity, entropy, and magnetic field induction in the MHD case) depend on a single phase function ǎrphi which is a function of the space and time variables. The simple wave ansatz requires that the wave normal and the normal speed of the wave front depend only on the phase function ǎrphi. This leads to an implicit equation for the phase function, and a generalisation of the concept of a plane wave. We obtain examples of Alfvén simple waves, based on the right eigenvector solutions for the Alfvén mode. The Alfvén mode solutions have six integrals, namely that the entropy, density, magnetic pressure and the group velocity (the sum of the Alfvén and fluid velocity) are constant throughout the wave. The eigen-equations require that the rate of change of the magnetic induction B with ǎrphi throughout the wave is perpendicular to both the wave normal n and B. Methods to construct simple wave solutions based on specifying either a solution ansatz for n(ǎrphi) or B(ǎrphi) are developed.

Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory

NASA Astrophysics Data System (ADS)

Karami, Behrouz; Shahsavari, Davood; Li, Li

2018-03-01

A size-dependent model is developed for the hygrothermal wave propagation analysis of an embedded viscoelastic single layer graphene sheet (SLGS) under the influence of in-plane magnetic field. The bi-Helmholtz nonlocal strain gradient theory involving three small scale parameters is introduced to account for the size-dependent effects. The size-dependent model is deduced based on Hamilton's principle. The closed-form solution of eigenfrequency relation between wave number and phase velocity is achieved. By studying the size-dependent effects on the flexural wave of SLGS, the dispersion relation predicted by the developed size-dependent model can show a good match with experimental data. The influence of in-plane magnetic field, temperature and moisture of environs, structural damping, damped substrate, lower and higher order nonlocal parameters and the material characteristic parameter on the phase velocity of SLGS is explored.

On the decay of solutions to the 2D Neumann exterior problem for the wave equation

NASA Astrophysics Data System (ADS)

Secchi, Paolo; Shibata, Yoshihiro

We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition and study the asymptotic behavior of the solution for large times. For possible application we are interested to show a decay estimate which does not involve weighted norms of the initial data. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.

Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

PubMed Central

Jing, Yun; Tao, Molei; Clement, Greg T.

2011-01-01

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed. PMID:21302985

Reflection and interference of electromagnetic waves in inhomogeneous media

NASA Technical Reports Server (NTRS)

Geiger, F. E.; Kyle, H. L.

1973-01-01

Solutions were obtained of the wave equation for a plane horizontally polarized electro-magnetic wave incident on a semi infinite two dimensional inhomogeneous medium. Two problems were considered: An inhomogeneous half space, and an inhomogeneous layer of arbitrary thickness. Solutions of the wave equation were obtained in terms of Hankel functions with complex arguments. Numerical calculations were made of the reflection coefficient R at the interface of the homogeneous medium. The startling results show that the reflection coefficient for a complex dielectric constant with gradient, can be less than that of the same medium with zero gradient.

Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces

NASA Astrophysics Data System (ADS)

Roshchin, B. S.; Chukhovsky, F. N.; Pavlyuk, M. D.; Opolchentsev, A. M.; Asadchikov, V. E.

2017-03-01

The applicability of different approaches to the description of hard X-ray scattering from rough surfaces is generally limited by a maximum surface roughness height of no more than 1 nm. Meanwhile, this value is several times larger for the surfaces of different materials subjected to treatment, especially in the initial treatment stages. To control the roughness parameters in all stages of surface treatment, a new approach has been developed, which is based on a series expansion of wavefield over the plane eigenstate-function waves describing the small-angle scattering of incident X-rays in terms of plane q-waves propagating through the interface between two media with a random function of relief heights. To determine the amplitudes of reflected and transmitted plane q-waves, a system of two linked integral equations was derived. The solutions to these equations correspond (in zero order) to the well-known Fresnel expressions for a smooth plane interface. Based on these solutions, a statistical fractal model of an isotropic rough interface is built in terms of root-mean-square roughness σ, two-point correlation length l, and fractal surface index h. The model is used to interpret X-ray scattering data for polished surfaces of single-crystal cadmium telluride samples.

Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces

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

Roshchin, B. S., E-mail: ross@crys.ras.ru; Chukhovsky, F. N.; Pavlyuk, M. D.

2017-03-15

The applicability of different approaches to the description of hard X-ray scattering from rough surfaces is generally limited by a maximum surface roughness height of no more than 1 nm. Meanwhile, this value is several times larger for the surfaces of different materials subjected to treatment, especially in the initial treatment stages. To control the roughness parameters in all stages of surface treatment, a new approach has been developed, which is based on a series expansion of wavefield over the plane eigenstate-function waves describing the small-angle scattering of incident X-rays in terms of plane q-waves propagating through the interface betweenmore » two media with a random function of relief heights. To determine the amplitudes of reflected and transmitted plane q-waves, a system of two linked integral equations was derived. The solutions to these equations correspond (in zero order) to the well-known Fresnel expressions for a smooth plane interface. Based on these solutions, a statistical fractal model of an isotropic rough interface is built in terms of root-mean-square roughness σ, two-point correlation length l, and fractal surface index h. The model is used to interpret X-ray scattering data for polished surfaces of single-crystal cadmium telluride samples.« less

Integral representations of solutions of the wave equation based on relativistic wavelets

NASA Astrophysics Data System (ADS)

Perel, Maria; Gorodnitskiy, Evgeny

2012-09-01

A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed.

Magnetic Helicity of Alfven Simple Waves

NASA Technical Reports Server (NTRS)

Webb, Gary M.; Hu, Q.; Dasgupta, B.; Zank, G. P.; Roberts, D.

2010-01-01

The magnetic helicity of fully nonlinear, multi-dimensional Alfven simple waves are investigated, by using relative helicity formulae and also by using an approach involving poloidal and toroidal decomposition of the magnetic field and magnetic vector potential. Different methods to calculate the magnetic vector potential are used, including the homotopy and Biot-Savart formulas. Two basic Alfven modes are identified: (a) the plane 1D Alfven simple wave given in standard texts, in which the Alfven wave propagates along the z-axis, with wave phase varphi=k_0(z-lambda t), where k_0 is the wave number and lambda is the group velocity of the wave, and (b)\\ the generalized Barnes (1976) simple Alfven wave in which the wave normal {bf n} moves in a circle in the xy-plane perpendicular to the mean field, which is directed along the z-axis. The plane Alfven wave (a) is analogous to the slab Alfven mode and the generalized Barnes solution (b) is analogous to the 2D mode in Alfvenic, incompressible turbulence. The helicity characteristics of these two basic Alfven modes are distinct. The helicity characteristics of more general multi-dimensional simple Alfven waves are also investigated. Applications to nonlinear Aifvenic fluctuations and structures observed in the solar wind are discussed.

The memory effect for plane gravitational waves

NASA Astrophysics Data System (ADS)

Zhang, P.-M.; Duval, C.; Gibbons, G. W.; Horvathy, P. A.

2017-09-01

We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einstein's vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zel'dovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the "velocity memory effect", considered by Braginsky, Thorne, Grishchuk, and Polnarev.

Invertible propagator for plane wave illumination of forward-scattering structures.

PubMed

Samelsohn, Gregory

2017-05-10

Propagation of directed waves in forward-scattering media is considered. It is assumed that the evolution of the wave field is governed by the standard parabolic wave equation. An efficient one-step momentum-space propagator, suitable for a tilted plane wave illumination of extended objects, is derived. It is expressed in terms of a propagation operator that transforms (the complex exponential of) a linogram of the illuminated object into a set of its diffraction patterns. The invertibility of the propagator is demonstrated, which permits a multiple-shot scatter correction to be performed, and makes the solution especially attractive for either projective or tomographic imaging. As an example, high-resolution tomograms are obtained in numerical simulations implemented for a synthetic phantom, with both refractive and absorptive inclusions.

Transmission of sound across a vortex layer enclosing a cylindrical column of jet

NASA Technical Reports Server (NTRS)

Luh, R.; Chao, C. C.

1982-01-01

An approximate solution to the problem of transmission of sound across a cylindrical vortex was obtained. Results are considerably different from the plane vortex sheet case because of the added role played by the curvature of the jet. In comparison with the plane case, the specularly transmitted waves are more complex and require some numerical integration. Resonance waves are identically predicted for M 2, but there is also a wave field whose modified effect appears to extend the region of resonance just as the instability waves cover a region in space and time. The instability waves are predicted to exist for all Mach numbers but vanish for wavelengths that are large compared to the jet radius. The region of propagation is similarly wavelength dependent.

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

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.

The Role of Angular Momentum in the Construction of Electromagnetic Multipolar Fields

ERIC Educational Resources Information Center

Tischler, Nora; Zambrana-Puyalto, Xavier; Molina-Terriza, Gabriel

2012-01-01

Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic fields, the multipolar solutions do not share a standard derivation or notation. As a result, expressions…

Soliton, rational, and periodic solutions for the infinite hierarchy of defocusing nonlinear Schrödinger equations.

PubMed

Ankiewicz, Adrian

2016-07-01

Analysis of short-pulse propagation in positive dispersion media, e.g., in optical fibers and in shallow water, requires assorted high-order derivative terms. We present an infinite-order "dark" hierarchy of equations, starting from the basic defocusing nonlinear Schrödinger equation. We present generalized soliton solutions, plane-wave solutions, and periodic solutions of all orders. We find that "even"-order equations in the set affect phase and "stretching factors" in the solutions, while "odd"-order equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are complex. There are various applications in optics and water waves.

Existence and stability of dispersive solutions to the Kadomtsev-Petviashvili equation in the presence of dispersion effect

NASA Astrophysics Data System (ADS)

Das, Amiya; Ganguly, Asish

2017-07-01

The paper deals with Kadomtsev-Petviashvili (KP) equation in presence of a small dispersion effect. The nature of solutions are examined under the dispersion effect by using Lyapunov function and dynamical system theory. We prove that when dispersion is added to the KP equation, in certain regions, yet there exist bounded traveling wave solutions in the form of solitary waves, periodic and elliptic functions. The general solution of the equation with or without the dispersion effect are obtained in terms of Weirstrass ℘ functions and Jacobi elliptic functions. New form of kink-type solutions are established by exploring a new technique based on factorization method, use of functional transformation and the Abel's first order nonlinear equation. Furthermore, the stability analysis of the dispersive solutions are examined which shows that the traveling wave velocity is a bifurcation parameter which governs between different classes of waves. We use the phase plane analysis and show that at a critical velocity, the solution has a transcritical bifurcation.

Novel high-gain, improved-bandwidth, finned-ladder V-band Traveling-Wave Tube slow-wave circuit design

NASA Technical Reports Server (NTRS)

Kory, Carol L.; Wilson, Jeffrey D.

1994-01-01

The V-band frequency range of 59-64 GHz is a region of the millimeter-wave spectrum that has been designated for inter-satellite communications. As a first effort to develop a high-efficiency V-band Traveling-Wave Tube (TWT), variations on a ring-plane slow-wave circuit were computationally investigated to develop an alternative to the more conventional ferruled coupled-cavity circuit. The ring-plane circuit was chosen because of its high interaction impedance, large beam aperture, and excellent thermal dissipation properties. Despite these advantages, however, low bandwidth and high voltage requirements have, until now, prevented its acceptance outside the laboratory. In this paper, the three-dimensional electrodynamic simulation code MAFIA (solution of MAxwell's Equation by the Finite-Integration-Algorithm) is used to investigate methods of increasing the bandwidth and lowering the operating voltage of the ring-plane circuit. Calculations of frequency-phase dispersion, beam on-axis interaction impedance, attenuation and small-signal gain per wavelength were performed for various geometric variations and loading distributions of the ring-plane TWT slow-wave circuit. Based on the results of the variations, a circuit termed the finned-ladder TWT slow-wave circuit was designed and is compared here to the scaled prototype ring-plane and a conventional ferruled coupled-cavity TWT circuit over the V-band frequency range. The simulation results indicate that this circuit has a much higher gain, significantly wider bandwidth, and a much lower voltage requirement than the scaled ring-plane prototype circuit, while retaining its excellent thermal dissipation properties. The finned-ladder circuit has a much larger small-signal gain per wavelength than the ferruled coupled-cavity circuit, but with a moderate sacrifice in bandwidth.

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.

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.

Development of attenuation and diffraction corrections for linear and nonlinear Rayleigh surface waves radiating from a uniform line source

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

Jeong, Hyunjo, E-mail: hjjeong@wku.ac.kr; Cho, Sungjong; Zhang, Shuzeng

2016-04-15

In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave ismore » defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.« less

A new class of exact solutions of the Klein-Gordon equation of a charged particle interacting with an electromagnetic plane wave in a medium

NASA Astrophysics Data System (ADS)

Varró, Sándor

2014-01-01

Exact solutions are presented of the Klein-Gordon equation of a charged particle moving in a transverse monochromatic plasmon wave of arbitrary high amplitude, which propagates in an underdense plasma. These solutions are expressed in terms of Ince polynomials, forming a doubly infinite set, parametrized by discrete momentum components of the charged particle’s de Broglie wave along the polarization vector and along the propagation direction of the plasmon radiation. The envelope of the exact wavefunctions describes a high-contrast periodic structure of the particle density on the plasma length scale, which may have relevance in novel particle acceleration mechanisms.

A Bridge between Two Important Problems in Optics and Electrostatics

ERIC Educational Resources Information Center

Capelli, R.; Pozzi, G.

2008-01-01

It is shown how the same physically appealing method can be applied to find analytic solutions for two difficult and apparently unrelated problems in optics and electrostatics. They are: (i) the diffraction of a plane wave at a perfectly conducting thin half-plane and (ii) the electrostatic field associated with a parallel array of stripes held at…

Bianchi class B spacetimes with electromagnetic fields

NASA Astrophysics Data System (ADS)

Yamamoto, Kei

2012-02-01

We carry out a thorough analysis on a class of cosmological space-times which admit three spacelike Killing vectors of Bianchi class B and contain electromagnetic fields. Using dynamical system analysis, we show that a family of electro-vacuum plane-wave solutions of the Einstein-Maxwell equations is the stable attractor for expanding universes. Phase dynamics are investigated in detail for particular symmetric models. We integrate the system exactly for some special cases to confirm the qualitative features. Some of the obtained solutions have not been presented previously to the best of our knowledge. Finally, based on those analyses, we discuss the relation between those homogeneous models and perturbations of open Friedmann-Lemaitre-Robertson-Walker universes. We argue that the electro-vacuum plane-wave modes correspond to a certain long-wavelength limit of electromagnetic perturbations.

X-ray EM simulation tool for ptychography dataset construction

NASA Astrophysics Data System (ADS)

Stoevelaar, L. Pjotr; Gerini, Giampiero

2018-03-01

In this paper, we present an electromagnetic full-wave modeling framework, as a support EM tool providing data sets for X-ray ptychographic imaging. Modeling the entire scattering problem with Finite Element Method (FEM) tools is, in fact, a prohibitive task, because of the large area illuminated by the beam (due to the poor focusing power at these wavelengths) and the very small features to be imaged. To overcome this problem, the spectrum of the illumination beam is decomposed into a discrete set of plane waves. This allows reducing the electromagnetic modeling volume to the one enclosing the area to be imaged. The total scattered field is reconstructed by superimposing the solutions for each plane wave illumination.

Two-dimensional model of the interaction of a plane acoustic wave with nozzle edge and wing trailing edge.

PubMed

Faranosov, Georgy A; Bychkov, Oleg P

2017-01-01

The interaction of a plane acoustic wave with two-dimensional model of nozzle edge and trailing edge is investigated theoretically by means of the Wiener-Hopf technique. The nozzle edge and the trailing edge are simulated by two half-planes with offset edges. Shear layer behind the nozzle edge is represented by a vortex sheet supporting Kelvin-Helmholtz instability waves. The considered configuration combines two well-known models (nozzle edge and trailing edge), and reveals additional interesting physical aspects. To obtain the solution, the matrix Wiener-Hopf equation is solved in conjunction with a requirement that the full Kutta condition is imposed at the edges. Factorization of the kernel matrix is performed by the combination of Padé approximation and the pole removal technique. This procedure is used to obtain numerical results. The results indicate that the diffracted acoustic field may be significantly intensified due to scattering of hydrodynamic instability waves into sound waves provided that the trailing edge is close enough to the vortex sheet. Similar mechanism may be responsible for the intensification of jet noise near a wing.

Electromagnetic scattering from two-dimensional thick material junctions

NASA Technical Reports Server (NTRS)

Ricoy, M. A.; Volakis, John L.

1990-01-01

The problem of the plane wave diffraction is examined by an arbitrary symmetric two dimensional junction, where Generalized Impedance Boundary Conditions (GIBCs) and Generalized Sheet Transition Conditions (GSTCs) are employed to simulate the slabs. GIBCs and GSTCs are constructed for multilayer planar slabs of arbitrary thickness and the resulting GIBC/GSTC reflection coefficients are compared with exact counterparts to evaluate the GIBCs/GSTCs. The plane wave diffraction by a multilayer material slab recessed in a perfectly conducting ground plane is formulated and solved via the Generalized Scattering Matrix Formulation (GDMF) in conjunction with the dual integral equation approach. Various scattering patterns are computed and validated with exact results where possible. The diffraction by a material discontinuity in a thick dielectric/ferrite slab is considered by modelling the constituent slabs with GSTCs. A non-unique solution in terms of unknown constants is obtained, and these constants are evaluated for the recessed slab geometry by comparison with the solution obtained therein. Several other simplified cases are also presented and discussed. An eigenfunction expansion method is introduced to determine the unknown solution constants in the general case. This procedure is applied to the non-unique solution in terms of unknown constants; and scattering patterns are presented for various slab junctions and compared with alternative results where possible.

Vacillations induced by interference of stationary and traveling planetary waves

NASA Technical Reports Server (NTRS)

Salby, Murry L.; Garcia, Rolando R.

1987-01-01

The interference pattern produced when a traveling planetary wave propagates over a stationary forced wave is explored, examining the interference signature in a variety of diagnostics. The wave field is first restricted to a diatomic spectrum consisting of two components: a single stationary wave and a single monochromatic traveling wave. A simple barotropic normal mode propagating over a simple stationary plane wave is considered, and closed form solutions are obtained. The wave fields are then restricted spatially, providing more realistic structures without sacrificing the advantages of an analytical solution. Both stationary and traveling wave fields are calculated numerically with the linearized Primitive Equations in a realistic basic state. The mean flow reaction to the fluctuating eddy forcing which results from interference is derived. Synoptic geopotential behavior corresponding to the combined wave and mean flow fields is presented, and the synoptic signature in potential vorticity on isentropic surfaces is examined.

Supersymmetric string waves

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

Bergshoeff, E.A.; Kallosh, R.; Ortin, T.

1993-06-15

We present plane-wave-type solutions of the lowest-order superstring effective action which have unbroken space-time supersymmetries. They are given by a stringy generalization of the Brinkmann metric, dialton, axion, and gauge fields. Some conspiracy between the metric and the axion field is required. The [alpha][prime] stringy corrections to the effective on-shell action, to the equations of motion (and therefore to the solutions themselves), and to the supersymmetry transformations are shown to vanish for a special class of these solutions that we call supersymmetric string waves (SSW's). In the SSW solutions, there exists a conspiracy not only between the metric and themore » axion field, but also between the gauge fields and the metric, since the embedding of the spin connection in the gauge group is required.« less

Relativistic nonlinear plasma waves in a magnetic field

NASA Technical Reports Server (NTRS)

Kennel, C. F.; Pellat, R.

1975-01-01

Five relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an 'electron-positron' plasma leads to equations which have the form of a one-dimensional potential well. The solutions indicate that a large-amplitude superluminous wave determines the average plasma properties.

Instabilities of Internal Gravity Wave Beams

NASA Astrophysics Data System (ADS)

Dauxois, Thierry; Joubaud, Sylvain; Odier, Philippe; Venaille, Antoine

2018-01-01

Internal gravity waves play a primary role in geophysical fluids: They contribute significantly to mixing in the ocean, and they redistribute energy and momentum in the middle atmosphere. Until recently, most studies were focused on plane wave solutions. However, these solutions are not a satisfactory description of most geophysical manifestations of internal gravity waves, and it is now recognized that internal wave beams with a confined profile are ubiquitous in the geophysical context. We discuss the reason for the ubiquity of wave beams in stratified fluids, which is related to the fact that they are solutions of the nonlinear governing equations. We focus more specifically on situations with a constant buoyancy frequency. Moreover, in light of recent experimental and analytical studies of internal gravity beams, it is timely to discuss the two main mechanisms of instability for those beams: (a) the triadic resonant instability generating two secondary wave beams and (b) the streaming instability corresponding to the spontaneous generation of a mean flow.

The three-wave equation on the half-line

NASA Astrophysics Data System (ADS)

Xu, Jian; Fan, Engui

2014-01-01

The Fokas method is used to analyze the initial-boundary value problem for the three-wave equation p-{bi-bj}/{ai-aj}p+∑k ({bk-bj}/{ak-aj}-{bi-bk}/{ai-ak})pp=0, i,j,k=1,2,3, on the half-line. Assuming that the solution p(x,t) exists, we show that it can be recovered from its initial and boundary values via the solution of a Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ.

Resonance energy transfer: The unified theory via vector spherical harmonics

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

Grinter, Roger, E-mail: r.grinter@uea.ac.uk; Jones, Garth A., E-mail: garth.jones@uea.ac.uk

2016-08-21

In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in terms of vector spherical harmonics while Hankel functions are used to define the radial component. This approach alleviates the problem of having to select physically correct solution from non-physical solutions, which seems to be inherentmore » in plane wave derivations. The spherical coordinate system allows one to easily decompose the photon’s fields into longitudinal and transverse components and offers a natural way to analyse near-, intermediate-, and far-zone RET within the context of the relative orientation of the transition dipole moments for the two molecules.« less

Propagation of thickness-twist waves in a piezoelectric ceramic plate with unattached electrodes.

PubMed

Qian, Zheng-Hua; Kishimoto, Kikuo; Yang, Jiashi

2009-06-01

We analyze the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with air gaps between the plate surfaces and two electrodes. These waves are also called anti-plane or shear-horizontal waves with one displacement component only. An exact solution is obtained from the equations of the linear theory of piezoelectricity. Dispersion relations of the waves are obtained and plotted. Results show that the wave frequency or speed is sensitive to the air gap thickness. This effect can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.

Scattering of In-Plane Waves by Elastic Wedges

NASA Astrophysics Data System (ADS)

Mohammadi, K.; Asimaki, D.; Fradkin, L.

2014-12-01

The scattering of seismic waves by elastic wedges has been a topic of interest in seismology and geophysics for many decades. Analytical, semi-analytical, experimental and numerical studies on idealized wedges have provided insight into the seismic behavior of continental margins, mountain roots and crustal discontinuities. Published results, however, have almost exclusively focused on incident Rayleigh waves and out-of-plane body (SH) waves. Complementing the existing body of work, we here present results from our study on the res­ponse of elastic wedges to incident P or SV waves, an idealized pro­blem that can provide valuable insight to the understanding and parameterization of topographic ampli­fication of seismic ground mo­tion. We first show our earlier work on explicit finite difference simulations of SV-wave scattering by elastic wedges over a wide range of internal angles. We next present a semi-analytical solution that we developed using the approach proposed by Gautesen, to describe the scattered wavefield in the immediate vicinity of the wedge's tip (near-field). We use the semi-analytical solution to validate the numerical analyses, and improve resolution of the amplification factor at the wedge vertex that spikes when the internal wedge angle approaches the critical angle of incidence.

On increasing stability in the two dimensional inverse source scattering problem with many frequencies

NASA Astrophysics Data System (ADS)

Entekhabi, Mozhgan Nora; Isakov, Victor

2018-05-01

In this paper, we will study the increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain Ω with a sufficiently smooth boundary. Using the Fourier transform in the frequency domain, bounds for the Hankel functions and for scattering solutions in the complex plane, improving bounds for the analytic continuation, and the exact observability for the wave equation led us to our goals which are a sharp uniqueness and increasing stability estimate when the wave number interval is growing.

New conformal mapping for adaptive resolving of the complex singularities of Stokes wave

PubMed Central

Dyachenko, Sergey A.; A. Silantyev, Denis

2017-01-01

A new highly efficient method is developed for computation of travelling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularities above the free surface for the analytical continuation of the travelling wave into the complex plane. An auxiliary conformal mapping is introduced which moves singularities away from the free surface thus dramatically speeding up numerical convergence by adapting the numerical grid for resolving singularities while being consistent with the fluid dynamics. The efficiency of that conformal mapping is demonstrated for the Stokes wave approaching the limiting Stokes wave (the wave of the greatest height) which significantly expands the family of numerically accessible solutions. It allows us to provide a detailed study of the oscillatory approach of these solutions to the limiting wave. Generalizations of the conformal mapping to resolve multiple singularities are also introduced. PMID:28690418

New conformal mapping for adaptive resolving of the complex singularities of Stokes wave.

PubMed

Lushnikov, Pavel M; Dyachenko, Sergey A; A Silantyev, Denis

2017-06-01

A new highly efficient method is developed for computation of travelling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularities above the free surface for the analytical continuation of the travelling wave into the complex plane. An auxiliary conformal mapping is introduced which moves singularities away from the free surface thus dramatically speeding up numerical convergence by adapting the numerical grid for resolving singularities while being consistent with the fluid dynamics. The efficiency of that conformal mapping is demonstrated for the Stokes wave approaching the limiting Stokes wave (the wave of the greatest height) which significantly expands the family of numerically accessible solutions. It allows us to provide a detailed study of the oscillatory approach of these solutions to the limiting wave. Generalizations of the conformal mapping to resolve multiple singularities are also introduced.

2008 Program of Study: Perspectives and Challenges in GFD (Geophysical Fluid Dynamics)

DTIC Science & Technology

2009-03-01

half of the complex k- plane , and Φ− is similarly well defined in the lower half of 338 PSfrag replacements Im k Re k−i +i Figure 2: Branch cuts in...domains ⊕ and , which include, respectively, the upper and lower half k- planes . The full Fourier transform of φ (and of h, d, etc.) is then well defined in...contour at infinity in the lower half k- plane ; the solution will only contain waves arising from poles located in the

Effects of refraction by means flow velocity gradients on the standing wave pattern in three-dimensional, rectangular waveguides

NASA Technical Reports Server (NTRS)

Hersh, A. S.

1979-01-01

The influence of a mean vortical flow on the connection between the standing wave pattern in a rectangular three dimensional waveguide and the corresponding duct axial impedance was determined analytically. The solution was derived using a perturbation scheme valid for low mean flow Mach numbers and plane wave sound frequencies. The results show that deviations of the standing wave pattern due to refraction by the mean flow gradients are small.

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.

Empty substrate integrated waveguide technology for E plane high-frequency and high-performance circuits

NASA Astrophysics Data System (ADS)

Belenguer, Angel; Cano, Juan Luis; Esteban, Héctor; Artal, Eduardo; Boria, Vicente E.

2017-01-01

Substrate integrated circuits (SIC) have attracted much attention in the last years because of their great potential of low cost, easy manufacturing, integration in a circuit board, and higher-quality factor than planar circuits. A first suite of SIC where the waves propagate through dielectric have been first developed, based on the well-known substrate integrated waveguide (SIW) and related technological implementations. One step further has been made with a new suite of empty substrate integrated waveguides, where the waves propagate through air, thus reducing the associated losses. This is the case of the empty substrate integrated waveguide (ESIW) or the air-filled substrate integrated waveguide (air-filled SIW). However, all these SIC are H plane structures, so classical H plane solutions in rectangular waveguides have already been mapped to most of these new SIC. In this paper a novel E plane empty substrate integrated waveguide (ESIW-E) is presented. This structure allows to easily map classical E plane solutions in rectangular waveguide to this new substrate integrated solution. It is similar to the ESIW, although more layers are needed to build the structure. A wideband transition (covering the frequency range between 33 GHz and 50 GHz) from microstrip to ESIW-E is designed and manufactured. Measurements are successfully compared with simulation, proving the validity of this new SIC. A broadband high-frequency phase shifter (for operation from 35 GHz to 47 GHz) is successfully implemented in ESIW-E, thus proving the good performance of this new SIC in a practical application.

Phase-plane analysis to an “anisotropic” higher-order traffic flow model

NASA Astrophysics Data System (ADS)

Wu, Chun-Xiu

2018-04-01

The qualitative theory of differential equations is applied to investigate the traveling wave solution to an “anisotropic” higher-order viscous traffic flow model under the Lagrange coordinate system. The types and stabilities of the equilibrium points are discussed in the phase plane. Through the numerical simulation, the overall distribution structures of trajectories are drawn to analyze the relation between the phase diagram and the selected conservative solution variables, and the influences of the parameters on the system are studied. The limit-circle, limit circle-spiral point, saddle-spiral point and saddle-nodal point solutions are obtained. These steady-state solutions provide good explanation for the phenomena of the oscillatory and homogeneous congestions in real-world traffic.

Radiation force of an arbitrary acoustic beam on an elastic sphere in a fluid

PubMed Central

Sapozhnikov, Oleg A.; Bailey, Michael R.

2013-01-01

A theoretical approach is developed to calculate the radiation force of an arbitrary acoustic beam on an elastic sphere in a liquid or gas medium. First, the incident beam is described as a sum of plane waves by employing conventional angular spectrum decomposition. Then, the classical solution for the scattering of a plane wave from an elastic sphere is applied for each plane-wave component of the incident field. The net scattered field is expressed as a superposition of the scattered fields from all angular spectrum components of the incident beam. With this formulation, the incident and scattered waves are superposed in the far field to derive expressions for components of the radiation stress tensor. These expressions are then integrated over a spherical surface to analytically describe the radiation force on an elastic sphere. Limiting cases for particular types of incident beams are presented and are shown to agree with known results. Finally, the analytical expressions are used to calculate radiation forces associated with two specific focusing transducers. PMID:23363086

Constant-intensity waves and their modulation instability in non-Hermitian potentials

NASA Astrophysics Data System (ADS)

Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2015-07-01

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.

A wavenumber approach to analysing the active control of plane waves with arrays of secondary sources

NASA Astrophysics Data System (ADS)

Elliott, Stephen J.; Cheer, Jordan; Bhan, Lam; Shi, Chuang; Gan, Woon-Seng

2018-04-01

The active control of an incident sound field with an array of secondary sources is a fundamental problem in active control. In this paper the optimal performance of an infinite array of secondary sources in controlling a plane incident sound wave is first considered in free space. An analytic solution for normal incidence plane waves is presented, indicating a clear cut-off frequency for good performance, when the separation distance between the uniformly-spaced sources is equal to a wavelength. The extent of the near field pressure close to the source array is also quantified, since this determines the positions of the error microphones in a practical arrangement. The theory is also extended to oblique incident waves. This result is then compared with numerical simulations of controlling the sound power radiated through an open aperture in a rigid wall, subject to an incident plane wave, using an array of secondary sources in the aperture. In this case the diffraction through the aperture becomes important when its size is compatible with the acoustic wavelength, in which case only a few sources are necessary for good control. When the size of the aperture is large compared to the wavelength, and diffraction is less important but more secondary sources need to be used for good control, the results then become similar to those for the free field problem with an infinite source array.

The Dynamics and Evolution of Poles and Rogue Waves for Nonlinear Schrödinger Equations*

NASA Astrophysics Data System (ADS)

Chiu, Tin Lok; Liu, Tian Yang; Chan, Hiu Ning; Wing Chow, Kwok

2017-09-01

Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schrödinger (NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.

Rogue waves and W-shaped solitons in the multiple self-induced transparency system.

PubMed

Wang, Xin; Liu, Chong; Wang, Lei

2017-09-01

We study localized nonlinear waves on a plane wave background in the multiple self-induced transparency (SIT) system, which describes an important enhancement of the amplification and control of optical waves compared to the single SIT system. A hierarchy of exact multiparametric rational solutions in a compact determinant representation is presented. We demonstrate that this family of solutions contain known rogue wave solutions and unusual W-shaped soliton solutions. State transitions between the fundamental rogue waves and W-shaped solitons as well as higher-order nonlinear superposition modes are revealed in the zero-frequency perturbation region by the suitable choice for the background wavenumber of the electric field component. Particularly, it is found that the multiple SIT system can admit both stationary and nonstationary W-shaped solitons in contrast to the stationary results in the single SIT system. Moreover, the W-shaped soliton complex which is formed by a certain number of fundamental W-shaped solitons with zero phase parameters and its decomposition mechanism in the case of the nonzero phase parameters are shown. Meanwhile, some important characteristics of the nonlinear waves including trajectories and spectrum are discussed through the numerical and analytical methods.

Scattering of elastic waves by a spheroidal inclusion

NASA Astrophysics Data System (ADS)

Johnson, Lane R.

2018-03-01

An analytical solution is presented for scattering of elastic waves by prolate and oblate spheroidal inclusions. The problem is solved in the frequency domain where separation of variables leads to a solution involving spheroidal wave functions of the angular and radial kind. Unlike the spherical problem, the boundary equations remain coupled with respect to one of the separation indices. Expanding the angular spheroidal wave functions in terms of associated Legendre functions and using their orthogonality properties leads to a set of linear equations that can be solved to simultaneously obtain solutions for all coupled modes of both scattered and interior fields. To illustrate some of the properties of the spheroidal solution, total scattering cross-sections for P, SV and SH plane waves incident at an oblique angle on a prolate spheroid, an oblate spheroid and a sphere are compared. The waveforms of the scattered field exterior to the inclusion are calculated for these same incident waves. The waveforms scattered by a spheroid are strongly dependent upon the angle of incidence, are different for incident SV and SH waves and are asymmetrical about the centre of the spheroid with the asymmetry different for prolate and oblate spheroids.

Scattering of E Polarized Plane Wave by Rectangular Cavity With Finite Flanges

NASA Astrophysics Data System (ADS)

Vinogradova, Elena D.

2017-11-01

The rigorous Method of Regularization is implemented for accurate analysis of wave scattering by rectangular cavity with finite flanges. The solution is free from limitations on problem parameters. The calculation of the induced surface current, bistatic radar cross section (RCS) and frequency dependence of monostatic RCS are performed with controlled accuracy in a wide frequency band.

Traveling-Wave Solutions of the Kolmogorov-Petrovskii-Piskunov Equation

NASA Astrophysics Data System (ADS)

Pikulin, S. V.

2018-02-01

We consider quasi-stationary solutions of a problem without initial conditions for the Kolmogorov-Petrovskii-Piskunov (KPP) equation, which is a quasilinear parabolic one arising in the modeling of certain reaction-diffusion processes in the theory of combustion, mathematical biology, and other areas of natural sciences. A new efficiently numerically implementable analytical representation is constructed for self-similar plane traveling-wave solutions of the KPP equation with a special right-hand side. Sufficient conditions for an auxiliary function involved in this representation to be analytical for all values of its argument, including the endpoints, are obtained. Numerical results are obtained for model examples.

How hairpin vortices emerge from exact invariant solutions

NASA Astrophysics Data System (ADS)

Schneider, Tobias M.; Farano, Mirko; de Palma, Pietro; Robinet, Jean-Christoph; Cherubini, Stefania

2017-11-01

Hairpin vortices are among the most commonly observed flow structures in wall-bounded shear flows. However, within the dynamical system approach to turbulence, those structures have not yet been described. They are not captured by known exact invariant solutions of the Navier-Stokes equations nor have other state-space structures supporting hairpins been identified. We show that hairpin structures are observed along an optimally growing trajectory leaving a well known exact traveling wave solution of plane Poiseuille flow. The perturbation triggering hairpins does not correspond to an unstable mode of the exact traveling wave but lies in the stable manifold where non-normality causes strong transient amplification.

Effect of flow on the acoustic performance of extended reaction lined ducts

NASA Technical Reports Server (NTRS)

Hersh, A. S.; Walker, B.

1983-01-01

A model is developed for the effects of uniform and boundary-layer mean flow on the attenuation and propagation of harmonically excited sound waves in an extended reaction lined cylindrical duct. A duct geometry consisting of an annular outer region of bulk material surrounding an inner cylinder of air is utilized. A numerical solution is obtained for the coupled wave equations governing the motion of the sound in both the inner and annular regions. It is found that the numerically predicted attenuation and propagations constants are in excellent agreement with measured values using Kevlar as the liner material for plane-wave mode (O,O) excitation over a wide range of mean flows and sound frequency. The boundary-layer effects are determined to be unimportant, at least for plane-wave sound. In addition, numerical studies indicate small differences between the use of either the radial velocity or the radial displacement boundary conditions.

A wideband fast multipole boundary element method for half-space/plane-symmetric acoustic wave problems

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Chen, Hai-Bo; Chen, Lei-Lei

2013-04-01

This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/plane-symmetric acoustic wave problems. The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only. Moreover, a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived, and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating, translating and saving the multipole/local expansion coefficients of the image domain. The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems. As for exterior acoustic problems, the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method. Details on the implementation of the present method are described, and numerical examples are given to demonstrate its accuracy and efficiency.

Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Zhang, Guoqiang

2018-01-01

Under investigation in this paper is the Kundu equation, which may be used to describe the propagation process of ultrashort optical pulses in nonlinear optics. The modulational instability of the plane-wave for the possible reason of the formation of the rogue wave (RW) is studied for the system. Based on our proposed generalized perturbation (n,N - n)-fold Darboux transformation (DT), some new higher-order implicit RW solutions in terms of determinants are obtained by means of the generalized perturbation (1,N - 1)-fold DT, when choosing different special parameters, these results will reduce to the RW solutions of the Kaup-Newell (KN) equation, Chen-Lee-Liu (CLL) equation and Gerjikov-Ivanov (GI) equation, respectively. The relevant wave structures are shown graphically, which display abundant interesting wave structures. The dynamical behaviors and propagation stability of the first-order and second-order RW solutions are discussed by using numerical simulations, the higher-order nonlinear terms for the Kundu equation have an impact on the propagation instability of the RW. The method can also be extended to find the higher-order RW or rational solutions of other integrable nonlinear equations.

Stability of the Superconducting d-Wave Pairing Toward the Intersite Coulomb Repulsion in CuO_2 Plane

NASA Astrophysics Data System (ADS)

Val'kov, V. V.; Dzebisashvili, D. M.; Korovushkin, M. M.; Barabanov, A. F.

2018-06-01

Taking into account the real crystalline structure of the CuO_2 plane and the strong spin-fermion coupling, we study the influence of the intersite Coulomb repulsion between holes on the Cooper instability of the spin-polaron quasiparticles in cuprate superconductors. The analysis shows that only the superconducting d-wave pairing is implemented in the whole region of doping, whereas the solutions of the self-consistent equations for the s-wave pairing are absent. It is shown that intersite Coulomb interaction V_1 between the holes located at the nearest oxygen ions does not affect the d-wave pairing, because its Fourier transform V_q vanishes in the kernel of the corresponding integral equation. The intersite Coulomb interaction V_2 of quasiparticles located at the next-nearest oxygen ions does not vanish in the integral equations, however, but it is also shown that the d-wave pairing is robust toward this interaction for physically reasonable values of V_2.

Stability of the Superconducting d-Wave Pairing Toward the Intersite Coulomb Repulsion in CuO_2 Plane

NASA Astrophysics Data System (ADS)

Val'kov, V. V.; Dzebisashvili, D. M.; Korovushkin, M. M.; Barabanov, A. F.

2018-03-01

Taking into account the real crystalline structure of the CuO_2 plane and the strong spin-fermion coupling, we study the influence of the intersite Coulomb repulsion between holes on the Cooper instability of the spin-polaron quasiparticles in cuprate superconductors. The analysis shows that only the superconducting d-wave pairing is implemented in the whole region of doping, whereas the solutions of the self-consistent equations for the s-wave pairing are absent. It is shown that intersite Coulomb interaction V_1 between the holes located at the nearest oxygen ions does not affect the d-wave pairing, because its Fourier transform V_q vanishes in the kernel of the corresponding integral equation. The intersite Coulomb interaction V_2 of quasiparticles located at the next-nearest oxygen ions does not vanish in the integral equations, however, but it is also shown that the d-wave pairing is robust toward this interaction for physically reasonable values of V_2.

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

PubMed

Kourakis, I; Shukla, P K

2005-07-01

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Transmission of singularities through a shock wave and the sound generation

NASA Technical Reports Server (NTRS)

Ting, L.

1974-01-01

The interaction of a plane shock wave of finite strength with a vortex line, point vortex, doublet or quadrupole of weak strength is studied. Based upon the physical condition that a free vortex line cannot support a pressure difference, rules are established which define the change of the linear intensity of the segment of the vortex line after its passage through the shock. The rules for point vortex, doublet, and quadrupole are then established as limiting cases. These rules can be useful for the construction of the solution of the entire flow field and for its physical interpretation. However, the solution can be obtained directly by the technique developed for shock diffraction problems. Explicit solutions and the associated sound generation are obtained for the passage of a point vortex through the shock wave.

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

NASA Astrophysics Data System (ADS)

Kilcrease, D. P.; Brookes, S.

2013-12-01

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. A simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert-Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. We also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.

Dynamics of coupled mode solitons in bursting neural networks

NASA Astrophysics Data System (ADS)

Nfor, N. Oma; Ghomsi, P. Guemkam; Moukam Kakmeni, F. M.

2018-02-01

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

Dynamics of coupled mode solitons in bursting neural networks.

PubMed

Nfor, N Oma; Ghomsi, P Guemkam; Moukam Kakmeni, F M

2018-02-01

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

Bistability By Self-Reflection In A Saturable Absorber

NASA Astrophysics Data System (ADS)

Roso-Franco, Luis

1987-01-01

Propagation of laser light through a saturable absorber is theoretically studied. Computed steady state solutions of the Maxwell equations describing the unidimensional propagation of a plane monochromatic wave without introducing the slowly-varying envelope approximation are presented showing how saturation effects can influence the absorption of the field. At a certain range of refractive index and extintion coefficients, computed solutions display a very susprising behaviour, and a self-reflected wave appears inside the absorber. This can be useful for a new kind of biestable device, similar to a standard bistable cavity but with the back mirror self-induced by the light.

Source Characterization of Microseismic Events using Empirical Green's Functions at the Basel EGS Project

NASA Astrophysics Data System (ADS)

Folesky, Jonas; Kummerow, Jörn

2015-04-01

The Empirical Green's Function (EGF) method uses pairs of events of high wave form similarity and adjacent hypocenters to decompose the influences of source time function, ray path, instrument site, and instrument response. The seismogram of the smaller event is considered as the Green's function which then can be deconvolved from the other seismogram. The result provides a reconstructed relative source time function (RSTF) of the larger event of that event pair. The comparison of the RSTFs at all stations of the observation systems produces information on the rupture process of the event based on an apparent directivity effect and possible changes in the RSTFs complexities. The Basel EGS dataset of 2006-2007 consists of about 2800 localized events of magnitudes between 0.0 < ML < 3.5 with event pairs of adequate magnitude difference for EGF analysis. The data has sufficient quality to analyse events with magnitudes down to ML = 0.0 for an apparent directivity effect although the approximate rupture duration for those events is of only a few milliseconds. The dataset shows a number of multiplets where fault plane solutions are known from earlier studies. Using the EGF method we compute rupture orientations for about 190 event pairs and compare them to the fault plane solutions of the multiplets. For the majority of events we observe a good consistency between the rupture direction found there and one of the previously determined nodal planes from fault plane solutions. In combination this resolves the fault plane ambiguity. Furthermore the rupture direction fitting yields estimates for projections of the rupture velocity on the horizontal plane. They seem to vary between the multiplets in the reservoir from 0.3 to 0.7 times the S-wave velocity. To our knowledge source characterization by EGF analysis has not yet been introduced to microseismic reservoirs with the data quality found in Basel. Our results show that EGF analysis can provide valuable additional insights on the distribution of rupture properties within the reservoir.

The acoustic field of a point source in a uniform boundary layer over an impedance plane

NASA Technical Reports Server (NTRS)

Zorumski, W. E.; Willshire, W. L., Jr.

1986-01-01

The acoustic field of a point source in a boundary layer above an impedance plane is investigated anatytically using Obukhov quasi-potential functions, extending the normal-mode theory of Chunchuzov (1984) to account for the effects of finite ground-plane impedance and source height. The solution is found to be asymptotic to the surface-wave term studies by Wenzel (1974) in the limit of vanishing wind speed, suggesting that normal-mode theory can be used to model the effects of an atmospheric boundary layer on infrasonic sound radiation. Model predictions are derived for noise-generation data obtained by Willshire (1985) at the Medicine Bow wind-turbine facility. Long-range downwind propagation is found to behave as a cylindrical wave, with attention proportional to the wind speed, the boundary-layer displacement thickness, the real part of the ground admittance, and the square of the frequency.

Monochromatic plane-fronted waves in conformal gravity are pure gauge

NASA Astrophysics Data System (ADS)

Fabbri, Luca; Paranjape, M. B.

2011-05-01

We consider plane-fronted, monochromatic gravitational waves on a Minkowski background, in a conformally invariant theory of general relativity. By this we mean waves of the form: gμν=ημν+γμνF(k·x), where γμν is a constant polarization tensor, and kμ is a lightlike vector. We also assume the coordinate gauge condition |g|-1/4∂τ(|g|1/4gστ)=0 which is the conformal analog of the harmonic gauge condition gμνΓμνσ=-|g|-1/2∂τ(|g|1/2gστ)=0, where det⁡[gμν]≡g. Requiring additionally the conformal gauge condition g=-1 surprisingly implies that the waves are both transverse and traceless. Although the ansatz for the metric is eminently reasonable when considering perturbative gravitational waves, we show that the metric is reducible to the metric of Minkowski space-time via a sequence of coordinate transformations which respect the gauge conditions, without any perturbative approximation that γμν be small. This implies that we have, in fact, exact plane-wave solutions; however, they are simply coordinate/conformal artifacts. As a consequence, they carry no energy. Our result does not imply that conformal gravity does not have gravitational wave phenomena. A different, more generalized ansatz for the deviation, taking into account the fourth-order nature of the field equation, which has the form gμν=ημν+Bμν(n·x)G(k·x), indeed yields waves which carry energy and momentum [P. D. Mannheim, Gen. Relativ. Gravit.GRGVA80001-7701 43, 703 (2010)10.1007/s10714-010-1088-z]. It is just surprising that transverse, traceless, plane-fronted gravitational waves, those that would be used in any standard, perturbative, quantum analysis of the theory, simply do not exist.

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.

Two-dimensional modulated ion-acoustic excitations in electronegative plasmas

NASA Astrophysics Data System (ADS)

Panguetna, Chérif S.; Tabi, Conrad B.; Kofané, Timoléon C.

2017-09-01

Two-dimensional modulated ion-acoustic waves are investigated in an electronegative plasma. Through the reductive perturbation expansion, the governing hydrodynamic equations are reduced to a Davey-Stewartson system with two-space variables. The latter is used to study the modulational instability of ion-acoustic waves along with the effect of plasma parameters, namely, the negative ion concentration ratio (α) and the electron-to-negative ion temperature ratio (σn). A parametric analysis of modulational instability is carried out, where regions of plasma parameters responsible for the emergence of modulated ion-acoustic waves are discussed, with emphasis on the behavior of the instability growth rate. Numerically, using perturbed plane waves as initial conditions, parameters from the instability regions give rise to series of dromion solitons under the activation of modulational instability. The sensitivity of the numerical solutions to plasma parameters is discussed. Some exact solutions in the form one- and two-dromion solutions are derived and their response to the effect of varying α and σn is discussed as well.

Radiation from a current filament driven by a traveling wave

NASA Technical Reports Server (NTRS)

Levine, D. M.; Meneghini, R.

1976-01-01

Solutions are presented for the electromagnetic fields radiated by an arbitrarily oriented current filament located above a perfectly conducting ground plane and excited by a traveling current wave. Both an approximate solution, valid in the fraunhofer region of the filament and predicting the radiation terms in the fields, and an exact solution, which predicts both near and far field components of the electromagnetic fields, are presented. Both solutions apply to current waveforms which propagate along the channel but are valid regardless of the actual waveshape. The exact solution is valid only for waves which propagate at the speed of light, and the approximate solution is formulated for arbitrary velocity of propagation. The spectrum-magnitude of the fourier transform-of the radiated fields is computed by assuming a compound exponential model for the current waveform. The effects of channel orientation and length, as well as velocity of propagation of the current waveform and location of the observer, are discussed. It is shown that both velocity of propagation and an effective channel length are important in determining the shape of the spectrum.

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-03-01

An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads

Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography.

PubMed

Johnson, R S

2018-01-28

This review makes a case for describing many of the flows observed in our oceans, simply based on the Euler equation, with (piecewise) constant density and with suitable boundary conditions. The analyses start from the Euler and mass conservation equations, expressed in a rotating, spherical coordinate system (but the f -plane and β -plane approximations are also mentioned); five examples are discussed. For three of them, a suitable non-dimensionalization is introduced, and a single small parameter is identified in each case. These three examples lead straightforwardly and directly to new results for: waves on the Pacific Equatorial Undercurrent (EUC) with a thermocline (in the f -plane); a nonlinear, three-dimensional model for EUC-type flows (in the β -plane); and a detailed model for large gyres. The other two examples are exact solutions of the complete system: a flow which corresponds to the underlying structure of the Pacific EUC; and a flow based on the necessary requirement to use a non-conservative body force, which produces the type of flow observed in the Antarctic Circumpolar Current. (All these examples have been discussed in detail in the references cited.) This review concludes with a few comments on how these solutions can be extended and expanded.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

Wavespace-Based Coherent Deconvolution

NASA Technical Reports Server (NTRS)

Bahr, Christopher J.; Cattafesta, Louis N., III

2012-01-01

Array deconvolution is commonly used in aeroacoustic analysis to remove the influence of a microphone array's point spread function from a conventional beamforming map. Unfortunately, the majority of deconvolution algorithms assume that the acoustic sources in a measurement are incoherent, which can be problematic for some aeroacoustic phenomena with coherent, spatially-distributed characteristics. While several algorithms have been proposed to handle coherent sources, some are computationally intractable for many problems while others require restrictive assumptions about the source field. Newer generalized inverse techniques hold promise, but are still under investigation for general use. An alternate coherent deconvolution method is proposed based on a wavespace transformation of the array data. Wavespace analysis offers advantages over curved-wave array processing, such as providing an explicit shift-invariance in the convolution of the array sampling function with the acoustic wave field. However, usage of the wavespace transformation assumes the acoustic wave field is accurately approximated as a superposition of plane wave fields, regardless of true wavefront curvature. The wavespace technique leverages Fourier transforms to quickly evaluate a shift-invariant convolution. The method is derived for and applied to ideal incoherent and coherent plane wave fields to demonstrate its ability to determine magnitude and relative phase of multiple coherent sources. Multi-scale processing is explored as a means of accelerating solution convergence. A case with a spherical wave front is evaluated. Finally, a trailing edge noise experiment case is considered. Results show the method successfully deconvolves incoherent, partially-coherent, and coherent plane wave fields to a degree necessary for quantitative evaluation. Curved wave front cases warrant further investigation. A potential extension to nearfield beamforming is proposed.

Ultrasonic waves in classical gases

NASA Astrophysics Data System (ADS)

Magner, A. G.; Gorenstein, M. I.; Grygoriev, U. V.

2017-12-01

The velocity and absorption coefficient for the plane sound waves in a classical gas are obtained by solving the Boltzmann kinetic equation, which describes the reaction of the single-particle distribution function to a periodic external field. Within the linear response theory, the nonperturbative dispersion equation valid for all sound frequencies is derived and solved numerically. The results are in agreement with the approximate analytical solutions found for both the frequent- and rare-collision regimes. These results are also in qualitative agreement with the experimental data for ultrasonic waves in dilute gases.

Basis for paraxial surface-plasmon-polariton packets

NASA Astrophysics Data System (ADS)

Martinez-Herrero, Rosario; Manjavacas, Alejandro

2016-12-01

We present a theoretical framework for the study of surface-plasmon polariton (SPP) packets propagating along a lossy metal-dielectric interface within the paraxial approximation. Using a rigorous formulation based on the plane-wave spectrum formalism, we introduce a set of modes that constitute a complete basis set for the solutions of Maxwell's equations for a metal-dielectric interface in the paraxial approximation. The use of this set of modes allows us to fully analyze the evolution of the transversal structure of SPP packets beyond the single plane-wave approximation. As a paradigmatic example, we analyze the case of a Gaussian SPP mode, for which, exploiting the analogy with paraxial optical beams, we introduce a set of parameters that characterize its propagation.

Spatial-heterodyne sampling requirements in the off-axis pupil plane recording geometry for deep-turbulence wavefront sensing

NASA Astrophysics Data System (ADS)

Banet, Matthias T.; Spencer, Mark F.

2017-09-01

Spatial-heterodyne interferometry is a robust solution for deep-turbulence wavefront sensing. With that said, this paper analyzes the focal-plane array sampling requirements for spatial-heterodyne systems operating in the off-axis pupil plane recording geometry. To assess spatial-heterodyne performance, we use a metric referred to as the field-estimated Strehl ratio. We first develop an analytical description of performance with respect to the number of focal-plane array pixels across the Fried coherence diameter and then verify our results with wave-optics simulations. The analysis indicates that at approximately 5 focal-plane array pixels across the Fried coherence diameter, the field-estimated Strehl ratios begin to exceed 0:9 which is indicative of largely diffraction-limited results.

Calculation of periodic flows in a continuously stratified fluid

NASA Astrophysics Data System (ADS)

Vasiliev, A.

2012-04-01

Analytic theory of disturbances generated by an oscillating compact source in a viscous continuously stratified fluid was constructed. Exact solution of the internal waves generation problem was constructed taking into account diffusivity effects. This analysis is based on set of fundamental equations of incompressible flows. The linearized problem of periodic flows in a continuously stratified fluid, generated by an oscillating part of the inclined plane was solved by methods of singular perturbation theory. A rectangular or disc placed on a sloping plane and oscillating linearly in an arbitrary direction was selected as a source of disturbances. The solutions include regularly perturbed on dissipative component functions describing internal waves and a family of singularly perturbed functions. One of the functions from the singular components family has an analogue in a homogeneous fluid that is a periodic or Stokes' flow. Its thickness is defined by a universal micro scale depending on kinematics viscosity coefficient and a buoyancy frequency with a factor depending on the wave slope. Other singular perturbed functions are specific for stratified flows. Their thickness are defined the diffusion coefficient, kinematic viscosity and additional factor depending on geometry of the problem. Fields of fluid density, velocity, vorticity, pressure, energy density and flux as well as forces acting on the source are calculated for different types of the sources. It is shown that most effective source of waves is the bi-piston. Complete 3D problem is transformed in various limiting cases that are into 2D problem for source in stratified or homogeneous fluid and the Stokes problem for an oscillating infinite plane. The case of the "critical" angle that is equality of the emitting surface and the wave cone slope angles needs in separate investigations. In this case, the number of singular component is saved. Patterns of velocity and density fields were constructed and analyzed by methods of computational mathematics. Singular components of the solution affect the flow pattern of the inhomogeneous stratified fluid, not only near the source of the waves, but at a large distance. Analytical calculations of the structure of wave beams are matched with laboratory experiments. Some deviations at large distances from the source are formed due to the contribution of background wave field associated with seiches in the laboratory tank. In number of the experiments vortices with closed contours were observed on some distances from the disk. The work was supported by Ministry of Education and Science RF (Goscontract No. 16.518.11.7059), experiments were performed on set up USU "HPC IPMec RAS".

New exact solutions of the Dirac and Klein-Gordon equations of a charged particle propagating in a strong laser field in an underdense plasma

NASA Astrophysics Data System (ADS)

Varró, Sándor

2014-03-01

Exact solutions are presented of the Dirac and Klein-Gordon equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave in a medium of index of refraction nm<1. In the Dirac case the solutions are expressed in terms of new complex polynomials, and in the Klein-Gordon case the found solutions are expressed in terms of Ince polynomials. In each case they form a doubly infinite set, labeled by two integer quantum numbers. These integer numbers represent quantized momentum components of the charged particle along the polarization vector and along the propagation direction of the electromagnetic radiation. Since this radiation may represent a plasmon wave of arbitrary high amplitude, propagating in an underdense plasma, the solutions obtained may have relevance in describing possible quantum features of novel acceleration mechanisms.

Ultrasonic standing wave preparation of a liquid cell for glucose measurements in urine by midinfrared spectroscopy and potential application to smart toilets.

PubMed

Yamamoto, Naoyuki; Kawashima, Natsumi; Kitazaki, Tomoya; Mori, Keita; Kang, Hanyue; Nishiyama, Akira; Wada, Kenji; Ishimaru, Ichiro

2018-05-01

Smart toilets could be used to monitor different components of urine in daily life for early detection of lifestyle-related diseases and prompt provision of treatment. For analysis of biological samples such as urine by midinfrared spectroscopy, thin-film samples like liquid cells are needed because of the strong absorption of midinfrared light by water. Conventional liquid cells or fixed cells are prepared based on the liquid membrane method and solution technique, but these are not quantitative and are difficult to set up and clean. We generated an ultrasonic standing wave reflection plane in a sample and produced an ultrasonic liquid cell. In this cell, the thickness of the optical path length was adjustable, as in the conventional method. The reflection plane could be generated at an arbitrary depth and internal reflected light could be detected by changing the frequency of the ultrasonic wave. We could generate refractive index boundaries using the density difference created by the ultrasonic standing wave. Creation of the reflection plane in the sample was confirmed by optical coherence tomography. Using the proposed method and midinfrared spectroscopy, we discriminated between normal urine samples spiked with glucose at different concentrations and obtained a high correlation coefficient. (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

DOE PAGES

Kilcrease, D. P.; Brookes, S.

2013-08-19

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. Additionally, a simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure formore » the Born cross-sections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. Furthermore, we also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.« less

Generalized self-similar unsteady gas flows behind the strong shock wave front

NASA Astrophysics Data System (ADS)

Bogatko, V. I.; Potekhina, E. A.

2018-05-01

Two-dimensional (plane and axially symmetric) nonstationary gas flows behind the front of a strong shock wave are considered. All the gas parameters are functions of the ratio of Cartesian coordinates to some degree of time tn, where n is a self-similarity index. The problem is solved in Lagrangian variables. It is shown that the resulting system of partial differential equations is suitable for constructing an iterative process. ¢he "thin shock layer" method is used to construct an approximate analytical solution of the problem. The limit solution of the problem is constructed. A formula for determining the path traversed by a gas particle in the shock layer along the front of a shock wave is obtained. A system of equations for determining the first approximation corrections is constructed.

Numerical modeling of the interaction of liquid drops and jets with shock waves and gas jets

NASA Astrophysics Data System (ADS)

Surov, V. S.

1993-02-01

The motion of a liquid drop (jet) and of the ambient gas is described, in the general case, by Navier-Stokes equations. An approximate solution to the interaction of a plane shock wave with a single liquid drop is presented. Based on the analysis, the general system of Navier-Stokes equations is reduced to two groups of equations, Euler equations for gas and Navier-Stokes equations for liquid; solutions to these equations are presented. The discussion also covers the modeling of the interaction of a shock wave with a drop screen, interaction of a liquid jet with a counterpropagating supersonic gas flow, and modeling of processes in a shock layer during the impact of a drop against an obstacle in gas flow.

In-plane dynamic Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

NASA Astrophysics Data System (ADS)

Ba, Zhenning; Kang, Zeqing; Liang, Jianwen

2018-04-01

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic (TI) half-space. The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces, which are then applied to the total system with the opposite sign. By adding solutions restricted in the loaded layer to solutions from the reaction forces, the global solutions in the wavenumber domain are obtained, and the dynamic Green's functions in the space domain are recovered by the inverse Fourier transform. The presented formulations can be reduced to the isotropic case developed by Wolf (1985), and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI half-space subjected to horizontally distributed loads which are special cases of the more general problem addressed. The deduced Green's functions, in conjunction with boundary element methods, will lead to significant advances in the investigation of a variety of wave scattering, wave radiation and soil-structure interaction problems in a layered TI site. Selected numerical results are given to investigate the influence of material anisotropy, frequency of excitation, inclination angle and layered on the responses of displacement and stress, and some conclusions are drawn.

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.

The scattering of electromagnetic pulses by a slit in a conducting screen

NASA Technical Reports Server (NTRS)

Ackerknecht, W. E., III; Chen, C.-L.

1975-01-01

A direct method for calculating the impulse response of a slit in a conducting screen is presented which is derived specifically for the analysis of transient scattering by two-dimensional objects illuminated by a plane incident wave. The impulse response is obtained by assuming that the total response is composed of two sequences of diffracted waves. The solution is determined for the first two waves in one sequence by using Green's functions and the equivalence principle, for additional waves in the sequence by iteration, and for the other sequence by a transformation of coordinates. The cases of E-polarization and H-polarization are considered.

Wave multiple scattering by a finite number of unclosed circular cylinders

NASA Technical Reports Server (NTRS)

Veliyev, E. I.; Veremey, V. V.

1984-01-01

The boundary value problem of plane H-polarized electromagnetic wave multiple scattering by a finite number of unclosed circular cylinders is solved. The solution is obtained by two different methods: the method of successive scattering and the method of partial matrix inversion for simultaneous dual equations. The advantages of the successive scattering method are shown. Computer calculations of the suface currents and the total cross section are presented for the structure of two screens.

Correspondence between discrete and continuous models of excitable media: trigger waves

NASA Technical Reports Server (NTRS)

Chernyak, Y. B.; Feldman, A. B.; Cohen, R. J.

1997-01-01

We present a theoretical framework for relating continuous partial differential equation (PDE) models of excitable media to discrete cellular automata (CA) models on a randomized lattice. These relations establish a quantitative link between the CA model and the specific physical system under study. We derive expressions for the CA model's plane wave speed, critical curvature, and effective diffusion constant in terms of the model's internal parameters (the interaction radius, excitation threshold, and time step). We then equate these expressions to the corresponding quantities obtained from solution of the PDEs (for a fixed excitability). This yields a set of coupled equations with a unique solution for the required CA parameter values. Here we restrict our analysis to "trigger" wave solutions obtained in the limiting case of a two-dimensional excitable medium with no recovery processes. We tested the correspondence between our CA model and two PDE models (the FitzHugh-Nagumo medium and a medium with a "sawtooth" nonlinear reaction source) and found good agreement with the numerical solutions of the PDEs. Our results suggest that the behavior of trigger waves is actually controlled by a small number of parameters.

Comparison of two leading uniform theories of edge diffraction with the exact uniform asymptotic solution

NASA Technical Reports Server (NTRS)

Boersma, J.; Rahmat-Samii, Y.

1980-01-01

The diffraction of an arbitrary cylindrical wave by a half-plane has been treated by Rahmat-Samii and Mittra who used a spectral domain approach. In this paper, their exact solution for the total field is expressed in terms of a new integral representation. For large wave number k, two rigorous procedures are described for the exact uniform asymptotic expansion of the total field solution. The uniform expansions obtained are valid in the entire space, including transition regions around the shadow boundaries. The final results are compared with the formulations of two leading uniform theories of edge diffraction, namely, the uniform asymptotic theory and the uniform theory of diffraction. Some unique observations and conclusions are made in relating the two theories.

Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

NASA Technical Reports Server (NTRS)

Baumeiste, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Receptivity of Supersonic Boundary Layers Due To Acoustic Disturbances Over Blunt Cones

NASA Technical Reports Server (NTRS)

Balakumar, P.

2007-01-01

Receptivity and stability of supersonic boundary layers over a 5-degree straight cone with a blunt tip are numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 106/inch. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The linear stability results showed that bluntness has less stabilizing effects on the stability of boundary layers over cones than on flat plates and wedges. The unsteady simulations of the interaction of plane threedimensional acoustic waves with the cone showed that the modulation of wavelength and the generation of instability waves first occurred near the leading edge in the plane where the constant acoustic phase lines are perpendicular to the cone axis. Further downstream, this instability region spreads in the azimuthal direction from this plane.

A method for distinguishing between propagons, diffusions, and locons

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

Seyf, Hamid Reza; Henry, Asegun; School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

2016-07-14

The majority of intuition on phonon transport has been derived from studies of homogenous crystalline solids, where the atomic composition and structure are periodic. For this specific class of materials, the solutions to the equations of motions for the atoms (in the harmonic limit) result in plane wave modulated velocity fields for the normal modes of vibration. However, it has been known for several decades that whenever a system lacks periodicity, either compositional or structural, the normal modes of vibration can still be determined (in the harmonic limit), but the solutions take on different characteristics and many modes may notmore » be plane wave modulated. Previous work has classified the types of vibrations into three primary categories, namely, propagons, diffusions, and locons. One can use the participation ratio to distinguish locons, from propagons and diffusons, which measures the extent to which a mode is localized. However, distinguishing between propagons and diffusons has remained a challenge, since both are spatially delocalized. Here, we present a new method that quantifies the extent to which a mode's character corresponds to a propagating mode, e.g., exhibits plane wave modulation. This then allows for clear and quantitative distinctions between propagons and diffusons. By resolving this issue quantitatively, one can now automate the classification of modes for any arbitrary material or structure, subject to a single constraint that the atoms must vibrate stably around their respective equilibrium sites. Several example test cases are studied including crystalline silicon and germanium, crystalline silicon with different defect concentrations, as well as amorphous silicon, germanium, and silica.« less

Plane Evanescent Waves and Interface Waves

NASA Astrophysics Data System (ADS)

Luppé, F.; Conoir, J. M.; El Kettani, M. Ech-Cherif; Lenoir, O.; Izbicki, J. L.; Duclos, J.; Poirée, B.

The evanescent plane wave formalism is used to obtain the characteristic equation of the normal vibration modes of a plane elastic solid embedded in a perfect fluid. Simple drawings of the real and imaginary parts of complex wave vectors make quite clear the choice of the Riemann sheets on which the roots of the characteristic equation are to be looked for. The generalized Rayleigh wave and the Scholte - Stoneley wave are then described. The same formalism is used to describe Lamb waves on an elastic plane plate immersed in water. The damping, due to energy leaking in the fluid, is shown to be directly given by the projection of evanescence vectors on the interface. Measured values of the damping coefficient are in good agreement with those derived from calculations. The width of the angular resonances associated to Lamb waves or Rayleigh waves is also directly related to this same evanescence vectors projection, as well as the excitation coefficient of a given Lamb wave excited by a plane incident wave. This study shows clearly the strong correlation between the resonance point of view and the wave one in plane interface problems.

Rational solutions to the KPI equation and multi rogue waves

NASA Astrophysics Data System (ADS)

Gaillard, Pierre

2016-04-01

We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in x, y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2 N(N + 1) in x, y and t depending on 2 N - 2 real parameters for each positive integer N. We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x , y) plane for different values of time t and parameters.

Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Ivanov, S. K.; Kamchatnov, A. M.; Congy, T.; Pavloff, N.

2017-12-01

We provide a classification of the possible flows of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as "magnetic excitation") obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferromagnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as the appearance of interesting elements—contact dispersive shock waves—that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations.

Harbingers and latecomers - the order of appearance of exact coherent structures in plane Poiseuille flow

NASA Astrophysics Data System (ADS)

Zammert, Stefan; Eckhardt, Bruno

2017-02-01

The transition to turbulence in plane Poiseuille flow (PPF) is connected with the presence of exact coherent structures. We here discuss a variety of different structures that are relevant for the transition, compare the critical Reynolds numbers and optimal wavelengths for their appearance, and explore the differences between flows operating at constant mass flux or at constant pressure drop. The Reynolds numbers quoted here are based on the mean flow velocity and refer to constant mass flux. Reynolds numbers based on constant pressure drop are always higher. The Tollmien-Schlichting (TS) waves bifurcate subcritically from the laminar profile at Re = 5772 at wavelength 6.16 and reach down to Re = 2610 at a different optimal wave length of 4.65. Their streamwise localised counter part bifurcates at the even lower value Re = 2334. Three-dimensional exact solutions appear at much lower Reynolds numbers. We describe one exact solutions that has a critical Reynolds number of 316. Streamwise localised versions of this state require higher Reynolds numbers, with the lowest bifurcation occurring near Re = 1018. The analysis shows that the various branches of TS-waves cannot be connected with transition observed near Re ≈ 1000 and that the exact coherent structures related to downstream vortices come in at lower Reynolds numbers and prepare for the transition.

Transversally periodic solitary gravity–capillary waves

PubMed Central

Milewski, Paul A.; Wang, Zhan

2014-01-01

When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity–capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity–capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles. PMID:24399922

Full-Wave Based Validation of Stripline Field Applicator For Low Frequency Material Measurements

DTIC Science & Technology

2009-03-01

16 3.3.1 Principal Solution. . . . . . . . . . . . . . . . . 17 3.3.2 Reflected Solution. . . . . . . . . . . . . . . . . 22 3.4 Applying...potential) [ 17 ]. The vector potential BCs are found to be Ax(x, y = ±h, z) = 0 ∀ x, z (3.2) ∂Ay(x, y = ±h, z) ∂y = 0 ∀ x, z (3.3) Az(x, y = ±h, z...solution at y = ±h, an inverse Fourier transform must be performed on the principal contribution 17 ηre ηim x x η-plane −jp jp Figure 3.2

Peakompactons: Peaked compact nonlinear waves

DOE PAGES

Christov, Ivan C.; Kress, Tyler; Saxena, Avadh

2017-04-20

This paper is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of nonstandard solitary waves termed peakompactons. We present that these peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg–de Vries-type models. Peakompactons, like the now-well-known compactons and unlike the soliton solutions of the Korteweg–de Vries equation, have finite support, i.e., they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, i.e., a higher spatial derivative suffers a jump discontinuity at the wave’s crest. Here, we construct such solutions exactly bymore » reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phase-plane analysis. Lastly, a simple, but reliable, finite-difference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solutions, the general physical features of the so-called K #(n,m) hierarchy of nonlinearly dispersive Korteweg–de Vries-type models are discussed as well.« less

Emergent rogue wave structures and statistics in spontaneous modulation instability.

PubMed

Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M

2015-05-20

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude "rogue waves" emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised "breather" or "soliton on finite background (SFB)" structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions.

Multidomain spectral solution of shock-turbulence interactions

NASA Technical Reports Server (NTRS)

Kopriva, David A.; Hussaini, M. Yousuff

1989-01-01

The use of a fitted-shock multidomain spectral method for solving the time-dependent Euler equations of gasdynamics is described. The multidomain method allows short spatial scale features near the shock to be resolved throughout the calculation. Examples presented are of a shock-plane wave, shock-hot spot and shock-vortex street interaction.

Classification of the line-soliton solutions of KPII

NASA Astrophysics Data System (ADS)

Chakravarty, Sarbarish; Kodama, Yuji

2008-07-01

In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169-90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation was found. The line-soliton solutions are solitary waves which decay exponentially in the (x, y)-plane except along certain rays. In this paper, it is shown that those solutions are classified by asymptotic information of the solution as |y| → ∞. The present work then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

PubMed

Tsitoura, F; Gietz, U; Chabchoub, A; Hoffmann, N

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

Tsitoura, F.; Gietz, U.; Chabchoub, A.; Hoffmann, N.

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Prediction of drag at subsonic and transonic speeds using Euler methods

NASA Technical Reports Server (NTRS)

Nikfetrat, K.; Van Dam, C. P.; Vijgen, P. M. H. W.; Chang, I. C.

1992-01-01

A technique for the evaluation of aerodynamic drag from flowfield solutions based on the Euler equations is discussed. The technique is limited to steady attached flows around three-dimensional configurations in the absence of active systems such as surface blowing/suction and propulsion. It allows the decomposition of the total drag into induced drag and wave drag and, consequently, it provides more information on the drag sources than the conventional surface-pressure integration technique. The induced drag is obtained from the integration of the kinetic energy (per unit distance) of the trailing vortex system on a wake plane and the wave drag is obtained from the integration of the entropy production on a plane just downstream of the shocks. The drag-evaluation technique is applied to three-dimensional flowfield solutions for the ONERA M6 wing as well as an aspect-ratio-7 wing with an elliptic spanwise chord distribution and an NACA-0012 section shape. Comparisons between the drag obtained with the present technique and the drag based on the integration of surface pressures are presented for two Euler codes.

Measurement of in-plane thermal conductivity in polymer films

NASA Astrophysics Data System (ADS)

Wei, Qingshuo; Uehara, Chinatsu; Mukaida, Masakazu; Kirihara, Kazuhiro; Ishida, Takao

2016-04-01

Measuring the in-plane thermal conductivity of organic thermoelectric materials is challenging but is critically important. Here, a method to study the in-plane thermal conductivity of free-standing films (via the use of commercial equipment) based on temperature wave analysis is explored in depth. This subject method required a free-standing thin film with a thickness larger than 10 μm and an area larger than 1 cm2, which are not difficult to obtain for most solution-processable organic thermoelectric materials. We evaluated thermal conductivities and anisotropic ratios for various types of samples including insulating polymers, undoped semiconducting polymers, doped conducting polymers, and one-dimensional carbon fiber bulky papers. This approach facilitated a rapid screening of in-plane thermal conductivities for various organic thermoelectric materials.

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.

Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods

NASA Astrophysics Data System (ADS)

Boronin, Ivan; Shevlyakov, Andrey

2018-03-01

Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.

Kinematics and dynamics of green water on a fixed platform in a large wave basin in focusing wave and random wave conditions

NASA Astrophysics Data System (ADS)

Chuang, Wei-Liang; Chang, Kuang-An; Mercier, Richard

2018-06-01

Green water kinematics and dynamics due to wave impingements on a simplified geometry, fixed platform were experimentally investigated in a large, deep-water wave basin. Both plane focusing waves and random waves were employed in the generation of green water. The focusing wave condition was designed to create two consecutive plunging breaking waves with one impinging on the frontal vertical wall of the fixed platform, referred as wall impingement, and the other directly impinging on the deck surface, referred as deck impingement. The random wave condition was generated using the JONSWAP spectrum with a significant wave height approximately equal to the freeboard. A total of 179 green water events were collected in the random wave condition. By examining the green water events in random waves, three different flow types are categorized: collapse of overtopping wave, fall of bulk water, and breaking wave crest. The aerated flow velocity was measured using bubble image velocimetry, while the void fraction was measured using fiber optic reflectometry. For the plane focusing wave condition, measurements of impact pressure were synchronized with the flow velocity and void fraction measurements. The relationship between the peak pressures and the pressure rise times is examined. For the high-intensity impact in the deck impingement events, the peak pressures are observed to be proportional to the aeration levels. The maximum horizontal velocities in the green water events in random waves are well represented by the lognormal distribution. Ritter's solution is shown to quantitatively describe the green water velocity distributions under both the focusing wave condition and the random wave condition. A prediction equation for green water velocity distribution under random waves is proposed.

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes

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

Konor, Celal S.; Randall, David A.

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia–gravity modes on a midlatitude f plane.The results of our normal-modemore » analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.« less

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes

DOE PAGES

Konor, Celal S.; Randall, David A.

2018-05-08

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia–gravity modes on a midlatitude f plane.The results of our normal-modemore » analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.« less

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations - Part 2: Quasi-geostrophic Rossby modes

NASA Astrophysics Data System (ADS)

Konor, Celal S.; Randall, David A.

2018-05-01

We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia-gravity modes on a midlatitude f plane.The results of our normal-mode analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.

An IBEM solution to the scattering of plane SH-waves by a lined tunnel in elastic wedge space

NASA Astrophysics Data System (ADS)

Liu, Zhongxian; Liu, Lei

2015-02-01

The indirect boundary element method (IBEM) is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave field can be constructed by applying virtual uniform loads on the surface of lined tunnel and the nearby wedge surface. The densities of virtual loads can be solved by establishing equations through the continuity conditions on the interface and zero-traction conditions on free surfaces. The total wave field is obtained by the superposition of free field and scattered-wave field in elastic wedge space. Numerical results indicate that the IBEM can solve the diffraction of elastic wave in elastic wedge space accurately and efficiently. The wave motion feature strongly depends on the wedge angle, the angle of incidence, incident frequency, the location of lined tunnel, and material parameters. The waves interference and amplification effect around the tunnel in wedge space is more significant, causing the dynamic stress concentration factor on rigid tunnel and the displacement amplitude of flexible tunnel up to 50.0 and 17.0, respectively, more than double that of the case of half-space. Hence, considerable attention should be paid to seismic resistant or anti-explosion design of the tunnel built on a slope or hillside.

Subharmonic edge waves on a large, shallow island

NASA Astrophysics Data System (ADS)

Foda, Mostafa A.

1988-08-01

Subharmonic resonance of edge waves by incident and reflected waves has been studied thus far for the case of a plane infinite beach. The analysis will be extended here to the case of a curved coastline, with a large radius of curvature and slowly varying beach slope in the longshore direction. It will be shown that the effects of such slow beach slope changes on a propagating edge wave are similar to the familiar shoaling effects on incident waves. The case of subharmonic edge wave generation on large shallow islands will be discussed in detail. The nonlinear analysis will show that within a certain range of island sizes, the generation mechanism can produce a stable standing edge wave around the island. For larger islands the solution disintegrates into two out-of-phase envelopes of opposite-going edge waves. For still larger islands, the generated progressive edge waves become unstable to sideband modulations.

Resonant triad in boundary-layer stability. Part 1: Fully nonlinear interaction

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

A first principles theory is developed to study the nonlinear spatial evolution of a near-resonance triad of instability waves in boundary layer transition. This triad consists of a plane wave at fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low frequency, high Reynolds number asymptotic scaling leads to a distinct critical layer where nonlinearity first becomes important; the development of the triad's waves is determined by the critical layer's nonlinear, viscous dynamics. The resulting theory is fully nonlinear in that all nonlinearly generated oscillatory and nonoscillatory components are accounted for. The presence of the plane wave initially causes exponential of exponential growth of the oblique waves. However, the plane wave continues to follow the linear theory, even when the oblique waves' amplitude attains the same order of magnitude as that of the plane wave. A fully interactive stage then comes into effect when the oblique waves exceed a certain level compared to that of the plane wave. The oblique waves react back on the fundamental, slowing its growth rate. The oblique waves' saturation results from their self-interaction - a mechanism that does not require the presence of the plane wave. The oblique waves' saturation level is independent of their initial level, but decreases as the obliqueness angle increases.

Acoustic backscattering and radiation force on a rigid elliptical cylinder in plane progressive waves.

PubMed

Mitri, F G

2016-03-01

This work proposes a formal analytical theory using the partial-wave series expansion (PWSE) method in cylindrical coordinates, to calculate the acoustic backscattering form function as well as the radiation force-per-length on an infinitely long elliptical (non-circular) cylinder in plane progressive waves. The major (or minor) semi-axis of the ellipse coincides with the direction of the incident waves. The scattering coefficients for the rigid elliptical cylinder are determined by imposing the Neumann boundary condition for an immovable surface and solving a resulting system of linear equations by matrix inversion. The present method, which utilizes standard cylindrical (Bessel and Hankel) wave functions, presents an advantage over the solution for the scattering that is ordinarily expressed in a basis of elliptical Mathieu functions (which are generally non-orthogonal). Furthermore, an integral equation showing the direct connection of the radiation force function with the square of the scattering form function in the far-field from the scatterer (applicable for plane waves only), is noted and discussed. An important application of this integral equation is the adequate evaluation of the radiation force function from a bistatic measurement (i.e., in the polar plane) of the far-field scattering from any 2D object of arbitrary shape. Numerical predictions are evaluated for the acoustic backscattering form function and the radiation force function, which is the radiation force per unit length, per characteristic energy density, and per unit cross-sectional surface of the ellipse, with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes, as well as the dimensionless size parameter kb, without the restriction to a particular range of frequencies. The results are particularly relevant in acoustic levitation, acousto-fluidics and particle dynamics applications. Copyright © 2015 Elsevier B.V. All rights reserved.

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

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

Ambrose, David M.; Wilkening, Jon

2008-12-11

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

Goedel, Penrose, anti-Mach: Extra supersymmetries of time-dependent plane waves

NASA Astrophysics Data System (ADS)

Blau, Matthias; Meessen, Patrick; O'Loughlin, Martin

2003-09-01

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Gödel-like metrics, show that the Penrose limit of the M-theory Gödel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves.

Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder

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

Mitri, F. G., E-mail: F.G.Mitri@ieee.org

2015-11-14

Using the partial-wave series expansion method in cylindrical coordinates, a formal analytical solution for the acoustical scattering of a 2D cylindrical quasi-Gaussian beam with an arbitrary angle of incidence θ{sub i}, focused on a rigid elliptical cylinder in a non-viscous fluid, is developed. The cylindrical focused beam expression is an exact solution of the Helmholtz equation. The scattering coefficients for the elliptical cylinder are determined by forcing the expression of the total (incident + scattered) field to satisfy the Neumann boundary condition for a rigid immovable surface, and performing the product of matrices involving an inversion procedure. Computations for the matrices elementsmore » require a single numerical integration procedure for each partial-wave mode. Numerical results are performed with particular emphasis on the focusing properties of the incident beam and its angle of incidence with respect to the major axis a of the ellipse as well as the aspect ratio a/b where b is the minor axis (assuming a > b). The method is validated and verified against previous results obtained via the T-matrix for plane waves. The present analysis is the first to consider an acoustical beam on an elliptic cylinder of variable cross-section as opposed to plane waves of infinite extent. Other 2D non-spherical and Chebyshev surfaces are mentioned that may be examined throughout this analytical formalism assuming a small deformation parameter ε.« less

An analytical model of a curved beam with a T shaped cross section

NASA Astrophysics Data System (ADS)

Hull, Andrew J.; Perez, Daniel; Cox, Donald L.

2018-03-01

This paper derives a comprehensive analytical dynamic model of a closed circular beam that has a T shaped cross section. The new model includes in-plane and out-of-plane vibrations derived using continuous media expressions which produces results that have a valid frequency range above those available from traditional lumped parameter models. The web is modeled using two-dimensional elasticity equations for in-plane motion and the classical flexural plate equation for out-of-plane motion. The flange is modeled using two sets of Donnell shell equations: one for the left side of the flange and one for the right side of the flange. The governing differential equations are solved with unknown wave propagation coefficients multiplied by spatial domain and time domain functions which are inserted into equilibrium and continuity equations at the intersection of the web and flange and into boundary conditions at the edges of the system resulting in 24 algebraic equations. These equations are solved to yield the wave propagation coefficients and this produces a solution to the displacement field in all three dimensions. An example problem is formulated and compared to results from finite element analysis.

Holonomy, quantum mechanics and the signal-tuned Gabor approach to the striate cortex

NASA Astrophysics Data System (ADS)

Torreão, José R. A.

2016-02-01

It has been suggested that an appeal to holographic and quantum properties will be ultimately required for the understanding of higher brain functions. On the other hand, successful quantum-like approaches to cognitive and behavioral processes bear witness to the usefulness of quantum prescriptions as applied to the analysis of complex non-quantum systems. Here, we show that the signal-tuned Gabor approach for modeling cortical neurons, although not based on quantum assumptions, also admits a quantum-like interpretation. Recently, the equation of motion for the signal-tuned complex cell response has been derived and proven equivalent to the Schrödinger equation for a dissipative quantum system whose solutions come under two guises: as plane-wave and Airy-packet responses. By interpreting the squared magnitude of the plane-wave solution as a probability density, in accordance with the quantum mechanics prescription, we arrive at a Poisson spiking probability — a common model of neuronal response — while spike propagation can be described by the Airy-packet solution. The signal-tuned approach is also proven consistent with holonomic brain theories, as it is based on Gabor functions which provide a holographic representation of the cell’s input, in the sense that any restricted subset of these functions still allows stimulus reconstruction.

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

High-frequency techniques for RCS prediction of plate geometries

NASA Technical Reports Server (NTRS)

Balanis, Constantine A.; Polka, Lesley A.

1992-01-01

The principal-plane scattering from perfectly conducting and coated strips and rectangular plates is examined. Previous reports have detailed Geometrical Theory of Diffraction/Uniform Theory of Diffraction (GTD/UTD) solutions for these geometries. The GTD/UTD solution for the perfectly conducting plate yields monostatic radar cross section (RCS) results that are nearly identical to measurements and results obtained using the Moment Method (MM) and the Extended Physical Theory of Diffraction (EPTD). This was demonstrated in previous reports. The previous analysis is extended to bistatic cases. GTD/UTD results for the principal-plane scattering from a perfectly conducting, infinite strip are compared to MM and EPTD data. A comprehensive overview of the advantages and disadvantages of the GTD/UTD and of the EPTD and a detailed analysis of the results from both methods are provided. Several previous reports also presented preliminary discussions and results for a GTD/UTD model of the RCS of a coated, rectangular plate. Several approximations for accounting for the finite coating thickness, plane-wave incidence, and far-field observation were discussed. Here, these approximations are replaced by a revised wedge diffraction coefficient that implicitly accounts for a coating on a perfect conductor, plane-wave incidence, and far-field observation. This coefficient is computationally more efficient than the previous diffraction coefficient because the number of Maliuzhinets functions that must be calculated using numerical integration is reduced by a factor of 2. The derivation and the revised coefficient are presented in detail for the hard polarization case. Computations and experimental data are also included. The soft polarization case is currently under investigation.

DETERMINATION OF ELASTIC WAVE VELOCITY AND RELATIVE HYPOCENTER LOCATIONS USING REFRACTED WAVES. II. APPLICATION TO THE HAICHENG, CHINA, AFTERSHOCK SEQUENCE.

USGS Publications Warehouse

Shedlock, Kaye M.; Jones, Lucile M.; Ma, Xiufang

1985-01-01

The authors located the aftershocks of the February 4, 1975 Haicheng, China, aftershock sequence using an arrival time difference (ATD) simultaneous inversion method for determining the near-source (in situ) velocity and the location of the aftershocks with respect to a master event. The aftershocks define a diffuse zone, 70 km multiplied by 25 km, trending west-northwest, perpendicular to the major structural trend of the region. The main shock and most of the large aftershocks have strike-slip fault plane solutions. The preferred fault plane strikes west-northwest, and the inferred sense of motion is left-lateral. The entire Haicheng earthauake sequence appears to have been the response of an intensely faulted range boundary to a primarily east-west crustal compression and/or north-south extension.

Numerical modelling and experimental analysis of acoustic emission

NASA Astrophysics Data System (ADS)

Gerasimov, S. I.; Sych, T. V.

2018-05-01

In the present paper, the authors report on the application of non-destructive acoustic waves technologies to determine the structural integrity of engineering components. In particular, a finite element (FE) system COSMOS/M is used to investigate propagation characteristics of ultrasonic waves in linear, plane and three-dimensional structures without and with geometric concentrators. In addition, the FE results obtained are compared to the analytical and experimental ones. The study illustrates the efficient use of the FE method to model guided wave propagation problems and demonstrates the FE method’s potential to solve problems when an analytical solution is not possible due to “complicated” geometry.

Design of the sample cell in near-field surface-enhanced Raman scattering by finite difference time domain method

NASA Astrophysics Data System (ADS)

Li, Yaqin; Jian, Guoshu; Wu, Shifa

2006-11-01

The rational design of the sample cell may improve the sensitivity of surface-enhanced Raman scattering (SERS) detection in a high degree. Finite difference time domain (FDTD) simulations of the configuration of Ag film-Ag particles illuminated by plane wave and evanescent wave are performed to provide physical insight for design of the sample cell. Numerical solutions indicate that the sample cell can provide more "hot spots' and the massive field intensity enhancement occurs in these "hot spots'. More information on the nanometer character of the sample can be got because of gradient-field Raman (GFR) of evanescent wave.

Topologically protected edge states for out-of-plane and in-plane bulk elastic waves.

PubMed

Huo, Shao-Yong; Chen, Jiu-Jiu; Huang, Hong-Bo

2018-04-11

Topological phononic insulators (TPnIs) show promise for application in the manipulation of acoustic waves for the design of low-loss transmission and perfectly integrated communication devices. Since solid phononic crystals exist as a transverse polarization mode and a mixed longitudinal-transverse polarization mode, the realization of topological edge states for both out-of-plane and in-plane bulk elastic waves is desirable to enhance the controllability of the edge waves in solid systems. In this paper, a two-dimensional (2D) solid/solid hexagonal-latticed phononic system that simultaneously supports the topologically protected edge states for out-of-plane and in-plane bulk elastic waves is investigated. Firstly, two pairs of two-fold Dirac cones, respectively corresponding to the out-of-plane and in-plane waves, are obtained at the same frequency by tuning the crystal parameters. Then, a strategy of zone folding is invoked to form double Dirac cones. By shrinking and expanding the steel scatterer, the lattice symmetry is broken, and band inversions induced, giving rise to an intriguing topological phase transition. Finally, the topologically protected edge states for both out-of-plane and in-plane bulk elastic waves, which can be simultaneously located at the frequency range from 1.223 to 1.251 MHz, are numerically observed. Robust pseudospin-dependent elastic edge wave propagation along arbitrary paths is further demonstrated. Our results will significantly broaden its practical application in the engineering field.

Topologically protected edge states for out-of-plane and in-plane bulk elastic waves

NASA Astrophysics Data System (ADS)

Huo, Shao-Yong; Chen, Jiu-Jiu; Huang, Hong-Bo

2018-04-01

Topological phononic insulators (TPnIs) show promise for application in the manipulation of acoustic waves for the design of low-loss transmission and perfectly integrated communication devices. Since solid phononic crystals exist as a transverse polarization mode and a mixed longitudinal-transverse polarization mode, the realization of topological edge states for both out-of-plane and in-plane bulk elastic waves is desirable to enhance the controllability of the edge waves in solid systems. In this paper, a two-dimensional (2D) solid/solid hexagonal-latticed phononic system that simultaneously supports the topologically protected edge states for out-of-plane and in-plane bulk elastic waves is investigated. Firstly, two pairs of two-fold Dirac cones, respectively corresponding to the out-of-plane and in-plane waves, are obtained at the same frequency by tuning the crystal parameters. Then, a strategy of zone folding is invoked to form double Dirac cones. By shrinking and expanding the steel scatterer, the lattice symmetry is broken, and band inversions induced, giving rise to an intriguing topological phase transition. Finally, the topologically protected edge states for both out-of-plane and in-plane bulk elastic waves, which can be simultaneously located at the frequency range from 1.223 to 1.251 MHz, are numerically observed. Robust pseudospin-dependent elastic edge wave propagation along arbitrary paths is further demonstrated. Our results will significantly broaden its practical application in the engineering field.

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.

Tilted string cosmologies

NASA Astrophysics Data System (ADS)

Clancy, Dominic; Feinstein, Alexander; Lidsey, James E.; Tavakol, Reza

1999-04-01

Global symmetries of the string effective action are employed to generate tilted, homogeneous Bianchi type VIh string cosmologies from a previously known stiff perfect fluid solution to Einstein gravity. The dilaton field is not constant on the surfaces of homogeneity. The future asymptotic state of the models is interpreted as a plane wave and is itself an exact solution to the string equations of motion to all orders in the inverse string tension. An inhomogeneous generalization of the Bianchi type III model is also found.

Strings on plane-waves and spin chains on orbifolds

NASA Astrophysics Data System (ADS)

Sadri, Darius

This thesis covers a number of topics in string theory focusing on various aspects of the AdS/CFT duality in various guises and regimes. In the first chapter we present a self-contained review of the Plane-wave/super-Yang-Mills duality. This duality is a specification of the usual AdS/CFT correspondence in the "Penrose limit". In chapter two we study the most general parallelizable pp-wave backgrounds which are non-dilatonic solutions in the NS-NS sector of type IIA and IIB string theories. We demonstrate that parallelizable pp-wave backgrounds are necessarily homogeneous plane-waves, and that a large class of homogeneous plane-waves are parallelizable, stating the necessary conditions. Quantization of string modes, their compactification and behaviour under T-duality are also studied, as are BPS Dp-branes on such backgrounds. In chapter three we consider giant gravitons on the maximally supersymmetric plane-wave background. We deduce the low energy effective light-cone Hamiltonian of the three-sphere giant graviton, and place sources in this effective gauge theory. Although non-vanishing net electric charge configurations are disallowed by Gauss' law, electric dipoles can be formed. From the string theory point of view these dipoles can be understood as open strings piercing the three-sphere, giving a two dimensional (worldsheet) description of giant gravitons. Chapter four presents some new ideas regarding the relation between super-conformal gauge theories and string theories with three-dimensional target spaces, possible relations of these systems to Hamiltonian lattice gauge theories, and integrable spin chains. We consider N = 1, D = 4 superconformal SU( N)px q Yang-Mills theories dual to AdS5 x S5/Zp x Zq orbifolds. We show that a specific sector of this dilatation operator can be thought of as the transfer matrix for a three-dimensional statistical mechanical system, which in turn is equivalent to a 2 + 1-dimensional string theory where the spatial slices are discretized on a triangular lattice, and comment on the integrability of this N = 1 gauge theory, its connection to three-dimensional lattice gauge theories, extensions to six-dimensional string theories, AdS/CFT type dualities and finally their construction via orbifolds and brane-box models. In the process we discover a new class of almost-BPS BMN type operators with large engineering dimensions but controllably small anomalous corrections.

Controlling the wave propagation through the medium designed by linear coordinate transformation

NASA Astrophysics Data System (ADS)

Wu, Yicheng; He, Chengdong; Wang, Yuzhuo; Liu, Xuan; Zhou, Jing

2015-01-01

Based on the principle of transformation optics, we propose to control the wave propagating direction through the homogenous anisotropic medium designed by linear coordinate transformation. The material parameters of the medium are derived from the linear coordinate transformation applied. Keeping the space area unchanged during the linear transformation, the polarization-dependent wave control through a non-magnetic homogeneous medium can be realized. Beam benders, polarization splitter, and object illusion devices are designed, which have application prospects in micro-optics and nano-optics. The simulation results demonstrate the feasibilities and the flexibilities of the method and the properties of these devices. Design details and full-wave simulation results are provided. The work in this paper comprehensively applies the fundamental theories of electromagnetism and mathematics. The method of obtaining a new solution of the Maxwell equations in a medium from a vacuum plane wave solution and a linear coordinate transformation is introduced. These have a pedagogical value and are methodologically and motivationally appropriate for physics students and teachers at the undergraduate and graduate levels.

Scattering of three-dimensional plane waves in a self-reinforced half-space lying over a triclinic half-space

NASA Astrophysics Data System (ADS)

Gupta, Shishir; Pramanik, Abhijit; Smita; Pramanik, Snehamoy

2018-06-01

The phenomenon of plane waves at the intersecting plane of a triclinic half-space and a self-reinforced half-space is discussed with possible applications during wave propagation. Analytical expressions of the phase velocities of reflection and refraction for quasi-compressional and quasi-shear waves under initial stress are discussed carefully. The closest form of amplitude proportions on reflection and refraction factors of three quasi-plane waves are developed mathematically by applying appropriate boundary conditions. Graphics are sketched to exhibit the consequences of initial stress in the three-dimensional plane wave on reflection and refraction coefficients. Some special cases that coincide with the fundamental properties of several layers are designed to express the reflection and refraction coefficients.

Ultrafast dynamic response of single crystal β-HMX

NASA Astrophysics Data System (ADS)

Zaug, Joseph M.; Armstrong, Michael R.; Crowhurst, Jonathan C.; Radousky, Harry B.; Ferranti, Louis; Swan, Raymond; Gross, Rick; Teslich, Nick E.; Wall, Mark A.; Austin, Ryan A.; Fried, Laurence E.

2017-01-01

We report results from ultrafast compression experiments conducted on β-HMX single crystals. Results consist of nominally 12 picosecond time-resolved wave profile data, (ultrafast time domain interferometry -TDI measurements), that were analyzed to determine high-velocity wave speeds as a function of piston velocity. TDI results are used to validate calculations of anisotropic stress-strain behavior of shocked loaded energetic materials. Our previous results derived using a 350 ps duration compression drive revealed anisotropic elastic wave response in single crystal β-HMX from (110) and (010) impact planes. Here we present results using a 1.05 ns duration compression drive with a 950 ps interferometry window to extend knowledge of the anisotropic dynamic response of β-HMX within eight microns of the initial impact plane. We observe two distinct wave profiles from (010) and three wave profiles from (010) impact planes. The (110) impact plane wave speeds typically exceed (010) impact plane wave speeds at the same piston velocities. The development of multiple hydrodynamic wave profiles begins at 20 GPa for the (110) impact plane and 28 GPa for the (10) impact plane. We compare our ultrafast TDI results with previous gun and plate impact results on β-HMX and PBX9501.

Scattering of SH wave by a semi-cylindrical salient near vertical interface in the bi-material half space

NASA Astrophysics Data System (ADS)

Qi, Hui; Zhang, Xi-meng

2017-10-01

With the aid of the Green function method and image method, the problem of scattering of SH-wave by a semi-cylindrical salient near vertical interface in bi-material half-space is considered to obtain its steady state response. Firstly, by the means of the image method, Green function which is the essential solution of displacement field is constructed to satisfy the stress-free condition on the horizontal boundary in a right-angle space including a semi-cylindrical salient and bearing a harmonic out-of-plane line source force at any point on the vertical boundary. Secondly, the bi-material is separated into two parts along the vertical interface, then unknown anti-plane forces are applied on the vertical interface, and according to the continuity condition, the first kind of Fredholm integral equations is established to determine unknown anti-plane forces by "the conjunction method", then the integral equations are reduced to the linear algebraic equations by effective truncation. Finally, the dynamic stress concentration factor (DSCF) around the edge of semi-cylindrical salient is calculated, and the influences of incident wave number, incident angle, effect of interface and different combination of material parameters, etc. on DSCF are discussed.

A high frequency analysis of electromagnetic plane wave scattering by perfectly-conducting semi-infinite parallel plate and rectangular waveguides with absorber coated inner walls

NASA Technical Reports Server (NTRS)

Noh, H. M.; Pathak, P. H.

1986-01-01

An approximate but sufficiently accurate high frequency solution which combines the uniform geometrical theory of diffraction (UTD) and the aperture integration (AI) method is developed for analyzing the problem of electromagnetic (EM) plane wave scattering by an open-ended, perfectly-conducting, semi-infinite hollow rectangular waveguide (or duct) with a thin, uniform layer of lossy or absorbing material on its inner wall, and with a planar termination inside. In addition, a high frequency solution for the EM scattering by a two dimensional (2-D), semi-infinite parallel plate waveguide with a absorber coating on the inner walls is also developed as a first step before analyzing the open-ended semi-infinite three dimensional (3-D) rectangular waveguide geometry. The total field scattered by the semi-infinite waveguide consists firstly of the fields scattered from the edges of the aperture at the open-end, and secondly of the fields which are coupled into the waveguide from the open-end and then reflected back from the interior termination to radiate out of the open-end. The first contribution to the scattered field can be found directly via the UTD ray method. The second contribution is found via the AI method which employs rays to describe the fields in the aperture that arrive there after reflecting from the interior termination. It is assumed that the direction of the incident plane wave and the direction of observation lie well inside the forward half space tht exists outside the half space containing the semi-infinite waveguide geometry. Also, the medium exterior to the waveguide is assumed to be free space.

The influence of air-filled structures on wave propagation and beam formation of a pygmy sperm whale (Kogia breviceps) in horizontal and vertical planes.

PubMed

Song, Zhongchang; Zhang, Yu; Thornton, Steven W; Li, Songhai; Dong, Jianchen

2017-10-01

The wave propagation, sound field, and transmission beam pattern of a pygmy sperm whale (Kogia breviceps) were investigated in both the horizontal and vertical planes. Results suggested that the signals obtained at both planes were similarly characterized with a high peak frequency and a relatively narrow bandwidth, close to the ones recorded from live animals. The sound beam measured outside the head in the vertical plane was narrower than that of the horizontal one. Cases with different combinations of air-filled structures in both planes were used to study the respective roles in controlling wave propagation and beam formation. The wave propagations and beam patterns in the horizontal and vertical planes elucidated the important reflection effect of the spermaceti and vocal chambers on sound waves, which was highly significant in forming intensive forward sound beams. The air-filled structures, the forehead soft tissues and skull structures formed wave guides in these two planes for emitted sounds to propagate forward.

Emergent rogue wave structures and statistics in spontaneous modulation instability

PubMed Central

Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M.

2015-01-01

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude “rogue waves” emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised “breather” or “soliton on finite background (SFB)” structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions. PMID:25993126

Analysis of an infinite array of rectangular microstrip patches with idealized probe feeds

NASA Technical Reports Server (NTRS)

Pozar, D. M.; Schaubert, D. H.

1984-01-01

A solution is presented to the problem of an infinite array of microstrip patches fed by idealized current probes. The input reflection coefficient is calculated versus scan angle in an arbitrary scan plane, and the effects of substrate parameters and grid spacing are considered. It is pointed out that even when a Galerkin method is used the impedance matrix is not symmetric due to phasing through a unit cell, as required for scanning. The mechanism by which scan blindness can occur is discussed. Measurement results are presented for the reflection coefficient magnitude variation with angle for E-plane, H-plane, and D-plane scans, for various substrate parameters. Measured results from waveguide simulators are also presented, and the scan blindness phenomenon is observed and discussed in terms of forced surface waves and a modified grating lobe diagram.

Corrections to the Thomson cross section caused by relativistic effects and by the presence of the drift velocity of a classical charged particle in the field of a monochromatic plane wave

NASA Astrophysics Data System (ADS)

Perestoronin, A. V.

2017-03-01

An approach to the solution of the relativistic problem of the motion of a classical charged particle in the field of a monochromatic plane wave with an arbitrary polarization (linear, circular, or elliptic) is proposed. It is based on the analysis of the 4-vector equation of motion of the charged particle together with the 4-vector and tensor equations for the components of the electromagnetic field tensor of a monochromatic plane wave. This approach provides analytical expressions for the time-averaged square of the 4-acceleration of the charge, as well as for the averaged values of any quantities periodic in the time of the reference frame. Expressions for the integral power of scattered radiation, which is proportional to the time-averaged square of the 4-acceleration of the charge, and for the integral scattering cross section, which is the ratio of the power of scattered radiation to the intensity of incident radiation, are obtained for an arbitrary inertial reference frame. An expression for the scattering cross section, which coincides with the known results at the circular and linear polarizations of the incident waves and describes the case of elliptic polarization of the incident wave, is obtained for the reference frame where the charged particle is on average at rest. An expression for the scattering cross section including relativistic effects and the nonzero drift velocity of a particle in this system is obtained for the laboratory reference frame, where the initial velocity of the charged particle is zero. In the case of the circular polarization of the incident wave, the scattering cross section in the laboratory frame is equal to the Thompson cross section.

Analysis of sound propagation in ducts using the wave envelope concept

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1974-01-01

A finite difference formulation is presented for sound propagation in a rectangular two-dimensional duct without steady flow for plane wave input. Before the difference equations are formulated, the governing Helmholtz equation is first transformed to a form whose solution does not oscillate along the length of the duct. This transformation reduces the required number of grid points by an order of magnitude, and the number of grid points becomes independent of the sound frequency. Physically, the transformed pressure represents the amplitude of the conventional sound wave. Example solutions are presented for sound propagation in a one-dimensional straight hard-wall duct and in a two-dimensional straight soft-wall duct without steady flow. The numerical solutions show evidence of the existence along the duct wall of a developing acoustic pressure diffusion boundary layer which is similar in nature to the conventional viscous flow boundary layer. In order to better illustrate this concept, the wave equation and boundary conditions are written such that the frequency no longer appears explicitly in them. The frequency effects in duct propagation can be visualized solely as an expansion and stretching of the suppressor duct.

Estimating Tsunami Runup with Fault Plane Parameters

NASA Astrophysics Data System (ADS)

Sepulveda, I.; Liu, P. L. F.

2016-12-01

The forecasting of tsunami runup has often been done by solving numerical models. The execution times, however, make them unsuitable for the purpose of warning. We offer an alternative method that provides analytical relationship between the runup height, the fault plane parameters and the characteristic of coastal bathymetry. The method uses the model of Okada (1985) to estimate the coseismic deformation and the corresponding sea surface displacement (η(x,0)). Once the tsunami waves are generated, Carrier & Greenspan (1958) solution (C&G) is adopted to yield analytical expressions for the shoreline elevation and velocity. Two types of problems are investigated. In the first, the bathymetry is modeled as a constant slope that is connected to a constant depth region, where a seismic event occurs. This is a boundary value problem (BVP). In the second, the bathymetry is further simplified as a constant slope, on which a seismic event occurs. This is an initial value problem (IVP). Both problems are depicted in Figure 1. We derive runup solutions in terms of the fault parameters. The earthquake is associated with vertical coseismic seafloor displacements by using Okada's elastic model. In addition to the simplifications considered in Okada's model, we further assume (1) a strike parallel to the shoreline, (2) a very long rupture area and (3) a fast earthquake so surface elevation mimics the seafloor displacements. Then the tsunami origin is modeled in terms of the fault depth (d), fault width (W), fault slip (s) and dip angle (δ). We describe the solution for the BVP. Madsen & Schaeffer (2010) utilized C&G to derive solutions for the shoreline elevation of sinusoidal waves imposed in the offshore boundary. A linear superposition of this solution represents any arbitrary incident wave. Furthermore, we can prescribe the boundary condition at the toe of sloping beach by adopting the linear shallow wave equations in the constant depth area. By means of a dimensional analysis, the runup R is determined by Eq.1. Kanoglu (2004) derived a non-dimensional expression for long wave runup originated over a sloping beach. In our work we determine an analytical expression for a sinusoidal initial condition. Following the same procedure as the BVP, the expression for the runup R in the IVP is given by Eq.2. The curves F1 and F2 are plotted in Figure 2.

Non-plane-wave Hartree-Fock states and nuclear homework potentials

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

Gutierrez, G.; Plastino, A.; de Llano, M.

1979-12-01

It is shown that non-plane-wave single-particle Hartree-Fock orbitals giving rise to a ''spin-density-wave-like'' structure give lower energy than plane waves beyond a certain relatively low density in both nuclear and neutron matter with homework pair potentials v/sub 1/ and v/sub 2/.

Bending of solitons in weak and slowly varying inhomogeneous plasma

NASA Astrophysics Data System (ADS)

Mukherjee, Abhik; Janaki, M. S.; Kundu, Anjan

2015-12-01

The bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using reductive perturbation technique, a modified Kadomtsev-Petviashvili equation is obtained with a chosen unperturbed ion density profile. The exact solution of the equation shows that the phase of the solitary wave gets modified by a function related to the unperturbed inhomogeneous ion density causing the soliton to bend in the two dimensional plane, while the amplitude of the soliton remains constant.

Bending of solitons in weak and slowly varying inhomogeneous plasma

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

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-12-15

The bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using reductive perturbation technique, a modified Kadomtsev-Petviashvili equation is obtained with a chosen unperturbed ion density profile. The exact solution of the equation shows that the phase of the solitary wave gets modified by a function related to the unperturbed inhomogeneous ion density causing the soliton to bend in the two dimensional plane, while the amplitude of the soliton remains constant.

Explosive plane-wave lens

DOEpatents

Marsh, Stanley P.

1988-01-01

An explosive plane-wave air lens which enables a spherical wave form to be converted to a planar wave without the need to specially machine or shape explosive materials is described. A disc-shaped impactor having a greater thickness at its center than around its periphery is used to convert the spherical wave into a plane wave. When the wave reaches the impactor, the center of the impactor moves first because the spherical wave reaches the center of the impactor first. The wave strikes the impactor later in time as one moves radially along the impactor. Because the impactor is thinner as one moves radially outward, the velocity of the impactor is greater at the periphery than at the center. An acceptor explosive is positioned so that the impactor strikes the acceptor simultaneously. Consequently, a plane detonation wave is propagated through the acceptor explosive.

Explosive plane-wave lens

DOEpatents

Marsh, S.P.

1988-03-08

An explosive plane-wave air lens which enables a spherical wave form to be converted to a planar wave without the need to specially machine or shape explosive materials is described. A disc-shaped impactor having a greater thickness at its center than around its periphery is used to convert the spherical wave into a plane wave. When the wave reaches the impactor, the center of the impactor moves first because the spherical wave reaches the center of the impactor first. The wave strikes the impactor later in time as one moves radially along the impactor. Because the impactor is thinner as one moves radially outward, the velocity of the impactor is greater at the periphery than at the center. An acceptor explosive is positioned so that the impactor strikes the acceptor simultaneously. Consequently, a plane detonation wave is propagated through the acceptor explosive. 4 figs.

Tissue elasticity of in vivo skeletal muscles measured in the transverse and longitudinal planes using shear wave elastography.

PubMed

Chino, Kentaro; Kawakami, Yasuo; Takahashi, Hideyuki

2017-07-01

The aim of the present study was to measure in vivo skeletal muscle elasticity in the transverse and longitudinal planes using shear wave elastography and then to compare the image stability, measurement values and measurement repeatability between these imaging planes. Thirty-one healthy males participated in this study. Tissue elasticity (shear wave velocity) of the medial gastrocnemius, rectus femoris, biceps brachii and rectus abdominis was measured in both the transverse and longitudinal planes using shear wave elastography. Image stability was evaluated by the standard deviation of the colour distribution in the shear wave elastography image. Measurement repeatability was assessed by the coefficient of variance obtained from three measurement values. Image stability of all tested muscles was significantly higher in the longitudinal plane (P<0·001), but measurement repeatability did not differ significantly between the imaging planes (P>0·05), except in the biceps brachii (P = 0·001). Measurement values of the medial gastrocnemius, rectus femoris and biceps brachii were significantly different between the imaging planes (P<0·001). Image stability and measurement values of shear wave elastography images varied with imaging plane, which indicates that imaging plane should be considered when measuring skeletal muscle tissue elasticity by shear wave elastography. © 2015 Scandinavian Society of Clinical Physiology and Nuclear Medicine. Published by John Wiley & Sons Ltd.

Analytical model for vibration prediction of two parallel tunnels in a full-space

NASA Astrophysics Data System (ADS)

He, Chao; Zhou, Shunhua; Guo, Peijun; Di, Honggui; Zhang, Xiaohui

2018-06-01

This paper presents a three-dimensional analytical model for the prediction of ground vibrations from two parallel tunnels embedded in a full-space. The two tunnels are modelled as cylindrical shells of infinite length, and the surrounding soil is modelled as a full-space with two cylindrical cavities. A virtual interface is introduced to divide the soil into the right layer and the left layer. By transforming the cylindrical waves into the plane waves, the solution of wave propagation in the full-space with two cylindrical cavities is obtained. The transformations from the plane waves to cylindrical waves are then used to satisfy the boundary conditions on the tunnel-soil interfaces. The proposed model provides a highly efficient tool to predict the ground vibration induced by the underground railway, which accounts for the dynamic interaction between neighbouring tunnels. Analysis of the vibration fields produced over a range of frequencies and soil properties is conducted. When the distance between the two tunnels is smaller than three times the tunnel diameter, the interaction between neighbouring tunnels is highly significant, at times in the order of 20 dB. It is necessary to consider the interaction between neighbouring tunnels for the prediction of ground vibrations induced underground railways.

Generation of higher-order rogue waves from multibreathers by double degeneracy in an optical fiber.

PubMed

Wang, Lihong; He, Jingsong; Xu, Hui; Wang, Ji; Porsezian, Kuppuswamy

2017-04-01

In this paper, we construct a special kind of breather solution of the nonlinear Schrödinger (NLS) equation, the so-called breather-positon (b-positon for short), which can be obtained by taking the limit λ_{j}→λ_{1} of the Lax pair eigenvalues in the order-n periodic solution, which is generated by the n-fold Darboux transformation from a special "seed" solution-plane wave. Further, an order-n b-positon gives an order-n rogue wave under a limit λ_{1}→λ_{0}. Here, λ_{0} is a special eigenvalue in a breather of the NLS equation such that its period goes to infinity. Several analytical plots of order-2 breather confirm visually this double degeneration. The last limit in this double degeneration can be realized approximately in an optical fiber governed by the NLS equation, in which an injected initial ideal pulse is created by a frequency comb system and a programable optical filter (wave shaper) according to the profile of an analytical form of the b-positon at a certain position z_{0}. We also suggest a new way to observe higher-order rogue waves generation in an optical fiber, namely, measure the patterns at the central region of the higher-order b-positon generated by above ideal initial pulses when λ_{1} is very close to the λ_{0}. The excellent agreement between the numerical solutions generated from initial ideal inputs with a low signal-to-noise ratio and analytical solutions of order-2 b-positon supports strongly this way in a realistic optical fiber system. Our results also show the validity of the generating mechanism of a higher-order rogue waves from a multibreathers through the double degeneration.

Propagation of Finite Amplitude Sound in Multiple Waveguide Modes.

NASA Astrophysics Data System (ADS)

van Doren, Thomas Walter

1993-01-01

This dissertation describes a theoretical and experimental investigation of the propagation of finite amplitude sound in multiple waveguide modes. Quasilinear analytical solutions of the full second order nonlinear wave equation, the Westervelt equation, and the KZK parabolic wave equation are obtained for the fundamental and second harmonic sound fields in a rectangular rigid-wall waveguide. It is shown that the Westervelt equation is an acceptable approximation of the full nonlinear wave equation for describing guided sound waves of finite amplitude. A system of first order equations based on both a modal and harmonic expansion of the Westervelt equation is developed for waveguides with locally reactive wall impedances. Fully nonlinear numerical solutions of the system of coupled equations are presented for waveguides formed by two parallel planes which are either both rigid, or one rigid and one pressure release. These numerical solutions are compared to finite -difference solutions of the KZK equation, and it is shown that solutions of the KZK equation are valid only at frequencies which are high compared to the cutoff frequencies of the most important modes of propagation (i.e., for which sound propagates at small grazing angles). Numerical solutions of both the Westervelt and KZK equations are compared to experiments performed in an air-filled, rigid-wall, rectangular waveguide. Solutions of the Westervelt equation are in good agreement with experiment for low source frequencies, at which sound propagates at large grazing angles, whereas solutions of the KZK equation are not valid for these cases. At higher frequencies, at which sound propagates at small grazing angles, agreement between numerical solutions of the Westervelt and KZK equations and experiment is only fair, because of problems in specifying the experimental source condition with sufficient accuracy.

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

PubMed

Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C

2017-08-01

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

Wind velocity profile reconstruction from intensity fluctuations of a plane wave propagating in a turbulent atmosphere.

PubMed

Banakh, V A; Marakasov, D A

2007-08-01

Reconstruction of a wind profile based on the statistics of plane-wave intensity fluctuations in a turbulent atmosphere is considered. The algorithm for wind profile retrieval from the spatiotemporal spectrum of plane-wave weak intensity fluctuations is described, and the results of end-to-end computer experiments on wind profiling based on the developed algorithm are presented. It is shown that the reconstructing algorithm allows retrieval of a wind profile from turbulent plane-wave intensity fluctuations with acceptable accuracy.

Explosive plane-wave lens

DOEpatents

Marsh, S.P.

1987-03-12

An explosive plane-wave air lens which enables a spherical wave form to be converted to a planar wave without the need to specially machine or shape explosive materials is described. A disc-shaped impactor having a greater thickness at its center than around its periphery is used to convert the spherical wave into a plane wave. When the wave reaches the impactor, the center of the impactor moves first because the spherical wave reaches the center of the impactor first. The wave strikes the impactor later in time as one moves radially along the impactor. Because the impactor is thinner as one moves radially outward, the velocity of the impactor is greater at the periphery than at the center. An acceptor explosive is positioned so that the impactor strikes the acceptor simultaneously. Consequently, a plane detonation wave is propagated through the acceptor explosive. 3 figs., 3 tabs.

Subcritical Kelvin-Helmholtz instability in a Hele-Shaw cell.

PubMed

Meignin, L; Gondret, P; Ruyer-Quil, C; Rabaud, M

2003-06-13

We investigate experimentally the subcritical behavior of the Kelvin-Helmholtz instability for a gas-liquid shearing flow in a Hele-Shaw cell. The subcritical curve separating the solutions of a stable plane interface and a fully saturated nonlinear wave train is determined. Experimental results are fitted by a fifth order complex Ginzburg-Landau equation whose linear coefficients are compared to theoretical ones.

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).

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.

Null hypersurfaces in de Sitter and anti-de Sitter cosmologies

NASA Astrophysics Data System (ADS)

Hogan, P. A.

The study of gravitational waves in the presence of a cosmological constant has led to interesting forms of the de Sitter and anti-de Sitter line elements based on families of null hypersurfaces. The forms are interesting because they focus attention on the geometry of null hypersurfaces in spacetimes of constant curvature. Two examples are worked out in some detail. The first originated in the study of collisions of impulsive gravitational waves in which the post-collision spacetime is a solution of Einstein’s field equations with a cosmological constant, and the second originated in the generalization of plane fronted gravitational waves with parallel rays to include a cosmological constant.

Fitting dynamic models to the Geosat sea level observations in the tropical Pacific Ocean. I - A free wave model

NASA Technical Reports Server (NTRS)

Fu, Lee-Lueng; Vazquez, Jorge; Perigaud, Claire

1991-01-01

Free, equatorially trapped sinusoidal wave solutions to a linear model on an equatorial beta plane are used to fit the Geosat altimetric sea level observations in the tropical Pacific Ocean. The Kalman filter technique is used to estimate the wave amplitude and phase from the data. The estimation is performed at each time step by combining the model forecast with the observation in an optimal fashion utilizing the respective error covariances. The model error covariance is determined such that the performance of the model forecast is optimized. It is found that the dominant observed features can be described qualitatively by basin-scale Kelvin waves and the first meridional-mode Rossby waves. Quantitatively, however, only 23 percent of the signal variance can be accounted for by this simple model.

Acoustic resonance scattering from a multilayered cylindrical shell with imperfect bonding.

PubMed

Rajabi, M; Hasheminejad, Seyyed M

2009-12-01

The method of wave function expansion is adopted to study the three dimensional scattering of a time-harmonic plane progressive sound field obliquely incident upon a multi-layered hollow cylinder with interlaminar bonding imperfection. For the generality of solution, each layer is assumed to be cylindrically orthotropic. An approximate laminate model in the context of the modal state equations with variable coefficients along with the classical T-matrix solution technique is set up for each layer to solve for the unknown modal scattering and transmission coefficients. A linear spring model is used to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the non-resonance (backgrounds) and resonance components. The solution is first used to investigate the effect of interlayer imperfection of an air-filled and water submerged bilaminate aluminium cylindrical shell on the resonances associated with various modes of wave propagation (i.e., symmetric/asymmetric Lamb waves, fluid-borne A-type waves, Rayleigh and Whispering Gallery waves) appearing in the backscattered spectrum, according to their polarization and state of stress. An illustrative numerical example is also given for a multi-layered (five-layered) cylindrical shell for which the stiffness of the adhesive interlayers is artificially varied. The sensitivity of resonance frequencies associated with higher mode numbers to the stiffness coefficients is demonstrated to be a good measure of the bonding strength. Limiting cases are considered and fair agreements with solutions available in the literature are established.

A dynamical systems approach to the tilted Bianchi models of solvable type

NASA Astrophysics Data System (ADS)

Coley, Alan; Hervik, Sigbjørn

2005-02-01

We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VIh and VIIh) with a perfect fluid and a linear barotropic γ-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi type VII0 models. We prove the important result that for non-inflationary Bianchi type VIIh models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VIIh invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exist closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VIIh models there is a bifurcation in which a set of equilibrium points turns into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VIIh models in this region the solution curves approach a compact surface which is topologically a torus.

P-Wave to Rayleigh-wave conversion coefficients for wedge corners; model experiments

USGS Publications Warehouse

Gangi, A.F.; Wesson, R.L.

1978-01-01

An analytic solution is not available for the diffraction of elastic waves by wedges; however, numerical solutions of finite-difference type are available for selected wedge angles. The P- to Rayleigh-wave conversion coefficients at wedge tips have been measured on two-dimensional seismic models for stress-free wedges with wedge angles, ??0, of 10, 30, 60, 90 and 120??. The conversion coefficients show two broad peaks and a minimum as a function of the angle between the wedge face and the direction of the incident P-wave. The minimum occurs for the P wave incident parallel to the wedge face and one maximum is near an incidence angle of 90?? to the wedge face. The amplitude of this maximum, relative to the other, decreases as the wedge angle increases. The asymmetry of the conversion coefficients, CPR(??; ??0), relative to parallel incidence (?? = 0) increases as the wedge angle increases. The locations of the maxima and the minimum as well as the asymmetry can be explained qualitatively. The conversion coefficients are measured with an accuracy of ??5% in those regions where there are no interfering waves. A comparison of the data for the 10?? wedge with the theoretical results for a half plane (0?? wedge) shows good correlation. ?? 1978.

C-plane Reconstructions from Sheaf Acquisition for Ultrasound Electrode Vibration Elastography.

PubMed

Ingle, Atul; Varghese, Tomy

2014-09-03

This paper presents a novel algorithm for reconstructing and visualizing ablated volumes using radiofrequency ultrasound echo data acquired with the electrode vibration elastography approach. The ablation needle is vibrated using an actuator to generate shear wave pulses that are tracked in the ultrasound image plane at different locations away from the needle. This data is used for reconstructing shear wave velocity maps for each imaging plane. A C-plane reconstruction algorithm is proposed which estimates shear wave velocity values on a collection of transverse planes that are perpendicular to the imaging planes. The algorithm utilizes shear wave velocity maps from different imaging planes that share a common axis of intersection. These C-planes can be used to generate a 3D visualization of the ablated region. Experimental validation of this approach was carried out using data from a tissue mimicking phantom. The shear wave velocity estimates were within 20% of those obtained from a clinical scanner, and a contrast of over 4 dB was obtained between the stiff and soft regions of the phantom.

Coded Excitation Plane Wave Imaging for Shear Wave Motion Detection

PubMed Central

Song, Pengfei; Urban, Matthew W.; Manduca, Armando; Greenleaf, James F.; Chen, Shigao

2015-01-01

Plane wave imaging has greatly advanced the field of shear wave elastography thanks to its ultrafast imaging frame rate and the large field-of-view (FOV). However, plane wave imaging also has decreased penetration due to lack of transmit focusing, which makes it challenging to use plane waves for shear wave detection in deep tissues and in obese patients. This study investigated the feasibility of implementing coded excitation in plane wave imaging for shear wave detection, with the hypothesis that coded ultrasound signals can provide superior detection penetration and shear wave signal-to-noise-ratio (SNR) compared to conventional ultrasound signals. Both phase encoding (Barker code) and frequency encoding (chirp code) methods were studied. A first phantom experiment showed an approximate penetration gain of 2-4 cm for the coded pulses. Two subsequent phantom studies showed that all coded pulses outperformed the conventional short imaging pulse by providing superior sensitivity to small motion and robustness to weak ultrasound signals. Finally, an in vivo liver case study on an obese subject (Body Mass Index = 40) demonstrated the feasibility of using the proposed method for in vivo applications, and showed that all coded pulses could provide higher SNR shear wave signals than the conventional short pulse. These findings indicate that by using coded excitation shear wave detection, one can benefit from the ultrafast imaging frame rate and large FOV provided by plane wave imaging while preserving good penetration and shear wave signal quality, which is essential for obtaining robust shear elasticity measurements of tissue. PMID:26168181

Transport Theory for Propagation and Reverberation

DTIC Science & Technology

2016-07-20

mentioned that our transport theory method is essentially 2-D (range and depth), so that out-of- plane forward scattering (a 3-D effect) is not treated...roughness spectrum, it is useful to consider scattering based on perturbation theory in some detail with a plane wave incident on the rough surface. The...the wave vector for the water wave. Let an incident acoustic plane wave have wave vector ki = kiH + kiz, where kiH denotes the horizontal component

Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field.

PubMed

Bayindir, Cihan

2016-03-01

In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the β parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant k and showed that the probability of rogue wave occurrence depends on k. Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schrödinger equation have also been presented.

Twisted electron-acoustic waves in plasmas

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

Aman-ur-Rehman, E-mail: amansadiq@gmail.com; Department of Physics and Applied Mathematics; Ali, S.

2016-08-15

In the paraxial limit, a twisted electron-acoustic (EA) wave is studied in a collisionless unmagnetized plasma, whose constituents are the dynamical cold electrons and Boltzmannian hot electrons in the background of static positive ions. The analytical and numerical solutions of the plasma kinetic equation suggest that EA waves with finite amount of orbital angular momentum exhibit a twist in its behavior. The twisted wave particle resonance is also taken into consideration that has been appeared through the effective wave number q{sub eff} accounting for Laguerre-Gaussian mode profiles attributed to helical phase structures. Consequently, the dispersion relation and the damping ratemore » of the EA waves are significantly modified with the twisted parameter η, and for η → ∞, the results coincide with the straight propagating plane EA waves. Numerically, new features of twisted EA waves are identified by considering various regimes of wavelength and the results might be useful for transport and trapping of plasma particles in a two-electron component plasma.« less

Solution of electromagnetic scattering and radiation problems using a spectral domain approach - A review

NASA Technical Reports Server (NTRS)

Mittra, R.; Ko, W. L.; Rahmat-Samii, Y.

1979-01-01

This paper presents a brief review of some recent developments on the use of the spectral-domain approach for deriving high-frequency solutions to electromagnetics scattering and radiation problems. The spectral approach is not only useful for interpreting the well-known Keller formulas based on the geometrical theory of diffraction (GTD), it can also be employed for verifying the accuracy of GTD and other asymptotic solutions and systematically improving the results when such improvements are needed. The problem of plane wave diffraction by a finite screen or a strip is presented as an example of the application of the spectral-domain approach.

Strong shock implosion, approximate solution

NASA Astrophysics Data System (ADS)

Fujimoto, Y.; Mishkin, E. A.; Alejaldre, C.

1983-01-01

The self-similar, center-bound motion of a strong spherical, or cylindrical, shock wave moving through an ideal gas with a constant, γ= cp/ cv, is considered and a linearized, approximate solution is derived. An X, Y phase plane of the self-similar solution is defined and the representative curved of the system behind the shock front is replaced by a straight line connecting the mappings of the shock front with that of its tail. The reduced pressure P(ξ), density R(ξ) and velocity U1(ξ) are found in closed, quite accurate, form. Comparison with numerically obtained results, for γ= {5}/{3} and γ= {7}/{5}, is shown.

Point force and point electric charge applied to the boundary of three-dimensional anisotropic piezoelectric solid

DOE PAGES

Borovikov, V. A.; Kalinin, S. V.; Khavin, Yu.; ...

2015-08-19

We derive the Green's functions for a three-dimensional semi-infinite fully anisotropic piezoelectric material using the plane wave theory method. The solution gives the complete set of electromechanical fields due to an arbitrarily oriented point force and a point electric charge applied to the boundary of the half-space. Moreover, the solution constitutes generalization of Boussinesq's and Cerruti's problems of elastic isotropy for the anisotropic piezoelectric materials. On the example of piezoceramics PZT-6B, the present results are compared with the previously obtained solution for the special case of transversely isotropic piezoelectric solid subjected to the same boundary condition.

Two-dimensional complex source point solutions: application to propagationally invariant beams, optical fiber modes, planar waveguides, and plasmonic devices.

PubMed

Sheppard, Colin J R; Kou, Shan S; Lin, Jiao

2014-12-01

Highly convergent beam modes in two dimensions are considered based on rigorous solutions of the scalar wave (Helmholtz) equation, using the complex source point formalism. The modes are applicable to planar waveguide or surface plasmonic structures and nearly concentric microcavity resonator modes in two dimensions. A novel solution is that of a vortex beam, where the direction of propagation is in the plane of the vortex. The modes also can be used as a basis for the cross section of propagationally invariant beams in three dimensions and bow-tie-shaped optical fiber modes.

Evanescent waves and deaf bands in sonic crystals

NASA Astrophysics Data System (ADS)

Romero-García, V.; Garcia-Raffi, L. M.; Sánchez-Pérez, J. V.

2011-12-01

The properties of sonic crystals (SC) are theoretically investigated in this work by solving the inverse problem k(ω) using the extended plane wave expansion (EPWE). The solution of the resulting eigenvalue problem gives the complex band structure which takes into account both the propagating and the evanescent modes. In this work we show the complete mathematical formulation of the EPWE for SC and the supercell approximation for its use in both a complete SC and a SC with defects. As an example we show a novel interpretation of the deaf bands in a complete SC in good agreement with multiple scattering simulations.

Wave-front propagation in a discrete model of excitable media

NASA Astrophysics Data System (ADS)

Feldman, A. B.; Chernyak, Y. B.; Cohen, R. J.

1998-06-01

We generalize our recent discrete cellular automata (CA) model of excitable media [Y. B. Chernyak, A. B. Feldman, and R. J. Cohen, Phys. Rev. E 55, 3215 (1997)] to incorporate the effects of inhibitory processes on the propagation of the excitation wave front. In the common two variable reaction-diffusion (RD) models of excitable media, the inhibitory process is described by the v ``controller'' variable responsible for the restoration of the equilibrium state following excitation. In myocardial tissue, the inhibitory effects are mainly due to the inactivation of the fast sodium current. We represent inhibition using a physical model in which the ``source'' contribution of excited elements to the excitation of their neighbors decreases with time as a simple function with a single adjustable parameter (a rate constant). We sought specific solutions of the CA state transition equations and obtained (both analytically and numerically) the dependence of the wave-front speed c on the four model parameters and the wave-front curvature κ. By requiring that the major characteristics of c(κ) in our CA model coincide with those obtained from solutions of a specific RD model, we find a unique set of CA parameter values for a given excitable medium. The basic structure of our CA solutions is remarkably similar to that found in typical RD systems (similar behavior is observed when the analogous model parameters are varied). Most notably, the ``turn-on'' of the inhibitory process is accompanied by the appearance of a solution branch of slow speed, unstable waves. Additionally, when κ is small, we obtain a family of ``eikonal'' relations c(κ) that are suitable for the kinematic analysis of traveling waves in the CA medium. We compared the solutions of the CA equations to CA simulations for the case of plane waves and circular (target) waves and found excellent agreement. We then studied a spiral wave using the CA model adjusted to a specific RD system and found good correspondence between the shapes of the RD and CA spiral arms in the region away from the tip where kinematic theory applies. Our analysis suggests that only four physical parameters control the behavior of wave fronts in excitable media.

Matrix basis for plane and modal waves in a Timoshenko beam.

PubMed

Claeyssen, Julio Cesar Ruiz; Tolfo, Daniela de Rosso; Tonetto, Leticia

2016-11-01

Plane waves and modal waves of the Timoshenko beam model are characterized in closed form by introducing robust matrix basis that behave according to the nature of frequency and wave or modal numbers. These new characterizations are given in terms of a finite number of coupling matrices and closed form generating scalar functions. Through Liouville's technique, these latter are well behaved at critical or static situations. Eigenanalysis is formulated for exponential and modal waves. Modal waves are superposition of four plane waves, but there are plane waves that cannot be modal waves. Reflected and transmitted waves at an interface point are formulated in matrix terms, regardless of having a conservative or a dissipative situation. The matrix representation of modal waves is used in a crack problem for determining the reflected and transmitted matrices. Their euclidean norms are seen to be dominated by certain components at low and high frequencies. The matrix basis technique is also used with a non-local Timoshenko model and with the wave interaction with a boundary. The matrix basis allows to characterize reflected and transmitted waves in spectral and non-spectral form.

Incident wave run-up into narrow sloping bays and estuaries

NASA Astrophysics Data System (ADS)

Sinan Özeren, M.; Postacioglu, Nazmi; Canlı, Umut

2015-04-01

The problem is investigated using Carrier Greenspan hodograph transformations.We perform a quasi-one-dimensional solution well into the bay, far enough of the mouth of the bay. The linearized boundary conditions at the mouth of the bay lead to an integral equation for 2-D geometry. A semi analytical optimization method has been developed to solve this integral equation. When the wavelength of the incident wave is much larger than the width of the bay, the conformalmapping of the bay and the semi infinite sea onto upper complex plane provides a solution of the integral equation in closed form. Particular emphasis is placed on the case where the frequency of the incident waves matches the real-part of the natural frequency of the oscillation of the bay. These natural frequencies are complex because of the radiation conditions imposed at the mouth of the bay. It is found that the complex part of these natural frequencies decreases with decreasing width of the bay. Thus the trapping of the waves in narrower bays leads to a strong resonance phenomenon when the frequency of the incident wave is equal to the real part of the natural frequency.

Introduction to Radar Polarimetry

DTIC Science & Technology

1991-04-23

Coulomb force 11 1,2 Static etectric fields 13 1.3 Summary 15 2 ELECTROMAGNETIC WAVES 16 2.1 Harmonic plane waves 16 2.2 The average intensity of a...harmonic plane wave 17 2.3 Spherical harmonic waves 18 2.4 Summary 19 3 THE POLARIZATION OF AN ELECTROMAGNETIC WAVE 20 3.1 The polarization ellipse 20 3.2...CHANGE OF POLARIZATION 31 4.1 Simple examples 31 4.2 Scattering at a plane interface 33 4.3 Summary 36 5 THE SCATTERING MATRIX 37 5.1 Transmission

Integrability and Linear Stability of Nonlinear Waves

NASA Astrophysics Data System (ADS)

Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo

2018-03-01

It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.

A numerical solution method for acoustic radiation from axisymmetric bodies

NASA Technical Reports Server (NTRS)

Caruthers, John E.; Raviprakash, G. K.

1995-01-01

A new and very efficient numerical method for solving equations of the Helmholtz type is specialized for problems having axisymmetric geometry. It is then demonstrated by application to the classical problem of acoustic radiation from a vibrating piston set in a stationary infinite plane. The method utilizes 'Green's Function Discretization', to obtain an accurate resolution of the waves using only 2-3 points per wave. Locally valid free space Green's functions, used in the discretization step, are obtained by quadrature. Results are computed for a range of grid spacing/piston radius ratios at a frequency parameter, omega R/c(sub 0), of 2 pi. In this case, the minimum required grid resolution appears to be fixed by the need to resolve a step boundary condition at the piston edge rather than by the length scale imposed by the wave length of the acoustic radiation. It is also demonstrated that a local near-field radiation boundary procedure allows the domain to be truncated very near the radiating source with little effect on the solution.

Determination of Focal Mechanisms of Non-Volcanic Tremors Based on S-Wave Polarization Data Corrected for the Effects of Anisotropy

NASA Astrophysics Data System (ADS)

Imanishi, K.; Uchide, T.; Takeda, N.

2014-12-01

We propose a method to determine focal mechanisms of non-volcanic tremors (NVTs) based on S-wave polarization angles. The successful retrieval of polarization angles in low S/N tremor signals owes much to the observation that NVTs propagate slowly and therefore they do not change their location immediately. This feature of NVTs enables us to use a longer window to compute a polarization angle (e.g., one minute or longer), resulting in a stack of particle motions. Following Zhang and Schwartz (1994), we first correct for the splitting effect to recover the source polarization angle (anisotropy-corrected angle). This is a key step, because shear-wave splitting distorts the particle motion excited by a seismic source. We then determine the best double-couple solution using anisotropy-corrected angles of multiple stations. The present method was applied to a tremor sequence at Kii Peninsula, southwest Japan, which occurred at the beginning of April 2013. A standard splitting and polarization analysis were subject to a one-minute-long moving window to determine the splitting parameters as well as anisotropy-corrected angles. A grid search approach was performed at each hour to determine the best double-couple solution satisfying one-hour average polarization angles. Most solutions show NW-dipping low-angle planes consistent with the plate boundary or SE-dipping high-angle planes. Because of 180 degrees ambiguity in polarization angles, the present method alone cannot distinguish compressional quadrant from dilatational one. Together with the observation of very low-frequency earthquakes near the present study area (Ito et al., 2007), it is reasonable to consider that they represent shear slip on low-angle thrust faults. It is also noted that some of solutions contain strike-slip component. Acknowledgements: Seismograph stations used in this study include permanent stations operated by NIED (Hi-net), JMA, Earthquake Research Institute, together with Geological Survey of Japan, AIST. This work was supported by JSPS KAKENHI Grant Number 24540463.

Sauter-Schwinger pair creation dynamically assisted by a plane wave

NASA Astrophysics Data System (ADS)

Torgrimsson, Greger; Schneider, Christian; Schützhold, Ralf

2018-05-01

We study electron-positron pair creation by a strong and constant electric field superimposed with a weaker transversal plane wave which is incident perpendicularly (or under some angle). Comparing the fully nonperturbative approach based on the world-line instanton method with a perturbative expansion into powers of the strength of the weaker plane wave, we find good agreement—provided that the latter is carried out to sufficiently high orders. As usual for the dynamically assisted Sauter-Schwinger effect, the additional plane wave induces an exponential enhancement of the pair-creation probability if the combined Keldysh parameter exceeds a certain threshold.

Near ground measure and theoretical model of plane wave covariance of intensity in anisotropic turbulence.

PubMed

Beason, Melissa; Smith, Christopher; Coffaro, Joseph; Belichki, Sara; Spychalsky, Jonathon; Titus, Franklin; Crabbs, Robert; Andrews, Larry; Phillips, Ronald

2018-06-01

Experimental measurements were recently made which displayed characteristics of plane wave propagation through anisotropic optical turbulence. A near-plane wave beam was propagated a distance of 1 and 2 km at a height of 2 m above the concrete runway at the Shuttle Landing Facility, Kennedy Space Center, Florida, during January and February of 2017. The spatial-temporal fluctuations of the beam were recorded, and the covariance of intensity was calculated. These data sets were compared to a theoretical calculation of covariance of intensity for a plane wave.

On pp wave limit for η deformed superstrings

NASA Astrophysics Data System (ADS)

Roychowdhury, Dibakar

2018-05-01

In this paper, based on the notion of plane wave string/gauge theory duality, we explore the pp wave limit associated with the bosonic sector of η deformed superstrings propagating in ( AdS 5 × S 5) η . Our analysis reveals that in the presence of NS-NS and RR fluxes, the pp wave limit associated to full ABF background satisfies type IIB equations in its standard form. However, the beta functions as well as the string Hamiltonian start receiving non trivial curvature corrections as one starts probing beyond pp wave limit which thereby takes solutions away from the standard type IIB form. Furthermore, using uniform gauge, we also explore the BMN dynamics associated with short strings and compute the corresponding Hamiltonian density. Finally, we explore the Penrose limit associated with the HT background and compute the corresponding stringy spectrum for the bosonic sector.

Electron acoustic solitary waves in a magnetized plasma with nonthermal electrons and an electron beam

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

Singh, S. V., E-mail: satyavir@iigs.iigm.res.in; Lakhina, G. S., E-mail: lakhina@iigs.iigm.res.in; University of the Western Cape, Belville

2016-08-15

A theoretical investigation is carried out to study the obliquely propagating electron acoustic solitary waves having nonthermal hot electrons, cold and beam electrons, and ions in a magnetized plasma. We have employed reductive perturbation theory to derive the Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation describing the nonlinear evolution of these waves. The two-dimensional plane wave solution of KdV-ZK equation is analyzed to study the effects of nonthermal and beam electrons on the characteristics of the solitons. Theoretical results predict negative potential solitary structures. We emphasize that the inclusion of finite temperature effects reduces the soliton amplitudes and the width of the solitons increasesmore » by an increase in the obliquity of the wave propagation. The numerical analysis is presented for the parameters corresponding to the observations of “burst a” event by Viking satellite on the auroral field lines.« less

An irregular lattice method for elastic wave propagation

NASA Astrophysics Data System (ADS)

O'Brien, Gareth S.; Bean, Christopher J.

2011-12-01

Lattice methods are a class of numerical scheme which represent a medium as a connection of interacting nodes or particles. In the case of modelling seismic wave propagation, the interaction term is determined from Hooke's Law including a bond-bending term. This approach has been shown to model isotropic seismic wave propagation in an elastic or viscoelastic medium by selecting the appropriate underlying lattice structure. To predetermine the material constants, this methodology has been restricted to regular grids, hexagonal or square in 2-D or cubic in 3-D. Here, we present a method for isotropic elastic wave propagation where we can remove this lattice restriction. The methodology is outlined and a relationship between the elastic material properties and an irregular lattice geometry are derived. The numerical method is compared with an analytical solution for wave propagation in an infinite homogeneous body along with comparing the method with a numerical solution for a layered elastic medium. The dispersion properties of this method are derived from a plane wave analysis showing the scheme is more dispersive than a regular lattice method. Therefore, the computational costs of using an irregular lattice are higher. However, by removing the regular lattice structure the anisotropic nature of fracture propagation in such methods can be removed.

First plasma wave observations at neptune.

PubMed

Gurnett, D A; Kurth, W S; Poynter, R L; Granroth, L J; Cairns, I H; Macek, W M; Moses, S L; Coroniti, F V; Kennel, C F; Barbosa, D D

1989-12-15

The Voyager 2 plasma wave instrument detected many familiar plasma waves during the encounter with Neptune, including electron plasma oscillations in the solar wind upstream of the bow shock, electrostatic turbulence at the bow shock, and chorus, hiss, electron cyclotron waves, and upper hybrid resonance waves in the inner magnetosphere. Low-frequency radio emissions, believed to be generated by mode conversion from the upper hybrid resonance emissions, were also observed propagating outward in a disklike beam along the magnetic equatorial plane. At the two ring plane crossings many small micrometer-sized dust particles were detected striking the spacecraft. The maximum impact rates were about 280 impacts per second at the inbound ring plane crossing, and about 110 impacts per second at the outbound ring plane crossing. Most of the particles are concentrated in a dense disk, about 1000 kilometers thick, centered on the equatorial plane. However, a broader, more tenuous distribution also extends many tens of thousands of kilometers from the equatorial plane, including over the northern polar region.

Screw-symmetric gravitational waves: A double copy of the vortex

NASA Astrophysics Data System (ADS)

Ilderton, A.

2018-07-01

Plane gravitational waves can admit a sixth 'screw' isometry beyond the usual five. The same is true of plane electromagnetic waves. From the point of view of integrable systems, a sixth isometry would appear to over-constrain particle dynamics in such waves; we show here, though, that no effect of the sixth isometry is independent of those from the usual five. Many properties of particle dynamics in a screw-symmetric gravitational wave are also seen in a (non-plane-wave) electromagnetic vortex; we make this connection explicit, showing that the screw-symmetric gravitational wave is the classical double copy of the vortex.

A plane wave generation method by wave number domain point focusing.

PubMed

Chang, Ji-Ho; Choi, Jung-Woo; Kim, Yang-Hann

2010-11-01

A method for generation of a wave-field that is a plane wave is described. This method uses an array of loudspeakers phased so that the field in the wave-number domain is nearly concentrated at a point, this point being at the wave-number vector of the desired plane wave. The method described here for such a wave-number concentration makes use of an expansion in spherical harmonics, and requires a relatively small number of measurement points for a good approximate achievement of a plane wave. The measurement points are on a spherical surface surrounding the array of loudspeakers. The input signals for the individual loudspeakers can be derived without a matrix inversion or without explicit assumptions about the loudspeakers. The mathematical development involves spherical harmonics and three-dimensional Fourier transforms. Some numerical examples are given, with various assumptions concerning the nature of the loudspeakers, that support the premise that the method described in the present paper may be useful in applications.

Breathers, quasi-periodic and travelling waves for a generalized ?-dimensional Yu-Toda-Sasa-Fukayama equation in fluids

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Zhao, Chen; Jia, Shu-Liang; Lan, Zhong-Zhou

2017-07-01

Under investigation in this paper is a generalized ?-dimensional Yu-Toda-Sasa-Fukayama equation for the interfacial wave in a two-layer fluid or the elastic quasi-plane wave in a liquid lattice. By virtue of the binary Bell polynomials, bilinear form of this equation is obtained. With the help of the bilinear form, N-soliton solutions are obtained via the Hirota method, and a bilinear Bäcklund transformation is derived to verify the integrability. Homoclinic breather waves are obtained according to the homoclinic test approach, which is not only the space-periodic breather but also the time-periodic breather via the graphic analysis. Via the Riemann theta function, quasi one-periodic waves are constructed, which can be viewed as a superposition of the overlapping solitary waves, placed one period apart. Finally, soliton-like, periodical triangle-type, rational-type and solitary bell-type travelling waves are obtained by means of the polynomial expansion method.

Towards ultrasound enhanced mid-IR spectroscopy for sensing bacteria in aqueous solutions

NASA Astrophysics Data System (ADS)

Freitag, Stephan; Schwaighofer, Andreas; Radel, Stefan; Lendl, Bernhard

2018-02-01

We employ attenuated total reflection (ATR) mid-IR technology for sensing of bacteria present in aqueous solution. In ATR spectroscopy, the penetration depth of the evanescent field extends to approx. 1-2 micrometers into the aqueous solution depending on the refractive index of the employed materials (Si, ZnS, Ge) used as attenuated total reflection (ATR) element and the geometry of the optical set-up. Due to the flow profile in the microfluidic cell, an additional force is required to bring particles into the evanescent field for measurement. For that purpose, we employ standing ultrasound waves produced between a sound source vibrating at approx. 2 MHz and the ATR crystal acting as a reflector. This ultrasonic trap is integrated into the microfluidic channel. As aqueous solution is passing through that acoustofluidic cell, particles are concentrated in the nodal plane of the standing ultrasound wave, forming particle conglomerates. By selecting appropriate experimental conditions, it is then possible to press bacteria against the crystal surface for interaction with the evanescent wave (as well as to keep them away from the ATR element). Our current work aims at establishing a custommade US-ATR-IR setup for signal enhancement of bacteria (e.g. E. coli, P. aeruginosa as well as Salmonella) in drinking water.

Ground-based observations and simulation of ionospheric VLF source in experiments on modification of the polar ionosphere

NASA Astrophysics Data System (ADS)

Lebed', O. M.; Fedorenko, Yu. V.; Blagoveshchenskaya, N. F.; Larchenko, A. V.; Grigor'ev, V. F.; Pil'gaev, S. V.

2017-11-01

The phase velocities of TE and TEM waves at frequencies of 1017 and 3017 Hz, as well as the effect of precipitations during auroras on the velocities, are estimated in the Earth-ionosphere waveguide on the basis of observations of electromagnetic fields of an ionospheric source in experiments on modification of the lower ionosphere by a modulated high-power short-wave signals performed by the Arctic and Antarctic Research Institute (AARI) at the EISCAT/Heating test bench in October 2016. Probable electron density profiles in the plane-stratified ionosphere are retrieved from the numerical solution of a wave equation, which are used for the calculation of the phase velocities close to measured ones.

Sinc-interpolants in the energy plane for regular solution, Jost function, and its zeros of quantum scattering

NASA Astrophysics Data System (ADS)

Annaby, M. H.; Asharabi, R. M.

2018-01-01

In a remarkable note of Chadan [Il Nuovo Cimento 39, 697-703 (1965)], the author expanded both the regular wave function and the Jost function of the quantum scattering problem using an interpolation theorem of Valiron [Bull. Sci. Math. 49, 181-192 (1925)]. These expansions have a very slow rate of convergence, and applying them to compute the zeros of the Jost function, which lead to the important bound states, gives poor convergence rates. It is our objective in this paper to introduce several efficient interpolation techniques to compute the regular wave solution as well as the Jost function and its zeros approximately. This work continues and improves the results of Chadan and other related studies remarkably. Several worked examples are given with illustrations and comparisons with existing methods.

Evanescent-wave particle velocimetry measurements of zeta-potentials in fused-silica microchannels.

PubMed

Cevheri, Necmettin; Yoda, Minami

2013-07-01

The wall ζ-potential ζ(w), the potential at the shear plane of the electric double layer, depends on the properties of the BGE solution such as the valence and type of electrolyte, the pH and the ionic strength. Most of the methods estimate ζ(w) from measurements of the EOF velocity magnitude ueo , usually spatially averaged over the entire capillary. In these initial studies, evanescent-wave particle velocimetry was used to measure ueo in steady EOF for a variety of monovalent aqueous solutions to evaluate the effect of small amounts of divalent cations, as well as the pH and ionic strength of BGE solutions. In brief, the magnitude of the EOF velocity of NaCl-NaOH and borate buffer-NaOH solutions was estimated from the measured velocities of radius α = 104 nm fluorescent polystyrene particles in 33 μm fused-silica microchannels. The particle ζ-potentials were measured separately using laser-Doppler micro-electrophoresis; ζ(w) was then determined from ueo. The results suggest that evanescent-wave particle velocimetry can be used to estimate ζ(w) for a variety of BGE solutions, and that it can be used in the future to estimate local wall ζ-potential, and hence spatial variations in ζ(w). © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Precursor Wave Emission Enhanced by Weibel Instability in Relativistic Shocks

NASA Astrophysics Data System (ADS)

Iwamoto, Masanori; Amano, Takanobu; Hoshino, Masahiro; Matsumoto, Yosuke

2018-05-01

We investigated the precursor wave emission efficiency in magnetized purely perpendicular relativistic shocks in pair plasmas. We extended our previous study to include the dependence of upstream magnetic field orientations. We performed two-dimensional particle-in-cell simulations and focused on two magnetic field orientations: the magnetic field in the simulation plane (i.e., in-plane configuration) and that perpendicular to the simulation plane (i.e., out-of-plane configuration). Our simulations in the in-plane configuration demonstrated that not only extraordinary but also ordinary mode waves are excited. We quantified the emission efficiency as a function of the magnetization parameter σ e and found that the large-amplitude precursor waves are emitted for a wide range of σ e . We found that especially at low σ e , the magnetic field generated by Weibel instability amplifies the ordinary mode wave power. The amplitude is large enough to perturb the upstream plasma, and transverse density filaments are generated as in the case of the out-of-plane configuration investigated in the previous study. We confirmed that our previous conclusion holds regardless of upstream magnetic field orientations with respect to the two-dimensional simulation plane. We discuss the precursor wave emission in three dimensions and the feasibility of wakefield acceleration in relativistic shocks based on our results.

Matrix basis for plane and modal waves in a Timoshenko beam

PubMed Central

Tolfo, Daniela de Rosso; Tonetto, Leticia

2016-01-01

Plane waves and modal waves of the Timoshenko beam model are characterized in closed form by introducing robust matrix basis that behave according to the nature of frequency and wave or modal numbers. These new characterizations are given in terms of a finite number of coupling matrices and closed form generating scalar functions. Through Liouville’s technique, these latter are well behaved at critical or static situations. Eigenanalysis is formulated for exponential and modal waves. Modal waves are superposition of four plane waves, but there are plane waves that cannot be modal waves. Reflected and transmitted waves at an interface point are formulated in matrix terms, regardless of having a conservative or a dissipative situation. The matrix representation of modal waves is used in a crack problem for determining the reflected and transmitted matrices. Their euclidean norms are seen to be dominated by certain components at low and high frequencies. The matrix basis technique is also used with a non-local Timoshenko model and with the wave interaction with a boundary. The matrix basis allows to characterize reflected and transmitted waves in spectral and non-spectral form. PMID:28018668

A highly accurate analytical solution for the surface fields of a short vertical wire antenna lying on a multilayer ground

NASA Astrophysics Data System (ADS)

Parise, M.

2018-01-01

A highly accurate analytical solution is derived to the electromagnetic problem of a short vertical wire antenna located on a stratified ground. The derivation consists of three steps. First, the integration path of the integrals describing the fields of the dipole is deformed and wrapped around the pole singularities and the two vertical branch cuts of the integrands located in the upper half of the complex plane. This allows to decompose the radiated field into its three contributions, namely the above-surface ground wave, the lateral wave, and the trapped surface waves. Next, the square root terms responsible for the branch cuts are extracted from the integrands of the branch-cut integrals. Finally, the extracted square roots are replaced with their rational representations according to Newton's square root algorithm, and residue theorem is applied to give explicit expressions, in series form, for the fields. The rigorous integration procedure and the convergence of square root algorithm ensure that the obtained formulas converge to the exact solution. Numerical simulations are performed to show the validity and robustness of the developed formulation, as well as its advantages in terms of time cost over standard numerical integration procedures.

Computing the Dynamic Response of a Stratified Elastic Half Space Using Diffuse Field Theory

NASA Astrophysics Data System (ADS)

Sanchez-Sesma, F. J.; Perton, M.; Molina Villegas, J. C.

2015-12-01

The analytical solution for the dynamic response of an elastic half-space for a normal point load at the free surface is due to Lamb (1904). For a tangential force, we have Chaós (1960) formulae. For an arbitrary load at any depth within a stratified elastic half space, the resulting elastic field can be given in the same fashion, by using an integral representation in the radial wavenumber domain. Typically, computations use discrete wave number (DWN) formalism and Fourier analysis allows for solution in space and time domain. Experimentally, these elastic Greeńs functions might be retrieved from ambient vibrations correlations when assuming a diffuse field. In fact, the field could not be totally diffuse and only parts of the Green's functions, associated to surface or body waves, are retrieved. In this communication, we explore the computation of Green functions for a layered media on top of a half-space using a set of equipartitioned elastic plane waves. Our formalism includes body and surface waves (Rayleigh and Love waves). These latter waves correspond to the classical representations in terms of normal modes in the asymptotic case of large separation distance between source and receiver. This approach allows computing Green's functions faster than DWN and separating the surface and body wave contributions in order to better represent Green's function experimentally retrieved.

Noise Equalization for Ultrafast Plane Wave Microvessel Imaging.

PubMed

Song, Pengfei; Manduca, Armando; Trzasko, Joshua D; Chen, Shigao

2017-11-01

Ultrafast plane wave microvessel imaging significantly improves ultrasound Doppler sensitivity by increasing the number of Doppler ensembles that can be collected within a short period of time. The rich spatiotemporal plane wave data also enable more robust clutter filtering based on singular value decomposition. However, due to the lack of transmit focusing, plane wave microvessel imaging is very susceptible to noise. This paper was designed to: 1) study the relationship between ultrasound system noise (primarily time gain compensation induced) and microvessel blood flow signal and 2) propose an adaptive and computationally cost-effective noise equalization method that is independent of hardware or software imaging settings to improve microvessel image quality.

Effect of pressurization on helical guided wave energy velocity in fluid-filled pipes.

PubMed

Dubuc, Brennan; Ebrahimkhanlou, Arvin; Salamone, Salvatore

2017-03-01

The effect of pressurization stresses on helical guided waves in a thin-walled fluid-filled pipe is studied by modeling leaky Lamb waves in a stressed plate bordered by fluid. Fluid pressurization produces hoop and longitudinal stresses in a thin-walled pipe, which corresponds to biaxial in-plane stress in a plate waveguide model. The effect of stress on guided wave propagation is accounted for through nonlinear elasticity and finite deformation theory. Emphasis is placed on the stress dependence of the energy velocity of the guided wave modes. For this purpose, an expression for the energy velocity of leaky Lamb waves in a stressed plate is derived. Theoretical results are presented for the mode, frequency, and directional dependent variations in energy velocity with respect to stress. An experimental setup is designed for measuring variations in helical wave energy velocity in a thin-walled water-filled steel pipe at different levels of pressure. Good agreement is achieved between the experimental variations in energy velocity for the helical guided waves and the theoretical leaky Lamb wave solutions. Copyright © 2016 Elsevier B.V. All rights reserved.

Exact simulation of polarized light reflectance by particle deposits

NASA Astrophysics Data System (ADS)

Ramezan Pour, B.; Mackowski, D. W.

2015-12-01

The use of polarimetric light reflection measurements as a means of identifying the physical and chemical characteristics of particulate materials obviously relies on an accurate model of predicting the effects of particle size, shape, concentration, and refractive index on polarized reflection. The research examines two methods for prediction of reflection from plane parallel layers of wavelength—sized particles. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a deposit of spherical particles that are exposed to a plane incident wave. We use a FORTRAN-90 implementation of this solution (the Multiple Sphere T Matrix (MSTM) code), coupled with parallel computational platforms, to directly simulate the reflection from particle layers. The second method examined is based upon the vector radiative transport equation (RTE). Mie theory is used in our RTE model to predict the extinction coefficient, albedo, and scattering phase function of the particles, and the solution of the RTE is obtained from adding—doubling method applied to a plane—parallel configuration. Our results show that the MSTM and RTE predictions of the Mueller matrix elements converge when particle volume fraction in the particle layer decreases below around five percent. At higher volume fractions the RTE can yield results that, depending on the particle size and refractive index, significantly depart from the exact predictions. The particle regimes which lead to dependent scattering effects, and the application of methods to correct the vector RTE for particle interaction, will be discussed.

Autonomous motion of metallic microrods propelled by ultrasound.

PubMed

Wang, Wei; Castro, Luz Angelica; Hoyos, Mauricio; Mallouk, Thomas E

2012-07-24

Autonomously moving micro-objects, or micromotors, have attracted the attention of the scientific community over the past decade, but the incompatibility of phoretic motors with solutions of high ionic strength and the use of toxic fuels have limited their applications in biologically relevant media. In this letter we demonstrate that ultrasonic standing waves in the MHz frequency range can levitate, propel, rotate, align, and assemble metallic microrods (2 μm long and 330 nm diameter) in water as well as in solutions of high ionic strength. Metallic rods levitated to the midpoint plane of a cylindrical cell when the ultrasonic frequency was tuned to create a vertical standing wave. Fast axial motion of metallic microrods at ~200 μm/s was observed at the resonant frequency using continuous or pulsed ultrasound. Segmented metal rods (AuRu or AuPt) were propelled unidirectionally with one end (Ru or Pt, respectively) consistently forward. A self-acoustophoresis mechanism based on the shape asymmetry of the metallic rods is proposed to explain this axial propulsion. Metallic rods also aligned and self-assembled into long spinning chains, which in the case of bimetallic rods had a head-to-tail alternating structure. These chains formed ring or streak patterns in the levitation plane. The diameter or distance between streaks was roughly half the wavelength of the ultrasonic excitation. The ultrasonically driven movement of metallic rods was insensitive to the addition of salt to the solution, opening the possibility of driving and controlling metallic micromotors in biologically relevant media using ultrasound.

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, Arnold D.

2012-01-01

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation. PMID:22435102

Features of sound propagation through and stability of a finite shear layer

NASA Technical Reports Server (NTRS)

Koutsoyannis, S. P.

1976-01-01

The plane wave propagation, the stability and the rectangular duct mode problems of a compressible inviscid linearly sheared parallel, but otherwise homogeneous flow, are shown to be governed by Whittaker's equation. The exact solutions for the perturbation quantities are essentially Whittaker M-functions. A number of known results are obtained as limiting cases of exact solutions. For the compressible finite thickness shear layer it is shown that no resonances and no critical angles exist for all Mach numbers, frequencies and shear layer velocity profile slopes except in the singular case of the vortex sheet.

Comment on "the one dimensional acoustic field with arbitrary mean axial temperature gradient and mean flow" (J.Li and A.S.Morgans, Journal of Sound and Vibration 400 (2017) 248-269)

NASA Astrophysics Data System (ADS)

Dokumaci, Erkan

2017-12-01

In a recent study, Li and Morgans [1] present an ingenious WKB approximation for the acoustic plane wave field in a straight uniform duct with mean temperature gradient and mean flow. The authors state that the previous solutions are limited to small linear mean temperature gradients and low mean flow Mach numbers and claim that their solution applies for arbitrary mean temperature profiles and moderate-to-large mean flow velocity Mach numbers at both low and high frequencies.

Multiparticle Solutions in 2+1 Gravity and Time Machines

NASA Astrophysics Data System (ADS)

Steif, Alan R.

Multiparticle solutions for sources moving at the speed of light and corresponding to superpositions of single-particle plane-wave solutions are constructed in 2+1 gravity. It is shown that the two-particle spacetimes admit closed timelike curves provided the center-of-momentum energy exceeds a certain critical value. This occurs, however, at the cost of unphysical boundary conditions which are analogous to those affecting Gott’s time machine. As the energy exceeds the critical value, the closed timelike curves first occur at spatial infinity, then migrate inward as the energy is further increased. The total mass of the system also becomes imaginary for particle energies greater than the critical value.

Darcy Flow in a Wavy Channel Filled with a Porous Medium

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

Gray, Donald D; Ogretim, Egemen; Bromhal, Grant S

2013-05-17

Flow in channels bounded by wavy or corrugated walls is of interest in both technological and geological contexts. This paper presents an analytical solution for the steady Darcy flow of an incompressible fluid through a homogeneous, isotropic porous medium filling a channel bounded by symmetric wavy walls. This packed channel may represent an idealized packed fracture, a situation which is of interest as a potential pathway for the leakage of carbon dioxide from a geological sequestration site. The channel walls change from parallel planes, to small amplitude sine waves, to large amplitude nonsinusoidal waves as certain parameters are increased. Themore » direction of gravity is arbitrary. A plot of piezometric head against distance in the direction of mean flow changes from a straight line for parallel planes to a series of steeply sloping sections in the reaches of small aperture alternating with nearly constant sections in the large aperture bulges. Expressions are given for the stream function, specific discharge, piezometric head, and pressure.« less

Shutterless solution for simultaneous focal plane array temperature estimation and nonuniformity correction in uncooled long-wave infrared camera.

PubMed

Cao, Yanpeng; Tisse, Christel-Loic

2013-09-01

In uncooled long-wave infrared (LWIR) microbolometer imaging systems, temperature fluctuations of the focal plane array (FPA) result in thermal drift and spatial nonuniformity. In this paper, we present a novel approach based on single-image processing to simultaneously estimate temperature variances of FPAs and compensate the resulting temperature-dependent nonuniformity. Through well-controlled thermal calibrations, empirical behavioral models are derived to characterize the relationship between the responses of microbolometer and FPA temperature variations. Then, under the assumption that strong dependency exists between spatially adjacent pixels, we estimate the optimal FPA temperature so as to minimize the global intensity variance across the entire thermal infrared image. We make use of the estimated FPA temperature to infer an appropriate nonuniformity correction (NUC) profile. The performance and robustness of the proposed temperature-adaptive NUC method are evaluated on realistic IR images obtained by a 640 × 512 pixels uncooled LWIR microbolometer imaging system operating in a significantly changed temperature environment.

Analysis of fluid-structure interaction in a frame pipe undergoing plastic deformations

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

Khamlichi, A.; Jezequel, L.; Jacques, Y.

1995-11-01

Water hammer pressure waves of sufficiently large magnitude can cause plastic flexural deformations in a frame pipe. In this study, the authors propose a modelization of this problem based on plane wave approximation for the fluid equations and approximation of the structure motion by a single-degree-of-freedom elastic-plastic oscillator. Direct analytical integration of elastic-plastic equations through pipe sections, then over the pipe length is performed in order to identify the oscillator parameters. Comparison of the global load-displacement relationship obtained with the finite element solution was considered and has shown good agreement. Fluid-structure coupling is achieved by assuming elbows to act likemore » plane monopole sources, where localized jumps of fluid velocity occur and where net pressure forces are exerted on the structure. The authors have applied this method to analyze the fluid-structure interaction in this range of deformations. Energy exchange between the fluid and the structure and energy dissipation are quantified.« less

Performance modeling of terahertz (THz) and millimeter waves (mmW) pupil plane imaging

NASA Astrophysics Data System (ADS)

Mohammadian, Nafiseh; Furxhi, Orges; Zhang, Lei; Offermans, Peter; Ghazi, Galia; Driggers, Ronald

2018-05-01

Terahertz- (THz) and millimeter-wave sensors are becoming more important in industrial, security, medical, and defense applications. A major problem in these sensing areas is the resolution, sensitivity, and visual acuity of the imaging systems. There are different fundamental parameters in designing a system that have significant effects on the imaging performance. The performance of THz systems can be discussed in terms of two characteristics: sensitivity and spatial resolution. New approaches for design and manufacturing of THz imagers are a vital basis for developing future applications. Photonics solutions have been at the technological forefront in THz band applications. A single scan antenna does not provide reasonable resolution, sensitivity, and speed. An effective approach to imaging is placing a high-performance antenna in a two-dimensional antenna array to achieve higher radiation efficiency and higher resolution in the imaging systems. Here, we present the performance modeling of a pupil plane imaging system to find the resolution and sensitivity efficiency of the imaging system.

Connection between in-plane upper critical field Hc 2 and gap symmetry in layered d -wave superconductors

NASA Astrophysics Data System (ADS)

Wang, Jing-Rong; Liu, Guo-Zhu; Zhang, Chang-Jin

2016-07-01

Angle-resolved upper critical field Hc 2 provides an efficient tool to probe the gap symmetry of unconventional superconductors. We revisit the behavior of in-plane Hc 2 in d -wave superconductors by considering both the orbital effect and Pauli paramagnetic effect. After carrying out systematic analysis, we show that the maxima of Hc 2 could be along either nodal or antinodal directions of a d -wave superconducting gap, depending on the specific values of a number of tuning parameters. This behavior is in contrast to the common belief that the maxima of in-plane Hc 2 are along the direction where the superconducting gap takes its maximal value. Therefore, identifying the precise d -wave gap symmetry through fitting experiments results of angle-resolved Hc 2 with model calculations at a fixed temperature, as widely used in previous studies, is difficult and practically unreliable. However, our extensive analysis of angle-resolved Hc 2 show that there is a critical temperature T*: in-plane Hc 2 exhibits its maxima along nodal directions at T

Perturbations of the seismic reflectivity of a fluid-saturated depth-dependent poroelastic medium.

PubMed

de Barros, Louis; Dietrich, Michel

2008-03-01

Analytical formulas are derived to compute the first-order effects produced by plane inhomogeneities on the point source seismic response of a fluid-filled stratified porous medium. The derivation is achieved by a perturbation analysis of the poroelastic wave equations in the plane-wave domain using the Born approximation. This approach yields the Frechet derivatives of the P-SV- and SH-wave responses in terms of the Green's functions of the unperturbed medium. The accuracy and stability of the derived operators are checked by comparing, in the time-distance domain, differential seismograms computed from these analytical expressions with complete solutions obtained by introducing discrete perturbations into the model properties. For vertical and horizontal point forces, it is found that the Frechet derivative approach is remarkably accurate for small and localized perturbations of the medium properties which are consistent with the Born approximation requirements. Furthermore, the first-order formulation appears to be stable at all source-receiver offsets. The porosity, consolidation parameter, solid density, and mineral shear modulus emerge as the most sensitive parameters in forward and inverse modeling problems. Finally, the amplitude-versus-angle response of a thin layer shows strong coupling effects between several model parameters.

Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance

NASA Technical Reports Server (NTRS)

Hwang, Y. M.

1974-01-01

The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.

Conformal mapping for the Helmholtz equation: acoustic wave scattering by a two dimensional inclusion with irregular shape in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala G; Khoo, Boo Cheong; Han, Feng; Liu, Dian Kui

2012-02-01

The complex variables method with mapping function was extended to solve the linear acoustic wave scattering by an inclusion with sharp/smooth corners in an infinite ideal fluid domain. The improved solutions of Helmholtz equation, shown as Bessel function with mapping function as the argument and fractional order Bessel function, were analytically obtained. Based on the mapping function, the initial geometry as well as the original physical vector can be transformed into the corresponding expressions inside the mapping plane. As all the physical vectors are calculated in the mapping plane (η,η), this method can lead to potential vast savings of computational resources and memory. In this work, the results are validated against several published works in the literature. The different geometries of the inclusion with sharp corners based on the proposed mapping functions for irregular polygons are studied and discussed. The findings show that the variation of angles and frequencies of the incident waves have significant influence on the bistatic scattering pattern and the far-field form factor for the pressure in the fluid. © 2012 Acoustical Society of America

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.

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

Stoynov, Y.; Dineva, P.

The stress, magnetic and electric field analysis of multifunctional composites, weakened by impermeable cracks, is of fundamental importance for their structural integrity and reliable service performance. The aim is to study dynamic behavior of a plane of functionally graded magnetoelectroelastic composite with more than one crack. The coupled material properties vary exponentially in an arbitrary direction. The plane is subjected to anti-plane mechanical and in-plane electric and magnetic load. The boundary value problem described by the partial differential equations with variable coefficients is reduced to a non-hypersingular traction boundary integral equation based on the appropriate functional transform and frequency-dependent fundamentalmore » solution derived in a closed form by Radon transform. Software code based on the boundary integral equation method (BIEM) is developed, validated and inserted in numerical simulations. The obtained results show the sensitivity of the dynamic stress, magnetic and electric field concentration in the cracked plane to the type and characteristics of the dynamic load, to the location and cracks disposition, to the wave-crack-crack interactions and to the magnitude and direction of the material gradient.« less

New knotted solutions of Maxwell's equations

NASA Astrophysics Data System (ADS)

Hoyos, Carlos; Sircar, Nilanjan; Sonnenschein, Jacob

2015-06-01

In this paper we have further developed the study of topologically non-trivial solutions of vacuum electrodynamics. We have discovered a novel method of generating such solutions by applying conformal transformations with complex parameters on known solutions expressed in terms of Bateman's variables. This has enabled us to obtain a wide class of solutions from the basic configuration, such as constant electromagnetic fields and plane-waves. We have introduced a covariant formulation of Bateman's construction and discussed the conserved charges associated with the conformal group as well as a set of four types of conserved helicities. We have also given a formulation in terms of quaternions. This led to a simple map between the electromagnetic knotted and linked solutions into flat connections of SU(2) gauge theory. We have computed the corresponding Chern-Simons charge in a class of solutions and the charge takes integer values.

Electromagnetic fields radiated from a lightning return stroke - Application of an exact solution to Maxwell's equations

NASA Technical Reports Server (NTRS)

Le Vine, D. M.; Meneghini, R.

1978-01-01

A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.

Letters: Noise Equalization for Ultrafast Plane Wave Microvessel Imaging

PubMed Central

Song, Pengfei; Manduca, Armando; Trzasko, Joshua D.

2017-01-01

Ultrafast plane wave microvessel imaging significantly improves ultrasound Doppler sensitivity by increasing the number of Doppler ensembles that can be collected within a short period of time. The rich spatiotemporal plane wave data also enables more robust clutter filtering based on singular value decomposition (SVD). However, due to the lack of transmit focusing, plane wave microvessel imaging is very susceptible to noise. This study was designed to: 1) study the relationship between ultrasound system noise (primarily time gain compensation-induced) and microvessel blood flow signal; 2) propose an adaptive and computationally cost-effective noise equalization method that is independent of hardware or software imaging settings to improve microvessel image quality. PMID:28880169

Correlated scattering states of N-body Coulomb systems

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

Berakdar, J.

1997-03-01

For N charged particles of equal masses moving in the field of a heavy residual charge, an approximate analytical solution of the many-body time-independent Schr{umlt o}dinger equation is derived at a total energy above the complete fragmentation threshold. All continuum particles are treated on equal footing. The proposed correlated wave function represents, to leading order, an exact solution of the many-body Schr{umlt o}dinger equation in the asymptotic region defined by large interparticle separations. Thus, in this asymptotic region the N-body Coulomb modifications to the plane-wave motion of free particles are rigorously estimated. It is shown that the Kato cusp conditionsmore » are satisfied by the derived wave function at all two-body coalescence points. An expression of the normalization of this wave function is also given. To render possible the calculations of scattering amplitudes for transitions leading to a four-body scattering state, an effective-charge method is suggested in which the correlations between the continuum particles are completely subsumed into effective interactions with the residual charge. Analytical expressions for these effective interactions are derived and discussed for physical situations. {copyright} {ital 1997} {ital The American Physical Society}« less

Numerical Modeling of Poroelastic-Fluid Systems Using High-Resolution Finite Volume Methods

NASA Astrophysics Data System (ADS)

Lemoine, Grady

Poroelasticity theory models the mechanics of porous, fluid-saturated, deformable solids. It was originally developed by Maurice Biot to model geophysical problems, such as seismic waves in oil reservoirs, but has also been applied to modeling living bone and other porous media. Poroelastic media often interact with fluids, such as in ocean bottom acoustics or propagation of waves from soft tissue into bone. This thesis describes the development and testing of high-resolution finite volume numerical methods, and simulation codes implementing these methods, for modeling systems of poroelastic media and fluids in two and three dimensions. These methods operate on both rectilinear grids and logically rectangular mapped grids. To allow the use of these methods, Biot's equations of poroelasticity are formulated as a first-order hyperbolic system with a source term; this source term is incorporated using operator splitting. Some modifications are required to the classical high-resolution finite volume method. Obtaining correct solutions at interfaces between poroelastic media and fluids requires a novel transverse propagation scheme and the removal of the classical second-order correction term at the interface, and in three dimensions a new wave limiting algorithm is also needed to correctly limit shear waves. The accuracy and convergence rates of the methods of this thesis are examined for a variety of analytical solutions, including simple plane waves, reflection and transmission of waves at an interface between different media, and scattering of acoustic waves by a poroelastic cylinder. Solutions are also computed for a variety of test problems from the computational poroelasticity literature, as well as some original test problems designed to mimic possible applications for the simulation code.

Generalized thermoelastic diffusive waves in heat conducting materials

NASA Astrophysics Data System (ADS)

Sharma, J. N.

2007-04-01

Keeping in view the applications of diffusion processes in geophysics and electronics industry, the aim of the present paper is to give a detail account of the plane harmonic generalized thermoelastic diffusive waves in heat conducting solids. According to the characteristic equation, three longitudinal waves namely, elastodiffusive (ED), mass diffusion (MD-mode) and thermodiffusive (TD-mode), can propagate in such solids in addition to transverse waves. The transverse waves get decoupled from rest of the fields and hence remain unaffected due to temperature change and mass diffusion effects. These waves travel without attenuation and dispersion. The other generalized thermoelastic diffusive waves are significantly influenced by the interacting fields and hence suffer both attenuation and dispersion. At low frequency mass diffusion and thermal waves do not exist but at high-frequency limits these waves propagate with infinite velocity being diffusive in character. Moreover, in the low-frequency regions, the disturbance is mainly dominant by mechanical process of transportation of energy and at high-frequency regions it is significantly dominated by a close to diffusive process (heat conduction or mass diffusion). Therefore, at low-frequency limits the waves like modes are identifiable with small amplitude waves in elastic materials that do not conduct heat. The general complex characteristic equation is solved by using irreducible case of Cardano's method with the help of DeMoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation of various modes. The propagation of waves in case of non-heat conducting solids is also discussed. Finally, the numerical solution is carried out for copper (solvent) and zinc (solute) materials and the obtained phase velocities, attenuation coefficients and specific loss factor of various thermoelastic diffusive waves are presented graphically.

Optimized norm-conserving Hartree-Fock pseudopotentials for plane-wave calculations

NASA Astrophysics Data System (ADS)

Al-Saidi, W. A.; Walter, E. J.; Rappe, A. M.

2008-02-01

We report Hartree-Fock (HF)-based pseudopotentials suitable for plane-wave calculations. Unlike typical effective core potentials, the present pseudopotentials are finite at the origin and exhibit rapid convergence in a plane-wave basis; the optimized pseudopotential method [A. M. Rappe , Phys. Rev. B 41, 1227 (1990)] improves plane-wave convergence. Norm-conserving HF pseudopotentials are found to develop long-range non-Coulombic behavior which does not decay faster than 1/r , and is nonlocal. This behavior, which stems from the nonlocality of the exchange potential, is remedied using a recently developed self-consistent procedure [J. R. Trail and R. J. Needs, J. Chem. Phys. 122, 014112 (2005)]. The resulting pseudopotentials slightly violate the norm conservation of the core charge. We calculated several atomic properties using these pseudopotentials, and the results are in good agreement with all-electron HF values. The dissociation energies, equilibrium bond lengths, and frequencies of vibration of several dimers obtained with these HF pseudopotentials and plane waves are also in good agreement with all-electron results.

Highly precise acoustic calibration method of ring-shaped ultrasound transducer array for plane-wave-based ultrasound tomography

NASA Astrophysics Data System (ADS)

Terada, Takahide; Yamanaka, Kazuhiro; Suzuki, Atsuro; Tsubota, Yushi; Wu, Wenjing; Kawabata, Ken-ichi

2017-07-01

Ultrasound computed tomography (USCT) is promising for a non-invasive, painless, operator-independent and quantitative system for breast-cancer screening. Assembly error, production tolerance, and aging-degradation variations of the hardwire components, particularly of plane-wave-based USCT systems, may hamper cost effectiveness, precise imaging, and robust operation. The plane wave is transmitted from a ring-shaped transducer array for receiving the signal at a high signal-to-noise-ratio and fast aperture synthesis. There are four signal-delay components: response delays in the transmitters and receivers and propagation delays depending on the positions of the transducer elements and their directivity. We developed a highly precise calibration method for calibrating these delay components and evaluated it with our prototype plane-wave-based USCT system. Our calibration method was found to be effective in reducing delay errors. Gaps and curves were eliminated from the plane wave, and echo images of wires were sharpened in the entire imaging area.

Grating tuned unstable resonator laser cavity

DOEpatents

Johnson, Larry C.

1982-01-01

An unstable resonator to be used in high power, narrow line CO.sub.2 pump lasers comprises an array of four reflectors in a ring configuration wherein spherical and planar wavefronts are separated from each other along separate optical paths and only the planar wavefronts are impinged on a plane grating for line tuning. The reflector array comprises a concave mirror for reflecting incident spherical waves as plane waves along an output axis to form an output beam. A plane grating on the output axis is oriented to reflect a portion of the output beam off axis onto a planar relay mirror spaced apart from the output axis in proximity to the concave mirror. The relay mirror reflects plane waves from the grating to impinge on a convex expanding mirror spaced apart from the output axis in proximity to the grating. The expanding mirror reflects the incident planar waves as spherical waves to illuminate the concave mirror. Tuning is provided by rotating the plane grating about an axis normal to the output axis.

A perfect Fresnel acoustic reflector implemented by a Fano-resonant metascreen

NASA Astrophysics Data System (ADS)

Amin, M.; Siddiqui, O.; Farhat, M.; Khelif, A.

2018-04-01

We propose a perfectly reflecting acoustic metasurface which is designed by replacing the curved segments of the traditional Fresnel reflector by flat Fano-resonant sub-wavelength unit cells. To preserve the original Fresnel focusing mechanism, the unit cell phase follows a specific phase profile which is obtained by applying the generalized Snell's law and Fermat's principle. The reflected curved phase fronts are thus created at the air-metasurface boundary by tailoring the metasurface dispersion as dictated by Huygens' principle. Since the unit cells are implemented by sub-wavelength double slit-shaped cavity resonators, the impinging sound waves are perfectly reflected producing acoustic focusing with negligible absorption. We use plane-wave solution and full-wave simulations to demonstrate the focusing effects. The simulation results closely follow the analytical predictions.

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

PubMed

Cao, Yanpeng; Tisse, Christel-Loic

2014-02-01

In this Letter, we propose an efficient and accurate solution to remove temperature-dependent nonuniformity effects introduced by the imaging optics. This single-image-based approach computes optics-related fixed pattern noise (FPN) by fitting the derivatives of correction model to the gradient components, locally computed on an infrared image. A modified bilateral filtering algorithm is applied to local pixel output variations, so that the refined gradients are most likely caused by the nonuniformity associated with optics. The estimated bias field is subtracted from the raw infrared imagery to compensate the intensity variations caused by optics. The proposed method is fundamentally different from the existing nonuniformity correction (NUC) techniques developed for focal plane arrays (FPAs) and provides an essential image processing functionality to achieve completely shutterless NUC for uncooled long-wave infrared (LWIR) imaging systems.

Pulse generation scheme for flying electromagnetic doughnuts

NASA Astrophysics Data System (ADS)

Papasimakis, Nikitas; Raybould, Tim; Fedotov, Vassili A.; Tsai, Din Ping; Youngs, Ian; Zheludev, Nikolay I.

2018-05-01

Transverse electromagnetic plane waves are fundamental solutions of Maxwells equations. It is less known that a radically different type of solutions has been described theoretically, but has never been realized experimentally, that exist only in the form of short bursts of electromagnetic energy propagating in free space at the speed of light. They are distinguished from transverse waves by a doughnutlike configuration of electric and magnetic fields with a strong field component along the propagation direction. Here, we demonstrate numerically that such flying doughnuts can be generated from conventional pulses using a singular metamaterial converter designed to manipulate both the spatial and spectral structure of the input pulse. The ability to generate flying doughnuts is of fundamental interest, as they shall interact with matter in unique ways, including nontrivial field transformations upon reflection from interfaces and the excitation of toroidal response and anapole modes in matter, hence offering opportunities for telecommunications, sensing, and spectroscopy.

Higher Order Bases in a 2D Hybrid BEM/FEM Formulation

NASA Technical Reports Server (NTRS)

Fink, Patrick W.; Wilton, Donald R.

2002-01-01

The advantages of using higher order, interpolatory basis functions are examined in the analysis of transverse electric (TE) plane wave scattering by homogeneous, dielectric cylinders. A boundary-element/finite-element (BEM/FEM) hybrid formulation is employed in which the interior dielectric region is modeled with the vector Helmholtz equation, and a radiation boundary condition is supplied by an Electric Field Integral Equation (EFIE). An efficient method of handling the singular self-term arising in the EFIE is presented. The iterative solution of the partially dense system of equations is obtained using the Quasi-Minimal Residual (QMR) algorithm with an Incomplete LU Threshold (ILUT) preconditioner. Numerical results are shown for the case of an incident wave impinging upon a square dielectric cylinder. The convergence of the solution is shown versus the number of unknowns as a function of the completeness order of the basis functions.

Scattering of acoustic evanescent waves by circular cylinders: Partial wave series solution

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2002-05-01

Evanescent acoustical waves occur in a variety of situations such as when sound is incident on a fluid interface beyond the critical angle and when flexural waves on a plate are subsonic with respect to the surrounding fluid. The scattering by circular cylinders at normal incidence was calculated to give insight into the consequences on the scattering of the evanescence of the incident wave. To analyze the scattering, it is necessary to express the incident wave using a modified expansion involving cylindrical functions. For plane evanescent waves, the expansion becomes a double summation with products of modified and ordinary Bessel functions. The resulting modified series is found for the scattering by a fluid cylinder in an unbounded medium. The perfectly soft and rigid cases are also examined. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on the transverse coordinate. The associated exponential dependence of the scattering on the location of a scatterer was previously demonstrated [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].

On a method computing transient wave propagation in ionospheric regions

NASA Technical Reports Server (NTRS)

Gray, K. G.; Bowhill, S. A.

1978-01-01

A consequence of an exoatmospheric nuclear burst is an electromagnetic pulse (EMP) radiated from it. In a region far enough away from the burst, where nonlinear effects can be ignored, the EMP can be represented by a large-amplitude narrow-time-width plane-wave pulse. If the ionosphere intervenes the origin and destination of the EMP, frequency dispersion can cause significant changes in the original pulse upon reception. A method of computing these dispersive effects of transient wave propagation is summarized. The method described is different from the standard transform techniques and provides physical insight into the transient wave process. The method, although exact, can be used in approximating the early-time transient response of an ionospheric region by a simple integration with only explicit knowledge of the electron density, electron collision frequency, and electron gyrofrequency required. As an illustration of the method, it is applied to a simple example and contrasted with the corresponding transform solution.

Electromagnetic resonances of plasma column between two metallic plates

NASA Astrophysics Data System (ADS)

Dvinin, Sergey; Dovzhenko, Vitaly; Sinkevich, Oleg

2015-09-01

It is known that there are two types of electrodynamic resonances of bounded supercritical plasma, placed between the two metal planes are possible. The first type is associated with the excitation of surface waves propagating along the lateral surface. The second one is caused by standing surface waves in the sheath at plasma-metal boundary. This work is concerned with theoretical study of the resonance properties of plasma slab in cases where both effects can be observed together. Resonance densities and frequencies are calculated. Solution of Maxwell's equations is demonstrated that directions of energy flows in first and second cases are opposite. Energy transfer to lateral surface waves is prevailing, if the field frequency is higher than the frequency, corresponding to the geometric plasma-sheath resonance. Amplitude of waves at plasma metal boundary becomes greater in opposite case. Discharge properties in both cases are calculated including joint excitation.

Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics

NASA Technical Reports Server (NTRS)

Roe, P. L.

1984-01-01

A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries.

Theory of free electron vortices

PubMed Central

Schattschneider, P.; Verbeeck, J.

2011-01-01

The recent creation of electron vortex beams and their first practical application motivates a better understanding of their properties. Here, we develop the theory of free electron vortices with quantized angular momentum, based on solutions of the Schrödinger equation for cylindrical boundary conditions. The principle of transformation of a plane wave into vortices with quantized angular momentum, their paraxial propagation through round magnetic lenses, and the effect of partial coherence are discussed. PMID:21930017

40 MHz high-frequency ultrafast ultrasound imaging.

PubMed

Huang, Chih-Chung; Chen, Pei-Yu; Peng, Po-Hsun; Lee, Po-Yang

2017-06-01

Ultrafast high-frame-rate ultrasound imaging based on coherent-plane-wave compounding has been developed for many biomedical applications. Most coherent-plane-wave compounding systems typically operate at 3-15 MHz, and the image resolution for this frequency range is not sufficient for visualizing microstructure tissues. Therefore, the purpose of this study was to implement a high-frequency ultrafast ultrasound imaging operating at 40 MHz. The plane-wave compounding imaging and conventional multifocus B-mode imaging were performed using the Field II toolbox of MATLAB in simulation study. In experiments, plane-wave compounding images were obtained from a 256 channel ultrasound research platform with a 40 MHz array transducer. All images were produced by point-spread functions and cyst phantoms. The in vivo experiment was performed from zebrafish. Since high-frequency ultrasound exhibits a lower penetration, chirp excitation was applied to increase the imaging depth in simulation. The simulation results showed that a lateral resolution of up to 66.93 μm and a contrast of up to 56.41 dB were achieved when using 75-angles plane waves in compounding imaging. The experimental results showed that a lateral resolution of up to 74.83 μm and a contrast of up to 44.62 dB were achieved when using 75-angles plane waves in compounding imaging. The dead zone and compounding noise are about 1.2 mm and 2.0 mm in depth for experimental compounding imaging, respectively. The structure of zebrafish heart was observed clearly using plane-wave compounding imaging. The use of fewer than 23 angles for compounding allowed a frame rate higher than 1000 frames per second. However, the compounding imaging exhibits a similar lateral resolution of about 72 μm as the angle of plane wave is higher than 10 angles. This study shows the highest operational frequency for ultrafast high-frame-rate ultrasound imaging. © 2017 American Association of Physicists in Medicine.

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.

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 5: Propagation of propeller tone noise through a fuselage boundary layer

NASA Technical Reports Server (NTRS)

Magliozzi, B.; Hanson, D. B.

1991-01-01

An analysis of tone noise propagation through a boundary layer and fuselage scattering effects was derived. This analysis is a three dimensional and the complete wave field is solved by matching analytical expressions for the incident and scattered waves in the outer flow to a numerical solution in the boundary layer flow. The outer wave field is constructed analytically from an incident wave appropriate to the source and a scattered wave in the standard Hankel function form. For the incident wave, an existing function - domain propeller noise radiation theory is used. In the boundary layer region, the wave equation is solved by numerical methods. The theoretical analysis is embodied in a computer program which allows the calculation of correction factors for the fuselage scattering and boundary layer refraction effects. The effects are dependent on boundary layer profile, flight speed, and frequency. Corrections can be derived for any point on the fuselage, including those on the opposite side from the source. The theory was verified using limited cases and by comparing calculations with available measurements from JetStar tests of model prop-fans. For the JetStar model scale, the boundary layer refraction effects produce moderate fuselage pressure reinforcements aft of and near the plane of rotation and significant attenuation forward of the plane of rotation at high flight speeds. At lower flight speeds, the calculated boundary layer effects result in moderate amplification over the fuselage area of interest. Apparent amplification forward of the plane of rotation is a result of effective changes in the source directivity due to boundary layer refraction effects. Full scale effects are calculated to be moderate, providing fuselage pressure amplification of about 5 dB at the peak noise location. Evaluation using available noise measurements was made under high-speed, high-altitude flight conditions. Comparisons of calculations made of free field noise, using a current frequency-domain propeller noise prediction method, and fuselage effects using this new procedure show good agreement with fuselage measurements over a wide range of flight speeds and frequencies. Correction factors for the JetStar measurements made on the fuselage are provided in an Appendix.

Maximal amplitudes of finite-gap solutions for the focusing Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Bertola, M.; Tovbis, A.

2017-09-01

Finite-gap (algebro-geometric) solutions to the focusing Nonlinear Schrödinger Equation (fNLS) i ψ_t + ψ_{xx} + 2|ψ|^2ψ=0, are quasi-periodic solutions that represent nonlinear multi-phase waves. In general, a finite-gap solution for (0-1) is defined by a collection of Schwarz symmetrical spectral bands and of real constants (initial phases), associated with the corresponding bands. In this paper we prove an interesting new formula for the maximal amplitude of a finite-gap solution to the focusing Nonlinear Schrödinger equation with given spectral bands: the amplitude does not exceed the sum of the imaginary parts of all the endpoints in the upper half plane. In the case of the straight vertical bands, that amounts to the half of the sum of the length of all the bands. The maximal amplitude will be attained for certain choices of the initial phases. This result is an important part of a criterion for the potential presence of the rogue waves in finite-gap solutions with a given set of spectral endpoints, obtained in Bertola et al. (Proc R Soc A, 2016. doi: 10.1098/rspa.2016.0340). A similar result was also obtained for the defocusing Nonlinear Schrödinger equation.

Moment tensor solutions estimated using optimal filter theory for 51 selected earthquakes, 1980-1984

USGS Publications Warehouse

Sipkin, S.A.

1987-01-01

The 51 global events that occurred from January 1980 to March 1984, which were chosen by the convenors of the Symposium on Seismological Theory and Practice, have been analyzed using a moment tensor inversion algorithm (Sipkin). Many of the events were routinely analyzed as part of the National Earthquake Information Center's (NEIC) efforts to publish moment tensor and first-motion fault-plane solutions for all moderate- to large-sized (mb>5.7) earthquakes. In routine use only long-period P-waves are used and the source-time function is constrained to be a step-function at the source (??-function in the far-field). Four of the events were of special interest, and long-period P, SH-wave solutions were obtained. For three of these events, an unconstrained inversion was performed. The resulting time-dependent solutions indicated that, for many cases, departures of the solutions from pure double-couples are caused by source complexity that has not been adequately modeled. These solutions also indicate that source complexity of moderate-sized events can be determined from long-period data. Finally, for one of the events of special interest, an inversion of the broadband P-waveforms was also performed, demonstrating the potential for using broadband waveform data in inversion procedures. ?? 1987.

Analysis of THG modes for femtosecond laser pulse

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Sidorov, Pavel S.

2017-05-01

THG is used nowadays in many practical applications such as a substance diagnostics, and biological objects imaging, and etc. With developing of new materials and technology (for example, photonic crystal) an attention to THG process analysis grow. Therefore, THG features understanding are a modern problem. Early we have developed new analytical approach based on using the problem invariant for analytical solution construction of the THG process. It should be stressed that we did not use a basic wave non-depletion approximation. Nevertheless, a long pulse duration approximation and plane wave approximation has applied. The analytical solution demonstrates, in particular, an optical bistability property (and may other regimes of frequency tripling) for the third harmonic generation process. But, obviously, this approach does not reflect an influence of a medium dispersion on the frequency tripling. Therefore, in this paper we analyze THG efficiency of a femtosecond laser pulse taking into account a second order dispersion affect as well as self- and crossmodulation of the interacting waves affect on the frequency conversion process. Analysis is made using a computer simulation on the base of Schrödinger equations describing the process under consideration.

Experimental Study on Ultrasonic Computed Tomography Using Transducers Arrayed on the Internal Surface of a Cylinder

NASA Astrophysics Data System (ADS)

Kim, Jung-Soon; Kim, Moo-Joon; Kim, Jung-Ho; Ha, Kang-Lyeol

2005-06-01

In this study, ultrasonic array transducers with 32 vibrators arranged on the internal surface of a part of a cylinder were fabricated. The vibrators were operated by the piezoelectric transverse effect. By controlling the phase of the input signal for every vibrator, a quasi plane wave was synthesized. Using the fabricated array, inverse scattering ultrasonic computed tomography (UCT) was carried out with a phantom specimen after checking the plane wave generation. It was confirmed that the plane wave was synthesized successfully and a sound velocity image of the phantom was obtained by the plane wave. Consequently, it was noted that the array could be employed as a transmitter and receiver for data acquisition in UCT.

Amplitudes on plane waves from ambitwistor strings

NASA Astrophysics Data System (ADS)

Adamo, Tim; Casali, Eduardo; Mason, Lionel; Nekovar, Stefan

2017-11-01

In marked contrast to conventional string theory, ambitwistor strings remain solvable worldsheet theories when coupled to curved background fields. We use this fact to consider the quantization of ambitwistor strings on plane wave metric and plane wave gauge field backgrounds. In each case, the worldsheet model is anomaly free as a consequence of the background satisfying the field equations. We derive vertex operators (in both fixed and descended picture numbers) for gravitons and gluons on these backgrounds from the worldsheet CFT, and study the 3-point functions of these vertex operators on the Riemann sphere. These worldsheet correlation functions reproduce the known results for 3-point scattering amplitudes of gravitons and gluons in gravitational and gauge theoretic plane wave backgrounds, respectively.

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

Implementation of dispersion-free slow acoustic wave propagation and phase engineering with helical-structured metamaterials

PubMed Central

Zhu, Xuefeng; Li, Kun; Zhang, Peng; Zhu, Jie; Zhang, Jintao; Tian, Chao; Liu, Shengchun

2016-01-01

The ability to slow down wave propagation in materials has attracted significant research interest. A successful solution will give rise to manageable enhanced wave–matter interaction, freewheeling phase engineering and spatial compression of wave signals. The existing methods are typically associated with constructing dispersive materials or structures with local resonators, thus resulting in unavoidable distortion of waveforms. Here we show that, with helical-structured acoustic metamaterials, it is now possible to implement dispersion-free sound deceleration. The helical-structured metamaterials present a non-dispersive high effective refractive index that is tunable through adjusting the helicity of structures, while the wavefront revolution plays a dominant role in reducing the group velocity. Finally, we numerically and experimentally demonstrate that the helical-structured metamaterials with designed inhomogeneous unit cells can turn a normally incident plane wave into a self-accelerating beam on the prescribed parabolic trajectory. The helical-structured metamaterials will have profound impact to applications in explorations of slow wave physics. PMID:27198887

Wave chaos in the elastic disk.

PubMed

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

Fields and coupling between coils embedded in conductive environments

NASA Astrophysics Data System (ADS)

Chu, Son; Vallecchi, Andrea; Stevens, Christopher J.; Shamonina, Ekaterina

2018-02-01

An approximate solution is developed for the mutual inductance of two circular coils enclosed by insulating cavities in a conducting medium. This solution is used to investigate the variation of the mutual inductance upon the conductivity of the background (e.g., soil, seawater or human body), as well as upon other parameters such as the vertical of the coils and the displacement of one of the coils in the horizontal plane. Our theoretical results are compared with full wave simulations and a previous solution valid when a conductive slab is inserted between two coupled resonant coils. The proposed approach can have direct impact on the design and optimisation of magnetoinductive waveguides and wireless power transfer for underground/underwater networks and embedded biomedical systems.

Generation of remote adaptive torsional shear waves with an octagonal phased array to enhance displacements and reduce variability of shear wave speeds: comparison with quasi-plane shear wavefronts.

PubMed

Ouared, Abderrahmane; Montagnon, Emmanuel; Cloutier, Guy

2015-10-21

A method based on adaptive torsional shear waves (ATSW) is proposed to overcome the strong attenuation of shear waves generated by a radiation force in dynamic elastography. During the inward propagation of ATSW, the magnitude of displacements is enhanced due to the convergence of shear waves and constructive interferences. The proposed method consists in generating ATSW fields from the combination of quasi-plane shear wavefronts by considering a linear superposition of displacement maps. Adaptive torsional shear waves were experimentally generated in homogeneous and heterogeneous tissue mimicking phantoms, and compared to quasi-plane shear wave propagations. Results demonstrated that displacement magnitudes by ATSW could be up to 3 times higher than those obtained with quasi-plane shear waves, that the variability of shear wave speeds was reduced, and that the signal-to-noise ratio of displacements was improved. It was also observed that ATSW could cause mechanical inclusions to resonate in heterogeneous phantoms, which further increased the displacement contrast between the inclusion and the surrounding medium. This method opens a way for the development of new noninvasive tissue characterization strategies based on ATSW in the framework of our previously reported shear wave induced resonance elastography (SWIRE) method proposed for breast cancer diagnosis.

Ultrafast Ultrasound Imaging of Ocular Anatomy and Blood Flow

PubMed Central

Urs, Raksha; Ketterling, Jeffrey A.; Silverman, Ronald H.

2016-01-01

Purpose Ophthalmic ultrasound imaging is currently performed with mechanically scanned single-element probes. These probes have limited capabilities overall and lack the ability to image blood flow. Linear-array systems are able to detect blood flow, but these systems exceed ophthalmic acoustic intensity safety guidelines. Our aim was to implement and evaluate a new linear-array–based technology, compound coherent plane-wave ultrasound, which offers ultrafast imaging and depiction of blood flow at safe acoustic intensity levels. Methods We compared acoustic intensity generated by a 128-element, 18-MHz linear array operated in conventionally focused and plane-wave modes and characterized signal-to-noise ratio (SNR) and lateral resolution. We developed plane-wave B-mode, real-time color-flow, and high-resolution depiction of slow flow in postprocessed data collected continuously at a rate of 20,000 frames/s. We acquired in vivo images of the posterior pole of the eye by compounding plane-wave images acquired over ±10° and produced images depicting orbital and choroidal blood flow. Results With the array operated conventionally, Doppler modes exceeded Food and Drug Administration safety guidelines, but plane-wave modalities were well within guidelines. Plane-wave data allowed generation of high-quality compound B-mode images, with SNR increasing with the number of compounded frames. Real-time color-flow Doppler readily visualized orbital blood flow. Postprocessing of continuously acquired data blocks of 1.6-second duration allowed high-resolution depiction of orbital and choroidal flow over the cardiac cycle. Conclusions Newly developed high-frequency linear arrays in combination with plane-wave techniques present opportunities for the evaluation of ocular anatomy and blood flow, as well as visualization and analysis of other transient phenomena such as vessel wall motion over the cardiac cycle and saccade-induced vitreous motion. PMID:27428169

Application of the wavenumber jump condition to the normal and oblique interaction of a plane acoustic wave and a plane shock

NASA Technical Reports Server (NTRS)

Kleinstein, G. G.; Gunzburger, M. D.

1977-01-01

The kinematics of normal and oblique interactions between a plane acoustic wave and a plane shock wave are investigated separately using an approach whereby the shock is considered as a sharp discontinuity surface separating two half-spaces, so that the dispersion relation on either side of the shock and the wavenumber jump condition across a discontinuity surface completely specify the kinematics of the problem in the whole space independently of the acoustic-field dynamics. The normal interaction is analyzed for a stationary shock, and the spectral change of the incident wave is investigated. The normal interaction is then examined for the case of a shock wave traveling into an ambient region where an acoustic disturbance is propagating in the opposite direction. Detailed attention is given to the consequences of the existence of a critical shock speed above which the frequency of the transmitted wave becomes negative. Finally, the oblique interaction with a fixed shock is considered, and the existence and nature of the transmitted wave is investigated, particularly as a function of the angle of incidence.

Damage detection in composite panels based on mode-converted Lamb waves sensed using 3D laser scanning vibrometer

NASA Astrophysics Data System (ADS)

Pieczonka, Łukasz; Ambroziński, Łukasz; Staszewski, Wiesław J.; Barnoncel, David; Pérès, Patrick

2017-12-01

This paper introduces damage identification approach based on guided ultrasonic waves and 3D laser Doppler vibrometry. The method is based on the fact that the symmetric and antisymmetric Lamb wave modes differ in amplitude of the in-plane and out-of-plane vibrations. Moreover, the modes differ also in group velocities and normally they are well separated in time. For a given time window both modes can occur simultaneously only close to the wave source or to a defect that leads to mode conversion. By making the comparison between the in-plane and out-of-plane wave vector components the detection of mode conversion is possible, allowing for superior and reliable damage detection. Experimental verification of the proposed damage identification procedure is performed on fuel tank elements of Reusable Launch Vehicles designed for space exploration. Lamb waves are excited using low-profile, surface-bonded piezoceramic transducers and 3D scanning laser Doppler vibrometer is used to characterize the Lamb wave propagation field. The paper presents theoretical background of the proposed damage identification technique as well as experimental arrangements and results.

Propagation of Gaussian wave packets in complex media and application to fracture characterization

NASA Astrophysics Data System (ADS)

Ding, Yinshuai; Zheng, Yingcai; Zhou, Hua-Wei; Howell, Michael; Hu, Hao; Zhang, Yu

2017-08-01

Knowledge of the subsurface fracture networks is critical in probing the tectonic stress states and flow of fluids in reservoirs containing fractures. We propose to characterize fractures using scattered seismic data, based on the theory of local plane-wave multiple scattering in a fractured medium. We construct a localized directional wave packet using point sources on the surface and propagate it toward the targeted subsurface fractures. The wave packet behaves as a local plane wave when interacting with the fractures. The interaction produces multiple scattering of the wave packet that eventually travels up to the surface receivers. The propagation direction and amplitude of the multiply scattered wave can be used to characterize fracture density, orientation and compliance. Two key aspects in this characterization process are the spatial localization and directionality of the wave packet. Here we first show the physical behaviour of a new localized wave, known as the Gaussian Wave Packet (GWP), by examining its analytical solution originally formulated for a homogenous medium. We then use a numerical finite-difference time-domain (FDTD) method to study its propagation behaviour in heterogeneous media. We find that a GWP can still be localized and directional in space even over a large propagation distance in heterogeneous media. We then propose a method to decompose the recorded seismic wavefield into GWPs based on the reverse-time concept. This method enables us to create a virtually recorded seismic data using field shot gathers, as if the source were an incident GWP. Finally, we demonstrate the feasibility of using GWPs for fracture characterization using three numerical examples. For a medium containing fractures, we can reliably invert for the local parameters of multiple fracture sets. Differing from conventional seismic imaging such as migration methods, our fracture characterization method is less sensitive to errors in the background velocity model. For a layered medium containing fractures, our method can correctly recover the fracture density even with an inaccurate velocity model.

Features of sound propagation through and stability of a finite shear layer

NASA Technical Reports Server (NTRS)

Koutsoyannis, S. P.

1977-01-01

The plane wave propagation, the stability, and the rectangular duct mode problems of a compressible, inviscid, linearly sheared, parallel, homogeneous flow are shown to be governed by Whittaker's equation. The exact solutions for the perturbation quantities are essentially the Whittaker M-functions where the nondimensional quantities have precise physical meanings. A number of known results are obtained as limiting cases of the exact solutions. For the compressible finite thickness shear layer it is shown that no resonances and no critical angles exist for all Mach numbers, frequencies, and shear layer velocity profile slopes except in the singular case of the vortex sheet.

Nonintegrable Schrodinger discrete breathers.

PubMed

Gómez-Gardeñes, J; Floría, L M; Peyrard, M; Bishop, A R

2004-12-01

In an extensive numerical investigation of nonintegrable translational motion of discrete breathers in nonlinear Schrödinger lattices, we have used a regularized Newton algorithm to continue these solutions from the limit of the integrable Ablowitz-Ladik lattice. These solutions are shown to be a superposition of a localized moving core and an excited extended state (background) to which the localized moving pulse is spatially asymptotic. The background is a linear combination of small amplitude nonlinear resonant plane waves and it plays an essential role in the energy balance governing the translational motion of the localized core. Perturbative collective variable theory predictions are critically analyzed in the light of the numerical results.

Plane waves and structures in turbulent channel flow

NASA Technical Reports Server (NTRS)

Sirovich, L.; Ball, K. S.; Keefe, L. R.

1990-01-01

A direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen-Loeve procedure, proper orthogonal decomposition). This analysis reveals the presence of propagating plane waves in the turbulent flow. The velocity of propagation is determined by the flow velocity at the location of maximal Reynolds stress. The analysis further suggests that the interaction of these waves appears to be essential to the local production of turbulence via bursting or sweeping events in the turbulent boundary layer, with the additional suggestion that the fast acting plane waves act as triggers.

GW/Bethe-Salpeter calculations for charged and model systems from real-space DFT

NASA Astrophysics Data System (ADS)

Strubbe, David A.

GW and Bethe-Salpeter (GW/BSE) calculations use mean-field input from density-functional theory (DFT) calculations to compute excited states of a condensed-matter system. Many parts of a GW/BSE calculation are efficiently performed in a plane-wave basis, and extensive effort has gone into optimizing and parallelizing plane-wave GW/BSE codes for large-scale computations. Most straightforwardly, plane-wave DFT can be used as a starting point, but real-space DFT is also an attractive starting point: it is systematically convergeable like plane waves, can take advantage of efficient domain parallelization for large systems, and is well suited physically for finite and especially charged systems. The flexibility of a real-space grid also allows convenient calculations on non-atomic model systems. I will discuss the interfacing of a real-space (TD)DFT code (Octopus, www.tddft.org/programs/octopus) with a plane-wave GW/BSE code (BerkeleyGW, www.berkeleygw.org), consider performance issues and accuracy, and present some applications to simple and paradigmatic systems that illuminate fundamental properties of these approximations in many-body perturbation theory.

A projection-free method for representing plane-wave DFT results in an atom-centered basis

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

Dunnington, Benjamin D.; Schmidt, J. R., E-mail: schmidt@chem.wisc.edu

2015-09-14

Plane wave density functional theory (DFT) is a powerful tool for gaining accurate, atomic level insight into bulk and surface structures. Yet, the delocalized nature of the plane wave basis set hinders the application of many powerful post-computation analysis approaches, many of which rely on localized atom-centered basis sets. Traditionally, this gap has been bridged via projection-based techniques from a plane wave to atom-centered basis. We instead propose an alternative projection-free approach utilizing direct calculation of matrix elements of the converged plane wave DFT Hamiltonian in an atom-centered basis. This projection-free approach yields a number of compelling advantages, including strictmore » orthonormality of the resulting bands without artificial band mixing and access to the Hamiltonian matrix elements, while faithfully preserving the underlying DFT band structure. The resulting atomic orbital representation of the Kohn-Sham wavefunction and Hamiltonian provides a gateway to a wide variety of analysis approaches. We demonstrate the utility of the approach for a diverse set of chemical systems and example analysis approaches.« less

Simple Harmonic Motion in Harmonic Plane Waves.

ERIC Educational Resources Information Center

Benumof, Reuben

1980-01-01

Discusses the distribution of kinetic and potential energy in transverse and longitudinal waves and examines the transmission of power and momentum. This discussion is intended to aid in understanding the simple harmonic motion of a particle involved in the propagation of a harmonic mechanical plane wave. (HM)

Accuracy and efficiency considerations for wide-angle wavefield extrapolators and scattering operators

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2005-10-01

Several observations are made concerning the numerical implementation of wide-angle one-way wave equations, using for illustration scalar waves obeying the Helmholtz equation in two space dimensions. This simple case permits clear identification of a sequence of physically motivated approximations of use when the mathematically exact pseudo-differential operator (PSDO) one-way method is applied. As intuition suggests, these approximations largely depend on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow-angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so-called `standard-ordering' PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane-wave synthesis lying at the heart of the calculations. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one-way propagator for the laterally varying case, representing the intuitive extension of classical integral-transform solutions for a laterally homogeneous medium. This exponential propagator permits larger forward stepsizes. Numerical comparisons with Helmholtz (i.e. full) wave-equation finite-difference solutions are presented for various canonical problems. These include propagation along an interfacial gradient, the effects of a compact inclusion and the formation of extended transmitted and backscattered wave trains by model roughness. The ideas extend to the 3-D, generally anisotropic case and to multiple scattering by invariant embedding. It is concluded that the method is very competitive, striking a new balance between simplifying approximations and computational labour. Complicated wave-scattering effects are retained without the need for expensive global solutions, providing a robust and flexible modelling tool.

Control of Love waves by resonant metasurfaces.

PubMed

Palermo, Antonio; Marzani, Alessandro

2018-05-08

Metasurfaces of mechanical resonators have been successfully used to control in-plane polarized surface waves for filtering, waveguiding and lensing applications across different length scales. In this work, we extend the concept of metasurfaces to anti-plane surface waves existing in semi-infinite layered media, generally known as Love waves. By means of an effective medium approach, we derive an original closed-form dispersion relation for the metasurface. This relation reveals the possibility to control the Love waves dispersive properties by varying the resonators mechanical parameters. We exploit this capability to manipulate the metasurface refractive index and design two gradient index (GRIN) metalenses, i.e. a Luneburg lens and a Maxwell lens. We confirm the performance of the designed lenses using full 3D finite element simulations. Our work demonstrates the possibility of realizing wave control devices for anti-plane waves.

Finite-surface method for the Maxwell equations with corner singularities

NASA Technical Reports Server (NTRS)

Vinokur, Marcel; Yarrow, Maurice

1994-01-01

The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line integrals appearing in the method. Numerical results are presented for a harmonic plane wave incident on a finite flat plate. Comparisons with exact solutions show good agreement.

Plane wave gravitons, curvature singularities and string physics

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

Brooks, R.

1991-03-21

This paper discusses bounded (compactifying) potentials arising from a conspiracy between plane wave graviton and dilaton condensates. So are string propagation and supersymmetry in spacetimes with curvature singularities.

Bumps of the wave structure function in non-Kolmogorov turbulence

NASA Astrophysics Data System (ADS)

Qiao, Chunhong; Lu, Lu; Zhang, Pengfei; Wang, Haitao; Huang, Honghua; Fan, Chengyu

2015-10-01

The analytical expressions for wave structure function of plane and spherical waves are derived both in the viscous dissipation and inertial range. Due to previously research, there is a discrepancy between theoretical results and the experimental datum in viscous dissipation range. In this paper, only considering the inertial range, taking plane waves for example, we give a comparison of results of WSF calculated by the analytical formula obtained in this paper and the numerical calculations of the definition at the fixed parameter (i.e., the generalized exponent α), it can be seen that the two results are in agreement with each other exactly. Based on non-Kolmogorov power spectrum, new characteristics for wave structure function (WSF) have been found for plane and spherical wave models when the different ratio of inner scale l0 and outer scale of turbulence L0 is obtained. In outer scale assumed finite case (i.e., L0 =1m), WSF obtains the maximum when α approximates to 3.3 both for plane and spherical wave models. In outer scale assumed infinite case (i.e., L0 = ∞), the WSF can be sorted into three parts, including two rapid-rising regions (i.e., 3.0 < α < 3.3 and 3.8 < α < 4.0 ) and one gently rising region (i.e., 3.3 < α < 3.8 ).Further, the changes of scaled WSF versus the ratio of separation distance and inner scale ( p/ l0 ) are investigated under mentioned above conditions for two models. In L0 = 1m case, both for plane and spherical waves, the value of α determines the bump position of WSF. In L0 = ∞ case, the bump of scaled WSF disappears when the generalized exponent has large values. The changings of scaled WSF monotonically increase as α increased when the generalized exponent is larger than11/3 for two models. Besides, the properties of spherical waves are similar to plane waves, except which the values of WSF and the scaled WSF are smaller than plane ones.

Effect of a Starting Model on the Solution of a Travel Time Seismic Tomography Problem

NASA Astrophysics Data System (ADS)

Yanovskaya, T. B.; Medvedev, S. V.; Gobarenko, V. S.

2018-03-01

In the problems of three-dimensional (3D) travel time seismic tomography where the data are travel times of diving waves and the starting model is a system of plane layers where the velocity is a function of depth alone, the solution turns out to strongly depend on the selection of the starting model. This is due to the fact that in the different starting models, the rays between the same points can intersect different layers, which makes the tomography problem fundamentally nonlinear. This effect is demonstrated by the model example. Based on the same example, it is shown how the starting model should be selected to ensure a solution close to the true velocity distribution. The starting model (the average dependence of the seismic velocity on depth) should be determined by the method of successive iterations at each step of which the horizontal velocity variations in the layers are determined by solving the two-dimensional tomography problem. An example illustrating the application of this technique to the P-wave travel time data in the region of the Black Sea basin is presented.

Procedure for noise prediction and optimization of advanced technology propellers

NASA Technical Reports Server (NTRS)

Jou, W. H.; Bernstein, S.

1979-01-01

The sound field due to a propeller operating at supersonic tip speed in a uniform flow was investigated. Using the fact that the wave front in a uniform stream is a convected sphere, the fundamental solution to the convected wave equation was easily obtained. The Fourier coefficients of the pressure signature were obtained by a far field approximation, and are expressed as an integral over the blade platform. It is shown that cones of silence exist fore and aft the propeller plane. The semiapex angles are shown. These angles are independent of the individual Mach components such as the flight Mach number and the rotation Mach number. The result is confirmed by the computation of the ray path of the emitted Mach waves. The Doppler amplification factor strengthens the signal behind the propeller while it weakens that upstream.

Propagation of magnetostatic spin waves in an yttrium iron garnet film for out-of-plane magnetic fields

NASA Astrophysics Data System (ADS)

Bang, Wonbae; Lim, Jinho; Trossman, Jonathan; Tsai, C. C.; Ketterson, John B.

2018-06-01

We have observed the propagation of spin waves across a thin yttrium iron garnet film on (1 1 1) gadolinium gallium garnet for magnetic fields inclined with respect to the film plane. Two principle planes were studied: that for H in the plane defined by the wave vector k and the plane normal, n, with limiting forms corresponding to the Backward Volume and Forward Volume modes, and that for H in the plane perpendicular to k, with limiting forms corresponding to the Damon-Eshbach and Forward Volume modes. By exciting the wave at one edge of the film and observing the field dependence of the phase of the received signal at the opposing edge we determined the frequency vs. wavevector relation, ω = ω (k), of various propagating modes in the film. Avoided crossings are observed in the Damon-Eshbach and Forward Volume regimes when the propagating mode intersects the higher, exchange split, volume modes, leading to an extinction of the propagating mode; analysis of the resulting behavior allows a determination of the exchange parameter. The experimental results are compared with theoretical simulations.

The Relativistic Wave Vector

ERIC Educational Resources Information Center

Houlrik, Jens Madsen

2009-01-01

The Lorentz transformation applies directly to the kinematics of moving particles viewed as geometric points. Wave propagation, on the other hand, involves moving planes which are extended objects defined by simultaneity. By treating a plane wave as a geometric object moving at the phase velocity, novel results are obtained that illustrate the…

An anisotropic lens for transitioning plane waves between media of different permittivities

NASA Astrophysics Data System (ADS)

Stone, Alexander P.; Baum, Carl E.

1988-11-01

A particularly simple geometry is considered in which an inhomogeneous and anisotropic lens is specified for the transition of plane waves between media of different permittivities. The permittivities of the regions outside of the lens can be constant, but the permittivity of the lens region depends on position. Results are presented for a plane wave in the second medium propagating normally to the assumed plane boundary of that medium. The results for the case of normal incidence are then generalized to the case of nonnormal incidence. The conditions of transit time conservation and impedance matching are related to the Brewster angle.

Helicons in uniform fields. I. Wave diagnostics with hodograms

NASA Astrophysics Data System (ADS)

Urrutia, J. M.; Stenzel, R. L.

2018-03-01

The wave equation for whistler waves is well known and has been solved in Cartesian and cylindrical coordinates, yielding plane waves and cylindrical waves. In space plasmas, waves are usually assumed to be plane waves; in small laboratory plasmas, they are often assumed to be cylindrical "helicon" eigenmodes. Experimental observations fall in between both models. Real waves are usually bounded and may rotate like helicons. Such helicons are studied experimentally in a large laboratory plasma which is essentially a uniform, unbounded plasma. The waves are excited by loop antennas whose properties determine the field rotation and transverse dimensions. Both m = 0 and m = 1 helicon modes are produced and analyzed by measuring the wave magnetic field in three dimensional space and time. From Ampère's law and Ohm's law, the current density and electric field vectors are obtained. Hodograms for these vectors are produced. The sign ambiguity of the hodogram normal with respect to the direction of wave propagation is demonstrated. In general, electric and magnetic hodograms differ but both together yield the wave vector direction unambiguously. Vector fields of the hodogram normal yield the phase flow including phase rotation for helicons. Some helicons can have locally a linear polarization which is identified by the hodogram ellipticity. Alternatively the amplitude oscillation in time yields a measure for the wave polarization. It is shown that wave interference produces linear polarization. These observations emphasize that single point hodogram measurements are inadequate to determine the wave topology unless assuming plane waves. Observations of linear polarization indicate wave packets but not plane waves. A simple qualitative diagnostics for the wave polarization is the measurement of the magnetic field magnitude in time. Circular polarization has a constant amplitude; linear polarization results in amplitude modulations.

Geometrical optics in the near field: local plane-interface approach with evanescent waves.

PubMed

Bose, Gaurav; Hyvärinen, Heikki J; Tervo, Jani; Turunen, Jari

2015-01-12

We show that geometrical models may provide useful information on light propagation in wavelength-scale structures even if evanescent fields are present. We apply a so-called local plane-wave and local plane-interface methods to study a geometry that resembles a scanning near-field microscope. We show that fair agreement between the geometrical approach and rigorous electromagnetic theory can be achieved in the case where evanescent waves are required to predict any transmission through the structure.

Exciting surface plasmon polaritons in the Kretschmann configuration by a light beam

NASA Astrophysics Data System (ADS)

Vinogradov, A. P.; Dorofeenko, A. V.; Pukhov, A. A.; Lisyansky, A. A.

2018-06-01

We consider exciting surface plasmon polaritons in the Kretschmann configuration. Contrary to common belief, we show that a plane-wave incident at an angle greater than the angle of total internal reflection does not excite surface plasmon polaritons. These excitations do arise, however, if the incident light forms a narrow beam composed of an infinite number of plane waves. The surface plasmon polariton is formed at the geometrical edge of the beam as a result of interference of reflected plane waves.

On a Free Boundary Problem for the Curvature Flow with Driving Force

NASA Astrophysics Data System (ADS)

Guo, Jong-Shenq; Matano, Hiroshi; Shimojo, Masahiko; Wu, Chang-Hong

2016-03-01

We study a free boundary problem associated with the curvature dependent motion of planar curves in the upper half plane whose two endpoints slide along the horizontal axis with prescribed fixed contact angles. Our first main result concerns the classification of solutions; every solution falls into one of the three categories, namely, area expanding, area bounded and area shrinking types. We then study in detail the asymptotic behavior of solutions in each category. Among other things we show that solutions are asymptotically self-similar both in the area expanding and the area shrinking cases, while solutions converge to either a stationary solution or a traveling wave in the area bounded case. We also prove results on the concavity properties of solutions. One of the main tools of this paper is the intersection number principle, however in order to deal with solutions with free boundaries, we introduce what we call "the extended intersection number principle", which turns out to be exceedingly useful in handling curves with moving endpoints.

Multiplane wave imaging increases signal-to-noise ratio in ultrafast ultrasound imaging.

PubMed

Tiran, Elodie; Deffieux, Thomas; Correia, Mafalda; Maresca, David; Osmanski, Bruno-Felix; Sieu, Lim-Anna; Bergel, Antoine; Cohen, Ivan; Pernot, Mathieu; Tanter, Mickael

2015-11-07

Ultrafast imaging using plane or diverging waves has recently enabled new ultrasound imaging modes with improved sensitivity and very high frame rates. Some of these new imaging modalities include shear wave elastography, ultrafast Doppler, ultrafast contrast-enhanced imaging and functional ultrasound imaging. Even though ultrafast imaging already encounters clinical success, increasing even more its penetration depth and signal-to-noise ratio for dedicated applications would be valuable. Ultrafast imaging relies on the coherent compounding of backscattered echoes resulting from successive tilted plane waves emissions; this produces high-resolution ultrasound images with a trade-off between final frame rate, contrast and resolution. In this work, we introduce multiplane wave imaging, a new method that strongly improves ultrafast images signal-to-noise ratio by virtually increasing the emission signal amplitude without compromising the frame rate. This method relies on the successive transmissions of multiple plane waves with differently coded amplitudes and emission angles in a single transmit event. Data from each single plane wave of increased amplitude can then be obtained, by recombining the received data of successive events with the proper coefficients. The benefits of multiplane wave for B-mode, shear wave elastography and ultrafast Doppler imaging are experimentally demonstrated. Multiplane wave with 4 plane waves emissions yields a 5.8  ±  0.5 dB increase in signal-to-noise ratio and approximately 10 mm in penetration in a calibrated ultrasound phantom (0.7 d MHz(-1) cm(-1)). In shear wave elastography, the same multiplane wave configuration yields a 2.07  ±  0.05 fold reduction of the particle velocity standard deviation and a two-fold reduction of the shear wave velocity maps standard deviation. In functional ultrasound imaging, the mapping of cerebral blood volume results in a 3 to 6 dB increase of the contrast-to-noise ratio in deep structures of the rodent brain.

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

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

Booth, George H., E-mail: george.booth@kcl.ac.uk; Tsatsoulis, Theodoros; Grüneis, Andreas, E-mail: a.grueneis@fkf.mpg.de

2016-08-28

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

Linear shoaling of free-surface waves in multi-layer non-hydrostatic models

NASA Astrophysics Data System (ADS)

Bai, Yefei; Cheung, Kwok Fai

2018-01-01

The capability to describe shoaling over sloping bottom is fundamental to modeling of coastal wave transformation. The linear shoaling gradient provides a metric to measure this property in non-hydrostatic models with layer-integrated formulations. The governing equations in Boussinesq form facilitate derivation of the linear shoaling gradient, which is in the form of a [ 2 P + 2 , 2 P ] expansion of the water depth parameter kd with P equal to 1 for a one-layer model and (4 N - 4) for an N-layer model. The expansion reproduces the analytical solution from Airy wave theory at the shallow water limit and maintains a reasonable approximation up to kd = 1.2 and 2 for the one and two-layer models. Additional layers provide rapid and monotonic convergence of the shoaling gradient into deep water. Numerical experiments of wave propagation over a plane slope illustrate manifestation of the shoaling errors through the transformation processes from deep to shallow water. Even though outside the zone of active wave transformation, shoaling errors from deep to intermediate water are cumulative to produce appreciable impact to the wave amplitude in shallow water.

The elliptical Gaussian wave transformation due to diffraction by an elliptical hologram

NASA Astrophysics Data System (ADS)

Janicijevic, L.

1985-03-01

Realized as an interferogram of a spherical and a cylindrical wave, the elliptical hologram is treated as a plane diffracting grating which produces Fresnel diffraction of a simple astigmatic Gaussian incident wave. It is shown that if the principal axes of the incident beam coincide with the principal axes of the hologram, the diffracted wave field is composed of three different astigmatic Gaussian waves, with their waists situated in parallel but distinct planes. The diffraction pattern, observed on a transverse screen, is the result of the interference of the three diffracted wave components. It consists of three systems of overlapped second-order curves, whose shape depends on the distance of the observation screen from the hologram, as well as on the parameters of the incident wave beam and the hologram. The results are specialized for gratings in the form of circular and linear holograms and for the case of a stigmatic Gaussian incident wave, as well as for the normal plane-wave incidence on the three mentioned types of hologram.

Exploring the Use of Alfven Waves in Magnetometer Calibration at Geosynchronous Orbit

NASA Technical Reports Server (NTRS)

Bentley, John; Sheppard, David; RIch, Frederick; Redmon, Robert; Loto'aniu, Paul; Chu, Donald

2016-01-01

An Alfven wave is a type magnetohydrodynamicwave that travels through a conducting fluid under the influence of a magnetic field. Researchers have successfully calculated offset vectors of magnetometers in interplanetary space by optimizing the offset to maximize certain Alfvenic properties of observed waves (Leinweber, Belcher). If suitable Alfven waves can be found in the magnetosphere at geosynchronous altitude then these techniques could be used to augment the overall calibration plan for magnetometers in this region such as on the GOES spacecraft, possibly increasing the time between regular maneuvers. Calibration maneuvers may be undesirable because they disrupt the activities of other instruments. Various algorithms to calculate an offset using Alfven waves were considered. A new variation of the Davis-Smith method was derived because it can be mathematically shown that the Davis-Smith method tolerates filtered data, which expands potential applications. The variant developed was designed to find only the offset in the plane normal to the main field because the overall direction of Earth's magnetic field rarely changes, and theory suggests the Alfvenic disturbances occur transverse to the main field. Other variations of the Davis-Smith method encounter problems with data containing waves that propagate in mostly the same direction. A searching algorithm was then designed to look for periods of time with potential Alfven waves in GOES 15 data based on parameters requiring that disturbances be normal to the main field and not change field magnitude. Final waves for calculation were hand-selected. These waves produced credible two-dimensional offset vectors when input to the Davis-Smith method. Multiple two-dimensional solutions in different planes can be combined to get a measurement of the complete offset. The resulting three dimensional offset did not show sufficient precision over several years to be used as a primary calibration method, but reflected changes in the offset fairly well, suggesting that the method could be helpful in monitoring trends of the offset vector when maneuvers cannot be used.

Isotropic transmission of magnon spin information without a magnetic field.

PubMed

Haldar, Arabinda; Tian, Chang; Adeyeye, Adekunle Olusola

2017-07-01

Spin-wave devices (SWD), which use collective excitations of electronic spins as a carrier of information, are rapidly emerging as potential candidates for post-semiconductor non-charge-based technology. Isotropic in-plane propagating coherent spin waves (magnons), which require magnetization to be out of plane, is desirable in an SWD. However, because of lack of availability of low-damping perpendicular magnetic material, a usually well-known in-plane ferrimagnet yttrium iron garnet (YIG) is used with a large out-of-plane bias magnetic field, which tends to hinder the benefits of isotropic spin waves. We experimentally demonstrate an SWD that eliminates the requirement of external magnetic field to obtain perpendicular magnetization in an otherwise in-plane ferromagnet, Ni 80 Fe 20 or permalloy (Py), a typical choice for spin-wave microconduits. Perpendicular anisotropy in Py, as established by magnetic hysteresis measurements, was induced by the exchange-coupled Co/Pd multilayer. Isotropic propagation of magnon spin information has been experimentally shown in microconduits with three channels patterned at arbitrary angles.

Isotropic transmission of magnon spin information without a magnetic field

PubMed Central

Haldar, Arabinda; Tian, Chang; Adeyeye, Adekunle Olusola

2017-01-01

Spin-wave devices (SWD), which use collective excitations of electronic spins as a carrier of information, are rapidly emerging as potential candidates for post-semiconductor non-charge-based technology. Isotropic in-plane propagating coherent spin waves (magnons), which require magnetization to be out of plane, is desirable in an SWD. However, because of lack of availability of low-damping perpendicular magnetic material, a usually well-known in-plane ferrimagnet yttrium iron garnet (YIG) is used with a large out-of-plane bias magnetic field, which tends to hinder the benefits of isotropic spin waves. We experimentally demonstrate an SWD that eliminates the requirement of external magnetic field to obtain perpendicular magnetization in an otherwise in-plane ferromagnet, Ni80Fe20 or permalloy (Py), a typical choice for spin-wave microconduits. Perpendicular anisotropy in Py, as established by magnetic hysteresis measurements, was induced by the exchange-coupled Co/Pd multilayer. Isotropic propagation of magnon spin information has been experimentally shown in microconduits with three channels patterned at arbitrary angles. PMID:28776033

Photoelectron wave function in photoionization: Plane wave or Coulomb wave? [Does photoionization of neutral targets produce Coulomb or plane waves?

DOE PAGES

Gozem, Samer; Gunina, Anastasia O.; Ichino, Takatoshi; ...

2015-10-28

The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectronmore » wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. Finally, the results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.« less

A combined representation method for use in band structure calculations. 1: Method

NASA Technical Reports Server (NTRS)

Friedli, C.; Ashcroft, N. W.

1975-01-01

A representation was described whose basis levels combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding levels. The chosen combination has a particularly simple dependence on the wave vector within the Brillouin Zone, and its use in reducing the standard one-electron band structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of the wave vector. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker (KKR), Augmented-Plane Wave (APW) and Orthogonalized-Plane Wave (OPW) methods are difficult to apply, the present method leads to results with satisfactory accuracy and convergence.

Modulational instability and discrete breathers in a nonlinear helicoidal lattice model

NASA Astrophysics Data System (ADS)

Ding, Jinmin; Wu, Tianle; Chang, Xia; Tang, Bing

2018-06-01

We investigate the problem on the discrete modulation instability of plane waves and discrete breather modes in a nonlinear helicoidal lattice model, which is described by a discrete nonlinear Schrödinger equation with the first-, second-, and third-neighbor coupling. By means of the linear stability analysis, we present an analytical expression of the instability growth rate and identify the regions of modulational instability of plane waves. It is shown that the introduction of the third-neighbor coupling will affect the shape of the areas of modulational instability significantly. Based on the results obtained by the modulational instability analysis, we predict the existence conditions for the stationary breather modes. Otherwise, by making use of the semidiscrete multiple-scale method, we obtain analytical solutions of discrete breather modes and analyze their properties for different types of nonlinearities. Our results show that the discrete breathers obtained are stable for a long time only when the system exhibits the repulsive nonlinearity. In addition, it is found that the existence of the stable bright discrete breather closely relates to the presence of the third-neighbor coupling.

Local spectrum analysis of field propagation in an anisotropic medium. Part II. Time-dependent fields.

PubMed

Tinkelman, Igor; Melamed, Timor

2005-06-01

In Part I of this two-part investigation [J. Opt. Soc. Am. A 22, 1200 (2005)], we presented a theory for phase-space propagation of time-harmonic electromagnetic fields in an anisotropic medium characterized by a generic wave-number profile. In this Part II, these investigations are extended to transient fields, setting a general analytical framework for local analysis and modeling of radiation from time-dependent extended-source distributions. In this formulation the field is expressed as a superposition of pulsed-beam propagators that emanate from all space-time points in the source domain and in all directions. Using time-dependent quadratic-Lorentzian windows, we represent the field by a phase-space spectral distribution in which the propagating elements are pulsed beams, which are formulated by a transient plane-wave spectrum over the extended-source plane. By applying saddle-point asymptotics, we extract the beam phenomenology in the anisotropic environment resulting from short-pulsed processing. Finally, the general results are applied to the special case of uniaxial crystal and compared with a reference solution.

Irregular focal mechanisms observed at Salton Sea Geothermal Field: Possible influences of anthropogenic stress perturbations

USGS Publications Warehouse

Crandall-Bear, Aren; Barbour, Andrew J.; Schoenball, Martin; Schoenball, Martin

2018-01-01

At the Salton Sea Geothermal Field (SSGF), strain accumulation is released through seismic slip and aseismic deformation. Earthquake activity at the SSGF often occurs in swarm-like clusters, some with clear migration patterns. We have identified an earthquake sequence composed entirely of focal mechanisms representing an ambiguous style of faulting, where strikes are similar but deformation occurs due to steeply-dipping normal faults with varied stress states. In order to more accurately determine the style of faulting for these events, we revisit the original waveforms and refine estimates of P and S wave arrival times and displacement amplitudes. We calculate the acceptable focal plane solutions using P-wave polarities and S/P amplitude ratios, and determine the preferred fault plane. Without constraints on local variations in stress, found by inverting the full earthquake catalog, it is difficult to explain the occurrence of such events using standard fault-mechanics and friction. Comparing these variations with the expected poroelastic effects from local production and injection of geothermal fluids suggests that anthropogenic activity could affect the style of faulting.

Surface enhanced Raman optical activity of molecules on orientationally averaged substrates: theory of electromagnetic effects.

PubMed

Janesko, Benjamin G; Scuseria, Gustavo E

2006-09-28

We present a model for electromagnetic enhancements in surface enhanced Raman optical activity (SEROA) spectroscopy. The model extends previous treatments of SEROA to substrates, such as metal nanoparticles in solution, that are orientationally averaged with respect to the laboratory frame. Our theoretical treatment combines analytical expressions for unenhanced Raman optical activity with molecular polarizability tensors that are dressed by the substrate's electromagnetic enhancements. We evaluate enhancements from model substrates to determine preliminary scaling laws and selection rules for SEROA. We find that dipolar substrates enhance Raman optical activity (ROA) scattering less than Raman scattering. Evanescent gradient contributions to orientationally averaged ROA scale to first or higher orders in the gradient of the incident plane-wave field. These evanescent gradient contributions may be large for substrates with quadrupolar responses to the plane-wave field gradient. Some substrates may also show a ROA contribution that depends only on the molecular electric dipole-electric dipole polarizability. These conclusions are illustrated via numerical calculations of surface enhanced Raman and ROA spectra from (R)-(-)-bromochlorofluoromethane on various model substrates.

Hydrodynamic waves in films flowing under an inclined plane

NASA Astrophysics Data System (ADS)

Rohlfs, Wilko; Pischke, Philipp; Scheid, Benoit

2017-04-01

This study addresses the fluid dynamics of two-dimensional falling films flowing underneath an inclined plane using the weighted integral boundary layer (WIBL) model and direct numerical simulations (DNSs). Film flows under an inclined plane are subject to hydrodynamic and Rayleigh-Taylor instabilities, leading to the formation of two- and three-dimensional waves, rivulets, and eventually dripping. The latter can only occur in film flows underneath an inclined plane such that the gravitational force acts in a destabilizing manner by pulling liquid into the gaseous atmosphere. The DNSs are performed using the solver interFoam of the open-source code OpenFOAM with a gradient limiter approach that avoids artificial oversharpening of the interface. We find good agreement between the two model approaches for wave amplitude and wave speed irrespectively of the orientation of the gravitational force and before the onset of dripping. The latter cannot be modeled with the WIBL model by nature as it is a single-value model. However, for large-amplitude solitarylike waves, the WIBL model fails to predict the velocity field within the wave, which is confirmed by a balance of viscous dissipation and the change in potential energy. In the wavy film flows, different flow features can occur such as circulating waves, i.e., circulating eddies in the main wave hump, or flow reversal, i.e., rotating vortices in the capillary minima of the wave. A phase diagram for all flow features is presented based on results of the WIBL model. Regarding the transition to circulating waves, we show that a critical ratio between the maximum and substrate film thickness (approximately 2.5) is also universal for film flows underneath inclined planes (independent of wavelength, inclination, viscous dissipation, and Reynolds number).

Plane wave packet formulation of atom-plus-diatom quantum reactive scattering.

PubMed

Althorpe, Stuart C

2004-07-15

We recently interpreted several reactive scattering experiments using a plane wave packet (PWP) formulation of quantum scattering theory [see, e.g., S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper presents the first derivation of this formulation for atom-plus-diatom reactive scattering, and explains its relation to conventional time-independent reactive scattering. We generalize recent results for spherical-particle scattering [S. C. Althorpe, Phys. Rev. A 69, 042702 (2004)] to atom-rigid-rotor scattering in the space-fixed frame, atom-rigid-rotor scattering in the body-fixed frame, and finally A+BC rearrangement scattering. The reactive scattering is initiated by a plane wave packet, describing the A+BC reagents in center-of-mass scattering coordinates, and is detected by projecting onto a series of AC+B (or AB+C) plane wave "probe" packets. The plane wave packets are localized at the closest distance from the scattering center at which the interaction potential can be neglected. The time evolution of the initial plane wave packet provides a clear visualization of the scattering into space of the reaction products. The projection onto the probe packets yields the time-independent, state-to-state scattering amplitude, and hence the differential cross section. We explain how best to implement the PWP approach in a numerical computation, and illustrate this with a detailed application to the H+D2 reaction. (c) 2004 American Institute of Physics

Interfacial instability of wormlike micellar solutions sheared in a Taylor-Couette cell

NASA Astrophysics Data System (ADS)

Mohammadigoushki, Hadi; Muller, Susan J.

2014-11-01

We report experiments on wormlike micellar solutions sheared in a custom-made Taylor-Couette (TC) cell. The computer controlled TC cell allows us to rotate both cylinders independently. Wormlike micellar solutions containing water, CTAB, and NaNo3 with different compositions are highly elastic and exhibit shear banding. We visualized the flow field in the θ-z as well as r-z planes, using multiple cameras. When subject to low shear rates, the flow is stable and azimuthal, but becomes unstable above a certain threshold shear rate. This shear rate coincides with the onset of shear banding. Visualizing the θ-z plane shows that this instability is characterized by stationary bands equally spaced in the z direction. Increasing the shear rate results to larger wave lengths. Above a critical shear rate, experiments reveal a chaotic behavior reminiscent of elastic turbulence. We also studied the effect of ramp speed on the onset of instability and report an acceleration below which the critical Weissenberg number for onset of instability is unaffected. Moreover, visualizations in the r-z direction reveals that the interface between the two bands undulates with shear bands evolving towards the outer cylinder regardless of which cylinder is rotating.

Second-harmonic generation in shear wave beams with different polarizations

NASA Astrophysics Data System (ADS)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

Wave propagation in media having negative permittivity and permeability.

PubMed

Ziolkowski, R W; Heyman, E

2001-11-01

Wave propagation in a double negative (DNG) medium, i.e., a medium having negative permittivity and negative permeability, is studied both analytically and numerically. The choices of the square root that leads to the index of refraction and the wave impedance in a DNG medium are determined by imposing analyticity in the complex frequency domain, and the corresponding wave properties associated with each choice are presented. These monochromatic concepts are then tested critically via a one-dimensional finite difference time domain (FDTD) simulation of the propagation of a causal, pulsed plane wave in a matched, lossy Drude model DNG medium. The causal responses of different spectral regimes of the medium with positive or negative refractive indices are studied by varying the carrier frequency of narrowband pulse excitations. The smooth transition of the phenomena associated with a DNG medium from its early-time nondispersive behavior to its late-time monochromatic response is explored with wideband pulse excitations. These FDTD results show conclusively that the square root choice leading to a negative index of refraction and positive wave impedance is the correct one, and that this choice is consistent with the overall causality of the response. An analytical, exact frequency domain solution to the scattering of a wave from a DNG slab is also given and is used to characterize several physical effects. This solution is independent of the choice of the square roots for the index of refraction and the wave impedance, and thus avoids any controversy that may arise in connection with the signs of these constituents. The DNG slab solution is used to critically examine the perfect lens concept suggested recently by Pendry. It is shown that the perfect lens effect exists only under the special case of a DNG medium with epsilon(omega)=mu(omega)=-1 that is both lossless and nondispersive. Otherwise, the closed form solutions for the field structure reveal that the DNG slab converts an incident spherical wave into a localized beam field whose parameters depend on the values of epsilon and mu. This beam field is characterized with a paraxial approximation of the exact DNG slab solution. These monochromatic concepts are again explored numerically via a causal two-dimensional FDTD simulation of the scattering of a pulsed cylindrical wave by a matched, lossy Drude model DNG slab. These FDTD results demonstrate conclusively that the monochromatic electromagnetic power flow through the DNG slab is channeled into beams rather then being focused and, hence, the Pendry perfect lens effect is not realizable with any realistic metamaterial.

Three-Dimensional Electromagnetic Scattering from Layered Media with Rough Interfaces for Subsurface Radar Remote Sensing

NASA Astrophysics Data System (ADS)

Duan, Xueyang

The objective of this dissertation is to develop forward scattering models for active microwave remote sensing of natural features represented by layered media with rough interfaces. In particular, soil profiles are considered, for which a model of electromagnetic scattering from multilayer rough surfaces with or without buried random media is constructed. Starting from a single rough surface, radar scattering is modeled using the stabilized extended boundary condition method (SEBCM). This method solves the long-standing instability issue of the classical EBCM, and gives three-dimensional full wave solutions over large ranges of surface roughnesses with higher computational efficiency than pure numerical solutions, e.g., method of moments (MoM). Based on this single surface solution, multilayer rough surface scattering is modeled using the scattering matrix approach and the model is used for a comprehensive sensitivity analysis of the total ground scattering as a function of layer separation, subsurface statistics, and sublayer dielectric properties. The buried inhomogeneities such as rocks and vegetation roots are considered for the first time in the forward scattering model. Radar scattering from buried random media is modeled by the aggregate transition matrix using either the recursive transition matrix approach for spherical or short-length cylindrical scatterers, or the generalized iterative extended boundary condition method we developed for long cylinders or root-like cylindrical clusters. These approaches take the field interactions among scatterers into account with high computational efficiency. The aggregate transition matrix is transformed to a scattering matrix for the full solution to the layered-medium problem. This step is based on the near-to-far field transformation of the numerical plane wave expansion of the spherical harmonics and the multipole expansion of plane waves. This transformation consolidates volume scattering from the buried random medium with the scattering from layered structure in general. Combined with scattering from multilayer rough surfaces, scattering contributions from subsurfaces and vegetation roots can be then simulated. Solutions of both the rough surface scattering and random media scattering are validated numerically, experimentally, or both. The experimental validations have been carried out using a laboratory-based transmit-receive system for scattering from random media and a new bistatic tower-mounted radar system for field-based surface scattering measurements.

Acoustic Monitoring of Gravity-Driven Controls on CaCO3 Precipitates in a Fracture

NASA Astrophysics Data System (ADS)

Xu, Z.; Sheets, J.; Zhang, L.; Kim, D.; Kneafsey, T. J.; Cole, D. R.; Jun, Y. S.; Pyrak-Nolte, L. J.

2017-12-01

Sealing fractures by mineral precipitation is an important process for improving caprock integrity in subsurface reservoirs. In this study, the ability to monitor precipitate distribution in fractures with buoyant fluids was examined. Fractures with uniform aperture distributions of 0.5, 1.0 and 2.0 mm were created from acrylic plates to enable direct imaging of precipitate formation over time. CaCO3 precipitation was induced in a fracture from invasion of 1M CaCl2 and 0.3M Na2CO3 solutions. During chemical invasion, a fracture plane was oriented either parallel or perpendicular to gravity. Acoustic (P) wave transmission ( 1 MHz) and optical imaging were used to monitor the sample prior to, during and after fluid injection. Complementary X-ray computed tomography was performed throughout the experiments on vertical fractures and post injection for the horizontal fractures. Precipitate particle sizes during formation were determined using SAXS and WAXS. In both horizontal and vertical fractures, the density contrast between the two solutions affected the spatial distribution of precipitation. In vertical fractures, the denser CaCl2 solution almost completely displaced the NaCO3 solution, causing strong localization of precipitates. However, in the horizontal fractures, flow stratification occurred in the 2 mm aperture fractures, with the less dense Na2CO3 flowing over the CaCl2 solution, resulting in a more even distribution of precipitates cross the fracture plane. P-wave amplitudes increased up to 8% and the arrival time decreased with precipitate accumulation in the horizontal fracture. This is consistent with a three-layered approach as the seismic impedance inside the fracture increases. The initial contact between the two was observed as a decrease in the P-wave amplitude. As precipitates accumulated, the amplitude recovered and increased, with greater increases observed along the mixing flow path. Fractures in the subsurface may seal differently depending on the orientation thus affecting the ability of a fracture to self-heal if oriented vertically. This work was supported by the Center for Nanoscale Controls on Geologic CO (NCGC), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # DE-AC02-05CH11231

On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the hyperbolicity of the Euler equation system and the first principle of plane (simple) wave propagation. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in ID, 2D and 3D space are illustrated to demonstrate its robustness in practical computations.

Roothaan approach in the thermodynamic limit

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

Gutierrez, G.; Plastino, A.

1982-02-01

A systematic method for the solution of the Hartree-Fock equations in the thermodynamic limit is presented. The approach is seen to be a natural extension of the one usually employed in the finite-fermion case, i.e., that developed by Roothaan. The new techniques developed here are applied, as an example, to neutron matter, employing the so-called V/sub 1/ Bethe homework potential. The results obtained are, by far, superior to those that the ordinary plane-wave Hartree-Fock theory yields.

On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

NASA Technical Reports Server (NTRS)

Loh, Ching Y.

2003-01-01

A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the first principle of non-reflecting, plane wave propagation and the hyperbolicity of the Euler equation system. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in 1D, 2D, and 3D space are illustrated to demonstrate its robustness in practical computations.

Evanescent-Wave Filtering in Images Using Remote Terahertz Structured Illumination

NASA Astrophysics Data System (ADS)

Flammini, M.; Pontecorvo, E.; Giliberti, V.; Rizza, C.; Ciattoni, A.; Ortolani, M.; DelRe, E.

2017-11-01

Imaging with structured illumination allows for the retrieval of subwavelength features of an object by conversion of evanescent waves into propagating waves. In conditions in which the object plane and the structured-illumination plane do not coincide, this conversion process is subject to progressive filtering of the components with high spatial frequency when the distance between the two planes increases, until the diffraction-limited lateral resolution is restored when the distance exceeds the extension of evanescent waves. We study the progressive filtering of evanescent waves by developing a remote super-resolution terahertz imaging system operating at a wavelength λ =1.00 mm , based on a freestanding knife edge and a reflective confocal terahertz microscope. In the images recorded with increasing knife-edge-to-object-plane distance, we observe the transition from a super-resolution of λ /17 ≃60 μ m to the diffraction-limited lateral resolution of Δ x ≃λ expected for our confocal microscope. The extreme nonparaxial conditions are analyzed in detail, exploiting the fact that, in the terahertz frequency range, the knife edge can be positioned at a variable subwavelength distance from the object plane. Electromagnetic simulations of radiation scattering by the knife edge reproduce the experimental super-resolution achieved.

Special discontinuities in nonlinearly elastic media

NASA Astrophysics Data System (ADS)

Chugainova, A. P.

2017-06-01

Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

On gravitational chirality as the genesis of astrophysical jets

NASA Astrophysics Data System (ADS)

Tucker, R. W.; Walton, T. J.

2017-02-01

It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of plane-fronted and pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. These solutions are classified in terms of their chirality and generate a family of non-stationary spacetime metrics. Particular members of these families are used as backgrounds in analysing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.

Probing the smearing effect by a pointlike graviton in the plane-wave matrix model

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

Lee, Bum-Hoon; Nam, Siyoung; Shin, Hyeonjoon

2010-08-15

We investigate the interaction between a flat membrane and pointlike graviton in the plane-wave matrix model. The one-loop effective potential in the large-distance limit is computed and is shown to be of r{sup -3} type where r is the distance between two objects. This type of interaction has been interpreted as the one incorporating the smearing effect due to the configuration of a flat membrane in a plane-wave background. Our results support this interpretation and provide more evidence about it.

Applicability of geometrical optics to in-plane liquid-crystal configurations.

PubMed

Sluijter, M; Xu, M; Urbach, H P; de Boer, D K G

2010-02-15

We study the applicability of geometrical optics to inhomogeneous dielectric nongyrotropic optically anisotropic media typically found in in-plane liquid-crystal configurations with refractive indices n(o)=1.5 and n(e)=1.7. To this end, we compare the results of advanced ray- and wave-optics simulations of the propagation of an incident plane wave to a special anisotropic configuration. Based on the results, we conclude that for a good agreement between ray and wave optics, a maximum change in optical properties should occur over a distance of at least 20 wavelengths.

A parallel orbital-updating based plane-wave basis method for electronic structure calculations

NASA Astrophysics Data System (ADS)

Pan, Yan; Dai, Xiaoying; de Gironcoli, Stefano; Gong, Xin-Gao; Rignanese, Gian-Marco; Zhou, Aihui

2017-11-01

Motivated by the recently proposed parallel orbital-updating approach in real space method [1], we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue problems. In addition, we propose two new modified parallel orbital-updating methods. Compared to the traditional plane-wave methods, our methods allow for two-level parallelization, which is particularly interesting for large scale parallelization. Numerical experiments show that these new methods are more reliable and efficient for large scale calculations on modern supercomputers.

Solid explosive plane-wave lenses pressed-to-shape with dies

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

Olinger, B.

2007-11-01

Solid-explosive plane-wave lenses 1", 2" and 4¼" in diameter have been mass-produced from components pressed-to-shape with aluminum dies. The method used to calculate the contour between the solid plane-wave lens components pressed-to-shape with the dies is explained. The steps taken to press, machine, and assemble the lenses are described. The method of testing the lenses, the results of those tests, and the corrections to the dies are reviewed. The work on the ½", 8", and 12" diameter lenses is also discussed.

RCS measurements, transformations, and comparisons under cylindrical and plane wave illumination

NASA Astrophysics Data System (ADS)

Vokura, V. J.; Balanis, Constantine A.; Birtcher, Craig R.

1994-03-01

Monostatic RCS measurements of a long bar (at X-band) and of a scale model aircraft (at C-band) were performed under the quasi-plane wave illumination produced by a dual parabolic-cylinder CATR. At Arizona State University's ElectroMagnetic Anechoic Chamber (EMAC) facility, these measurements were repeated under the cylindrical wave illumination produced by a March Microwave Single-Plane Collimating Range (SPCR). The SPRC measurements were corrected using corrected using the 'reference target method.' The corrected SPCR measurements are in good agreement with the CATR measurements.

Understanding the power reflection and transmission coefficients of a plane wave at a planar interface

NASA Astrophysics Data System (ADS)

Ye, Qian; Jiang, Yikun; Lin, Haoze

2017-03-01

In most textbooks, after discussing the partial transmission and reflection of a plane wave at a planar interface, the power (energy) reflection and transmission coefficients are introduced by calculating the normal-to-interface components of the Poynting vectors for the incident, reflected and transmitted waves, separately. Ambiguity arises among students since, for the Poynting vector to be interpreted as the energy flux density, on the incident (reflected) side, the electric and magnetic fields involved must be the total fields, namely, the sum of incident and reflected fields, instead of the partial fields which are just the incident (reflected) fields. The interpretation of the cross product of partial fields as energy flux has not been obviously justified in most textbooks. Besides, the plane wave is actually an idealisation that is only ever found in textbooks, then what do the reflection and transmission coefficients evaluated for a plane wave really mean for a real beam of limited extent? To provide a clearer physical picture, we exemplify a light beam of finite transverse extent by a fundamental Gaussian beam and simulate its reflection and transmission at a planar interface. Due to its finite transverse extent, we can then insert the incident fields or reflected fields as total fields into the expression of the Poynting vector to evaluate the energy flux and then power reflection and transmission coefficients. We demonstrate that the power reflection and transmission coefficients of a beam of finite extent turn out to be the weighted sum of the corresponding coefficients for all constituent plane wave components that form the beam. The power reflection and transmission coefficients of a single plane wave serve, in turn, as the asymptotes for the corresponding coefficients of a light beam as its width expands infinitely.

Strings on AdS_3 x S^3 and the Plane-Wave Limit. Issues on PP-Wave/CFT Holography

NASA Astrophysics Data System (ADS)

Zapata, Oswaldo

2005-10-01

In this thesis we give explicit results for bosonic string amplitudes on AdS_3 x S^3 and the corresponding plane-wave limit. We also analyze the consequences of our approach for understanding holography in this set up, as well as its possible generalization to other models.

The Relativistic Transformation for an Electromagnetic Plane Wave with General Time Dependence

ERIC Educational Resources Information Center

Smith, Glenn S.

2012-01-01

In special relativity, the transformation between inertial frames for an electromagnetic plane wave is usually derived for the time-harmonic case (the field is a sinusoid of infinite duration), even though all practical waves are of finite duration and may not even contain a dominant sinusoid. This paper presents an alternative derivation in which…

Dispersion of gravitational waves in cold spherical interstellar medium

NASA Astrophysics Data System (ADS)

Barta, Dániel; Vasúth, Mátyás

We investigate the propagation of locally plane, small-amplitude, monochromatic gravitational waves (GWs) through cold compressible interstellar gas in order to provide a more accurate picture of expected waveforms for direct detection. The quasi-isothermal gas is concentrated in a spherical symmetric cloud held together by self-gravitation. Gravitational waves can be treated as linearized perturbations on the background inner Schwarzschild spacetime. The perturbed quantities lead to the field equations governing the gas dynamics and describe the interaction of gravitational waves with matter. We have shown that the transport equation of these amplitudes provides numerical solutions for the frequency-alteration. The decrease in frequency is driven by the energy dissipating process of GW-matter interactions. The decrease is significantly smaller than the magnitude of the original frequency and too small to be detectable by present second-generation and planned third-generation detectors. It exhibits a power-law relationship between original and decreased frequencies. The frequency deviation was examined particularly for the transient signal GW150914.

Shock wave interactions in hypervelocity flow

NASA Astrophysics Data System (ADS)

Sanderson, S. R.; Sturtevant, B.

1994-08-01

The impingement of shock waves on blunt bodies in steady supersonic flow is known to cause extremely high local heat transfer rates and surface pressures. Although these problems have been studied in cold hypersonic flow, the effects of dissociative relaxation processes are unknown. In this paper we report a model aimed at determining the boundaries of the possible interaction regimes for an ideal dissociating gas. Local analysis about shock wave intersection points in the pressure-flow deflection angle plane with continuation of singular solutions is the fundamental tool employed. Further, we discuss an experimental investigation of the nominally two-dimensional mean flow that results from the impingement of an oblique shock wave on the leading edge of a cylinder. The effects of variations in shock impingement geometry were visualized using differential interferometry. Generally, real gas effects are seen to increase the range of shock impingement points for which enhanced heating occurs. They also reduce the type 4 interaction supersonic jet width and influence the type 2-3 transition process.

Nonlinear and linear wave equations for propagation in media with frequency power law losses

NASA Astrophysics Data System (ADS)

Szabo, Thomas L.

2003-10-01

The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.

Plane waves in magneto-thermoelastic anisotropic medium based on (L-S) theory under the effect of Coriolis and centrifugal forces

NASA Astrophysics Data System (ADS)

Alesemi, Meshari

2018-04-01

The objective of this research is to illustrate the effectiveness of the thermal relaxation time based on the theory of Lord-Shulman (L-S), Coriolis and Centrifugal Forces on the reflection coefficients of plane waves in an anisotropic magneto-thermoelastic medium. Assuming the elastic medium is rotating with stable angular velocity and the imposed magnetic field is parallel to the boundary of the half-space. The basic equations of a transversely isotropic rotating magneto-thermoelastic medium are formulated according to thermoelasticity theory of Lord-Shulman (L-S). Next to that, getting the velocity equation which is illustrated to show existence of three quasi-plane waves propagating in the medium. The amplitude ratios coefficients of these plane waves have been given and then computed numerically and plotted graphically to demonstrate the influences of the rotation on the Zinc material.

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.

Fast, purely growing collisionless reconnection as an eigenfunction problem related to but not involving linear whistler waves

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

Bellan, Paul M.

If either finite electron inertia or finite resistivity is included in 2D magnetic reconnection, the two-fluid equations become a pair of second-order differential equations coupling the out-of-plane magnetic field and vector potential to each other to form a fourth-order system. The coupling at an X-point is such that out-of-plane even-parity electric and odd-parity magnetic fields feed off each other to produce instability if the scale length on which the equilibrium magnetic field changes is less than the ion skin depth. The instability growth rate is given by an eigenvalue of the fourth-order system determined by boundary and symmetry conditions. Themore » instability is a purely growing mode, not a wave, and has growth rate of the order of the whistler frequency. The spatial profile of both the out-of-plane electric and magnetic eigenfunctions consists of an inner concave region having extent of the order of the electron skin depth, an intermediate convex region having extent of the order of the equilibrium magnetic field scale length, and a concave outer exponentially decaying region. If finite electron inertia and resistivity are not included, the inner concave region does not exist and the coupled pair of equations reduces to a second-order differential equation having non-physical solutions at an X-point.« less

Innovative Technologies for Maskless Lithography and Non-Conventional Patterning

DTIC Science & Technology

2008-08-01

wave sources are used and quantitative data is produced on the local field intensities and scattered plane and plasmon wave amplitudes and phases...transistors”, Transducers 2007, Lyon, France, 3EH5.P, 2007. 9. D. Huang and V. Subramanian “Iodine-doped pentacene schottky diodes for high-frequency RFID...wave sources are used and quantitative data is produced on the local field intensities and scattered plane and plasmon wave amplitudes and phases

Reflection coefficient of qP, qS and SH at a plane boundary between viscoelastic TTI media

NASA Astrophysics Data System (ADS)

Wang, Hongwei; Peng, Suping

2016-01-01

This paper introduces a calculation method for the effective elastic stiffness tensor matrix of the viscous-elastic TTI medium based on the Chapman theory. We then obtain the phase velocity formula and seismic wave polarization formula of the viscous-elastic TTI medium, by solving the Christoffel equation; solve the phase angle of reflection and transmission wave through the numerical method in accordance with the wave slowness ellipsoid; on the basis of this assumption, and assuming that qP, qS and SH waves occurred simultaneously at the viscous-elastic anisotropic interface, establish the sixth-order Zoeppritz equation in accordance with the boundary conditions; establish the models for the upper and lower media which are viscous-elastic HTI, TTI, etc., on the basis of the sixth-order Zoeppritz equation; and study the impact of fracture dip angle, azimuth angle and frequency on the reflection coefficient. From this we obtain the following conclusions: the reflection coefficient can identify the fracture strike and dip when any information pertaining to the media is unknown; dispersion phenomenon is obvious on the axial plane of symmetry and weakened in the plane vertical to the axial plane of symmetry; the vertical-incidence longitudinal wave can stimulate the qS wave when the dip angle is not 0° or 90° under the condition of coincidence between the symmetry planes of the upper and lower media; when the symmetry planes of the upper and lower media do not coincide and the dip angle is not 0° or 90°, then the vertical-incidence qP will stimulate the qS and SH waves at the same time; the dip angle can cause the reflection coefficient curve to have a more obvious dispersion phenomenon, while the included angle between the symmetry planes of the upper and lower media will weaken the dispersion except SH; and the intercept of reflection coefficient is affected by the fracture dip and included angle between the symmetry planes of the upper and lower media.

Coherent scattering of a spherical wave from an irregular surface. [antenna pattern effects

NASA Technical Reports Server (NTRS)

Fung, A. K.

1983-01-01

The scattering of a spherical wave from a rough surface using the Kirchhoff approximation is considered. An expression representing the measured coherent scattering coefficient is derived. It is shown that the sphericity of the wavefront and the antenna pattern can become an important factor in the interpretation of ground-based measurements. The condition under which the coherent scattering-coefficient expression reduces to that corresponding to a plane wave incidence is given. The condition under which the result reduces to the standard image solution is also derived. In general, the consideration of antenna pattern and sphericity is unimportant unless the surface-height standard deviation is small, i.e., unless the coherent scattering component is significant. An application of the derived coherent backscattering coefficient together with the existing incoherent scattering coefficient to interpret measurements from concrete and asphalt surfaces is shown.

Seismic Waves, 4th order accurate

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

2013-08-16

SW4 is a program for simulating seismic wave propagation on parallel computers. SW4 colves the seismic wave equations in Cartesian corrdinates. It is therefore appropriate for regional simulations, where the curvature of the earth can be neglected. SW4 implements a free surface boundary condition on a realistic topography, absorbing super-grid conditions on the far-field boundaries, and a kinematic source model consisting of point force and/or point moment tensor source terms. SW4 supports a fully 3-D heterogeneous material model that can be specified in several formats. SW4 can output synthetic seismograms in an ASCII test format, or in the SAC finarymore » format. It can also present simulation information as GMT scripts, whixh can be used to create annotated maps. Furthermore, SW4 can output the solution as well as the material model along 2-D grid planes.« less

Forward volume and surface magnetostatic modes in an yttrium iron garnet film for out-of-plane magnetic fields: Theory and experiment

NASA Astrophysics Data System (ADS)

Lim, Jinho; Bang, Wonbae; Trossman, Jonathan; Amanov, Dovran; Ketterson, John B.

2018-05-01

We present experimental and theoretical results on the propagation of magnetostatic spin waves in a film of yttrium iron garnet (YIG) for out-of-plane magnetic fields for which propagation in opposite directions is nonreciprocal in the presence of a metal layer. The plane studied is defined by the film normal n and n × k where k is the wave vector of the mode. Spin waves in this setting are classified as forward volume waves or surface waves and display non-reciprocity in the presence of an adjacent metal layer except for when H//n. The measurements are carried out in a transmission geometry, and a microwave mixer is used to measure the change of phase, and with it the evolution of wavevector, of the arriving spin wave with external magnetic field.

TSOS and TSOS-FK hybrid methods for modelling the propagation of seismic waves

NASA Astrophysics Data System (ADS)

Ma, Jian; Yang, Dinghui; Tong, Ping; Ma, Xiao

2018-05-01

We develop a new time-space optimized symplectic (TSOS) method for numerically solving elastic wave equations in heterogeneous isotropic media. We use the phase-preserving symplectic partitioned Runge-Kutta method to evaluate the time derivatives and optimized explicit finite-difference (FD) schemes to discretize the space derivatives. We introduce the averaged medium scheme into the TSOS method to further increase its capability of dealing with heterogeneous media and match the boundary-modified scheme for implementing free-surface boundary conditions and the auxiliary differential equation complex frequency-shifted perfectly matched layer (ADE CFS-PML) non-reflecting boundaries with the TSOS method. A comparison of the TSOS method with analytical solutions and standard FD schemes indicates that the waveform generated by the TSOS method is more similar to the analytic solution and has a smaller error than other FD methods, which illustrates the efficiency and accuracy of the TSOS method. Subsequently, we focus on the calculation of synthetic seismograms for teleseismic P- or S-waves entering and propagating in the local heterogeneous region of interest. To improve the computational efficiency, we successfully combine the TSOS method with the frequency-wavenumber (FK) method and apply the ADE CFS-PML to absorb the scattered waves caused by the regional heterogeneity. The TSOS-FK hybrid method is benchmarked against semi-analytical solutions provided by the FK method for a 1-D layered model. Several numerical experiments, including a vertical cross-section of the Chinese capital area crustal model, illustrate that the TSOS-FK hybrid method works well for modelling waves propagating in complex heterogeneous media and remains stable for long-time computation. These numerical examples also show that the TSOS-FK method can tackle the converted and scattered waves of the teleseismic plane waves caused by local heterogeneity. Thus, the TSOS and TSOS-FK methods proposed in this study present an essential tool for the joint inversion of local, regional, and teleseismic waveform data.

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.

Relating Stellar Cycle Periods to Dynamo Calculations

NASA Technical Reports Server (NTRS)

Tobias, S. M.

1998-01-01

Stellar magnetic activity in slowly rotating stars is often cyclic, with the period of the magnetic cycle depending critically on the rotation rate and the convective turnover time of the star. Here we show that the interpretation of this law from dynamo models is not a simple task. It is demonstrated that the period is (unsurprisingly) sensitive to the precise type of non-linearity employed. Moreover the calculation of the wave-speed of plane-wave solutions does not (as was previously supposed) give an indication of the magnetic period in a more realistic dynamo model, as the changes in length-scale of solutions are not easily captured by this approach. Progress can be made, however, by considering a realistic two-dimensional model, in which the radial length-scale of waves is included. We show that it is possible in this case to derive a more robust relation between cycle period and dynamo number. For all the non-linearities considered in the most realistic model, the magnetic cycle period is a decreasing function of IDI (the amplitude of the dynamo number). However, discriminating between different non-linearities is difficult in this case and care must therefore be taken before advancing explanations for the magnetic periods of stars.

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.

Root finding in the complex plane for seismo-acoustic propagation scenarios with Green's function solutions.

PubMed

McCollom, Brittany A; Collis, Jon M

2014-09-01

A normal mode solution to the ocean acoustic problem of the Pekeris waveguide with an elastic bottom using a Green's function formulation for a compressional wave point source is considered. Analytic solutions to these types of waveguide propagation problems are strongly dependent on the eigenvalues of the problem; these eigenvalues represent horizontal wavenumbers, corresponding to propagating modes of energy. The eigenvalues arise as singularities in the inverse Hankel transform integral and are specified by roots to a characteristic equation. These roots manifest themselves as poles in the inverse transform integral and can be both subtle and difficult to determine. Following methods previously developed [S. Ivansson et al., J. Sound Vib. 161 (1993)], a root finding routine has been implemented using the argument principle. Using the roots to the characteristic equation in the Green's function formulation, full-field solutions are calculated for scenarios where an acoustic source lies in either the water column or elastic half space. Solutions are benchmarked against laboratory data and existing numerical solutions.

Sound field reconstruction within an entire cavity by plane wave expansions using a spherical microphone array.

PubMed

Wang, Yan; Chen, Kean

2017-10-01

A spherical microphone array has proved effective in reconstructing an enclosed sound field by a superposition of spherical wave functions in Fourier domain. It allows successful reconstructions surrounding the array, but the accuracy will be degraded at a distance. In order to extend the effective reconstruction to the entire cavity, a plane-wave basis in space domain is used owing to its non-decaying propagating characteristic and compared with the conventional spherical wave function method in a low frequency sound field within a cylindrical cavity. The sensitivity to measurement noise, the effects of the numbers of plane waves, and measurement positions are discussed. Simulations show that under the same measurement conditions, the plane wave function method is superior in terms of reconstruction accuracy and data processing efficiency, that is, the entire sound field imaging can be achieved by only one time calculation instead of translations of local sets of coefficients with respect to every measurement position into a global one. An experiment was conducted inside an aircraft cabin mock-up for validation. Additionally, this method provides an alternative possibility to recover the coefficients of high order spherical wave functions in a global coordinate system without coordinate translations with respect to local origins.

An Apparatus for Constructing an Electromagnetic Plane Wave Model

ERIC Educational Resources Information Center

Kneubil, Fabiana Botelho; Loures, Marcus Vinicius Russo; Amado, William

2015-01-01

In this paper we report on an activity aimed at building an electromagnetic wave. This was part of a class on the concept of mass offered to a group of 20 pre-service Brazilian physics teachers. The activity consisted of building a plane wave using an apparatus in which it is possible to fit some rods representing electric and magnetic fields into…

Globally Convergent Inverse Reconstruction Algorithm for Detection of IEDs via Imaging of Spatially Distributed Dielectric Constants using Microwave

DTIC Science & Technology

2010-04-27

Dirichlet boundary data DP̃ (x, y) at the entire plane P̃ . Then one can solve the following boundary value problem in the half space below P̃ ∆w − s2w...which we wanted to be a plane wave when reaching the bottom side of the prism of Figure 1, where measurements were conducted. But actually this 14 was a...initializing wave field is a plane wave. On the other hand, a visual inspection of the output experimental data has revealed to us that actually we had a

Plane-wave scattering by self-complementary metasurfaces in terms of electromagnetic duality and Babinet's principle

NASA Astrophysics Data System (ADS)

Nakata, Yosuke; Urade, Yoshiro; Nakanishi, Toshihiro; Kitano, Masao

2013-11-01

We investigate theoretically electromagnetic plane-wave scattering by self-complementary metasurfaces. By using Babinet's principle extended to metasurfaces with resistive elements, we show that the frequency-independent transmission and reflection are realized for normal incidence of a circularly polarized plane wave onto a self-complementary metasurface, even if there is diffraction. Next, we consider two special classes of self-complementary metasurfaces. We show that self-complementary metasurfaces with rotational symmetry can act as coherent perfect absorbers, and those with translational symmetry compatible with their self-complementarity can split the incident power equally, even for oblique incidences.

Generalized thermoelastic wave band gaps in phononic crystals without energy dissipation

NASA Astrophysics Data System (ADS)

Wu, Ying; Yu, Kaiping; Li, Xiao; Zhou, Haotian

2016-01-01

We present a theoretical investigation of the thermoelastic wave propagation in the phononic crystals in the context of Green-Nagdhi theory by taking thermoelastic coupling into account. The thermal field is assumed to be steady. Thermoelastic wave band structures of 3D and 2D are derived by using the plane wave expansion method. For the 2D problem, the anti-plane shear mode is not affected by the temperature difference. Thermoelastic wave bands of the in-plane x-y mode are calculated for lead/silicone rubber, aluminium/silicone rubber, and aurum/silicone rubber phononic crystals. The new findings in the numerical results indicate that the thermoelastic wave bands are composed of the pure elastic wave bands and the thermal wave bands, and that the thermal wave bands can serve as the low boundary of the first band gap when the filling ratio is low. In addition, for the lead/silicone rubber phononic crystals the effects of lattice type (square, rectangle, regular triangle, and hexagon) and inclusion shape (circle, oval, and square) on the normalized thermoelastic bandwidth and the upper/lower gap boundaries are analysed and discussed. It is concluded that their effects on the thermoelastic wave band structure are remarkable.

Scattering Matrix for the Interaction between Solar Acoustic Waves and Sunspots. I. Measurements

NASA Astrophysics Data System (ADS)

Yang, Ming-Hsu; Chou, Dean-Yi; Zhao, Hui

2017-01-01

Assessing the interaction between solar acoustic waves and sunspots is a scattering problem. The scattering matrix elements are the most commonly used measured quantities to describe scattering problems. We use the wavefunctions of scattered waves of NOAAs 11084 and 11092 measured in the previous study to compute the scattering matrix elements, with plane waves as the basis. The measured scattered wavefunction is from the incident wave of radial order n to the wave of another radial order n‧, for n=0{--}5. For a time-independent sunspot, there is no mode mixing between different frequencies. An incident mode is scattered into various modes with different wavenumbers but the same frequency. Working in the frequency domain, we have the individual incident plane-wave mode, which is scattered into various plane-wave modes with the same frequency. This allows us to compute the scattering matrix element between two plane-wave modes for each frequency. Each scattering matrix element is a complex number, representing the transition from the incident mode to another mode. The amplitudes of diagonal elements are larger than those of the off-diagonal elements. The amplitude and phase of the off-diagonal elements are detectable only for n-1≤slant n\\prime ≤slant n+1 and -3{{Δ }}k≤slant δ {k}x≤slant 3{{Δ }}k, where δ {k}x is the change in the transverse component of the wavenumber and Δk = 0.035 rad Mm-1.

Response of a shell structure subject to distributed harmonic excitation

NASA Astrophysics Data System (ADS)

Cao, Rui; Bolton, J. Stuart

2016-09-01

Previously, a coupled, two-dimensional structural-acoustic ring model was constructed to simulate the dynamic and acoustical behavior of pneumatic tires. Analytical forced solutions were obtained and were experimentally verified through laser velocimeter measurement made using automobile tires. However, the two-dimensional ring model is incapable of representing higher order, in-plane modal motion in either the circumferential or axial directions. Therefore, in this paper, a three-dimensional pressurized circular shell model is proposed to study the in-plane shearing motion and the effect of different forcing conditions. Closed form analytical solutions were obtained for both free and forced vibrations of the shell under simply supported boundary conditions. Dispersion relations were calculated and different wave types were identified by their different speeds. Shell surface mobility results under various input distributions were also studied and compared. Spatial Fourier series decompositions were also performed on the spatial mobility results to give the forced dispersion relations, which illustrate clearly the influence of input force spatial distribution. Such a model has practical application in identifying the sources of noise and vibration problems in automotive tires.

Experimental Basis for IED Particle Model

NASA Astrophysics Data System (ADS)

Zheng-Johansson, J.

2009-03-01

The internally electrodynamic (IED) particle model is built on three experimental facts: a) electric charges present in all matter particles, b) an accelerated charge generates electromagnetic (EM) waves by Maxwell's equations and Planck energy equation, and c) source motion gives Doppler effect. A set of well-kwon basic particle equations have been predicted based on first-principles solutions for IED particle (e.g. J Phys CS128, 012019, 2008); the equations are long experimentally validated. A critical review of the key experiments suggests that the IED process underlies these equations not just sufficiently but also necessarily. E.g.: 1) A free IED electron solution is a plane wave ψ= Ce^i(kdX-φT) requisite for producing the diffraction fringe in a Davisson-Germer experiment, and of also all basic point-like attributes facilitated by a linear momentum kd and the model structure. It needs not further be a wave packet which produces not a diffraction fringe. 2)The radial partial EM waves, hence the total ψ, of an IED electron will, on both EM theory and experiment basis -not by assumption, enter two slits at the same time, as is requisite for an electron to interfere with itself as shown in double slit experiments. 3) On annihilation, an electron converts (from mass m) to a radiation energy φ without an acceleration which is externally observable and yet requisite by EM theory. So a charge oscillation of frequency φ and its EM waves must regularly present internal of a normal electron, whence the IED model.

Argand-plane vorticity singularities in complex scalar optical fields: an experimental study using optical speckle.

PubMed

Rothschild, Freda; Bishop, Alexis I; Kitchen, Marcus J; Paganin, David M

2014-03-24

The Cornu spiral is, in essence, the image resulting from an Argand-plane map associated with monochromatic complex scalar plane waves diffracting from an infinite edge. Argand-plane maps can be useful in the analysis of more general optical fields. We experimentally study particular features of Argand-plane mappings known as "vorticity singularities" that are associated with mapping continuous single-valued complex scalar speckle fields to the Argand plane. Vorticity singularities possess a hierarchy of Argand-plane catastrophes including the fold, cusp and elliptic umbilic. We also confirm their connection to vortices in two-dimensional complex scalar waves. The study of vorticity singularities may also have implications for higher-dimensional fields such as coherence functions and multi-component fields such as vector and spinor fields.

Influence of Tissue Microstructure on Shear Wave Speed Measurements in Plane Shear Wave Elastography: A Computational Study in Lossless Fibrotic Liver Media.

PubMed

Wang, Yu; Jiang, Jingfeng

2018-01-01

Shear wave elastography (SWE) has been used to measure viscoelastic properties for characterization of fibrotic livers. In this technique, external mechanical vibrations or acoustic radiation forces are first transmitted to the tissue being imaged to induce shear waves. Ultrasonically measured displacement/velocity is then utilized to obtain elastographic measurements related to shear wave propagation. Using an open-source wave simulator, k-Wave, we conducted a case study of the relationship between plane shear wave measurements and the microstructure of fibrotic liver tissues. Particularly, three different virtual tissue models (i.e., a histology-based model, a statistics-based model, and a simple inclusion model) were used to represent underlying microstructures of fibrotic liver tissues. We found underlying microstructures affected the estimated mean group shear wave speed (SWS) under the plane shear wave assumption by as much as 56%. Also, the elastic shear wave scattering resulted in frequency-dependent attenuation coefficients and introduced changes in the estimated group SWS. Similarly, the slope of group SWS changes with respect to the excitation frequency differed as much as 78% among three models investigated. This new finding may motivate further studies examining how elastic scattering may contribute to frequency-dependent shear wave dispersion and attenuation in biological tissues.

The observation of AE events under uniaxial compression and the quantitative relationship between the anisotropy index and the main failure plane

NASA Astrophysics Data System (ADS)

Zhang, Zhibo; Wang, Enyuan; Chen, Dong; Li, Xuelong; Li, Nan

2016-11-01

In this paper, the P-wave velocities in different directions of sandstone samples under uniaxial compression are measured. The results indicate that the changes in the P-wave velocity in different directions are almost the same. In the initial stage of loading, the P-wave velocity exhibits a rising trend due to compaction and closure of preexisting fissures. As the stress increase, preexisting fissures are closed but induced fractures are not yet generated. The sandstone samples become denser and more uniform. The P-wave velocity remains in a steady state at a high level. In the late stage of loading, the P-wave velocity drops significantly due to the expansion and breakthrough of induced fractures. The P-wave velocity anisotropy index ε is analyzed during the process of loading. It can be observed that the change in the degree of wave velocity anisotropy can be divided into three stages: the AB stage, the BC stage and the CD stage, with a changing trend from decline to incline. In the initial stage of loading, the preexisting fissures have a randomized distribution, and the change is large-scale and uniform. The difference in each spatial point decreases gradually, and synchronization increases gradually. Thus, the P-wave velocity anisotropy declines. As the stress increases gradually, with the expansion and breakthrough of induced fractures, the difference in each spatial point increases. Before failure of rock samples, the violent change region of the rock samples' internal structure is focused on a narrow two-dimensional zone, and the rock samples' structural change is obviously local. Therefore, the degree of velocity anisotropy rises after declining, and it also has good corresponding relation among the AE count, the location of AE events and the degree of wave velocity anisotropy. The projection plane of the main fracture plane on the axis plane is recorded as M plane. Based on the AFF equation, for the CD stage, we analyze the quantitative relationship between the velocity anisotropy index ε and angle θ, which is the difference between the angle of the M plane and the X plane and the angle of the M plane and the Y plane from the theoretical point. The results indicate that 1/ε and cotθ/2 have good negative linear relationship that can be expressed as cotθ/2 = a ∗1/ε + b. According to experimental data, the linear fit of 1/ε and cotθ/2 is found, obtaining cotθ/2 = - 0.04721/ε + 0.03, with a linear fit index of 0.908. From an experimental point of view, the linear relationship between 1/ε and cotθ/2 is verified. Through this research, we propose a new method for quantitatively predicting the main fracture occurrence position by P-wave velocity anisotropy. This work has an important significance for understanding buckling failure of rocks.

Effective equations for matter-wave gap solitons in higher-order transversal states.

PubMed

Mateo, A Muñoz; Delgado, V

2013-10-01

We demonstrate that an important class of nonlinear stationary solutions of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) exhibiting nontrivial transversal configurations can be found and characterized in terms of an effective one-dimensional (1D) model. Using a variational approach we derive effective equations of lower dimensionality for BECs in (m,n(r)) transversal states (states featuring a central vortex of charge m as well as n(r) concentric zero-density rings at every z plane) which provides us with a good approximate solution of the original 3D problem. Since the specifics of the transversal dynamics can be absorbed in the renormalization of a couple of parameters, the functional form of the equations obtained is universal. The model proposed finds its principal application in the study of the existence and classification of 3D gap solitons supported by 1D optical lattices, where in addition to providing a good estimate for the 3D wave functions it is able to make very good predictions for the μ(N) curves characterizing the different fundamental families. We have corroborated the validity of our model by comparing its predictions with those from the exact numerical solution of the full 3D GPE.

Numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Calini, A.; Schober, C. M.

2013-09-01

In this article we present the results of a broad numerical investigation on the stability of breather-type solutions of the nonlinear Schrödinger (NLS) equation, specifically the one- and two-mode breathers for an unstable plane wave, which are frequently used to model rogue waves. The numerical experiments involve large ensembles of perturbed initial data for six typical random perturbations. Ensemble estimates of the "closeness", A(t), of the perturbed solution to an element of the respective unperturbed family indicate that the only neutrally stable breathers are the ones of maximal dimension, that is: given an unstable background with N unstable modes, the only neutrally stable breathers are the N-dimensional ones (obtained as a superimposition of N simple breathers via iterated Backlund transformations). Conversely, breathers which are not fully saturated are sensitive to noisy environments and are unstable. Interestingly, A(t) is smallest for the coalesced two-mode breather indicating the coalesced case may be the most robust two-mode breather in a laboratory setting. The numerical simulations confirm and provide a realistic realization of the stability behavior established analytically by the authors.