A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion

NASA Astrophysics Data System (ADS)

Perumpanani, Abbey J.; Sherratt, Jonathan A.; Norbury, John; Byrne, Helen M.

1999-02-01

Invasive cells variously show changes in adhesion, protease production and motility. In this paper the authors develop and analyse a model for malignant invasion, brought about by a combination of proteolysis and haptotaxis. A common feature of these two mechanisms is that they can be produced by contact with the extracellular matrix through the mediation of a class of surface receptors called integrins. An unusual feature of the model is the absence of cell diffusion. By seeking travelling wave solutions the model is reduced to a system of ordinary differential equations which can be studied using phase plane analysis. The authors demonstrate the presence of a singular barrier in the phase plane and a “hole” in this singular barrier which admits a phase trajectory. The model admits a family of travelling waves which depend on two parameters, i.e. the tissue concentration of connective tissue and the rate of decay of the initial spatial profile of the invading cells. The slowest member of this family corresponds to the phase trajectory which goes through the “hole” in the singular barrier. Using a power series method the authors derive an expression relating the minimum wavespeed to the tissue concentration of the extracellular matrix which is arbitrary. The model is applicable in a wide variety of biological settings which combine haptotaxis with proteolysis. By considering various functional forms the authors show that the key mathematical features of the particular model studied in the early parts of the paper are exhibited by a wider class of models which characterise the behaviour of invading cells.

Broadband Control of Topological Nodes in Electromagnetic Fields

NASA Astrophysics Data System (ADS)

Song, Alex Y.; Catrysse, Peter B.; Fan, Shanhui

2018-05-01

We study topological nodes (phase singularities) in electromagnetic wave interactions with structures. We show that, when the nodes exist, it is possible to bind certain nodes to a specific plane in the structure by a combination of mirror and time-reversal symmetry. Such binding does not rely on any resonances in the structure. As a result, the nodes persist on the plane over a wide wavelength range. As an implication of such broadband binding, we demonstrate that the topological nodes can be used for hiding of metallic objects over a broad wavelength range.

High-order integral equation methods for problems of scattering by bumps and cavities on half-planes.

PubMed

Pérez-Arancibia, Carlos; Bruno, Oscar P

2014-08-01

This paper presents high-order integral equation methods for the evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced in this paper apply to eight classical scattering problems, namely, scattering by a dielectric bump on a perfectly conducting or a dielectric half-plane, and scattering by a filled, overfilled, or void dielectric cavity on a perfectly conducting or a dielectric half-plane. In all cases field representations based on single-layer potentials for appropriately chosen Green functions are used. The numerical far fields and near fields exhibit excellent convergence as discretizations are refined-even at and around points where singular fields and infinite currents exist.

Multi-domain boundary element method for axi-symmetric layered linear acoustic systems

NASA Astrophysics Data System (ADS)

Reiter, Paul; Ziegelwanger, Harald

2017-12-01

Homogeneous porous materials like rock wool or synthetic foam are the main tool for acoustic absorption. The conventional absorbing structure for sound-proofing consists of one or multiple absorbers placed in front of a rigid wall, with or without air-gaps in between. Various models exist to describe these so called multi-layered acoustic systems mathematically for incoming plane waves. However, there is no efficient method to calculate the sound field in a half space above a multi layered acoustic system for an incoming spherical wave. In this work, an axi-symmetric multi-domain boundary element method (BEM) for absorbing multi layered acoustic systems and incoming spherical waves is introduced. In the proposed BEM formulation, a complex wave number is used to model absorbing materials as a fluid and a coordinate transformation is introduced which simplifies singular integrals of the conventional BEM to non-singular radial and angular integrals. The radial and angular part are integrated analytically and numerically, respectively. The output of the method can be interpreted as a numerical half space Green's function for grounds consisting of layered materials.

Mitotic Cortical Waves Predict Future Division Sites by Encoding Positional and Size Information.

PubMed

Xiao, Shengping; Tong, Cheesan; Yang, Yang; Wu, Min

2017-11-20

Dynamic spatial patterns such as traveling waves could theoretically encode spatial information, but little is known about whether or how they are employed by biological systems, especially higher eukaryotes. Here, we show that concentric target or spiral waves of active Cdc42 and the F-BAR protein FBP17 are invoked in adherent cells at the onset of mitosis. These waves predict the future sites of cell divisions and represent the earliest known spatial cues for furrow assembly. Unlike interphase waves, the frequencies and wavelengths of the mitotic waves display size-dependent scaling properties. While the positioning role of the metaphase waves requires microtubule dynamics, spindle and microtubule-independent inhibitory signals are propagated by the mitotic waves to ensure the singularity of furrow formation. Taken together, we propose that metaphase cortical waves integrate positional and cell size information for division-plane specification in adhesion-dependent cytokinesis. Copyright © 2017 Elsevier Inc. All rights reserved.

Scattering of electromagnetic waves by a graphene-coated thin cylinder of left-handed metamaterial

NASA Astrophysics Data System (ADS)

Pashaeiadl, Hamid; Naserpour, Mahin; Zapata-Rodríguez, Carlos J.

2018-04-01

In this paper we explored the scattering behavior of thin cylinders made of LHM and coated by a monoatomic graphene layer. A spectral tunability of the resonance peaks is evidenced by altering the chemical potential of the graphene coating, a fact that occurs at any state of polarization of the incident plane wave in opposition to the case of scatterers of dielectric core. On the contrary, no invisibility condition can be satisfied for dielectric environments. A singular performance is also found for cylinders with permittivity and permeability near zero. Practical implementations of our results can be carried out in sensing and wave manipulation driven by metamaterials.

Measuring the light scattering and orientation of a spheroidal particle using in-line holography.

PubMed

Seo, Kyung Won; Byeon, Hyeok Jun; Lee, Sang Joon

2014-07-01

The light scattering properties of a horizontally and vertically oriented spheroidal particle under laser illumination are experimentally investigated using digital in-line holography. The reconstructed wave field shows the bright singular points as a result of the condensed beam formed by a transparent spheroidal particle acting as a lens. The in-plane (θ) and out-of-plane (ϕ) rotating angles of an arbitrarily oriented spheroidal particle are measured by using these scattering properties. As a feasibility test, the 3D orientation of a transparent spheroidal particle suspended in a microscale pipe flow is successfully reconstructed by adapting the proposed method.

Non-singular acoustic cloak derived by the ray tracing method with rotationally symmetric transformations

PubMed Central

Wu, Linzhi

2016-01-01

Recently, the ray tracing method has been used to derive the non-singular cylindrical invisibility cloaks for out-of-plane shear waves, which is impossible via the transformation method directly owing to the singular push-forward mapping. In this paper, the method is adopted to design a kind of non-singular acoustic cloak. Based on Hamilton's equations of motion, eikonal equation and pre-designed ray equations, we derive several constraint equations for bulk modulus and density tensor. On the premise that the perfect matching conditions are satisfied, a series of non-singular physical profiles can be obtained by arranging the singular terms reasonably. The physical profiles derived by the ray tracing method will degenerate to the transformation-based solutions when taking the transport equation into consideration. This illuminates the essence of the newly designed cloaks that they are actually the so-called eikonal cloaks that can accurately control the paths of energy flux but with small disturbance in energy distribution along the paths. The near-perfect invisible performance has been demonstrated by the numerical ray tracing results and the pressure distribution snapshots. Finally, a kind of reduced cloak is conceived, and the good invisible performance has been measured quantitatively by the normalized scattering width. PMID:27118884

The effect of spherical aberration on the phase singularities of focused dark-hollow Gaussian beams

NASA Astrophysics Data System (ADS)

Luo, Yamei; Lü, Baida

2009-06-01

The phase singularities of focused dark-hollow Gaussian beams in the presence of spherical aberration are studied. It is shown that the evolution behavior of phase singularities of focused dark-hollow Gaussian beams in the focal region depends not only on the truncation parameter and beam order, but also on the spherical aberration. The spherical aberration leads to an asymmetric spatial distribution of singularities outside the focal plane and to a shift of singularities near the focal plane. The reorganization process of singularities and spatial distribution of singularities are additionally dependent on the sign of the spherical aberration. The results are illustrated by numerical examples.

Acoustic scattering on spheroidal shapes near boundaries

NASA Astrophysics Data System (ADS)

Miloh, Touvia

2016-11-01

A new expression for the Lamé product of prolate spheroidal wave functions is presented in terms of a distribution of multipoles along the axis of the spheroid between its foci (generalizing a corresponding theorem for spheroidal harmonics). Such an "ultimate" singularity system can be effectively used for solving various linear boundary-value problems governed by the Helmholtz equation involving prolate spheroidal bodies near planar or other boundaries. The general methodology is formally demonstrated for the axisymmetric acoustic scattering problem of a rigid (hard) spheroid placed near a hard/soft wall or inside a cylindrical duct under an axial incidence of a plane acoustic wave.

The crack problem in bonded nonhomogeneous materials

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Kaya, A. C.; Joseph, P. F.

1988-01-01

The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.

The crack problem in bonded nonhomogeneous materials

NASA Technical Reports Server (NTRS)

Erdogan, F.; Joseph, P. F.; Kaya, A. C.

1991-01-01

The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip termination at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.

Nonlinear Waves, Instabilities and Singularities in Plasma and Hydrodynamics

NASA Astrophysics Data System (ADS)

Silantyev, Denis Albertovich

Nonlinear effects are present in almost every area of science as soon as one tries to go beyond the first order approximation. In particular, nonlinear waves emerge in such areas as hydrodynamics, nonlinear optics, plasma physics, quantum physics, etc. The results of this work are related to nonlinear waves in two areas, plasma physics and hydrodynamics, united by concepts of instability, singularity and advanced numerical methods used for their investigation. The first part of this work concentrates on Langmuir wave filamentation instability in the kinetic regime of plasma. In Internal Confinement Fusion Experiments (ICF) at National Ignition Facility (NIF), where attempts are made to achieve fusion by compressing a small target by many powerful lasers to extremely high temperatures and pressures, plasma is created in the first moments of the laser reaching the target and undergoes complicated dynamics. Some of the most challenging difficulties arise from various plasma instabilities that occur due to interaction of the laser beam and a plasma surrounding the target. In this work we consider one of such instabilities that describes a decay of nonlinear plasma wave, initially excited due to interaction of the laser beam with the plasma, into many filaments in direction perpendicular to the laser beam, therefore named Langmuir filamentation instability. This instability occurs in the kinetic regime of plasma, klambda D > 0.2, where k is the wavenumber and lambda D is the Debye length. The filamentation of Langmuir waves in turn leads to the saturation of the stimulated Raman scattering (SRS) in laser-plasma interaction experiments which plays an essential role in ICF experiments. The challenging part of this work was that unlike in hydrodynamics we needed to use fully kinetic description of plasma to capture the physics in question properly, meaning that we needed to consider the distribution function of charged particles and its evolution in time not only with respect to spatial coordinates but with respect to velocities as well. To study Langmuir filamentation instability in its simplest form we performed 2D+2V numerical simulations. Taking into account that the distribution function in question was 4-dimensional function, making these simulation quite challenging, we developed an efficient numerical method making these simulations possible on modern desktop computers. Using the developed numerical method we studied how Langmuir wave filamentation instability depends on the parameters of the Langmuir wave such as wave length and amplitude that are relevant to ICF experiments. We considered several types of Langmuir waves, including nonlinear Langmuir waves exited by external electric field as well as an idealized approximation of such Langmuir waves by a particular family of Bernstein-Greene-Kruskal (BGK) modes that bifurcates from the linear Langmuir wave. The results of these simulations were compared to the theoretical predictions in our recent papers. An alternative approach to overcome computational difficulty of this problem was considered by our research group in Ref. It involves reducing the number of transverse direction in the model therefore lowering computational difficulty at a cost of lesser accuracy of the model. The second part of this work concentrates on 2D free surface hydrodynamics and in particular on computing Stokes waves with high-precision using conformal maps and spectral methods. Stokes waves are fully nonlinear periodic gravity waves propagating with the constant velocity on a free surface of two-dimensional potential flow of the ideal incompressible fluid of infinite depth. The increase of the scaled wave height H/lambda, where H is the wave height and lambda is the wavelength, from H/lambda = 0 to the critical value Hmax/lambda marks the transition from almost linear wave to a strongly nonlinear limiting Stokes wave. The Stokes wave of the greatest height H = Hmax has an angle of 120° at the crest. To obtain Stokes wave fully nonlinear Euler equations describing the flow can be reformulated in terms of conformal map of the fluid domain into the complex lower half-plane, with fluid free surface mapped into the real line. This description is convenient for analysis and numerical simulations since the whole problem is then reduced to a single nonlinear equation on the real line. Having computed solutions on the real line we extend them to the rest of the complex plane to analyze the singularities above real line. The distance vc from the closest singularity in the upper half-plane to the real line goes to zero as we approach the limiting Stokes wave with maximum hight Hmax/lambda, which is the reason for the widening of the solution's Fourier spectrum. (Abstract shortened by ProQuest.).

An integrated analysis-synthesis array system for spatial sound fields.

PubMed

Bai, Mingsian R; Hua, Yi-Hsin; Kuo, Chia-Hao; Hsieh, Yu-Hao

2015-03-01

An integrated recording and reproduction array system for spatial audio is presented within a generic framework akin to the analysis-synthesis filterbanks in discrete time signal processing. In the analysis stage, a microphone array "encodes" the sound field by using the plane-wave decomposition. Direction of arrival of plane-wave components that comprise the sound field of interest are estimated by multiple signal classification. Next, the source signals are extracted by using a deconvolution procedure. In the synthesis stage, a loudspeaker array "decodes" the sound field by reconstructing the plane-wave components obtained in the analysis stage. This synthesis stage is carried out by pressure matching in the interior domain of the loudspeaker array. The deconvolution problem is solved by truncated singular value decomposition or convex optimization algorithms. For high-frequency reproduction that suffers from the spatial aliasing problem, vector panning is utilized. Listening tests are undertaken to evaluate the deconvolution method, vector panning, and a hybrid approach that combines both methods to cover frequency ranges below and above the spatial aliasing frequency. Localization and timbral attributes are considered in the subjective evaluation. The results show that the hybrid approach performs the best in overall preference. In addition, there is a trade-off between reproduction performance and the external radiation.

Managing focal fields of vector beams with multiple polarization singularities.

PubMed

Han, Lei; Liu, Sheng; Li, Peng; Zhang, Yi; Cheng, Huachao; Gan, Xuetao; Zhao, Jianlin

2016-11-10

We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.

Topological resolution of gauge theory singularities

NASA Astrophysics Data System (ADS)

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-01

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

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.

Modeling and analysis of several classes of self-oscillating inverters. I - State-plane representations. II - Model extension, classification, and duality relationships

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1982-01-01

The present investigation is concerned with an important class of power conditioning networks, taking into account self-oscillating dc-to-square-wave transistor inverters. The considered circuits are widely used both as the principal power converting and processing means in many systems and as low-power analog-to-discrete-time converters for controlling the switching of the output-stage semiconductors in a variety of power conditioning systems. Aspects of piecewise-linear modeling are discussed, taking into consideration component models, and an equivalent-circuit model. Questions of singular point analysis and state plane representation are also investigated, giving attention to limit cycles, starting circuits, the region of attraction, a hard oscillator, and a soft oscillator.

Topological resolution of gauge theory singularities

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

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-21

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit themore » singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.« less

Short time propagation of a singular wave function: Some surprising results

NASA Astrophysics Data System (ADS)

Marchewka, A.; Granot, E.; Schuss, Z.

2007-08-01

The Schrödinger evolution of an initially singular wave function was investigated. First it was shown that a wide range of physical problems can be described by initially singular wave function. Then it was demonstrated that outside the support of the initial wave function the time evolution is governed to leading order by the values of the wave function and its derivatives at the singular points. Short-time universality appears where it depends only on a single parameter—the value at the singular point (not even on its derivatives). It was also demonstrated that the short-time evolution in the presence of an absorptive potential is different than in the presence of a nonabsorptive one. Therefore, this dynamics can be harnessed to the determination whether a potential is absorptive or not simply by measuring only the transmitted particles density.

Nonlinear excited waves on the interventricular septum

NASA Astrophysics Data System (ADS)

Bekki, Naoaki; Harada, Yoshifumi; Kanai, Hiroshi

2012-11-01

Using a novel ultrasonic noninvasive imaging method, we observe some phase singularities in propagating excited waves on a human cardiac interventricular septum (IVS) for a healthy young male. We present a possible physical model explaining one-dimensional dynamics of phase singularities in nonlinearly excited waves on the IVS. We show that at least one of the observed phase singularities in the excited waves on the IVS can be explained by the Bekki-Nozaki hole solution of the complex Ginzburg-Landau equation without any adjustable parameters. We conclude that the complex Ginzburg-Landau equation is such a suitable model for one-dimensional dynamics of cardiac phase singularities in nonlinearly excited waves on the IVS.

Solitary Waves, Periodic Peakons and Pseudo-Peakons of the Nonlinear Acoustic Wave Model in Rotating Magnetized Plasma

NASA Astrophysics Data System (ADS)

Li, Jibin

The dynamical model of the nonlinear acoustic wave in rotating magnetized plasma is governed by a partial differential equation system. Its traveling system is a singular traveling wave system of first class depending on two parameters. By using the bifurcation theory and method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as different solitary wave solutions.

Wave-front singularities for two-dimensional anisotropic elastic waves.

NASA Technical Reports Server (NTRS)

Payton, R. G.

1972-01-01

Wavefront singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d to the -1/2 power, where d measures distance away from the front. However, in certain exceptional cases singularities of order d to the -n power, where n = 1/4, 2/3, 3/4, may be encountered.

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.

Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

PubMed Central

Donoho, David L.

1999-01-01

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1. PMID:10051554

Resolution of quantum singularities

NASA Astrophysics Data System (ADS)

Konkowski, Deborah; Helliwell, Thomas

2017-01-01

A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.

Stress singularities at the vertex of a cylindrically anisotropic wedge

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.; Boduroglu, H.

1980-01-01

The plane elasticity problem for a cylindrically anisotropic solid is formulated. The form of the solution for an infinite wedge shaped domain with various homogeneous boundary conditions is derived and the nature of the stress singularity at the vertex of the wedge is studied. The characteristic equations giving the stress singularity and the angular distribution of the stresses around the vertex of the wedge are obtained for three standard homogeneous boundary conditions. The numerical examples show that the singular behavior of the stresses around the vertex of an anisotropic wedge may be significantly different from that of the isotropic material. Some of the results which may be of practical importance are that for a half plane the stress state at r = 0 may be singular and for a crack the power of stress singularity may be greater or less than 1/2.

Singularities in the classical Rayleigh-Taylor flow - Formation and subsequent motion

NASA Technical Reports Server (NTRS)

Tanveer, S.

1993-01-01

The creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms our previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

Singularities in the classical Rayleigh-Taylor flow: Formation and subsequent motion

NASA Technical Reports Server (NTRS)

Tanveer, S.

1992-01-01

The creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms our previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

Dark Energy and Dark Matter Phenomena and the Universe with Variable Gravitational Mass

NASA Astrophysics Data System (ADS)

Gorkavyi, N.

2005-12-01

Generation of high-frequency gravitational waves near the singularity is a crucial factor for understanding the origin and dynamics of the Universe. Emission of gravitational waves increases with a decreasing radius of collapsed object much faster than a gravitational force itself. Gravitationally unstable matter of the Universe will be completely converted into gravitational radiation during the Big Crunch. According to Misner, Thorne & Wheeler (Gravitation, 1977, p.959) plane gravitational waves have not gravitational mass or spacetime is flat everywhere outside the pulse. We can propose that the gravitational mass of the Universe is vanished after converting matter into gravitational waves. This hypothesis in the framework of Einstein's theory of gravitation can solve the problem of singularity without contradiction with theorems by Penrose-Hawking; explain the acceleration of our Universe as the effect of a retarded gravitational potential (Gorkavyi, BAAS, 2003, 35, #3) and the low quadrupole in fluctuations in CMB as result of blue-shift effect in a gravitational field. Proposed solution of dark energy problem free from coincidence problems. The hypothesis keeps best parts of Big Bang theory and inflation model without any unknown physical fields or new dimensions. According to this hypothesis a relic sea of high-frequency gravitational radiation in our Universe can be very dense. Interaction of relic gravitational waves with gravitational fields of galaxies and stars can create an additional dynamical effects like pressure of relic radiation that proportional to gravitational potential GM/(Rc2). This effect can be responsible for dark matter phenomena in galaxies and the Pioneer acceleration in the solar system (Gorkavyi, BAAS, 2005, 37, #2).

A multiwave range test for obstacle reconstructions with unknown physical properties

NASA Astrophysics Data System (ADS)

Potthast, Roland; Schulz, Jochen

2007-08-01

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A `range test' for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533-547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhauser, Basel, 1986, pp. 93-102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Gottingen, 1999]. In particular, we propose a new version of the Kirsch-Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.

Conical refraction of elastic waves in absorbing crystals

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

Alshits, V. I., E-mail: alshits@ns.crys.ras.ru; Lyubimov, V. N.

2011-10-15

The absorption-induced acoustic-axis splitting in a viscoelastic crystal with an arbitrary anisotropy is considered. It is shown that after 'switching on' absorption, the linear vector polarization field in the vicinity of the initial degeneracy point having an orientation singularity with the Poincare index n = {+-}1/2, transforms to a planar distribution of ellipses with two singularities n = {+-}1/4 corresponding to new axes. The local geometry of the slowness surface of elastic waves is studied in the vicinity of new degeneracy points and a self-intersection line connecting them. The absorption-induced transformation of the classical picture of conical refraction is studied.more » The ellipticity of waves at the edge of the self-intersection wedge in a narrow interval of propagation directions drastically changes from circular at the wedge ends to linear in the middle of the wedge. For the wave normal directed to an arbitrary point of this wedge, during movement of the displacement vector over the corresponding polarization ellipse, the wave ray velocity s runs over the same cone describing refraction in a crystal without absorption. In this case, the end of the vector moves along a universal ellipse whose plane is orthogonal to the acoustic axis for zero absorption. The areal velocity of this movement differs from the angular velocity of the displacement vector on the polarization ellipse only by a constant factor, being delayed by {pi}/2 in phase. When the wave normal is localized at the edge of the wedge in its central region, the movement of vector s along the universal ellipse becomes drastically nonuniform and the refraction transforms from conical to wedge-like.« less

Regular scattering patterns from near-cloaking devices and their implications for invisibility cloaking

NASA Astrophysics Data System (ADS)

Kocyigit, Ilker; Liu, Hongyu; Sun, Hongpeng

2013-04-01

In this paper, we consider invisibility cloaking via the transformation optics approach through a ‘blow-up’ construction. An ideal cloak makes use of singular cloaking material. ‘Blow-up-a-small-region’ construction and ‘truncation-of-singularity’ construction are introduced to avoid the singular structure, however, giving only near-cloaks. The study in the literature is to develop various mechanisms in order to achieve high-accuracy approximate near-cloaking devices, and also from a practical viewpoint to nearly cloak an arbitrary content. We study the problem from a different viewpoint. It is shown that for those regularized cloaking devices, the corresponding scattering wave fields due to an incident plane wave have regular patterns. The regular patterns are both a curse and a blessing. On the one hand, the regular wave pattern betrays the location of a cloaking device which is an intrinsic defect due to the ‘blow-up’ construction, and this is particularly the case for the construction by employing a high-loss layer lining. Indeed, our numerical experiments show robust reconstructions of the location, even by implementing the phaseless cross-section data. The construction by employing a high-density layer lining shows a certain promising feature. On the other hand, it is shown that one can introduce an internal point source to produce the canceling scattering pattern to achieve a near-cloak of an arbitrary order of accuracy.

Periodic Peakons, Pseudo-Peakons and Compactons of Ion-Acoustic Wave Model in Electronegative Plasmas with Electrons Featuring Tsallis Distribution

NASA Astrophysics Data System (ADS)

Li, Jibin

The dynamical model of the nonlinear ion-acoustic oscillations is governed by a partial differential equation system. Its traveling system is just a singular traveling wave system of first class depending on four parameters. By using the method of dynamical systems and the theory of singular traveling wave systems, in this paper, we show that there exist parameter groups such that this singular system has pseudo-peakons, periodic peakons and compactons as well as kink and anti-kink wave solutions.

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.

Electromechanical vortex filaments during cardiac fibrillation

NASA Astrophysics Data System (ADS)

Christoph, J.; Chebbok, M.; Richter, C.; Schröder-Schetelig, J.; Bittihn, P.; Stein, S.; Uzelac, I.; Fenton, F. H.; Hasenfuß, G.; Gilmour, R. F., Jr.; Luther, S.

2018-03-01

The self-organized dynamics of vortex-like rotating waves, which are also known as scroll waves, are the basis of the formation of complex spatiotemporal patterns in many excitable chemical and biological systems. In the heart, filament-like phase singularities that are associated with three-dimensional scroll waves are considered to be the organizing centres of life-threatening cardiac arrhythmias. The mechanisms that underlie the onset, maintenance and control of electromechanical turbulence in the heart are inherently three-dimensional phenomena. However, it has not previously been possible to visualize the three-dimensional spatiotemporal dynamics of scroll waves inside cardiac tissues. Here we show that three-dimensional mechanical scroll waves and filament-like phase singularities can be observed deep inside the contracting heart wall using high-resolution four-dimensional ultrasound-based strain imaging. We found that mechanical phase singularities co-exist with electrical phase singularities during cardiac fibrillation. We investigated the dynamics of electrical and mechanical phase singularities by simultaneously measuring the membrane potential, intracellular calcium concentration and mechanical contractions of the heart. We show that cardiac fibrillation can be characterized using the three-dimensional spatiotemporal dynamics of mechanical phase singularities, which arise inside the fibrillating contracting ventricular wall. We demonstrate that electrical and mechanical phase singularities show complex interactions and we characterize their dynamics in terms of trajectories, topological charge and lifetime. We anticipate that our findings will provide novel perspectives for non-invasive diagnostic imaging and therapeutic applications.

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.

Measurements of the scattering of sound by a line vortex

NASA Technical Reports Server (NTRS)

Horne, W. C.

1983-01-01

This paper presents measurements of the phase and magnitude of the scattered field arising from the incidence of a monochromatic plane sound field as a steady vortex. The amplitude of the scattered field was found to vary linearly with the vortex strength, and with the incident wave amplitude and frequency as predicted by solutions based on the Born approximation. The scattered field was observed to be nonsingular in the incidence direction, and this was similar to predictions by the Parabolic Equation Method (PEM) rather than the Born approximation, which predicts singular behavior in the incidence direction.

Some boundary-value problems for anisotropic quarter plane

NASA Astrophysics Data System (ADS)

Arkhypenko, K. M.; Kryvyi, O. F.

2018-04-01

To solve the mixed boundary-value problems of the anisotropic elasticity for the anisotropic quarter plane, a method based on the use of the space of generalized functions {\\Im }{\\prime }({\\text{R}}+2) with slow growth properties was developed. The two-dimensional integral Fourier transform was used to construct the system of fundamental solutions for the anisotropic quarter plane in this space and a system of eight boundary integral relations was obtained, which allows one to reduce the mixed boundary-value problems for the anisotropic quarter plane directly to systems of singular integral equations with fixed singularities. The exact solutions of these systems were found by using the integral Mellin transform. The asymptotic behavior of solutions was investigated at the vertex of the quarter plane.

Lee waves, benign and malignant

NASA Technical Reports Server (NTRS)

Wurtele, M. G.; Datta, A.

1992-01-01

The flow of an incompressible, stratified fluid over an obstacle will produce an oscillation in which buoyancy is the restoring force, called a gravity wave. For disturbances of this scale, the atmosphere may be treated as incompressible; and even the linear approximation will explain many of the phenomena observed in the lee of mountains. However, nonlinearities arise in two ways: (1) through the large (scaled) size of the mountain, and (2) from dynamically singular levels in the fluid field. These produce a complicated array of phenomena that present hazards to aircraft and to lee surface areas. If there is no dynamic barrier, these waves can penetrate vertically into the middle atmosphere (30-100 km attitude), where recent observations show them to be of a length scale that must involve the Coriolis force in any modeling. At these altitudes, the amplitude of the waves is very large, and the waves are studied with a view to their potential impact on the projected National Aerospace Plane. This paper presents the results of analyses and state-of-the-art numerical simulations, validated where possible by observational data.

Electric and magnetic polarization singularities of first-order Laguerre-Gaussian beams diffracted at a half-plane screen.

PubMed

Luo, Yamei; Gao, Zenghui; Tang, Bihua; Lü, Baida

2013-08-01

Based on the vector Fresnel diffraction integrals, analytical expressions for the electric and magnetic components of first-order Laguerre-Gaussian beams diffracted at a half-plane screen are derived and used to study the electric and magnetic polarization singularities in the diffraction field for both two- and three-dimensional (2D and 3D) cases. It is shown that there exist 2D and 3D electric and magnetic polarization singularities in the diffraction field, which do not coincide each other in general. By suitably varying the waist width ratio, off-axis displacement parameter, amplitude ratio, or propagation distance, the motion, pair-creation, and annihilation of circular polarization singularities, and the motion of linear polarization singularities take place in 2D and 3D electric and magnetic fields. The V point, at which two circular polarization singularities with the same topological charge but opposite handedness collide, appears in the 2D electric field under certain conditions in the diffraction field and free-space propagation. A comparison with the free-space propagation is also made.

Spacetime Singularities in Quantum Gravity

NASA Astrophysics Data System (ADS)

Minassian, Eric A.

2000-04-01

Recent advances in 2+1 dimensional quantum gravity have provided tools to study the effects of quantization of spacetime on black hole and big bang/big crunch type singularities. I investigate effects of quantization of spacetime on singularities of the 2+1 dimensional BTZ black hole and the 2+1 dimensional torus universe. Hosoya has considered the BTZ black hole, and using a "quantum generalized affine parameter" (QGAP), has shown that, for some specific paths, quantum effects "smear" the singularities. Using gaussian wave functions as generic wave functions, I found that, for both BTZ black hole and the torus universe, there are families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, offer further support for this conclusion. Currently work is in progress to study more realistic quantum gravity effects for BTZ black holes and other spacetime models.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

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

Meek, Garrett A.; Levine, Benjamin G., E-mail: levine@chemistry.msu.edu

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplingsmore » at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.« less

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-05-01

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

PubMed

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Null cosmological singularities and free strings

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

Narayan, K.

2010-03-15

We continue exploring free strings in the background of null Kasner-like cosmological singularities, following K. Narayan, arXiv:0904.4532. We study the free string Schrodinger wave functional along the lines of K. Narayan, arXiv:0807.1517. We find the wave functional to be nonsingular in the vicinity of singularities whose Kasner exponents satisfy certain relations. We compare this with the description in other variables. We then study certain regulated versions of these singularities where the singular region is replaced by a substringy but nonsingular region and study the string spectra in these backgrounds. The string modes can again be solved for exactly, giving somemore » insight into how string oscillator states get excited near the singularity.« less

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.

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.

Complete particle-pair annihilation as a dynamical signature of the spectral singularity

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

Li, G.R.; Zhang, X.Z.; Song, Z., E-mail: nkquantum@gmail.com

2014-10-15

Motivated by the physical relevance of a spectral singularity of interacting many-particle system, we explore the dynamics of two bosons as well as fermions in one-dimensional system with imaginary delta interaction strength. Based on the exact solution, it shows that the two-particle collision leads to amplitude-reduction of the wave function. For fermion pair, the amplitude-reduction depends on the spin configuration of two particles. In both cases, the residual amplitude can vanish when the relative group velocity of two single-particle Gaussian wave packets with equal width reaches the magnitude of the interaction strength, exhibiting complete particle-pair annihilation at the spectral singularity.more » - Highlights: • We investigate the physical relevance of a spectral singularity. • The two-particle collision leads to amplitude-reduction of the wave function. • There is a singularity spectrum which leads to complete particle-pair annihilation. • Complete particle-pair annihilation can only occur for two distinguishable bosons and singlet fermions. • Pair annihilation provides a detection method of the spectral singularity in the experiment.« less

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.

Electromagnetic analysis of arbitrarily shaped pinched carpets

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

Dupont, Guillaume; Guenneau, Sebastien; Enoch, Stefan

2010-09-15

We derive the expressions for the anisotropic heterogeneous tensors of permittivity and permeability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth curves whereas in the latter case we map an arbitrary region of the plane onto smooth surfaces. Importantly, these carpets display no singularity of the permeability and permeability tensor components. Moreover, a reduced set of parameters leads to nonmagnetic two-dimensional carpets in p polarization (i.e., for a magnetic field orthogonal to the plane containing the carpet). Such an arbitrarily shaped carpet is shown to work over amore » finite bandwidth when it is approximated by a checkerboard with 190 homogeneous cells of piecewise constant anisotropic permittivity. We finally perform some finite element computations in the full vector three-dimensional case for a plane wave in normal incidence and a Gaussian beam in oblique incidence. The latter requires perfectly matched layers set in a rotated coordinate axis which exemplifies the role played by geometric transforms in computational electromagnetism.« less

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

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Hennig, Jörg

2018-03-01

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

Spontaneous generation of singularities in paraxial optical fields.

PubMed

Aiello, Andrea

2016-04-01

In nonrelativistic quantum mechanics, the spontaneous generation of singularities in smooth and finite wave functions is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schrödinger equation and the optical paraxial wave equation to define a new class of square-integrable paraxial optical fields that develop a spatial singularity in the focal point of a weakly focusing thin lens. These fields are characterized by a single real parameter whose value determines the nature of the singularity. This novel field enhancement mechanism may stimulate fruitful research for diverse technological and scientific applications.

Quantum probe of Hořava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

Gurtug, O.; Mangut, M.

2018-04-01

Particle probe analysis of the Kehagias-Sfetsos black hole spacetime of Hořava-Lifshitz gravity is extended to wave probe analysis within the framework of quantum mechanics. The time-like naked singularity that develops when ωM2 < 1/2 is probed with quantum fields obeying Klein-Gordon and Chandrasekhar-Dirac equations. The quantum field probe of the naked singularity has revealed that both the spatial part of the wave and the Hamiltonian operators of Klein-Gordon and Chandrasekhar-Dirac equations are essentially self-adjoint, and thus, the naked singularity in the Kehagias-Sfetsos spacetime becomes quantum mechanically non-singular.

Phase geometries of two-dimensional excitable waves govern self-organized morphodynamics of amoeboid cells

PubMed Central

Taniguchi, Daisuke; Ishihara, Shuji; Oonuki, Takehiko; Honda-Kitahara, Mai; Kaneko, Kunihiko; Sawai, Satoshi

2013-01-01

In both randomly moving Dictyostelium and mammalian cells, phosphatidylinositol (3,4,5)-trisphosphate and F-actin are known to propagate as waves at the membrane and act to push out the protruding edge. To date, however, the relationship between the wave geometry and the patterns of amoeboid shape change remains elusive. Here, by using phase map analysis, we show that morphology dynamics of randomly moving Dictyostelium discoideum cells can be characterized by the number, topology, and position of spatial phase singularities, i.e., points that represent organizing centers of rotating waves. A single isolated singularity near the cellular edge induced a rotational protrusion, whereas a pair of singularities supported a symmetric extension. These singularities appeared by strong phase resetting due to de novo nucleation at the back of preexisting waves. Analysis of a theoretical model indicated excitability of the system that is governed by positive feedback from phosphatidylinositol (3,4,5)-trisphosphate to PI3-kinase activation, and we showed experimentally that this requires F-actin. Furthermore, by incorporating membrane deformation into the model, we demonstrated that geometries of competing waves explain most of the observed semiperiodic changes in amoeboid morphology. PMID:23479620

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

PubMed

Reintjes, Moritz; Temple, Blake

2015-05-08

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

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

PubMed Central

Reintjes, Moritz; Temple, Blake

2015-01-01

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

Experimental verification of free-space singular boundary conditions in an invisibility cloak

NASA Astrophysics Data System (ADS)

Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile

2016-04-01

A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.

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.

On gravitational waves in Born-Infeld inspired non-singular cosmologies

NASA Astrophysics Data System (ADS)

Beltrán Jiménez, Jose; Heisenberg, Lavinia; Olmo, Gonzalo J.; Rubiera-Garcia, Diego

2017-10-01

We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisation of the gravitational waves evolution. We extend our analysis to more general Born-Infeld inspired theories where analogous solutions are found. As a general conclusion, we obtain that the bouncing solutions are generally more prone to instabilities, while the asymptotically Minkowski solutions can be rendered stable, making them appealing models for the early universe.

On gravitational waves in Born-Infeld inspired non-singular cosmologies

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

Jiménez, Jose Beltrán; Heisenberg, Lavinia; Olmo, Gonzalo J.

We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisation of themore » gravitational waves evolution. We extend our analysis to more general Born-Infeld inspired theories where analogous solutions are found. As a general conclusion, we obtain that the bouncing solutions are generally more prone to instabilities, while the asymptotically Minkowski solutions can be rendered stable, making them appealing models for the early universe.« less

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

Propagation of the Lissajous singularity dipole emergent from non-paraxial polychromatic beams

NASA Astrophysics Data System (ADS)

Haitao, Chen; Gao, Zenghui; Wang, Wanqing

2017-06-01

The propagation of the Lissajous singularity dipole (LSD) emergent from the non-paraxial polychromatic beams is studied. It is found that the handedness reversal of Lissajous singularities, the change in the shape of Lissajous figures, as well as the creation and annihilation of the LSD may take place by varying the propagation distance, off-axis parameter, wavelength, or amplitude factor. Comparing with the LSD emergent from paraxial polychromatic beams, the output field of non-paraxial polychromatic beams is more complicated, which results in some richer dynamic behaviors of Lissajous singularities, such as more Lissajous singularities and no vanishing of a single Lissajous singularity at the plane z>0.

Spatial Distribution of Phase Singularities in Optical Random Vector Waves.

PubMed

De Angelis, L; Alpeggiani, F; Di Falco, A; Kuipers, L

2016-08-26

Phase singularities are dislocations widely studied in optical fields as well as in other areas of physics. With experiment and theory we show that the vectorial nature of light affects the spatial distribution of phase singularities in random light fields. While in scalar random waves phase singularities exhibit spatial distributions reminiscent of particles in isotropic liquids, in vector fields their distribution for the different vector components becomes anisotropic due to the direct relation between propagation and field direction. By incorporating this relation in the theory for scalar fields by Berry and Dennis [Proc. R. Soc. A 456, 2059 (2000)], we quantitatively describe our experiments.

Stanley Corrsin Award Talk: The role of singularities in hydrodynamics

NASA Astrophysics Data System (ADS)

Eggers, Jens

2017-11-01

If a tap is opened slowly, a drop will form. The separation of the drop is described by a singularity of the Navier-Stokes equation with a free surface. Shock waves are singular solutions of the equations of ideal, compressible hydrodynamics. These examples show that singularities are characteristic for the tendency of the hydrodynamic equations to develop small scale features spontaneously, starting from smooth initial conditions. As a result, new structures are created, which form the building blocks of more complicated flows. The mathematical structure of singularities is self-similar, and their characteristics are fixed by universal properties. This will be illustrated by physical examples, as well as by applications to engineering problems such as printing, coating, or air entrainment. Finally, more recent developments will be discussed: the increasing complexity underlying the self-similar behavior of some singularities, and the spatial structure of shock waves.

Appearance of singularities of optical fields under torsion of crystals containing threefold symmetry axes.

PubMed

Skab, Ihor; Vasylkiv, Yurij; Zapeka, Bohdan; Savaryn, Viktoriya; Vlokh, Rostyslav

2011-07-01

We present an analysis of the effect of torsion stresses on the spatial distribution of optical birefringence in crystals of different point symmetry groups. The symmetry requirements needed so that the optical beam carries dislocations of the phase front are evaluated for the case when the crystals are twisted and the beam closely corresponds to a plane wave. It is shown that the torsion stresses can produce screw-edge, pure screw, or pure edge dislocations of the phase front in the crystals belonging to cubic and trigonal systems. The conditions for appearance of canonical and noncanonical vortices in the conditions of crystal torsion are analyzed. © 2011 Optical Society of America

Nonlinear Spectral Singularity and Laser Output Intensity for the TE and TM Modes

NASA Astrophysics Data System (ADS)

Ghaemidizicheh, Hamed; Mostafazadeh, Ali

The nonlinear spectral singularity arising from a Kerr nonlinearity is explored in. This reference studies the effect of nonlinearity in Lasing condition and shows that Kerr nonlinearity with spectral singularity for a normally incident wave provides an explanation of lasing at gain coefficient g. Lasing occurs when it exceeds threshold gain g0. For oblique waves, Ref. looks at the behavior of threshold gain coefficient g0 which is given by the condition that there is a linear spectral singularity. We investigated imposing the condition of the existence of nonlinear spectral singularity in the TE / TM modes of a mirrorless slab of gain materials and studied the θ-dependence of intensity. Supported by TUBITAK Project No: 114F357 and by the Turkish Academy of Science (TUBA).

Splash singularity for water waves.

PubMed

Castro, Angel; Córdoba, Diego; Fefferman, Charles L; Gancedo, Francisco; Gómez-Serrano, Javier

2012-01-17

We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time.

Splash singularity for water waves

PubMed Central

Castro, Angel; Córdoba, Diego; Fefferman, Charles L.; Gancedo, Francisco; Gómez-Serrano, Javier

2012-01-01

We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time. PMID:22219372

Measurement of in-plane displacements using the phase singularities generated by directional wavelet transforms of speckle pattern images.

PubMed

Vadnjal, Ana Laura; Etchepareborda, Pablo; Federico, Alejandro; Kaufmann, Guillermo H

2013-03-20

We present a method to determine micro and nano in-plane displacements based on the phase singularities generated by application of directional wavelet transforms to speckle pattern images. The spatial distribution of the obtained phase singularities by the wavelet transform configures a network, which is characterized by two quasi-orthogonal directions. The displacement value is determined by identifying the intersection points of the network before and after the displacement produced by the tested object. The performance of this method is evaluated using simulated speckle patterns and experimental data. The proposed approach is compared with the optical vortex metrology and digital image correlation methods in terms of performance and noise robustness, and the advantages and limitations associated to each method are also discussed.

Plasmonic Surface Lattice Resonances: A Review of Properties and Applications.

PubMed

Kravets, V G; Kabashin, A V; Barnes, W L; Grigorenko, A N

2018-06-27

When metal nanoparticles are arranged in an ordered array, they may scatter light to produce diffracted waves. If one of the diffracted waves then propagates in the plane of the array, it may couple the localized plasmon resonances associated with individual nanoparticles together, leading to an exciting phenomenon, the drastic narrowing of plasmon resonances, down to 1-2 nm in spectral width. This presents a dramatic improvement compared to a typical single particle resonance line width of >80 nm. The very high quality factors of these diffractively coupled plasmon resonances, often referred to as plasmonic surface lattice resonances, and related effects have made this topic a very active and exciting field for fundamental research, and increasingly, these resonances have been investigated for their potential in the development of practical devices for communications, optoelectronics, photovoltaics, data storage, biosensing, and other applications. In the present review article, we describe the basic physical principles and properties of plasmonic surface lattice resonances: the width and quality of the resonances, singularities of the light phase, electric field enhancement, etc. We pay special attention to the conditions of their excitation in different experimental architectures by considering the following: in-plane and out-of-plane polarizations of the incident light, symmetric and asymmetric optical (refractive index) environments, the presence of substrate conductivity, and the presence of an active or magnetic medium. Finally, we review recent progress in applications of plasmonic surface lattice resonances in various fields.

Quantum spreading of a self-gravitating wave-packet in singularity free gravity

NASA Astrophysics Data System (ADS)

Buoninfante, Luca; Lambiase, Gaetano; Mazumdar, Anupam

2018-01-01

In this paper we will study for the first time how the wave-packet of a self-gravitating meso-scopic system spreads in theories beyond Einstein's general relativity. In particular, we will consider a ghost-free infinite derivative gravity, which resolves the 1 / r singularity in the potential - such that the gradient of the potential vanishes within the scale of non-locality. We will show that a quantum wave-packet spreads faster for a ghost-free and singularity-free gravity as compared to the Newtonian case, therefore providing us a unique scenario for testing classical and quantum properties of short-distance gravity in a laboratory in the near future.

Geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem

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

Mandel, Ilya

The most promising way to compute the gravitational waves emitted by binary black holes (BBHs) in their last dozen orbits, where post-Newtonian techniques fail, is a quasistationary approximation introduced by Detweiler and being pursued by Price and others. In this approximation the outgoing gravitational waves at infinity and downgoing gravitational waves at the holes' horizons are replaced by standing waves so as to guarantee that the spacetime has a helical Killing vector field. Because the horizon generators will not, in general, be tidally locked to the holes' orbital motion, the standing waves will destroy the horizons, converting the black holesmore » into naked singularities that resemble black holes down to near the horizon radius. This paper uses a spherically symmetric, scalar-field model problem to explore in detail the following BBH issues: (i) The destruction of a horizon by the standing waves. (ii) The accuracy with which the resulting naked singularity resembles a black hole. (iii) The conversion of the standing-wave spacetime (with a destroyed horizon) into a spacetime with downgoing waves by the addition of a 'radiation-reaction field'. (iv) The accuracy with which the resulting downgoing waves agree with the downgoing waves of a true black-hole spacetime (with horizon). The model problem used to study these issues consists of a Schwarzschild black hole endowed with spherical standing waves of a scalar field, whose wave frequency and near-horizon energy density are chosen to match those of the standing gravitational waves of the BBH quasistationary approximation. It is found that the spacetime metric of the singular, standing-wave spacetime, and its radiation-reaction-field-constructed downgoing waves are quite close to those for a Schwarzschild black hole with downgoing waves--sufficiently close to make the BBH quasistationary approximation look promising for non-tidally-locked black holes.« less

Spectral singularities and Bragg scattering in complex crystals

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

Longhi, S.

2010-02-15

Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and secularities that arise in Bragg diffraction patterns. Signatures of spectral singularities in a scattering process with wave packets are elucidated for a PT-symmetric complex crystal.

Persistence and Lifelong Fidelity of Phase Singularities in Optical Random Waves.

PubMed

De Angelis, L; Alpeggiani, F; Di Falco, A; Kuipers, L

2017-11-17

Phase singularities are locations where light is twisted like a corkscrew, with positive or negative topological charge depending on the twisting direction. Among the multitude of singularities arising in random wave fields, some can be found at the same location, but only when they exhibit opposite topological charge, which results in their mutual annihilation. New pairs can be created as well. With near-field experiments supported by theory and numerical simulations, we study the persistence and pairing statistics of phase singularities in random optical fields as a function of the excitation wavelength. We demonstrate how such entities can encrypt fundamental properties of the random fields in which they arise.

Persistence and Lifelong Fidelity of Phase Singularities in Optical Random Waves

NASA Astrophysics Data System (ADS)

De Angelis, L.; Alpeggiani, F.; Di Falco, A.; Kuipers, L.

2017-11-01

Phase singularities are locations where light is twisted like a corkscrew, with positive or negative topological charge depending on the twisting direction. Among the multitude of singularities arising in random wave fields, some can be found at the same location, but only when they exhibit opposite topological charge, which results in their mutual annihilation. New pairs can be created as well. With near-field experiments supported by theory and numerical simulations, we study the persistence and pairing statistics of phase singularities in random optical fields as a function of the excitation wavelength. We demonstrate how such entities can encrypt fundamental properties of the random fields in which they arise.

Phase singularities of the transverse field component of high numerical aperture dark-hollow Gaussian beams in the focal region

NASA Astrophysics Data System (ADS)

Liu, Pusheng; Lü, Baida

2007-04-01

By using the vectorial Debye diffraction theory, phase singularities of high numerical aperture (NA) dark-hollow Gaussian beams in the focal region are studied. The dependence of phase singularities on the truncation parameter δ and semi-aperture angle α (or equally, NA) is illustrated numerically. A comparison of phase singularities of high NA dark-hollow Gaussian beams with those of scalar paraxial Gaussian beams and high NA Gaussian beams is made. For high NA dark-hollow Gaussian beams the beam order n additionally affects the spatial distribution of phase singularities, and there exist phase singularities outside the focal plane, which may be created or annihilated by variation of the semi-aperture angle in a certain region.

The nature of spherical collapse and a study of black hole dynamics

NASA Astrophysics Data System (ADS)

Nampalliwar, Sourabh

Gravitational waves and singularities are two of the most significant predictions of General Relativity. Binary systems are the most promising sources of gravitational waves that are expected to be detected with the current ground-based and upcoming space-based gravitational wave detectors. During the merger of binary compact objects, an important stage is the plunge. A small part of the gravitational waveform, it marks the end of early inspiral and determines the quasinormal ringing (QNR) of the final product of the merger. It is also the part of the waveform where most of the gravitational energy is released. But, unlike early inspiral and late ringdown, it is poorly understood in terms of phenomenology. This thesis introduces a novel approach combining the Fourier domain Green's function in the particle perturbation approximation and a simple model to understand this crucial stage. The resulting understanding is successful in explaining QNR for a Schwarzschild black hole and opens a new approach to understanding binary inspiral. It holds the promise of a much improved understanding, and improved efficiency in making astrophysical estimates of gravitational wave source strength. Singularities are known to be the ultimate fate of all massive stars undergoing gravitational collapse. The cosmic censorship hypothesis predicts that all these singularities are generically covered by event horizons, i.e., all collapsing stars, if they result in a singularity, end up as black holes. Although several theoretical examples of non-hidden (naked) singularities have been found, the question of the genericity of naked singularities is far from settled. This thesis presents a study of the causal structure of spherically symmetric models of dust collapse and its perturbations to investigate the genericity of naked singularities.

Dynamic crack propagation in a 2D elastic body: The out-of-plane case

NASA Astrophysics Data System (ADS)

Nicaise, Serge; Sandig, Anna-Margarete

2007-05-01

Already in 1920 Griffith has formulated an energy balance criterion for quasistatic crack propagation in brittle elastic materials. Nowadays, a generalized energy balance law is used in mechanics [F. Erdogan, Crack propagation theories, in: H. Liebowitz (Ed.), Fracture, vol. 2, Academic Press, New York, 1968, pp. 498-586; L.B. Freund, Dynamic Fracture Mechanics, Cambridge Univ. Press, Cambridge, 1990; D. Gross, Bruchmechanik, Springer-Verlag, Berlin, 1996] in order to predict how a running crack will grow. We discuss this situation in a rigorous mathematical way for the out-of-plane state. This model is described by two coupled equations in the reference configuration: a two-dimensional scalar wave equation for the displacement fields in a cracked bounded domain and an ordinary differential equation for the crack position derived from the energy balance law. We handle both equations separately, assuming at first that the crack position is known. Then the weak and strong solvability of the wave equation will be studied and the crack tip singularities will be derived under the assumption that the crack is straight and moves tangentially. Using the energy balance law and the crack tip behavior of the displacement fields we finally arrive at an ordinary differential equation for the motion of the crack tip.

Expansions for infinite or finite plane circular time-reversal mirrors and acoustic curtains for wave-field-synthesis.

PubMed

Mellow, Tim; Kärkkäinen, Leo

2014-03-01

An acoustic curtain is an array of microphones used for recording sound which is subsequently reproduced through an array of loudspeakers in which each loudspeaker reproduces the signal from its corresponding microphone. Here the sound originates from a point source on the axis of symmetry of the circular array. The Kirchhoff-Helmholtz integral for a plane circular curtain is solved analytically as fast-converging expansions, assuming an ideal continuous array, to speed up computations and provide insight. By reversing the time sequence of the recording (or reversing the direction of propagation of the incident wave so that the point source becomes an "ideal" point sink), the curtain becomes a time reversal mirror and the analytical solution for this is given simultaneously. In the case of an infinite planar array, it is demonstrated that either a monopole or dipole curtain will reproduce the diverging sound field of the point source on the far side. However, although the real part of the sound field of the infinite time-reversal mirror is reproduced, the imaginary part is an approximation due to the missing singularity. It is shown that the approximation may be improved by using the appropriate combination of monopole and dipole sources in the mirror.

Study of nonlinear MHD equations governing the wave propagation in twisted coronal loops

NASA Technical Reports Server (NTRS)

Parhi, S.; DeBruyne, P.; Goossens, M.; Zhelyazkov, I.

1995-01-01

The solar corona, modelled by a low beta, resistive plasma slab, sustains MHD wave propagations due to shearing footpoint motions in the photosphere. By using a numerical algorithm the excitation and nonlinear development of MHD waves in twisted coronal loops are studied. The plasma responds to the footpoint motion by sausage waves if there is no twist. The twist in the magnetic field of the loop destroys initially developed sausage-like wave modes and they become kinks. The transition from sausage to kink modes is analyzed. The twist brings about mode degradation producing high harmonics and this generates more complex fine structures. This can be attributed to several local extrema in the perturbed velocity profiles. The Alfven wave produces remnants of the ideal 1/x singularity both for zero and non-zero twist and this pseudo-singularity becomes less pronounced for larger twist. The effect of nonlinearity is clearly observed by changing the amplitude of the driver by one order of magnitude. The magnetosonic waves also exhibit smoothed remnants of ideal logarithmic singularities when the frequency of the driver is correctly chosen. This pseudo-singularity for fast waves is absent when the coronal loop does not undergo any twist but becomes pronounced when twist is included. On the contrary, it is observed for slow waves even if there is no twist. Increasing the twist leads to a higher heating rate of the loop. The larger twist shifts somewhat uniformly distributed heating to layers inside the slab corresponding to peaks in the magnetic field strength.

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle

PubMed Central

Brzezicki, Samuel J.

2017-01-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function. PMID:28690412

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle.

PubMed

Crowdy, Darren G; Brzezicki, Samuel J

2017-06-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function.

Two Dimensional Dendritic Crystal Growth for Weak Undercooling

NASA Technical Reports Server (NTRS)

Tanveer, S.; Kunka, M. D.; Foster, M. R.

1999-01-01

We discuss the framework and issues brought forth in the recent work of Kunka, Foster & Tanveer, which incorporates small but nonzero surface energy effects in the nonlinear dynamics of a conformal mapping function z(zeta,t) that maps the upper-half zeta plane into the exterior of a dendrite. In this paper, surface energy effects on the singularities of z(zeta,t) in the lower-half plane were examined, as they move toward the real axis from below. In particular, the dynamics of complex singularities manifests itself in predictions on nature and growth rate of disturbances, as well as of coarsening.

Singular boundary method for wave propagation analysis in periodic structures

NASA Astrophysics Data System (ADS)

Fu, Zhuojia; Chen, Wen; Wen, Pihua; Zhang, Chuanzeng

2018-07-01

A strong-form boundary collocation method, the singular boundary method (SBM), is developed in this paper for the wave propagation analysis at low and moderate wavenumbers in periodic structures. The SBM is of several advantages including mathematically simple, easy-to-program, meshless with the application of the concept of origin intensity factors in order to eliminate the singularity of the fundamental solutions and avoid the numerical evaluation of the singular integrals in the boundary element method. Due to the periodic behaviors of the structures, the SBM coefficient matrix can be represented as a block Toeplitz matrix. By employing three different fast Toeplitz-matrix solvers, the computational time and storage requirements are significantly reduced in the proposed SBM analysis. To demonstrate the effectiveness of the proposed SBM formulation for wave propagation analysis in periodic structures, several benchmark examples are presented and discussed The proposed SBM results are compared with the analytical solutions, the reference results and the COMSOL software.

Singularities of Floquet scattering and tunneling

NASA Astrophysics Data System (ADS)

Landa, H.

2018-04-01

We study quasibound states and scattering with short-range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S matrix can cross the real energy axis as a function of the drive amplitude, making the S matrix nonanalytic at a singular point. For the corresponding quasibound states that can tunnel out of (or get captured within) a potential well, this results in a discontinuous jump in both the angular momentum and energy of emitted (absorbed) waves. We also analyze elastic and inelastic scattering of slow particles in the time-dependent potential. For a drive amplitude at the singular point, there is a total absorption of incoming low-energy (s wave) particles and their conversion to high-energy outgoing (mostly p ) waves. We examine the relation of such Floquet singularities, lacking in an effective time-independent approximation, with well-known "spectral singularities" (or "exceptional points"). These results are based on an analytic approach for obtaining eigensolutions of time-dependent periodic Hamiltonians with mixed cylindrical and spherical symmetry, and apply broadly to particles interacting via power-law forces and subject to periodic fields, e.g., co-trapped ions and atoms.

Wave Geometry: a Plurality of Singularities

NASA Astrophysics Data System (ADS)

Berry, M. V.

Five interconnected wave singularities are discussed: phase monopoles, at eigenvalue degeneracies in parameter space, where the 2-form generating the geomeeic phase is singular, phase dislocations, at zeros of complex wavefunctions in position space, where different wavefronts (surfaces of constant phase) meet; caustics, that is envelopes (foci) of families of classical paths or geometrical rays, where real rays are born violently and which are complementary to dislocations; Stokes sets, at which a complex ray is born gently where it is maximally dominated by another ray; and complex degeneracies, which are the sources of adiabatic quantum transtions in analytic Hamiltonians.

Laser singular Theta-pinch

NASA Astrophysics Data System (ADS)

Okulov, A. Yu.

2010-10-01

The interaction of the two counter-propagating ultrashort laser pulses with singular wavefronts in the thin slice of the underdense plasma is considered. It is shown that ion-acoustic wave is excited via Brillouin three-wave resonance by corkscrew interference pattern of paraxial singular laser beams. The orbital angular momentum carried by light is transferred to plasma ion-acoustic vortex. The rotation of the density perturbations of electron fluid is the cause of helical current which produces the kilogauss axial quasi-static magnetic field. The exact analytical configurations are presented for an ion-acoustic current field and magnetic induction. The range of experimentally accessible parameters is evaluated.

String loops in the field of braneworld spherically symmetric black holes and naked singularities

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

Stuchlík, Z.; Kološ, M., E-mail: zdenek.stuchlik@fpf.slu.cz, E-mail: martin.kolos@fpf.slu.cz

We study motion of current-carrying string loops in the field of braneworld spherically symmetric black holes and naked singularities. The spacetime is described by the Reissner-Nordström geometry with tidal charge b reflecting the non-local tidal effects coming from the external dimension; both positive and negative values of the spacetime parameter b are considered. We restrict attention to the axisymmetric motion of string loops when the motion can be fully governed by an appropriately defined effective potential related to the energy and angular momentum of the string loops. In dependence on these two constants of the motion, the string loops canmore » be captured, trapped, or can escape to infinity. In close vicinity of stable equilibrium points at the centre of trapped states the motion is regular. We describe how it is transformed to chaotic motion with growing energy of the string loop. In the field of naked singularities the trapped states located off the equatorial plane of the system exist and trajectories unable to cross the equatorial plane occur, contrary to the trajectories in the field of black holes where crossing the equatorial plane is always admitted. We concentrate our attention to the so called transmutation effect when the string loops are accelerated in the deep gravitational field near the black hole or naked singularity by transforming the oscillatory energy to the energy of the transitional motion. We demonstrate that the influence of the tidal charge can be substantial especially in the naked singularity spacetimes with b > 1 where the acceleration to ultrarelativistic velocities with Lorentz factor γ ∼ 100 can be reached, being more than one order higher in comparison with those obtained in the black hole spacetimes.« less

Removing singular refractive indices with sculpted surfaces

PubMed Central

Horsley, S. A. R.; Hooper, I. R.; Mitchell–Thomas, R. C.; Quevedo–Teruel, O.

2014-01-01

The advent of Transformation Optics established the link between geometry and material properties, and has resulted in a degree of control over electromagnetic fields that was previously impossible. For waves confined to a surface it is known that there is a simpler, but related, geometrical equivalence between the surface shape and the refractive index, and here we demonstrate that conventional devices possessing a singularity — that is, the requirement of an infinite refractive index — can be realised for waves confined to an appropriately sculpted surface. In particular, we redesign three singular omnidirectional devices: the Eaton lens, the generalized Maxwell Fish–Eye, and the invisible sphere. Our designs perfectly reproduce the behaviour of these singular devices, and can be achieved with simple isotropic media of low refractive index contrast. PMID:24786649

Bound states in the continuum and polarization singularities in periodic arrays of dielectric rods

NASA Astrophysics Data System (ADS)

Bulgakov, Evgeny N.; Maksimov, Dmitrii N.

2017-12-01

We consider optical bound states in the continuum (BICs) in periodic arrays of dielectric rods. The full classification of BICs in the above system is provided, including the modes propagating along the axes of the rods and bidirectional BICs propagating both along the axes of the rods and the axis of periodicity. It is shown that the leaky zones supporting the BICs generally have elliptically polarized far-field radiation patterns, with the polarization ellipses collapsing on approach to the BICs in momentum space. That allowed us to apply the concept of polarization singularities and demonstrate that the BICs possess a topological charge defined as the winding number of the polarization direction [Phys. Rev. Lett. 113, 257401 (2014), 10.1103/PhysRevLett.113.257401]. It is found that the evolution of the BICs, including their creation and annihilation, under variation of geometric parameters is controlled by the topological charge. Three scenarios of such evolution for different leaky zones are described. Finally, it is shown that the topological properties of the BICs can be extracted from transmission spectra when the system is illuminated by a plane wave of circular polarization.

Naked singularities are not singular in distorted gravity

NASA Astrophysics Data System (ADS)

Garattini, Remo; Majumder, Barun

2014-07-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.

Dynamical characteristics of an electromagnetic field under conditions of total reflection

NASA Astrophysics Data System (ADS)

Bekshaev, Aleksandr Ya

2018-04-01

The dynamical characteristics of electromagnetic fields include energy, momentum, angular momentum (spin) and helicity. We analyze their spatial distributions near the planar interface between two transparent and non-dispersive media, when the incident monochromatic plane wave with arbitrary polarization is totally reflected, and an evanescent wave is formed in the medium with lower optical density. Based on the recent arguments in favor of the Minkowski definition of the electromagnetic momentum in a material medium (Philbin 2011 Phys. Rev. A 83 013823; Philbin and Allanson 2012 86 055802; Bliokh et al 2017 Phys. Rev. Lett. 119 073901), we derive the explicit expressions for the dynamical characteristics in both media, with special attention to their behavior at the interface. In particular, the ‘extraordinary’ spin and momentum components orthogonal to the plane of incidence are described, and a canonical (spin-orbital) momentum decomposition is performed that contains no singular terms. The field energy, helicity, the spin momentum and orbital momentum components are everywhere regular but experience discontinuities at the interface; the spin components parallel to the interface appear to be continuous, which testifies to the consistency of the adopted Minkowski picture. The results supply a meaningful example of the electromagnetic momentum decomposition, with separation of spatial and polarization degrees of freedom, in inhomogeneous media, and can be used in engineering the structured fields designed for optical sorting, dispatching and micromanipulation.

A note on singularities of the 3-D Euler equation

NASA Technical Reports Server (NTRS)

Tanveer, S.

1994-01-01

In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

Stress singularities in a model of a wood disk under sinusoidal pressure

Treesearch

Jay A. Johnson; John C. Hermanson; Steven M. Cramer; Charles Amundson

2005-01-01

A thin, solid, circular wood disk, cut from the transverse plane of a tree stem, can be modeled as a cylindrically orthotropic elastic material. It is known that a stress singularity can occur at the center of a cylindrically orthotropic disk subjected to uniform pressure. If a solid cylindrically orthotropic disk is subjected to sinusoidal pressure distributions, then...

Nonlinear analysis of a family of LC tuned inverters

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1975-01-01

Four widely used self-oscillating dc-to-square-wave parallel inverters which employ an inductor-capacitor tuned network to determine the oscillation frequency are reduced to a common equivalent RLC network, The techniques of singular-point analysis and state-plane interpretations are employed to describe the steady-state and transient behavior of these circuits and to elucidate the three possible modes of operation: quasi-harmonic, relaxation, and discontinuous. Design guidelines are provided through a study of the influence of circuit parameter variations on the characteristics of oscillation and on frequency stability. Several examples are provided to illustrate the usefulness of this analysis when studying such problems as transistor emitter-to-base junction breakdown during oscillations and the design of starting circuits to insure self-excited oscillations in these inverters.

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.

Making waves round a structured cloak: lattices, negative refraction and fringes

PubMed Central

Colquitt, D. J.; Jones, I. S.; Movchan, N. V.; Movchan, A. B.; Brun, M.; McPhedran, R. C.

2013-01-01

Using the framework of transformation optics, this paper presents a detailed analysis of a non-singular square cloak for acoustic, out-of-plane shear elastic and electromagnetic waves. Analysis of wave propagation through the cloak is presented and accompanied by numerical illustrations. The efficacy of the regularized cloak is demonstrated and an objective numerical measure of the quality of the cloaking effect is provided. It is demonstrated that the cloaking effect persists over a wide range of frequencies. As a demonstration of the effectiveness of the regularized cloak, a Young's double slit experiment is presented. The stability of the interference pattern is examined when a cloaked and uncloaked obstacle are successively placed in front of one of the apertures. This novel link with a well-known quantum mechanical experiment provides an additional method through which the quality of cloaks may be examined. In the second half of the paper, it is shown that an approximate cloak may be constructed using a discrete lattice structure. The efficiency of the approximate lattice cloak is analysed and a series of illustrative simulations presented. It is demonstrated that effective cloaking may be obtained by using a relatively simple lattice structure, particularly, in the low-frequency regime. PMID:24062625

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.

Rapid near-optimal aerospace plane trajectory generation and guidance

NASA Technical Reports Server (NTRS)

Calise, A. J.; Corban, J. E.; Markopoulos, N.

1991-01-01

Effort was directed toward the problems of the real time trajectory optimization and guidance law development for the National Aerospace Plane (NASP) applications. In particular, singular perturbation methods were used to develop guidance algorithms suitable for onboard, real time implementation. The progress made in this research effort is reported.

Realization of non-holonomic constraints and singular perturbation theory for plane dumbbells

NASA Astrophysics Data System (ADS)

Koshkin, Sergiy; Jovanovic, Vojin

2017-10-01

We study the dynamics of pairs of connected masses in the plane, when nonholonomic (knife-edge) constraints are realized by forces of viscous friction, in particular its relation to constrained dynamics, and its approximation by the method of matching asymptotics of singular perturbation theory when the mass to friction ratio is taken as the small parameter. It turns out that long term behaviors of the frictional and constrained systems may differ dramatically no matter how small the perturbation is, and when this happens is not determined by any transparent feature of the equations of motion. The choice of effective time scales for matching asymptotics is also subtle and non-obvious, and secular terms appearing in them can not be dealt with by the classical methods. Our analysis is based on comparison to analytic solutions, and we present a reduction procedure for plane dumbbells that leads to them in some cases.

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

NASA Technical Reports Server (NTRS)

Sharma, A.; Cogley, A. C.

1982-01-01

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid

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

Prochnow, Bo; O'Reilly, Ossian; Dunham, Eric M.

In this paper, we develop a high-order finite difference scheme for axisymmetric wave propagation in a cylindrical conduit filled with a viscous fluid. The scheme is provably stable, and overcomes the difficulty of the polar coordinate singularity in the radial component of the diffusion operator. The finite difference approximation satisfies the principle of summation-by-parts (SBP), which is used to establish stability using the energy method. To treat the coordinate singularity without losing the SBP property of the scheme, a staggered grid is introduced and quadrature rules with weights set to zero at the endpoints are considered. Finally, the accuracy ofmore » the scheme is studied both for a model problem with periodic boundary conditions at the ends of the conduit and its practical utility is demonstrated by modeling acoustic-gravity waves in a magmatic conduit.« less

A laboratory analogue of the event horizon using slow light in an atomic medium.

PubMed

Leonhardt, Ulf

2002-01-24

Singularities underlie many optical phenomena. The rainbow, for example, involves a particular type of singularity-a ray catastrophe-in which light rays become infinitely intense. In practice, the wave nature of light resolves these infinities, producing interference patterns. At the event horizon of a black hole, time stands still and waves oscillate with infinitely small wavelengths. However, the quantum nature of light results in evasion of the catastrophe and the emission of Hawking radiation. Here I report a theoretical laboratory analogue of an event horizon: a parabolic profile of the group velocity of light brought to a standstill in an atomic medium can cause a wave singularity similar to that associated with black holes. In turn, the quantum vacuum is forced to create photon pairs with a characteristic spectrum, a phenomenon related to Hawking radiation. The idea may initiate a theory of 'quantum' catastrophes, extending classical catastrophe theory.

Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid

DOE PAGES

Prochnow, Bo; O'Reilly, Ossian; Dunham, Eric M.; ...

2017-03-16

In this paper, we develop a high-order finite difference scheme for axisymmetric wave propagation in a cylindrical conduit filled with a viscous fluid. The scheme is provably stable, and overcomes the difficulty of the polar coordinate singularity in the radial component of the diffusion operator. The finite difference approximation satisfies the principle of summation-by-parts (SBP), which is used to establish stability using the energy method. To treat the coordinate singularity without losing the SBP property of the scheme, a staggered grid is introduced and quadrature rules with weights set to zero at the endpoints are considered. Finally, the accuracy ofmore » the scheme is studied both for a model problem with periodic boundary conditions at the ends of the conduit and its practical utility is demonstrated by modeling acoustic-gravity waves in a magmatic conduit.« less

Nonlinear spectral singularities for confined nonlinearities.

PubMed

Mostafazadeh, Ali

2013-06-28

We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrödinger operators involving a confined nonlinearity. The presence of the nonlinearity does not break the parity-reflection symmetry of spectral singularities but makes them amplitude dependent. Nonlinear spectral singularities are, therefore, associated with a resonance effect that produces amplified waves with a specific amplitude-wavelength profile. We explore the consequences of this phenomenon for a complex δ-function potential that is subject to a general confined nonlinearity.

Central charge from adiabatic transport of cusp singularities in the quantum Hall effect

NASA Astrophysics Data System (ADS)

Can, Tankut

2017-04-01

We study quantum Hall (QH) states on a punctured Riemann sphere. We compute the Berry curvature under adiabatic motion in the moduli space in the large N limit. The Berry curvature is shown to be finite in the large N limit and controlled by the conformal dimension of the cusp singularity, a local property of the mean density. Utilizing exact sum rules obtained from a Ward identity, we show that for the Laughlin wave function, the dimension of a cusp singularity is given by the central charge, a robust geometric response coefficient in the QHE. Thus, adiabatic transport of curvature singularities can be used to determine the central charge of QH states. We also consider the effects of threaded fluxes and spin-deformed wave functions. Finally, we give a closed expression for all moments of the mean density in the integer QH state on a punctured disk.

Role of a triangle singularity in the π N (1535 ) contribution to γ p →p π0η

NASA Astrophysics Data System (ADS)

Debastiani, V. R.; Sakai, S.; Oset, E.

2017-08-01

We have studied the γ p →p π0η reaction paying attention to the two main mechanisms at low energies, the γ p →Δ (1700 )→η Δ (1232 ) and the γ p →Δ (1700 )→π N (1535 ) . Both are driven by the photoexcitation of the Δ (1700 ) and the second one involves a mechanism that leads to a triangle singularity. We are able to evaluate quantitatively the cross section for this process and show that it agrees with the experimental determination. Yet there are some differences with the standard partial wave analysis which does not include explicitly the triangle singularity. The exercise also shows the convenience of exploring possible triangle singularities in other reactions and how a standard partial wave analysis can be extended to accommodate them.

COED Transactions, Vol. IX, No. 1, January 1977. Rapid Production of System Phase-Plane Portraits on the EAI 380 Hybrid/Analog Computer.

ERIC Educational Resources Information Center

Marcovitz, Alan B., Ed.

The method of phase-plane presentation as an educational tool in the study of the dynamic behavior of systems is discussed. In the treatment of nonlinear or piecewise-linear systems, the phase-plane portrait is used to exhibit the nature of singular points, regions of stability, and switching lines to aid comprehension. A technique is described by…

Opening of an interface flaw in a layered elastic half-plane under compressive loading

NASA Technical Reports Server (NTRS)

Kennedy, J. M.; Fichter, W. B.; Goree, J. G.

1984-01-01

A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.

Solution of plane cascade flow using improved surface singularity methods

NASA Technical Reports Server (NTRS)

Mcfarland, E. R.

1981-01-01

A solution method has been developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those found in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.

Quantum healing of spacetime singularities: A review

NASA Astrophysics Data System (ADS)

Konkowski, D. A.; Helliwell, T. M.

2018-02-01

Singularities are commonplace in general relativistic spacetimes. It is natural to hope that they might be “healed” (or resolved) by the inclusion of quantum mechanics, either in the theory itself (quantum gravity) or, more modestly, in the description of the spacetime geodesic paths used to define them. We focus here on the latter, mainly using a procedure proposed by Horowitz and Marolf to test whether singularities in broad classes of spacetimes can be resolved by replacing geodesic paths with quantum wave packets. We list the spacetime singularities that various authors have studied in this context, and distinguish those which are healed quantum mechanically (QM) from those which remain singular. Finally, we mention some alternative approaches to healing singularities.

Some classes of gravitational shock waves from higher order theories of gravity

NASA Astrophysics Data System (ADS)

Oikonomou, V. K.

2017-02-01

We study the gravitational shock wave generated by a massless high energy particle in the context of higher order gravities of the form F(R,R_{μν}R^{μν},R_{μναβ}R^{μν αβ}). In the case of F(R) gravity, we investigate the gravitational shock wave solutions corresponding to various cosmologically viable gravities, and as we demonstrate the solutions are rescaled versions of the Einstein-Hilbert gravity solution. Interestingly enough, other higher order gravities result to the general relativistic solution, except for some specific gravities of the form F(R_{μν}R^{μν}) and F(R,R_{μν}R^{μν}), which we study in detail. In addition, when realistic Gauss-Bonnet gravities of the form R+F(G) are considered, the gravitational shock wave solutions are identical to the general relativistic solution. Finally, the singularity structure of the gravitational shock waves solutions is studied, and it is shown that the effect of higher order gravities makes the singularities milder in comparison to the general relativistic solutions, and in some particular cases the singularities seem to be absent.

Problems of interaction longitudinal shear waves with V-shape tunnels defect

NASA Astrophysics Data System (ADS)

Popov, V. G.

2018-04-01

The problem of determining the two-dimensional dynamic stress state near a tunnel defect of V-shaped cross-section is solved. The defect is located in an infinite elastic medium, where harmonic longitudinal shear waves are propagating. The initial problem is reduced to a system of two singular integral or integro-differential equations with fixed singularities. A numerical method for solving these systems with regard to the true asymptotics of the unknown functions is developed.

General method of solving the Schroedinger equation of atoms and molecules

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

Nakatsuji, Hiroshi

2005-12-15

We propose a general method of solving the Schroedinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schroedinger equation and related principles, we can avoid the singularity problem of atoms and molecules and formulate a general method of calculating the exact wave functions in an analytical expansion form. We choose initial function {psi}{sub 0} and scaling g function, and then the ICI method automatically generates the wave function that hasmore » the exact structure by using the Hamiltonian of the system. The Hamiltonian contains all the information of the system. The free ICI method provides a flexible and variationally favorable procedure of constructing the exact wave function. We explain the computational procedure of the analytical ICI method routinely performed in our laboratory. Simple examples are given using hydrogen atom for the nuclear singularity case, the Hooke's atom for the electron singularity case, and the helium atom for both cases.« less

Fundamental formulae for wave-energy conversion

PubMed Central

Falnes, Johannes; Kurniawan, Adi

2015-01-01

The time-average wave power that is absorbed from an incident wave by means of a wave-energy conversion (WEC) unit, or by an array of WEC units—i.e. oscillating immersed bodies and/or oscillating water columns (OWCs)—may be mathematically expressed in terms of the WEC units' complex oscillation amplitudes, or in terms of the generated outgoing (diffracted plus radiated) waves, or alternatively, in terms of the radiated waves alone. Following recent controversy, the corresponding three optional expressions are derived, compared and discussed in this paper. They all provide the correct time-average absorbed power. However, only the first-mentioned expression is applicable to quantify the instantaneous absorbed wave power and the associated reactive power. In this connection, new formulae are derived that relate the ‘added-mass’ matrix, as well as a couple of additional reactive radiation-parameter matrices, to the difference between kinetic energy and potential energy in the water surrounding the immersed oscillating WEC array. Further, a complex collective oscillation amplitude is introduced, which makes it possible to derive, by a very simple algebraic method, various simple expressions for the maximum time-average wave power that may be absorbed by the WEC array. The real-valued time-average absorbed power is illustrated as an axisymmetric paraboloid defined on the complex collective-amplitude plane. This is a simple illustration of the so-called ‘fundamental theorem for wave power’. Finally, the paper also presents a new derivation that extends a recently published result on the direction-average maximum absorbed wave power to cases where the WEC array's radiation damping matrix may be singular and where the WEC array may contain OWCs in addition to oscillating bodies. PMID:26064612

Fundamental formulae for wave-energy conversion.

PubMed

Falnes, Johannes; Kurniawan, Adi

2015-03-01

The time-average wave power that is absorbed from an incident wave by means of a wave-energy conversion (WEC) unit, or by an array of WEC units-i.e. oscillating immersed bodies and/or oscillating water columns (OWCs)-may be mathematically expressed in terms of the WEC units' complex oscillation amplitudes, or in terms of the generated outgoing (diffracted plus radiated) waves, or alternatively, in terms of the radiated waves alone. Following recent controversy, the corresponding three optional expressions are derived, compared and discussed in this paper. They all provide the correct time-average absorbed power. However, only the first-mentioned expression is applicable to quantify the instantaneous absorbed wave power and the associated reactive power. In this connection, new formulae are derived that relate the 'added-mass' matrix, as well as a couple of additional reactive radiation-parameter matrices, to the difference between kinetic energy and potential energy in the water surrounding the immersed oscillating WEC array. Further, a complex collective oscillation amplitude is introduced, which makes it possible to derive, by a very simple algebraic method, various simple expressions for the maximum time-average wave power that may be absorbed by the WEC array. The real-valued time-average absorbed power is illustrated as an axisymmetric paraboloid defined on the complex collective-amplitude plane. This is a simple illustration of the so-called 'fundamental theorem for wave power'. Finally, the paper also presents a new derivation that extends a recently published result on the direction-average maximum absorbed wave power to cases where the WEC array's radiation damping matrix may be singular and where the WEC array may contain OWCs in addition to oscillating bodies.

Solution of plane cascade flow using improved surface singularity methods. [application of panel method to internal aerodynamics

NASA Technical Reports Server (NTRS)

Mcfarland, E. R.

1981-01-01

A solution method was developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.

Perturbation analysis of the limit cycle of the free van der Pol equation

NASA Technical Reports Server (NTRS)

Dadfar, M. B.; Geer, J.; Anderson, C. M.

1983-01-01

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Signature of phase singularities in diffusive regimes in disordered waveguide lattices: interplay and qualitative analysis

NASA Astrophysics Data System (ADS)

Ghosh, Somnath

2018-05-01

Co-existence and interplay between mesoscopic light dynamics with singular optics in spatially random but temporally coherent disordered waveguide lattices is reported. Two CW light beams of 1.55 micron operating wavelength are launched as inputs to 1D waveguide lattices with controllable weak disorder in refractive index profile. Direct observation of phase singularities in the speckle pattern along the length is numerically demonstrated. Quantitative analysis of onset of such singular behavior and diffusive wave propagation is analyzed for the first time.

Mode-coupling and wave-particle interactions for unstable ion-acoustic waves.

NASA Technical Reports Server (NTRS)

Martin, P.; Fried, B. D.

1972-01-01

A theory for the spatial development of linearly unstable, coupled waves is presented in which both quasilinear and mode-coupling effects are treated in a self-consistent manner. Steady-state excitation of two waves is assumed at the boundary x = 0, the plasma being homogeneous in the y and z directions. Coupled equations are derived for the x dependence of the amplitudes of the primary waves and the secondary waves, correct through terms of second order in the wave amplitude, but without the usual approximation of small growth rates. This general formalism is then applied to the case of coupled ion-acoustic waves driven unstable by an ion beam streaming in the direction of the x axis. If the modifications of the ion beam by the waves (quasilinear effects) are ignored, explosive instabilities (singularities in all of the amplitudes at finite x) are found even when all of the waves have positive energy. If these wave-particle interactions are included, the solutions are no longer singular, and all of the amplitudes have finite maxima.

Mode coupling and wave particle interactions for unstable ion acoustic waves

NASA Technical Reports Server (NTRS)

Martin, P.; Fried, B. D.

1972-01-01

A theory for the spatial development of linearly unstable, coupled waves is presented in which both quasi-linear and mode coupling effects are treated in a self-consistent manner. Steady state excitation of two waves is assumed at the boundary x = 0, the plasma being homogeneous in the y and z directions. Coupled equations are derived for the x dependence of the amplitudes of the primary waves and the secondary waves, correct through second order terms in the wave amplitude, but without usual approximation of small growth rates. This general formalism is then applied to the case of coupled ion acoustic waves driven unstable by an ion beam streaming in the direction of the x axis. If the modifications of the ion beam by the waves (quasi-linear effects) are ignored, explosive instabilities (singularities in all of the amplitudes at finite x) are found, even when all of the waves have positive energy. If these wave-particle interactions are included, the solutions are no longer singular, and all of the amplitudes have finite maxima.

Excitation of Continuous and Discrete Modes in Incompressible Boundary Layers

NASA Technical Reports Server (NTRS)

Ashpis, David E.; Reshotko, Eli

1998-01-01

This report documents the full details of the condensed journal article by Ashpis & Reshotko (JFM, 1990) entitled "The Vibrating Ribbon Problem Revisited." A revised formal solution of the vibrating ribbon problem of hydrodynamic stability is presented. The initial formulation of Gaster (JFM, 1965) is modified by application of the Briggs method and a careful treatment of the complex double Fourier transform inversions. Expressions are obtained in a natural way for the discrete spectrum as well as for the four branches of the continuous spectra. These correspond to discrete and branch-cut singularities in the complex wave-number plane. The solutions from the continuous spectra decay both upstream and downstream of the ribbon, with the decay in the upstream direction being much more rapid than that in the downstream direction. Comments and clarification of related prior work are made.

Singular trajectories: space-time domain topology of developing speckle fields

NASA Astrophysics Data System (ADS)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time domain, or evolution of transverse coordinates(x, y) in some fixed plane z0. The dynamics of generic developing speckle fields was realized experimentally by laser induced scattering in LiNbO3:Fe photorefractive crystal. The space-time trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration. Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z0, t) point, their movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of singularities nucleation in various points (xi yi, ti) and following annihilation of both singularities in other space-time points with alien singularities of opposite topological indices. Their topology and properties are established. Chain topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural developing speckle fields are presented.

Wave propagation in metamaterials mimicking the topology of a cosmic string

NASA Astrophysics Data System (ADS)

Fernández-Núñez, Isabel; Bulashenko, Oleg

2018-04-01

We study the interference and diffraction of light when it propagates through a metamaterial medium mimicking the spacetime of a cosmic string—a topological defect with curvature singularity. The phenomenon may look like a gravitational analogue of the Aharonov-Bohm effect, since the light propagates in a region where the Riemann tensor vanishes, being nonetheless affected by the non-zero curvature confined to the string core. We carry out the full-wave numerical simulation of the metamaterial medium and give the analytical interpretation of the results by use of the asymptotic theory of diffraction, which turns out to be in excellent agreement. In particular, we show that the main features of wave propagation in a medium with conical singularity can be explained by four-wave interference involving two geometrical optics and two diffracted waves.

Laboratory demonstration of an optical vortex mask coronagraph using photonic crystal

NASA Astrophysics Data System (ADS)

Murakami, N.; Baba, N.; Ise, A.; Sakamoto, M.; Oka, K.

2010-10-01

Photonic crystal, artificial periodic nanostructure, is an attractive device for constructing focal-plane phase-mask coronagraphs such as segmented phase masks (four-quadrant, eight-octant, and 4N-segmented ones) and an optical vortex mask (OVM), because of its extremely small manufacturing defect. Recently, speckle-noise limited contrast has been demonstrated for two monochromatic lasers by using the eight-octant phase-mask made of the photonic crystal (Murakami et al. 2010, ApJ, 714, 772). We applied the photonic-crystal device to the OVM coronagraph. The OVM is more advantageous over the segmented phase masks because it does not have discontinuities other than a central singular point and provides a full on-sky field of view. For generating an achromatic optical vortex, we manufactured an axially-symmetric half-wave plate (ASHWP). It is expected that a size of the manufacturing defect due to the central singularity is an order of several hundreds nanometers. The ASHWP is placed between two circular polarizers for modulating a Pancharatnam phase. A continuous spiral phase modulation is then implemented achromatically. We carried out preliminary laboratory demonstration of the OVM coronagraph using two monochromatic lasers as a model star (wavelengths of 532 nm and 633 nm). We report a principle of the achromatic optical-vortex generation, and results of the laboratory demonstration of the OVM coronagraph.

The Movement- and Load-Dependent Differences in the EMG Patterns of the Human Arm Muscles during Two-Joint Movements (A Preliminary Study)

PubMed Central

Tomiak, Tomasz; Abramovych, Tetiana I.; Gorkovenko, Andriy V.; Vereshchaka, Inna V.; Mishchenko, Viktor S.; Dornowski, Marcin; Kostyukov, Alexander I.

2016-01-01

Slow circular movements of the hand with a fixed wrist joint that were produced in a horizontal plane under visual guidance during conditions of action of the elastic load directed tangentially to the movement trajectory were studied. The positional dependencies of the averaged surface EMGs in the muscles of the elbow and shoulder joints were compared for four possible combinations in the directions of load and movements. The EMG intensities were largely correlated with the waves of the force moment computed for a corresponding joint in the framework of a simple geometrical model of the system: arm - experimental setup. At the same time, in some cases the averaged EMGs exit from the segments of the trajectory restricted by the force moment singular points (FMSPs), in which the moments exhibited altered signs. The EMG activities display clear differences for the eccentric and concentric zones of contraction that are separated by the joint angle singular points (JASPs), which present extreme at the joint angle traces. We assumed that the modeled patterns of FMSPs and JASPs may be applied for an analysis of the synergic interaction between the motor commands arriving at different muscles in arbitrary two-joint movements. PMID:27375496

Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?

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

Haro, Jaume de, E-mail: jaime.haro@upc.edu

It is stated that holonomy corrections in loop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation is obtained in an inconsistent way, what means that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem is that holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, to a non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent waymore » to deal with the big rip singularity avoidance is to disregard modification in the gravitational part of the Hamiltonian, and only consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, the big rip singularity survives in loop quantum cosmology. Another way to deal with the big rip avoidance is to take into account geometric quantum effects given by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, the expectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantum cosmology, one can conclude that the big rip singularity survives when one takes into account these quantum effects. However, the spreading of the wave packets prevents the recover of the semiclassical time, and thus, one might conclude that the classical evolution of the universe come to and end before the big rip is reached. This is not conclusive because. as we will see, it always exists other external times that allows us to define the classical and quantum evolution of the universe up to the big rip singularity.« less

The dynamics of a shear band

NASA Astrophysics Data System (ADS)

Giarola, Diana; Capuani, Domenico; Bigoni, Davide

2018-03-01

A shear band of finite length, formed inside a ductile material at a certain stage of a continued homogeneous strain, provides a dynamic perturbation to an incident wave field, which strongly influences the dynamics of the material and affects its path to failure. The investigation of this perturbation is presented for a ductile metal, with reference to the incremental mechanics of a material obeying the J2-deformation theory of plasticity (a special form of prestressed, elastic, anisotropic, and incompressible solid). The treatment originates from the derivation of integral representations relating the incremental mechanical fields at every point of the medium to the incremental displacement jump across the shear band faces, generated by an impinging wave. The boundary integral equations (under the plane strain assumption) are numerically approached through a collocation technique, which keeps into account the singularity at the shear band tips and permits the analysis of an incident wave impinging a shear band. It is shown that the presence of the shear band induces a resonance, visible in the incremental displacement field and in the stress intensity factor at the shear band tips, which promotes shear band growth. Moreover, the waves scattered by the shear band are shown to generate a fine texture of vibrations, parallel to the shear band line and propagating at a long distance from it, but leaving a sort of conical shadow zone, which emanates from the tips of the shear band.

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

Solution of two-body relativistic bound state equations with confining plus Coulomb interactions

NASA Technical Reports Server (NTRS)

Maung, Khin Maung; Kahana, David E.; Norbury, John W.

1992-01-01

Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus Linear Confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound state problem. Such a treatment is most easily carried out in momentum space. However, the position space Linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities exactly and thereby solve the Schroedinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistic kernels in four dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactions for all partial waves.

Bonded half planes containing an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Aksogan, O.

1973-01-01

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin transforms, the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given include the stress intensity factors, tHe strain energy release rates, and tHe probable cleavage angles giving the direction of crack propagation.

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.

Coplanar three-beam interference and phase edge dislocations

NASA Astrophysics Data System (ADS)

Patorski, Krzysztof; SłuŻewski, Łukasz; Trusiak, Maciej; Pokorski, Krzysztof

2016-12-01

We present a comprehensive analysis of grating three-beam interference to discover a broad range of the ratio of amplitudes A of +/-1 diffraction orders and the zero order amplitude C providing phase edge dislocations. We derive a condition A/C > 0.5 for the occurrence of phase edge dislocations in three-beam interference self-image planes. In the boundary case A/C = 0.5 singularity conditions are met in those planes (once per interference field period), but the zero amplitude condition is not accompanied by an abrupt phase change. For A/C > 0.5 two adjacent singularities in a single field period show opposite sign topological charges. The occurrence of edge dislocations for selected values of A/C was verified by processing fork fringes obtained by introducing the fourth beam in the plane perpendicular to the one containing three coplanar diffraction orders. Two fork pattern processing methods are described, 2D CWT (two-dimensional continuous wavelet transform) and 2D spatial differentiation.

Tailored vectorial light fields: flower, spider web and hybrid structures

NASA Astrophysics Data System (ADS)

Otte, Eileen; Alpmann, Christina; Denz, Cornelia

2017-04-01

We present the realization and analysis of tailored vector fields including polarization singularities. The fields are generated by a holographic method based on an advanced system including a spatial light modulator. We demonstrate our systems capabilities realizing specifically customized vector fields including stationary points of defined polarization in its transverse plane. Subsequently, vectorial flowers and spider webs as well as unique hybrid structures of these are introduced, and embedded singular points are characterized. These sophisticated light fields reveal attractive properties that pave the way to advanced application in e.g. optical micromanipulation. Beyond particle manipulation, they contribute essentially to actual questions in singular optics.

Vortex formation through inertial wave focusing

NASA Astrophysics Data System (ADS)

Duran-Matute, Matias; Flor, Jan-Bert; Godeferd, Fabien

2011-11-01

We present a novel experimental and numerical study on the formation of columnar vortical structures by inertial waves in a rotating fluid. Two inertial-wave cones are generated by a vertically oscillating torus in a fluid in solid body rotation At the tip of the cones, there is a singular point towards which the energy of the waves gets focused. The particularity of this configuration, as compared to those of previous experiments (e.g. oscillating sphere or disc), is that the singular point's position within the fluid leads to complex non-linear wave interaction, which may lead to the formation of a localized vortex that expands in the vertical in the form of a Taylor column. Using detailed PIV measurements we consider the flow evolution from the localized wave overturning motion to the Taylor column formation as well as the inertial wave dynamics during this process, The results are discussed in the context of turbulence in rotating fluids. We acknowledge financial support from projects ANR ANISO and CIBLE.

Matrix Approach of Seismic Wave Imaging: Application to Erebus Volcano

NASA Astrophysics Data System (ADS)

Blondel, T.; Chaput, J.; Derode, A.; Campillo, M.; Aubry, A.

2017-12-01

This work aims at extending to seismic imaging a matrix approach of wave propagation in heterogeneous media, previously developed in acoustics and optics. More specifically, we will apply this approach to the imaging of the Erebus volcano in Antarctica. Volcanoes are actually among the most challenging media to explore seismically in light of highly localized and abrupt variations in density and wave velocity, extreme topography, extensive fractures, and the presence of magma. In this strongly scattering regime, conventional imaging methods suffer from the multiple scattering of waves. Our approach experimentally relies on the measurement of a reflection matrix associated with an array of geophones located at the surface of the volcano. Although these sensors are purely passive, a set of Green's functions can be measured between all pairs of geophones from ice-quake coda cross-correlations (1-10 Hz) and forms the reflection matrix. A set of matrix operations can then be applied for imaging purposes. First, the reflection matrix is projected, at each time of flight, in the ballistic focal plane by applying adaptive focusing at emission and reception. It yields a response matrix associated with an array of virtual geophones located at the ballistic depth. This basis allows us to get rid of most of the multiple scattering contribution by applying a confocal filter to seismic data. Iterative time reversal is then applied to detect and image the strongest scatterers. Mathematically, it consists in performing a singular value decomposition of the reflection matrix. The presence of a potential target is assessed from a statistical analysis of the singular values, while the corresponding eigenvectors yield the corresponding target images. When stacked, the results obtained at each depth give a three-dimensional image of the volcano. While conventional imaging methods lead to a speckle image with no connection to the actual medium's reflectivity, our method enables to highlight a chimney-shaped structure inside Erebus volcano with true positive rates ranging from 80% to 95%. Although computed independently, the results at each depth are spatially consistent, substantiating their physical reliability. The identified structure is therefore likely to describe accurately the internal structure of the Erebus volcano.

Coulomb wave functions in momentum space

DOE PAGES

Eremenko, V.; Upadhyay, N. J.; Thompson, I. J.; ...

2015-10-15

We present an algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p → q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of vertical bar eta vertical barmore » in the range of 10 -1 to 10, and thus is particularly suited for momentum space calculations of nuclear reactions.« less

Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation

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

Liu, Y.; Rizzo, F.J.

1997-08-01

In this paper, the composite boundary integral equation (BIE) formulation is applied to scattering of elastic waves from thin shapes with small but {ital finite} thickness (open cracks or thin voids, thin inclusions, thin-layer interfaces, etc.), which are modeled with {ital two surfaces}. This composite BIE formulation, which is an extension of the Burton and Miller{close_quote}s formulation for acoustic waves, uses a linear combination of the conventional BIE and the hypersingular BIE. For thin shapes, the conventional BIE, as well as the hypersingular BIE, will degenerate (or nearly degenerate) if they are applied {ital individually} on the two surfaces. Themore » composite BIE formulation, however, will not degenerate for such problems, as demonstrated in this paper. Nearly singular and hypersingular integrals, which arise in problems involving thin shapes modeled with two surfaces, are transformed into sums of weakly singular integrals and nonsingular line integrals. Thus, no finer mesh is needed to compute these nearly singular integrals. Numerical examples of elastic waves scattered from penny-shaped cracks with varying openings are presented to demonstrate the effectiveness of the composite BIE formulation. {copyright} {ital 1997 Acoustical Society of America.}« less

Signature of phase singularities in diffusive regimes in disordered waveguide lattices: interplay and qualitative analysis.

PubMed

Ghosh, Somnath

2018-05-10

Coexistence and interplay between mesoscopic light dynamics with singular optics in spatially disordered waveguide lattices are reported. Two CW light beams of a 1.55 μm operating wavelength are launched as inputs to 1D waveguide lattices with controllable weak disorder in a complex refractive index profile. Direct observation of phase singularities in the speckle pattern along the length is numerically demonstrated. Quantitative analysis of the onset of such singular behavior and diffusive wave propagation is analyzed for the first time, to the best of our knowledge.

On the freestream matching condition for stagnation point turbulent flows

NASA Technical Reports Server (NTRS)

Speziale, C. G.

1989-01-01

The problem of plane stagnation point flow with freestream turbulence is examined from a basic theoretical standpoint. It is argued that the singularity which arises from the standard kappa-epsilon model is not due to a defect in the model but results from the use of an inconsistent freestream boundary condition. The inconsistency lies in the implementation of a production equals dissipation equilibrium hypothesis in conjunction with a freestream mean velocity field that corresponds to homogeneous plane strain - a turbulent flow which does not reach such a simple equilibrium. Consequently, the adjustment that has been made in the constants of the epsilon-transport equation to eliminate this singularity is not self-consistent since it is tantamount to artificially imposing an equilibrium structure on a turbulent flow which is known not to have one.

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.

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

PubMed

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

2017-04-01

In this study, a method is proposed that eliminates spiral waves in a locally connected chaotic neural network (CNN) under some simplified conditions, using a dynamic phase space constraint (DPSC) as a control method. In this method, a control signal is constructed from the feedback internal states of the neurons to detect phase singularities based on their amplitude reduction, before modulating a threshold value to truncate the refractory internal states of the neurons and terminate the spirals. Simulations showed that with appropriate parameter settings, the network was directed from a spiral wave state into either a plane wave (PW) state or a synchronized oscillation (SO) state, where the control vanished automatically and left the original CNN model unaltered. Each type of state had a characteristic oscillation frequency, where spiral wave states had the highest, and the intra-control dynamics was dominated by low-frequency components, thereby indicating slow adjustments to the state variables. In addition, the PW-inducing and SO-inducing control processes were distinct, where the former generally had longer durations but smaller average proportions of affected neurons in the network. Furthermore, variations in the control parameter allowed partial selectivity of the control results, which were accompanied by modulation of the control processes. The results of this study broaden the applicability of DPSC to chaos control and they may also facilitate the utilization of locally connected CNNs in memory retrieval and the exploration of traveling wave dynamics in biological neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Polarization Utilization in Radar Target Reconstruction: C-Wide (Multi-Frequency) Band Relationship of a Target’s Characteristic Operators with Its Unique Set of Natural Eigenfrequencies.

DTIC Science & Technology

1983-12-14

the left half of the s- plane . These are representation independent. We shall be interested in these poles only. These poles are the complex...on the Left Half Plane Asymptotic Behavior of the SEM Expansion of Surface Currents, Published in Special Issue on the Singularity Expansion Method...precisely, the polarization chart is an orthogonal projection of the Poincare Sphere on a plane , having polar coordinates p= cos (2-) and

The supersonic triplet - A new aerodynamic panel singularity with directional properties. [internal wave elimination

NASA Technical Reports Server (NTRS)

Woodward, F. A.; Landrum, E. J.

1979-01-01

A new supersonic triplet singularity has been developed which eliminates internal waves generated by panels having supersonic edges. The triplet is a linear combination of source and vortex distributions which provides the desired directional properties in the flow field surrounding the panel. The theoretical development of the triplet is described, together with its application to the calculation of surface pressure on arbitrary body shapes. Examples are presented comparing the results of the new method with other supersonic panel methods and with experimental data.

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.

Modeling of Graphene Planar Grating in the THz Range by the Method of Singular Integral Equations

NASA Astrophysics Data System (ADS)

Kaliberda, Mstislav E.; Lytvynenko, Leonid M.; Pogarsky, Sergey A.

2018-04-01

Diffraction of the H-polarized electromagnetic wave by the planar graphene grating in the THz range is considered. The scattering and absorption characteristics are studied. The scattered field is represented in the spectral domain via unknown spectral function. The mathematical model is based on the graphene surface impedance and the method of singular integral equations. The numerical solution is obtained by the Nystrom-type method of discrete singularities.

Loop quantum cosmology and singularities.

PubMed

Struyve, Ward

2017-08-15

Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.

New method for detecting singularities in experimental incompressible flows

NASA Astrophysics Data System (ADS)

Kuzzay, Denis; Saw, Ewe-Wei; Martins, Fabio J. W. A.; Faranda, Davide; Foucaut, Jean-Marc; Daviaud, François; Dubrulle, Bérengère

2017-06-01

We introduce two new criteria based on the work of Duchon and Robert (2000 Nonlinearity 13 249) and Eyink (2006 Phys. Rev. E 74 066302), which allow for the local detection of Navier-Stokes singularities in experimental flows. We discuss the difference between non-dissipative or dissipative Euler quasi-singularities and genuine Navier-Stokes dissipative singularites, and classify them with respect to their Hölder exponent h. We show that our criteria allow us to detect areas in a flow where the velocity field is no more regular than Hölder continuous with some Hölder exponent h ≤slant 1/2 . We illustrate our discussion using classical tomographic particle image velocimetry (TPIV) measurements obtained inside a high Reynolds number flow generated in the boundary layer of a wind tunnel. Our study shows that, in order to detect singularities or quasi-singularities, one does not need to have access to the whole velocity field inside a volume, but can instead look for them from stereoscopic PIV data on a plane. We also provide a discussion about the link between areas detected by our criteria and areas corresponding to large vorticity. We argue that this link might provide either a clue about the genesis of these quasi-singularities or a way to discriminate dissipative Euler quasi-singularities and genuine Navier-Stokes singularities.

Generalization of helicoidal beams for short pulses.

PubMed

Thomas, Jean-Louis; Brunet, Thomas; Coulouvrat, François

2010-01-01

A generalization to the transient regime is developed for waves with a phase singularity of the screw type. These singular waves are commonly called vortices for all kind of waves as, for instance, optical vortex or acoustical vortex. We generalize the definition of vortices to get an azimuthal velocity invariant for all the frequency components contained in the broad spectrum of a short pulse. This generalization leads to a modification of the orbital angular momentum definition. Another generalization is introduced by considering helicoidal waves with a finite number of turns. We demonstrate that, in this last case, the topological charge is no longer an integer. This provides a physical interpretation to vortices of fractional charge that are involved here to take into account the diffraction occurring at both tips of the now finite helical wave front. We show that shortening the pulse implies an angular localization of the wave energy and, as a consequence, a spreading of the angular momentum amplitude due to the uncertainty principle.

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.

Strong Evidence for Nucleon Resonances near 1900 MeV

DOE PAGES

Anisovich, A. V.; Burkert, V.; Hadžimehmedović, M.; ...

2017-08-11

Data on the reaction yp→K +A from the CLAS experiments are used to derive the leading multipoles, E 0+, M 1-, E 1+, and M 1+, from the production threshold to 2180 MeV in 24 slices of the invariant mass. The four multipoles are determined without any constraints. The multipoles are fitted using a multichannel L+P model that allows us to search for singularities and to extract the positions of poles on the complex energy plane in an almost model-independent method. The multipoles are also used as additional constraints in an energy-dependent analysis of a large body of pion andmore » photoinduced reactions within the Bonn-Gatchina partial wave analysis. The study confirms the existence of poles due to nucleon resonances with spin parity J P=1/2 -, 1/2 +, and 3/2 + in the region at about 1.9 GeV.« less

Strong Evidence for Nucleon Resonances near 1900 MeV

NASA Astrophysics Data System (ADS)

Anisovich, A. V.; Burkert, V.; Hadžimehmedović, M.; Ireland, D. G.; Klempt, E.; Nikonov, V. A.; Omerović, R.; Osmanović, H.; Sarantsev, A. V.; Stahov, J.; Švarc, A.; Thoma, U.

2017-08-01

Data on the reaction γ p →K+Λ from the CLAS experiments are used to derive the leading multipoles, E0 +, M1 -, E1 +, and M1 +, from the production threshold to 2180 MeV in 24 slices of the invariant mass. The four multipoles are determined without any constraints. The multipoles are fitted using a multichannel L +P model that allows us to search for singularities and to extract the positions of poles on the complex energy plane in an almost model-independent method. The multipoles are also used as additional constraints in an energy-dependent analysis of a large body of pion and photoinduced reactions within the Bonn-Gatchina partial wave analysis. The study confirms the existence of poles due to nucleon resonances with spin parity JP=1 /2- , 1 /2+ , and 3 /2+ in the region at about 1.9 GeV.

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

PubMed

Abbasi, Bilal; Craig, Walter

2014-09-08

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

Determination of Rayleigh wave ellipticity using single-station and array-based processing of ambient seismic noise

NASA Astrophysics Data System (ADS)

Workman, Eli Joseph

We present a single-station method for the determination of Rayleigh wave ellipticity, or Rayleigh wave horizontal to vertical amplitude ratio (H/V) using Frequency Dependent Polarization Analysis (FDPA). This procedure uses singular value decomposition of 3-by-3 spectral covariance matrices over 1-hr time windows to determine properties of the ambient seismic noise field such as particle motion and dominant wave-type. In FPDA, if the noise is mostly dominated by a primary singular value and the phase difference is roughly 90° between the major horizontal axis and the vertical axis of the corresponding singular vector, we infer that Rayleigh waves are dominant and measure an H/V ratio for that hour and frequency bin. We perform this analysis for all available data from the Earthscope Transportable Array between 2004 and 2014. We compare the observed Rayleigh wave H/V ratios with those previously measured by multicomponent, multistation noise cross-correlation (NCC), as well as classical noise spectrum H/V ratio analysis (NSHV). At 8 sec the results from all three methods agree, suggesting that the ambient seismic noise field is Rayleigh wave dominated. Between 10 and 30 sec, while the general pattern agrees well, the results from FDPA and NSHV are persistently slightly higher ( 2%) and significantly higher (>20%), respectively, than results from the array-based NCC. This is likely caused by contamination from other wave types (i.e., Love waves, body waves, and tilt noise) in the single station methods, but it could also reflect a small, persistent error in NCC. Additionally, we find that the single station method has difficulty retrieving robust Rayleigh wave H/V ratios within major sedimentary basins, such as the Williston Basin and Mississippi Embayment, where the noise field is likely dominated by reverberating Love waves.

Determination of Rayleigh wave ellipticity across the Earthscope Transportable Array using single-station and array-based processing of ambient seismic noise

NASA Astrophysics Data System (ADS)

Workman, Eli; Lin, Fan-Chi; Koper, Keith D.

2017-01-01

We present a single station method for the determination of Rayleigh wave ellipticity, or Rayleigh wave horizontal to vertical amplitude ratio (H/V) using Frequency Dependent Polarization Analysis (FDPA). This procedure uses singular value decomposition of 3-by-3 spectral covariance matrices over 1-hr time windows to determine properties of the ambient seismic noise field such as particle motion and dominant wave-type. In FPDA, if the noise is mostly dominated by a primary singular value and the phase difference is roughly 90° between the major horizontal axis and the vertical axis of the corresponding singular vector, we infer that Rayleigh waves are dominant and measure an H/V ratio for that hour and frequency bin. We perform this analysis for all available data from the Earthscope Transportable Array between 2004 and 2014. We compare the observed Rayleigh wave H/V ratios with those previously measured by multicomponent, multistation noise cross-correlation (NCC), as well as classical noise spectrum H/V ratio analysis (NSHV). At 8 s the results from all three methods agree, suggesting that the ambient seismic noise field is Rayleigh wave dominated. Between 10 and 30 s, while the general pattern agrees well, the results from FDPA and NSHV are persistently slightly higher (˜2 per cent) and significantly higher (>20 per cent), respectively, than results from the array-based NCC. This is likely caused by contamination from other wave types (i.e. Love waves, body waves, and tilt noise) in the single station methods, but it could also reflect a small, persistent error in NCC. Additionally, we find that the single station method has difficulty retrieving robust Rayleigh wave H/V ratios within major sedimentary basins, such as the Williston Basin and Mississippi Embayment, where the noise field is likely dominated by reverberating Love waves and tilt noise.

Development of the triplet singularity for the analysis of wings and bodies in supersonic flow

NASA Technical Reports Server (NTRS)

Woodward, F. A.

1981-01-01

A supersonic triplet singularity was developed which eliminates internal waves generated by panels having supersonic edges. The triplet is a linear combination of source and vortex distributions which gives directional properties to the perturbation flow field surrounding the panel. The theoretical development of the triplet singularity is described together with its application to the calculation of surface pressures on wings and bodies. Examples are presented comparing the results of the new method with other supersonic methods and with experimental data.

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.

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.

Stress intensity factors for bonded orthotropic strips with cracks

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1978-01-01

The elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. It is assumed that the plane contains a series of collinear cracks perpendicular to the interfaces and is loaded in tension away from and perpendicular to the cracks. Cracks fully imbedded into the homogenous strips were analyzed as well as the singular behavior of the stresses for two special crack geometries. The analysis of cracks crossing interfaces indicates that, for certain orthotropic material combinations, the stress state at the point of intersection of a crack and an interface may be bounded. A number of numerical examples are worked out in order to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters.

Ground Signatures of EMIC Waves obtained From a 3D Global Wave Model

NASA Astrophysics Data System (ADS)

Rankin, R.; Sydorenko, D.; Zong, Q.; Zhang, L.

2016-12-01

EMIC waves generated in the inner magnetosphere are important drivers of radiation belt particle loss. Van Allen Probes and ground observations of EMIC waves suggest that localized magnetospheric sources inject waves that are guided along geomagnetic field lines and then reflected and refracted in the low altitude magnetosphere [Kim, E.-H., and J. R. Johnson (2016), Geophys. Res. Lett., 43, 13-21, doi:10.1002/2015GL066978] before entering the ionosphere. The waves then spread horizontally within the F-region waveguide and propagate to the ground. To understand the observed properties of EMIC waves, a global 3D model of ULF waves in Earth's magnetosphere, ionosphere, and neutral atmosphere has been developed. The simulation domain extends from Earth's surface to a spherical boundary a few tens of thousands of km in radius. The model uses spherical coordinates and incorporates an overset Yin-Yang grid that eliminates the singularity at the polar axis and improves uniformity of the grid in the polar areas [Kageyama, A., and T. Sato (2004), Geochem. Geophys. Geosyst., 5, Q09005, doi:10.1029/2004GC000734]. The geomagnetic field in the model is general, but is dipole in this study. The plasma is described as a set of electron and multiple species ion conducting fluids. Realistic 3D density profiles of various ion species as well as thermospheric parameters are provided by the Canadian Ionosphere Atmosphere Model (C-IAM) [Martynenko O.V. et al. (2014), J. Atmos. Solar-Terr. Phys., 120, 51-61, doi:10.1016/j.jastp.2014.08.014]. The global ULF wave model is applied to study propagation of EMIC waves excited in the equatorial plane near L=7. Wave propagation along field lines, reflection and refraction in the zone of critical frequencies, and further propagation through the ionosphere to the ground are discussed.

A feasibility study of the use of bounded beams resembling the shape of evanescent and inhomogeneous waves.

PubMed

Declercq, Nico F; Leroy, Oswald

2011-08-01

Plane waves are solutions of the visco-elastic wave equation. Their wave vector can be real for homogeneous plane waves or complex for inhomogeneous and evanescent plane waves. Although interesting from a theoretical point of view, complex wave vectors normally only emerge naturally when propagation or scattering is studied of sound under the appearance of damping effects. Because of the particular behavior of inhomogeneous and evanescent waves and their estimated efficiency for surface wave generation, bounded beams, experimentally mimicking their infinite counterparts similar to (wide) Gaussian beams imitating infinite harmonic plane waves, are of special interest in this report. The study describes the behavior of bounded inhomogeneous and bounded evanescent waves in terms of amplitude and phase distribution as well as energy flow direction. The outcome is of importance to the applicability of bounded inhomogeneous ultrasonic waves for nondestructive testing. Copyright © 2011. Published by Elsevier B.V.

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/.

Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Park, C.B.

1999-01-01

The shear-wave (S-wave) velocity of near-surface materials (soil, rocks, pavement) and its effect on seismic-wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Rayleigh-wave phase velocity of a layered-earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers. Analysis of the Jacobian matrix provides a measure of dispersion-curve sensitivity to earth properties. S-wave velocities are the dominant influence on a dispersion curve in a high-frequency range (>5 Hz) followed by layer thickness. An iterative solution technique to the weighted equation proved very effective in the high-frequency range when using the Levenberg-Marquardt and singular-value decomposition techniques. Convergence of the weighted solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Synthetic examples demonstrated calculation efficiency and stability of inverse procedures. We verify our method using borehole S-wave velocity measurements.Iterative solutions to the weighted equation by the Levenberg-Marquardt and singular-value decomposition techniques are derived to estimate near-surface shear-wave velocity. Synthetic and real examples demonstrate the calculation efficiency and stability of the inverse procedure. The inverse results of the real example are verified by borehole S-wave velocity measurements.

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.

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

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

Teodorescu, Razvan; Lee, S - Y; Wiegmann, P

We investigate the hydrodynamics of a Hele-Shaw flow as the free boundary evolves from smooth initial conditions into a generic cusp singularity (of local geometry type x{sup 3} {approx} y{sup 2}), and then into a density shock wave. This novel solution preserves the integrability of the dynamics and, unlike all the weak solutions proposed previously, is not underdetermined. The evolution of the shock is such that the net vorticity remains zero, as before the critical time, and the shock can be interpreted as a singular line distribution of fluid deficit.

Bonded orthotropic strips with cracks

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1979-01-01

The elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. It is assumed that the plane contains a series of collinear cracks perpendicular to the interfaces and is loaded in tension away from and perpendicular to the cracks. The problem of cracks fully imbedded into the homogeneous strips is considered. The singular behavior of the stresses for two special crack geometries is studied. The first is the case of a broken laminate in which the crack tips touch the interfaces. The second is the case of cracks crossing the interfaces. An interesting result found from the analysis of the latter is that for certain orthotropic material combinations the stress state at the point of intersection of a crack and an interface may be bounded whereas in isotropic materials at this point stresses are always singular. A number of numerical examples are worked out to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters. Some numerical results are given for the stress intensity factors in certain basic crack geometries and for typical material combinations.

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.

Holographic signatures of cosmological singularities.

PubMed

Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T

2014-09-19

To gain insight into the quantum nature of cosmological singularities, we study anisotropic Kasner solutions in gauge-gravity duality. The dual description of the bulk evolution towards the singularity involves N=4 super Yang-Mills theory on the expanding branch of deformed de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlators show a strong signature of the singularity around horizon scales and decay at large boundary separation at different rates in different directions. More generally, the boundary evolution exhibits a process of particle creation similar to that in inflation. This leads us to conjecture that information on the quantum nature of cosmological singularities is encoded in long-wavelength features of the boundary wave function.

Geometrical shock dynamics, formation of singularities and topological bifurcations of converging shock fronts

NASA Astrophysics Data System (ADS)

Suramlishvili, Nugzar; Eggers, Jens; Fontelos, Marco

2014-11-01

We are concerned with singularities of the shock fronts of converging perturbed shock waves. Our considerations are based on Whitham's theory of geometrical shock dynamics. The recently developed method of local analysis is applied in order to determine generic singularities. In this case the solutions of partial differential equations describing the geometry of the shock fronts are presented as families of smooth maps with state variables and the set of control parameters dependent on Mach number, time and initial conditions. The space of control parameters of the singularities is analysed, the unfoldings describing the deformations of the canonical germs of shock front singularities are found and corresponding bifurcation diagrams are constructed. Research is supported by the Leverhulme Trust, Grant Number RPG-2012-568.

Quantum space and quantum completeness

NASA Astrophysics Data System (ADS)

Jurić, Tajron

2018-05-01

Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.

Lump solutions of the BKP equation

NASA Astrophysics Data System (ADS)

Gilson, C. R.; Nimmo, J. J. C.

1990-07-01

Rational solutions of the BKP equation which decay to zero in all directions in the plane are obtained. These solutions are analogous to the lump solutions of the KPI equation. Properties of the single lump solution are described and the form of the N-lump solution is given. It is shown that single lump solutions are only non-singular for spectral parameters lying in certain regions of the complex plane.

Similarity solutions of time-dependent relativistic radiation-hydrodynamical plane-parallel flows

NASA Astrophysics Data System (ADS)

Fukue, Jun

2018-04-01

Similarity solutions are examined for the frequency-integrated relativistic radiation-hydrodynamical flows, which are described by the comoving quantities. The flows are vertical plane-parallel time-dependent ones with a gray opacity coefficient. For adequate boundary conditions, the flows are accelerated in a somewhat homologous manner, but terminate at some singular locus, which originates from the pathological behavior in relativistic radiation moment equations truncated in finite orders.

Similarity solutions of time-dependent relativistic radiation-hydrodynamical plane-parallel flows

NASA Astrophysics Data System (ADS)

Fukue, Jun

2018-06-01

Similarity solutions are examined for the frequency-integrated relativistic radiation-hydrodynamical flows, which are described by the comoving quantities. The flows are vertical plane-parallel time-dependent ones with a gray opacity coefficient. For adequate boundary conditions, the flows are accelerated in a somewhat homologous manner, but terminate at some singular locus, which originates from the pathological behavior in relativistic radiation moment equations truncated in finite orders.

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.

Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution

NASA Astrophysics Data System (ADS)

Kazei, Vladimir; Alkhalifah, Tariq

2018-05-01

Various parametrizations have been suggested to simplify inversions of first arrivals, or P waves, in orthorhombic anisotropic media, but the number and type of retrievable parameters have not been decisively determined. We show that only six parameters can be retrieved from the dynamic linearized inversion of P waves. These parameters are different from the six parameters needed to describe the kinematics of P waves. Reflection-based radiation patterns from the P-P scattered waves are remapped into the spectral domain to allow for our resolution analysis based on the effective angle of illumination concept. Singular value decomposition of the spectral sensitivities from various azimuths, offset coverage scenarios and data bandwidths allows us to quantify the resolution of different parametrizations, taking into account the signal-to-noise ratio in a given experiment. According to our singular value analysis, when the primary goal of inversion is determining the velocity of the P waves, gradually adding anisotropy of lower orders (isotropic, vertically transversally isotropic and orthorhombic) in hierarchical parametrization is the best choice. Hierarchical parametrization reduces the trade-off between the parameters and makes gradual introduction of lower anisotropy orders straightforward. When all the anisotropic parameters affecting P-wave propagation need to be retrieved simultaneously, the classic parametrization of orthorhombic medium with elastic stiffness matrix coefficients and density is a better choice for inversion. We provide estimates of the number and set of parameters that can be retrieved from surface seismic data in different acquisition scenarios. To set up an inversion process, the singular values determine the number of parameters that can be inverted and the resolution matrices from the parametrizations can be used to ascertain the set of parameters that can be resolved.

Phase singularities, correlation singularities, and conditions for complete destructive interference.

PubMed

Rosenbury, Christopher; Gu, Yalong; Gbur, Greg

2012-04-01

A previously derived condition for the complete destructive interference of partially coherent light emerging from a trio of pinholes in an opaque screen is generalized to the case when the coherence properties of the field are asymmetric. It is shown by example that the interference condition is necessary, but not sufficient, and that the existence of complete destructive interference also depends on the intensity of light emerging from the pinholes and the system geometry; more general conditions for such interference are derived. The phase of the wave field exhibits both phase singularities and correlation singularities, and a number of nonintuitive situations in which complete destructive interference occurs are described and explained.

On the possibility of singularities in the acoustic field of supersonic sources when BEM is applied to a wave equation

NASA Technical Reports Server (NTRS)

De Bernardis, E.; Farassat, F.

1989-01-01

Using a time domain method based on the Ffowcs Williams-Hawkings equation, a reliable explanation is provided for the origin of singularities observed in the numerical prediction of supersonic propeller noise. In the last few years Tam and, more recently, Amiet have analyzed the phenomenon from different points of view. The method proposed here offers a clear interpretation of the singularities based on a new description of sources, relating to the behavior of lines where the propeller blade surface exhibit slope discontinuity.

Investigations of dark, bright, combined dark-bright optical and other soliton solutions in the complex cubic nonlinear Schrödinger equation with δ-potential

NASA Astrophysics Data System (ADS)

Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan; Aktürk, Tolga

2018-03-01

In this study, using the extended sinh-Gordon equation expansion method, we construct the dark, bright, combined dark-bright optical, singular, combined singular solitons and singular periodic waves solutions to the complex cubic nonlinear Schrödinger equation with δ-potential. The conditions for the existence of the obtained solutions are given. To present the physical feature of the acquired result, the 2D and 3D graphs are plotted under the choice of suitable values of the parameters.

The best of both Reps—Diabatized Gaussians on adiabatic surfaces

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-11-01

When simulating nonadiabatic molecular dynamics, choosing an electronic representation requires consideration of well-known trade-offs. The uniqueness and spatially local couplings of the adiabatic representation come at the expense of an electronic wave function that changes discontinuously with nuclear motion and associated singularities in the nonadiabatic coupling matrix elements. The quasi-diabatic representation offers a smoothly varying wave function and finite couplings, but identification of a globally well-behaved quasi-diabatic representation is a system-specific challenge. In this work, we introduce the diabatized Gaussians on adiabatic surfaces (DGAS) approximation, a variant of the ab initio multiple spawning (AIMS) method that preserves the advantages of both electronic representations while avoiding their respective pitfalls. The DGAS wave function is expanded in a basis of vibronic functions that are continuous in both electronic and nuclear coordinates, but potentially discontinuous in time. Because the time-dependent Schrödinger equation contains only first-order derivatives with respect to time, singularities in the second-derivative nonadiabatic coupling terms (i.e., diagonal Born-Oppenheimer correction; DBOC) at conical intersections are rigorously absent, though singular time-derivative couplings remain. Interpolation of the electronic wave function allows the accurate prediction of population transfer probabilities even in the presence of the remaining singularities. We compare DGAS calculations of the dynamics of photoexcited ethene to AIMS calculations performed in the adiabatic representation, including the DBOC. The 28 fs excited state lifetime observed in DGAS simulations is considerably shorter than the 50 fs lifetime observed in the adiabatic simulations. The slower decay in the adiabatic representation is attributable to the large, repulsive DBOC in the neighborhood of conical intersections. These repulsive DBOC terms are artifacts of the discontinuities in the individual adiabatic vibronic basis functions and therefore cannot reflect the behavior of the exact molecular wave function, which must be continuous.

Visualizing polarization singularities in Bessel-Poincaré beams.

PubMed

Shvedov, V; Karpinski, P; Sheng, Y; Chen, X; Zhu, W; Krolikowski, W; Hnatovsky, C

2015-05-04

We demonstrate that an annulus of light whose polarization is linear at each point, but the plane of polarization gradually rotates by π radians can be used to generate Bessel-Poincaré beams. In any transverse plane this beam exhibits concentric rings of polarization singularities in the form of L-lines, where the polarization is purely linear. Although the L-lines are invisible in terms of light intensity variations, we present a simple way to visualize them as dark rings around a sharp peak of intensity in the beam center. To do this we use a segmented polarizer whose transmission axes are oriented differently in each segment. The radius of the first L-line is always smaller than the radius of the central disk of the zero-order Bessel beam that would be produced if the annulus were homogeneously polarized and had no phase circulation along it.

Experimental Study of Saddle Point of Attachment in Laminar Juncture Flow

NASA Technical Reports Server (NTRS)

Coon, Michael D.; Tobak, Murray

1995-01-01

An experimental study of laminar horseshoe vortex flows upstream of a cylinder/flat plate juncture has been conducted to verify the existence of saddle-point-of-attachment topologies. In the classical depiction of this flowfield, a saddle point of separation exists on the flat plate upstream of the cylinder, and the boundary layer separates from the surface. Recent computations have indicated that the topology may actually involve a saddle point of attachment on the surface and additional singular points in the flow. Laser light sheet flow visualizations have been performed on the symmetry plane and crossflow planes to identify the saddle-point-of-attachment flowfields. The visualizations reveal that saddle-point-of-attachment topologies occur over a range of Reynolds numbers in both single and multiple vortex regimes. An analysis of the flow topologies is presented that describes the existence and evolution of the singular points in the flowfield.

Matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation for aeroassisted plane-change maneuvers

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Melamed, Nahum

1993-01-01

In this paper we develop a general procedure for constructing a matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation based on the method of characteristics. The development is for a class of perturbation problems whose solution exhibits two-time-scale behavior. A regular expansion for problems of this type is inappropriate since it is not uniformly valid over a narrow range of the independent variable. Of particular interest here is the manner in which matching and boundary conditions are enforced when the expansion is carried out to first order. Two cases are distinguished - one where the left boundary condition coincides with or lies to the right of the singular region and one where the left boundary condition lies to the left of the singular region. A simple example is used to illustrate the procedure, and its potential application to aeroassisted plane change is described.

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

Inclined edge crack in two bonded elastic quarter planes under out-of-plane loading

NASA Astrophysics Data System (ADS)

Hwang, E. H.; Choi, S. R.; Earmme, Y. Y.

1992-08-01

The problem of the interfacial edge crack in which the crack-inclination angle = zero is solved analytically by means of the Wiener-Hopf technique with the Mellin transform. The results are found to confirm the result by Bassani and Erdogan (1979) showing that there is no stress singularity for the interface perpendicular to the free boundary at the junction with a straight inclined interface with no crack.

A review of electron-phonon coupling seen in the high-Tc superconductors by angle-resolved photoemission studies (ARPES)

NASA Astrophysics Data System (ADS)

Cuk, T.; Lu, D. H.; Zhou, X. J.; Shen, Z.-X.; Devereaux, T. P.; Nagaosa, N.

2005-01-01

This issue of pss (b) - basic solid state physics contains a collection of Review Articles on the rather controversially discussed topic of Electron-Phonon Interaction in High-Temperature Superconductors, guest-edited by Miodrag Kuli, Johann Wolfgang Goethe-Universität Frankfurt/Main, Germany, with a Preface written by V. L. Ginzburg and E. G. Maksimov [1].The cover picture, taken from the review [2] by T. Cuk et al., shows plots of the electron-phonon coupling vertex, g2(k, k), where k, k are the initial and final electron momentum for electrons scattered by the bond-buckling phonon B1g (the out-of-phase vibration of the in-plane oxygen) in a tight-binding model of the copper-oxygen plane. The momentum dependence of this vertex, along with the d-wave superconducting gap and the van Hove singularity at the anti-node, accounts for the momentum dependence of the collective mode coupling seen in angle-resolved photoemission data on Bi2212.The present issue also sees the start of our rapid research letters, the fastest peer-reviewed publication medium in solid state physics. For more information see www.pss-rapid.com and the Editorial by the Editor-in-Chief Martin Stutzmann on page 7 [3].

Reflections on the Hyperbolic Plane

NASA Astrophysics Data System (ADS)

Lecian, Orchidea Maria

2013-12-01

The most general solution to the Einstein equations in 4 = 3 + 1 dimensions in the asymptotic limit close to the cosmological singularity under the BKL (Belinskii-Khalatnikov-Lifshitz) hypothesis can be visualized by the behavior of a billiard ball in a triangular domain on the Upper Poincaré Half Plane (UPHP). The billiard system (named "big billiard") can be schematized by dividing the successions of trajectories according to Poincaré return map on the sides of the billiard table, according to the paradigms implemented by the BKL investigation and by the CB-LKSKS (Chernoff-Barrow-Lifshitz-Khalatnikov-Sinai-Khanin-Shchur) one. Different maps are obtained, according to different symmetry-quotienting mechanisms used to analyze the dynamics. In the inhomogeneous case, new structures have been uncovered, such that, in this framework, the billiard table (named "small billiard") consists of 1/6 of the previous one. The connections between the symmetry-quotienting mechanisms are further investigated on the UPHP. The relation between the complete billiard and the small billiard are also further explained according to the role of Weyl reflections. The quantum properties of the system are sketched as well, and the physical interpretation of the wave function is further developed. In particular, a physical interpretation for the symmetry-quotienting maps is proposed.

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.

Non-singular cloaks allow mimesis

NASA Astrophysics Data System (ADS)

Diatta, André; Guenneau, Sébastien

2011-02-01

We design non-singular cloaks enabling objects to scatter waves like objects with smaller size and very different shapes. We consider the Schrödinger equation, which is valid, for example, in the contexts of geometrical and quantum optics. More precisely, we introduce a generalized non-singular transformation for star domains, and numerically demonstrate that an object of nearly any given shape surrounded by a given cloak scatters waves in exactly the same way as a smaller object of another shape. When a source is located inside the cloak, it scatters waves as if it were located some distance away from a small object. Moreover, the invisibility region actually hosts almost trapped eigenstates. Mimetism is numerically shown to break down for the quantified energies associated with confined modes. If we further allow for non-isomorphic transformations, our approach leads to the design of quantum super-scatterers: a small size object surrounded by a quantum cloak described by a negative anisotropic heterogeneous effective mass and a negative spatially varying potential scatters matter waves like a larger nano-object of different shape. Potential applications might be, for instance, in quantum dots probing. The results in this paper, as well as the corresponding derived constitutive tensors, are valid for cloaks with any arbitrary star-shaped boundary cross sections, although for numerical simulations we use examples with piecewise linear or elliptic boundaries.

Diffraction of a plane wave by a three-dimensional corner

NASA Technical Reports Server (NTRS)

Ting, L.; Kung, F.

1971-01-01

By the superposition of the conical solution for the diffraction of a plane pulse by a three dimensional corner, the solution for a general incident plane wave is constructed. A numerical program is presented for the computation of the pressure distribution on the surface due to an incident plane wave of any wave form and at any incident angle. Numerical examples are presented to show the pressure signature at several points on the surface due to incident wave with a front shock wave, two shock waves in succession, or a compression wave with same peak pressure. The examples show that when the distance of a point on the surface from the edges or the vertex is comparable to the distance for the front pressure raise to reach the maximum, the peak pressure at that point can be much less than that given by a regular reflection, because the diffracted wave front arrives at that point prior to the arrival of the peak incident wave.

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

Stress-free end problem in layered materials

NASA Technical Reports Server (NTRS)

Erdogan, F.; Bakioglu, M.

1977-01-01

In this paper the plane elastostatic problem for a medium which consists of periodically arranged two sets of bonded dissimilar layers or strips is considered. First it is assumed that one set of strips contains a crack which crosses the bimaterial interfaces. Then, by letting the collinear cracks join, the stress-free end problem is formulated. The singular behavior of the solutions at the point on intersection of the stress-free boundary and the interfaces is examined and appropriate stress intensity factors are defined. The results of some numerical examples are then presented which include the cases of both plane stress and plane strain.

Cosmic ray-modified stellar winds. I - Solution topologies and singularities

NASA Technical Reports Server (NTRS)

Ko, C. M.; Webb, G. M.

1987-01-01

In the present two-fluid hydrodynamical model for stellar wind flow modification due to its interaction with Galactic cosmic rays, these rays are coupled to the stellar wind by either hydromagnetic wave scattering or background flow irregularity propagation. The background flow is modified by the cosmic rays via their pressure gradient. The system of equations used possesses a line of singularities in (r, u, P sub c)-space, or a two-dimensional hypersurface of singularities in (r, u, P sub c, dP sub c/dr)-space, where r, u, and P sub c are respectively the radial distance from the star, the radial wind flow speed, and the cosmic ray pressure. The singular points may be nodes, foci, or saddle points.

Classical and quantum analysis of repulsive singularities in four-dimensional extended supergravity

NASA Astrophysics Data System (ADS)

Gaida, I.; Hollmann, H. R.; Stewart, J. M.

1999-07-01

Non-minimal repulsive singularities (`repulsons') in extended supergravity theories are investigated. The short-distance antigravity properties of the repulsons are tested at the classical and the quantum level by a scalar test-particle. Using a partial wave expansion it is shown that the particle is totally reflected at the origin. A high-frequency incoming particle undergoes a phase shift of icons/Journals/Common/pi" ALT="pi" ALIGN="TOP"/>/2. However, the phase shift for a low-frequency particle depends upon the physical data of the repulson. The curvature singularity at a finite distance rh turns out to be transparent for the scalar test-particle and the coordinate singularity at the origin serves as the repulsive barrier to bounce back the particles.

Twisted gravitational waves

NASA Astrophysics Data System (ADS)

Bini, Donato; Chicone, Carmen; Mashhoon, Bahram

2018-03-01

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

Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd-Bullough-Mikhailov equation

NASA Astrophysics Data System (ADS)

Ilhan, O. A.; Bulut, H.; Sulaiman, T. A.; Baskonus, H. M.

2018-02-01

In this study, the modified exp ( - Φ (η )) -expansion function method is used in constructing some solitary wave solutions to the Oskolkov-Benjamin-Bona-Mahony-Burgers, one-dimensional Oskolkov equations and the Dodd-Bullough-Mikhailov equation. We successfully construct some singular solitons and singular periodic waves solutions with the hyperbolic, trigonometric and exponential function structures to these three nonlinear models. Under the choice of some suitable values of the parameters involved, we plot the 2D and 3D graphics to some of the obtained solutions in this study. All the obtained solutions in this study verify their corresponding equation. We perform all the computations in this study with the help of the Wolfram Mathematica software. The obtained solutions in this study may be helpful in explaining some practical physical problems.

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.

Singular Atom Optics with Spinor BECs

NASA Astrophysics Data System (ADS)

Schultz, Justin T.; Hansen, Azure; Bigelow, Nicholas P.

2015-05-01

We create and study singular spin textures in pseudo-spin-1/2 BECs. A series of two-photon Raman interactions allows us to not only engineer the spinor wavefunction but also perform the equivalent of atomic polarimetry on the BEC. Adapting techniques from optical polarimetry, we can image two-dimensional maps of the atomic Stokes parameters, thereby fully reconstructing the atomic wavefunction. In a spin-1/2 system, we can represent the local spin superposition with ellipses in a Cartesian basis. The patterns that emerge from the major axes of the ellipses provide fingerprints of the singularities that enable us to classify them as lemons, stars, saddles, or spirals similar to classification schemes for singularities in singular optics, condensed matter, and liquid crystals. These techniques may facilitate the study of geometric Gouy phases in matter waves as well as provide an avenue for utilizing topological structures as quantum gates.

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.

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

PubMed

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

2012-09-14

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

Polarization singularity indices in Gaussian laser beams

NASA Astrophysics Data System (ADS)

Freund, Isaac

2002-01-01

Two types of point singularities in the polarization of a paraxial Gaussian laser beam are discussed in detail. V-points, which are vector point singularities where the direction of the electric vector of a linearly polarized field becomes undefined, and C-points, which are elliptic point singularities where the ellipse orientations of elliptically polarized fields become undefined. Conventionally, V-points are characterized by the conserved integer valued Poincaré-Hopf index η, with generic value η=±1, while C-points are characterized by the conserved half-integer singularity index IC, with generic value IC=±1/2. Simple algorithms are given for generating V-points with arbitrary positive or negative integer indices, including zero, at arbitrary locations, and C-points with arbitrary positive or negative half-integer or integer indices, including zero, at arbitrary locations. Algorithms are also given for generating continuous lines of these singularities in the plane, V-lines and C-lines. V-points and C-points may be transformed one into another. A topological index based on directly measurable Stokes parameters is used to discuss this transformation. The evolution under propagation of V-points and C-points initially embedded in the beam waist is studied, as is the evolution of V-dipoles and C-dipoles.

Lee waves: Benign and malignant

NASA Technical Reports Server (NTRS)

Wurtele, M. G.; Datta, A.; Sharman, R. D.

1993-01-01

The flow of an incompressible fluid over an obstacle will produce an oscillation in which buoyancy is the restoring force, called a gravity wave. For disturbances of this scale, the atmosphere may be treated as dynamically incompressible, even though there exists a mean static upward density gradient. Even in the linear approximation - i.e., for small disturbances - this model explains a great many of the flow phenomena observed in the lee of mountains. However, nonlinearities do arise importantly, in three ways: (1) through amplification due to the decrease of mean density with height; (2) through the large (scaled) size of the obstacle, such as a mountain range; and (3) from dynamically singular levels in the fluid field. These effects produce a complicated array of phenomena - large departure of the streamlines from their equilibrium levels, high winds, generation of small scales, turbulence, etc. - that present hazards to aircraft and to lee surface areas. The nonlinear disturbances also interact with the larger-scale flow in such a manner as to impact global weather forecasts and the climatological momentum balance. If there is no dynamic barrier, these waves can penetrate vertically into the middle atmosphere (30-100 km), where recent observations show them to be of a length scale that must involve the coriolis force in any modeling. At these altitudes, the amplitude of the waves is very large, and the phenomena associated with these wave dynamics are being studied with a view to their potential impact on high performance aircraft, including the projected National Aerospace Plane (NASP). The presentation shows the results of analysis and of state-of-the-art numerical simulations, validated where possible by observational data, and illustrated with photographs from nature.

An omnidirectional retroreflector based on the transmutation of dielectric singularities.

PubMed

Ma, Yun Gui; Ong, C K; Tyc, Tomás; Leonhardt, Ulf

2009-08-01

Transformation optics is a concept used in some metamaterials to guide light on a predetermined path. In this approach, the materials implement coordinate transformations on electromagnetic waves to create the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here, on the basis of transformation optics, we implement a microwave device that would normally require a dielectric singularity, an infinity in the refractive index. To fabricate such a device, we transmute a dielectric singularity in virtual space into a mere topological defect in a real metamaterial. In particular, we demonstrate an omnidirectional retroreflector, a device for faithfully reflecting images and for creating high visibility from all directions. Our method is robust, potentially broadband and could also be applied to visible light using similar techniques.

Bi-material plane with interface crack for the model of semi-linear material

NASA Astrophysics Data System (ADS)

Domanskaya, T. O.; Malkov, V. M.; Malkova, Yu. V.

2018-05-01

The singular plane problems of nonlinear elasticity (plane strain and plane stress) are considered for bi-material infinite plane with interface crack. The plane is formed of two half-planes. Mechanical properties of half-planes are described by the model of semi-linear material. Using model of this harmonic material has allowed to apply the theory of complex functions and to obtain exact analytical global solutions of some nonlinear problems. Among them the problem of bi-material plane with the stresses and strains jumps at an interface is considered. As an application of the problem of jumps, the problem of interface crack is solved. The values of nominal (Piola) and Cauchy stresses and displacements are founded. Based on the global solutions the asymptotic expansions are constructed for stresses and displacements in a vicinity of crack tip. As an example the case of a free crack in bi-material plane subjected to constant stresses at infinity is studied. As a special case, the analytical solution of the problem of a crack in a homogeneous plane is obtained from the problem for bi-material plane with interface crack.

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

Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg–de Vries equation

PubMed Central

Bridges, Thomas J.

2016-01-01

Multiphase wavetrains are multiperiodic travelling waves with a set of distinct wavenumbers and distinct frequencies. In conservative systems, such families are associated with the conservation of wave action or other conservation law. At generic points (where the Jacobian of the wave action flux is non-degenerate), modulation of the wavetrain leads to the dispersionless multiphase conservation of wave action. The main result of this paper is that modulation of the multiphase wavetrain, when the Jacobian of the wave action flux vector is singular, morphs the vector-valued conservation law into the scalar Korteweg–de Vries (KdV) equation. The coefficients in the emergent KdV equation have a geometrical interpretation in terms of projection of the vector components of the conservation law. The theory herein is restricted to two phases to simplify presentation, with extensions to any finite dimension discussed in the concluding remarks. Two applications of the theory are presented: a coupled nonlinear Schrödinger equation and two-layer shallow-water hydrodynamics with a free surface. Both have two-phase solutions where criticality and the properties of the emergent KdV equation can be determined analytically. PMID:28119546

Formation of a wave on an ice-sheet above the dipole, moving in a fluid

NASA Astrophysics Data System (ADS)

Il'ichev, A. T.; Savin, A. A.; Savin, A. S.

2012-05-01

Theory of wave motions of a fluid with an ice-sheet was developed due to the necessity of solving of a number of problems of marine and land physics. The main attention in these investigations was focused on propagation and interaction of free waves, and also on appearance of waves under action of different loadings on the ice-sheet. From the other side, the problems dealing with waves on the fluid surface, free from the ice due to motion in the mass of the fluid of rigid bodies, has the known solutions. In this connection, it seems natural to disserminate the formulation and methods of such problems to the case of the fluid with the ice-sheet. In the present note we describe the character of formation of waves from the singularity, localized in the fluid of infinite depth beneath the ice-sheet. We use the example of the dipole, which models a cylinder in the infinite mass of the fluid. The character of the formation does not depend on the type of singularity. The ice-sheet is considered as a thin elastic plate of a constant width, floating on the water surface.

Gravity–capillary waves in finite depth on flows of constant vorticity

PubMed Central

Hsu, Hung-Chu; Francius, Marc; Kharif, Christian

2016-01-01

This paper considers two-dimensional periodic gravity–capillary waves propagating steadily in finite depth on a linear shear current (constant vorticity). A perturbation series solution for steady periodic waves, accurate up to the third order, is derived using a classical Stokes expansion procedure, which allows us to include surface tension effects in the analysis of wave–current interactions in the presence of constant vorticity. The analytical results are then compared with numerical computations with the full equations. The main results are (i) the phase velocity is strongly dependent on the value of the vorticity; (ii) the singularities (Wilton singularities) in the Stokes expansion in powers of wave amplitude that correspond to a Bond number of 1/2 and 1/3, which are the consequences of the non-uniformity in the ordering of the Fourier coefficients, are found to be influenced by vorticity; (iii) different surface profiles of capillary–gravity waves are computed and the effect of vorticity on those profiles is shown to be important, in particular that the solutions exhibit type-2-like wave features, characterized by a secondary maximum on the surface profile with a trough between the two maxima. PMID:27956873

EDITORIAL: The plurality of optical singularities

NASA Astrophysics Data System (ADS)

Berry, Michael; Dennis, Mark; Soskin, Marat

2004-05-01

This collection of papers arose from an Advanced Research Workshop on Singular Optics, held at the Bogolyubov Institute in Kiev, Ukraine, during 24-28 June 2003. The workshop was generously financed by NATO, with welcome additional support from Institute of Physics Publishing and the National Academy of Sciences of Ukraine. There had been two previous international meetings devoted to singular optics, in Crimea in 1997 and 2000, reflecting the strong involvement of former Soviet Union countries in this research. Awareness of singular optics is growing within the wider optics community, indicated by symposia on the subject at several general optics meetings. As the papers demonstrate, the field of singular optics has reached maturity. Although the subject originated in an observation on ultrasound, it has been largely theory-driven until recently. Now, however, there is close contact between theory and experiment, and we speculate that this is one reason for its accelerated development. To single out particular papers for mention here would be invidious, and since the papers speak for themselves it is not necessary to describe them all. Instead, we will confine ourselves to a brief description of the main areas included in singular optics, to illustrate the broad scope of the subject. Optical vortices are lines of phase singularity: nodal lines where the intensity of the light, represented by a complex scalar field, vanishes. The subject has emerged from flatland, where the vortices are points characterized by topological charges, into the much richer world of vortex lines in three dimensions. By combining Laguerre-Gauss or Bessel beams, or reflecting light from plates with spiral steps, intricate arrangements can be generated, with vortices that are curved, looped, knotted, linked or braided. With light whose state of polarization varies with position, different singularities occur, associated with the vector nature of light. These are also lines, on which the electric (or magnetic) polarization ellipse is purely circular (C lines) or purely linear (L lines). The patterns of ellipse-fields are different for purely paraxial and fully three-dimensional fields. White-light diffraction generates richly coloured vortices—the colours of dark light. The description of these chromatic effects, and also those associated with polarization singularities, leads to new applications of coherence theory. For non-monochromatic light, it is natural to seek singularities of the full electromagnetic field, rather than of the electric or magnetic field separately. Such electromagnetic singularities are the Riemann-Silberstein vortices; these are relativistically covariant nodal lines of a complex scalar field constructed from the electromagnetic field. Optical fields have dynamical aspects, particularly those associated with angular momentum. Although angular momentum is not inevitably associated with optical singularities, in practice the two phenomena can occur together. Orbital angular momentum is associated with the spatial structure of light, and in beams with optical vortices it can be used to rotate particles in the field. Spin angular momentum is associated with the polarization structure of the light. There are tricky questions associated with the angular momentum of light in a refracting medium, echoing the Abraham-Minkowski controversy about linear momentum. In optically nonlinear materials (leading to second-harmonic generation, for example), new classes of phenomena can occur, such as, for example, dynamical interaction between vortex lines, whose stability needs to be considered. At a more fundamental level, it is important to investigate quantum effects associated with optical singularities, and a start has been made. The dark centre of an optical vortex can be regarded as a window onto the vacuum fluctuations of quantum optics, with the quantum core emerging as a distinct entity when the classical light is intense. And for light in a rapidly and inhomogeneously flowing material, horizons can develop, analogous to those surrounding black holes in general relativity, and these new optical singularities can be regarded as wave catastrophes, and new associated quantum effects anticipated. Three decades after wave dislocations were introduced as ‘a new concept in ... wave theory’, these phase singularities have been extensively explored and are now familiar. New ideas—in addition to those described in this special issue—continue to emerge. For example, x-ray vortices were observed recently; there is a proposal to create lenses to form atomic beams containing vortices; and astrophysical applications have been suggested for both photon orbital angular momentum and optical vortices. We can safely assume that the science of wave singularities will develop further, and diffuse into new areas of physics.

Inversion of residual stress profiles from ultrasonic Rayleigh wave dispersion data

NASA Astrophysics Data System (ADS)

Mora, P.; Spies, M.

2018-05-01

We investigate theoretically and with synthetic data the performance of several inversion methods to infer a residual stress state from ultrasonic surface wave dispersion data. We show that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. We focus on two methods, one based on a Taylor-expansion, and another one based on a piecewise linear expansion regularized by a singular value decomposition. We explain the instabilities of the Taylor-based method by highlighting singularities in the series of coefficients. At the same time, we show that the other method can successfully provide performances which only weakly depend on the material.

A special method for finding body distortions that reduce the wave drag of wing and body combinations at supersonic speeds

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Heaslet, Max A

1956-01-01

For a given wing and supersonic Mach number, the problem of shaping an adjoining fuselage so that the combination will have a low wave drag is considered. Only fuselages that can be simulated by singularities (multipoles) distributed along the body axis are studied. However, the optimum variations of such singularities are completely specified in terms of the given wing geometry. An application is made to an elliptic wing having a biconvex section, a thickness-chord ratio equal to 0.05 at the root, and an aspect ratio equal to 3. A comparison of the theoretical results with a wind-tunnel experiment is also presented.

Quantum solitonic wave-packet of a meso-scopic system in singularity free gravity

NASA Astrophysics Data System (ADS)

Buoninfante, Luca; Lambiase, Gaetano; Mazumdar, Anupam

2018-06-01

In this paper we will discuss how to localise a quantum wave-packet due to self-gravitating meso-scopic object by taking into account gravitational self-interaction in the Schrödinger equation beyond General Relativity. In particular, we will study soliton-like solutions in infinite derivative ghost free theories of gravity, which resolves the gravitational 1 / r singularity in the potential. We will show a unique feature that the quantum spread of such a gravitational system is larger than that of the Newtonian gravity, therefore enabling us a window of opportunity to test classical and quantum properties of such theories of gravity in the near future at a table-top experiment.

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.

Asymptotic dynamics of the exceptional Bianchi cosmologies

NASA Astrophysics Data System (ADS)

Hewitt, C. G.; Horwood, J. T.; Wainwright, J.

2003-05-01

In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly, it is generic within the class of non-tilted SH cosmologies, being of the same generality as the models of Bianchi types VIII and IX. Secondly, it is the SH limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies. Using the orthonormal frame formalism and Hubble-normalized variables, we show that the exceptional Bianchi cosmologies differ from the non-exceptional Bianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the models exhibit an oscillatory approach to the initial singularity and hence are not asymptotically self-similar. Secondly, at late times, although the models are asymptotically self-similar, the future attractor for the vacuum-dominated models is the so-called Robinson-Trautman SH model instead of the vacuum SH plane wave models.

Shocks and finite-time singularities in Hele-Shaw flow

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

Teodorescu, Razvan; Wiegmann, P; Lee, S-y

Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusplike singularities. We show that the ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating in the viscous fluid. The graph of shocks grows and branches. Velocity and pressure jump across the shock. We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve. We study in details the most genericmore » (2,3) cusp singularity which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.« less

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1974-01-01

The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1976-01-01

The paper deals with the plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

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

NASA Astrophysics Data System (ADS)

Lazar, Markus; Pellegrini, Yves-Patrick

2016-11-01

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

Validation of zero-order feedback strategies for medium range air-to-air interception in a horizontal plane

NASA Technical Reports Server (NTRS)

Shinar, J.

1982-01-01

A zero order feedback solution of a variable speed interception game between two aircraft in the horizontal plane, obtained by using the method of forced singular perturbation (FSP), is compared with the exact open loop solution. The comparison indicates that for initial distances of separation larger than eight turning radii of the evader, the accuracy of the feedback approximation is better than one percent. The result validates the zero order FSP approximation for medium range air combat analysis.

Steady sliding frictional contact problem for a 2d elastic half-space with a discontinuous friction coefficient and related stress singularities

NASA Astrophysics Data System (ADS)

Ballard, Patrick

2016-12-01

The steady sliding frictional contact problem between a moving rigid indentor of arbitrary shape and an isotropic homogeneous elastic half-space in plane strain is extensively analysed. The case where the friction coefficient is a step function (with respect to the space variable), that is, where there are jumps in the friction coefficient, is considered. The problem is put under the form of a variational inequality which is proved to always have a solution which, in addition, is unique in some cases. The solutions exhibit different kinds of universal singularities that are explicitly given. In particular, it is shown that the nature of the universal stress singularity at a jump of the friction coefficient is different depending on the sign of the jump.

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.

Guided solitary waves.

PubMed

Miles, J

1980-04-01

Transversely periodic solitary-wave solutions of the Boussinesq equations (which govern wave propagation in a weakly dispersive, weakly nonlinear physical system) are determined. The solutions for negative dispersion (e.g., gravity waves) are singular and therefore physically unacceptable. The solutions for positive dispersion (e.g., capillary waves or magnetosonic waves in a plasma) are physically acceptable except in a limited parametric interval, in which they are complex. The two end points of this interval are associated with (two different) resonant interactions among three basic solitary waves, two of which are two-dimensional complex conjugates and the third of which is one-dimensional and real.

Light focusing through a multiple scattering medium: ab initio computer simulation

NASA Astrophysics Data System (ADS)

Danko, Oleksandr; Danko, Volodymyr; Kovalenko, Andrey

2018-01-01

The present study considers ab initio computer simulation of the light focusing through a complex scattering medium. The focusing is performed by shaping the incident light beam in order to obtain a small focused spot on the opposite side of the scattering layer. MSTM software (Auburn University) is used to simulate the propagation of an arbitrary monochromatic Gaussian beam and obtain 2D distribution of the optical field in the selected plane of the investigated volume. Based on the set of incident and scattered fields, the pair of right and left eigen bases and corresponding singular values were calculated. The pair of right and left eigen modes together with the corresponding singular value constitute the transmittance eigen channel of the disordered media. Thus, the scattering process is described in three steps: 1) initial field decomposition in the right eigen basis; 2) scaling of decomposition coefficients for the corresponding singular values; 3) assembling of the scattered field as the composition of the weighted left eigen modes. Basis fields are represented as a linear combination of the original Gaussian beams and scattered fields. It was demonstrated that 60 independent control channels provide focusing the light into a spot with the minimal radius of approximately 0.4 μm at half maximum. The intensity enhancement in the focal plane was equal to 68 that coincided with theoretical prediction.

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.

Active listening room compensation for massive multichannel sound reproduction systems using wave-domain adaptive filtering.

PubMed

Spors, Sascha; Buchner, Herbert; Rabenstein, Rudolf; Herbordt, Wolfgang

2007-07-01

The acoustic theory for multichannel sound reproduction systems usually assumes free-field conditions for the listening environment. However, their performance in real-world listening environments may be impaired by reflections at the walls. This impairment can be reduced by suitable compensation measures. For systems with many channels, active compensation is an option, since the compensating waves can be created by the reproduction loudspeakers. Due to the time-varying nature of room acoustics, the compensation signals have to be determined by an adaptive system. The problems associated with the successful operation of multichannel adaptive systems are addressed in this contribution. First, a method for decoupling the adaptation problem is introduced. It is based on a generalized singular value decomposition and is called eigenspace adaptive filtering. Unfortunately, it cannot be implemented in its pure form, since the continuous adaptation of the generalized singular value decomposition matrices to the variable room acoustics is numerically very demanding. However, a combination of this mathematical technique with the physical description of wave propagation yields a realizable multichannel adaptation method with good decoupling properties. It is called wave domain adaptive filtering and is discussed here in the context of wave field synthesis.

A kinematic analysis of the Space Station remote manipulator system (SSRMS)

NASA Technical Reports Server (NTRS)

Crane, Carl D., III; Duffy, Joseph; Carnahan, Tim

1991-01-01

An efficient reverse analysis of three 6-degree-of-freedom (dof) subchains of the 7-dof SSRMS is presented. The first subchain is formed by locking the seventh joint. The second subchain is formed by locking the second joint, while the third subchain is formed by locking the first joint (the grounded joint is counted as the first joint in the chain). There are a maximum of eight different arm configurations in each of the three subchains, and these were determined by employing a computer-efficient algorithm, which required the rooting of only at most quadratic polynomials. The algorithms were implemented, and the SSRMS was employed in an animated environment to perform and practice a number of useful tasks for Space Station servicing. The locking of the second joint has the advantage in that an operator can choose the orientation of the plane that contains the two longest links so as to avoid collisions with obstacles. However, it has the disadvantage that when the second joint angle equals 0 deg or 180 deg, the manipulator is in a singularity configuration. This plane can also be oriented by specifying the first joint angle, so that the plane can be oriented arbitrarily and, in this, the singularity is avoided.

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

NASA Astrophysics Data System (ADS)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

The crack problem for a half plane stiffened by elastic cover plates

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

An elastic half plane containing a crack and stiffened by a cover plate is discussed. The asymptotic nature of the stress state in the half plane around an end point of the stiffener to determine the likely orientation of a possible fracture initiation and growth was studied. The problem is formulated for an arbitrary oriented radial crack in a system of singular integral equations. For an internal crack and for an edge crack, the problem is solved and the stress intensity factors at the crack tips and the interface stress are calculated. A cracked half plane with two symmetrically located cover plates is also considered. It is concluded that the case of two stiffeners appears to be more severe than that of a single stiffener.

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.

High order Nyström method for elastodynamic scattering

NASA Astrophysics Data System (ADS)

Chen, Kun; Gurrala, Praveen; Song, Jiming; Roberts, Ron

2016-02-01

Elastic waves in solids find important applications in ultrasonic non-destructive evaluation. The scattering of elastic waves has been treated using many approaches like the finite element method, boundary element method and Kirchhoff approximation. In this work, we propose a novel accurate and efficient high order Nyström method to solve the boundary integral equations for elastodynamic scattering problems. This approach employs high order geometry description for the element, and high order interpolation for fields inside each element. Compared with the boundary element method, this approach makes the choice of the nodes for interpolation based on the Gaussian quadrature, which renders matrix elements for far field interaction free from integration, and also greatly simplifies the process for singularity and near singularity treatment. The proposed approach employs a novel efficient near singularity treatment that makes the solver able to handle extreme geometries like very thin penny-shaped crack. Numerical results are presented to validate the approach. By using the frequency domain response and performing the inverse Fourier transform, we also report the time domain response of flaw scattering.

Interaction between a circular inclusion and an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.; Ratwani, M.

1975-01-01

The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Nakagaki, M.; Kathiresan, K.

1980-01-01

In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

Integrals and integral equations in linearized wing theory

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Heaslet, Max A; Fuller, Franklyn B

1951-01-01

The formulas of subsonic and supersonic wing theory for source, doublet, and vortex distributions are reviewed and a systematic presentation is provided which relates these distributions to the pressure and to the vertical induced velocity in the plane of the wing. It is shown that care must be used in treating the singularities involved in the analysis and that the order of integration is not always reversible. Concepts suggested by the irreversibility of order of integration are shown to be useful in the inversion of singular integral equations when operational techniques are used. A number of examples are given to illustrate the methods presented, attention being directed to supersonic flight speed.

Dry granular avalanche impact force on a rigid wall: Analytic shock solution versus discrete element simulations

NASA Astrophysics Data System (ADS)

Albaba, Adel; Lambert, Stéphane; Faug, Thierry

2018-05-01

The present paper investigates the mean impact force exerted by a granular mass flowing down an incline and impacting a rigid wall of semi-infinite height. First, this granular flow-wall interaction problem is modeled by numerical simulations based on the discrete element method (DEM). These DEM simulations allow computing the depth-averaged quantities—thickness, velocity, and density—of the incoming flow and the resulting mean force on the rigid wall. Second, that problem is described by a simple analytic solution based on a depth-averaged approach for a traveling compressible shock wave, whose volume is assumed to shrink into a singular surface, and which coexists with a dead zone. It is shown that the dead-zone dynamics and the mean force on the wall computed from DEM can be reproduced reasonably well by the analytic solution proposed over a wide range of slope angle of the incline. These results are obtained by feeding the analytic solution with the thickness, the depth-averaged velocity, and the density averaged over a certain distance along the incline rather than flow quantities taken at a singular section before the jump, thus showing that the assumption of a shock wave volume shrinking into a singular surface is questionable. The finite length of the traveling wave upstream of the grains piling against the wall must be considered. The sensitivity of the model prediction to that sampling length remains complicated, however, which highlights the need of further investigation about the properties and the internal structure of the propagating granular wave.

Quantum descriptions of singularities leading to pair creation. [of gravitons

NASA Technical Reports Server (NTRS)

Misner, C. W.

1974-01-01

A class of cosmological models is analyzed which provide a mathematically convenient (but idealized) description of a cosmological singularity that develops into a pair creation epoch and terminates in an adiabatic expansion with redshifting particle energies. This class of models was obtained by Gowdy (1971, 1974) as a set of exact solutions of the classical empty space Einstein equations describing inhomogeneous universes populated only by gravitational waves. It is shown that these models can be used to exhibit simplified models of quantized gravitational fields, and that a quantum description can be given arbitrarily near a cosmological singularity. Graviton pair creation occurs, and can be seen to convert anisotropic expansion rates into the energy of graviton pairs.

Symmetry breaking and singularity structure in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Commeford, K. A.; Garcia-March, M. A.; Ferrando, A.; Carr, Lincoln D.

2012-08-01

We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity and a Magnus force that introduces a torque about the axis of symmetry. For the analytical noninteracting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wave function, showing less than 0.5% error for an impulse strength of v=0.00005. We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry-breaking potential does not significantly change the dynamics of the system as long as the strength is below v=0.0005.

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.

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

USGS Publications Warehouse

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

2010-01-01

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

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.

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.

Stress state of a piecewise uniform layered space with doubly periodic internal cracks

NASA Astrophysics Data System (ADS)

Hakobyan, V. N.; Dashtoyan, L. L.

2018-04-01

The present paper deals with the stress state of a piecewise homogeneous plane formed by alternation junction of two distinct strips of equal height manufactured of different materials. There is a doubly periodic system of cracks on the plane. The governing system of singular integral equations of the first kind for the density of the crack dislocation is derived. The solution of the problem in the case where only one of the repeated strips contains one doubly-periodic crack is obtained by the method of mechanical quadratures.

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)

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.

Pulsation of black holes

NASA Astrophysics Data System (ADS)

Gao, Changjun; Lu, Youjun; Shen, You-Gen; Faraoni, Valerio

2018-01-01

The Hawking-Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually an outer and an inner apparent horizon, resembling the Reissner-Nordström situation. For a distant observer the horizon crossing occurs in an infinite time and the pulsations of the black hole quantum "beating heart" are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any.

Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories

NASA Astrophysics Data System (ADS)

Gao, Changjun; Lu, Youjun; Yu, Shuang; Shen, You-Gen

2018-05-01

A stationary and spherically symmetric black hole (e.g., Reissner-Nordström black hole or Kerr-Newman black hole) has, at most, one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? The de Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves or the black hole continuum spectrum.

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.

Cauchy problem with general discontinuous initial data along a smooth curve for 2-d Euler system

NASA Astrophysics Data System (ADS)

Chen, Shuxing; Li, Dening

2014-09-01

We study the Cauchy problems for the isentropic 2-d Euler system with discontinuous initial data along a smooth curve. All three singularities are present in the solution: shock wave, rarefaction wave and contact discontinuity. We show that the usual restrictive high order compatibility conditions for the initial data are automatically satisfied. The local existence of piecewise smooth solution containing all three waves is established.

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.

Existence and Stability of Spatial Plane Waves for the Incompressible Navier-Stokes in R^3

NASA Astrophysics Data System (ADS)

Correia, Simão; Figueira, Mário

2018-03-01

We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a L^∞ family of global spatial plane wave solutions, which are connected with the two-dimensional equation. We then proceed to prove local well-posedness over a space which includes L^3(R^3) and these solutions. Finally, we prove L^3-stability of spatial plane waves, with no condition on their size.

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.

Phononic band gaps and phase singularities in the ultrasonic response from toughened composites

NASA Astrophysics Data System (ADS)

Smith, Robert A.; Nelson, Luke J.; Mienczakowski, Martin J.

2018-04-01

Ultrasonic 3D characterization of ply-level features in layered composites, such as out-of-plane wrinkles and ply drops, is now possible with carefully applied analytic-signal analysis. Study of instantaneous amplitude, phase and frequency in the ultrasonic response has revealed some interesting effects, which become more problematic for 3D characterization as the inter-ply resin-layer thicknesses increase. In modern particle-toughened laminates, the thicker resin layers cause phase singularities to be observed; these are locations where the instantaneous amplitude is zero, so the instantaneous phase is undefined. The depth at which these occur has been observed experimentally to vary with resin- layer thickness, such that a phase-singularity surface is formed; beyond this surface, the ultrasonic response is reduced and significantly more difficult to interpret, so a method for removing the effect would be advantageous. The underlying physics has been studied using an analytical one-dimensional multi-layer model. This has been sufficient to determine that the cause is linked to a phononic band gap in the ultrasound transmitted through multiple equally-spaced partial reflectors. As a result, the phase singularity also depends on input-pulse center frequency and bandwidth. Various methods for overcoming the confusing effects in the data have been proposed and subsequently investigated using the analytical model. This paper will show experimental and modelled evidence of phase-singularities and phase-singularity surfaces, as well as the success of methods for reducing their effects.

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

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.

Confining potential in momentum space

NASA Technical Reports Server (NTRS)

Norbury, John W.; Kahana, David E.; Maung, Khin Maung

1992-01-01

A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations.

Nature's optics and our understanding of light

NASA Astrophysics Data System (ADS)

Berry, M. V.

2015-01-01

Optical phenomena visible to everyone have been central to the development of, and abundantly illustrate, important concepts in science and mathematics. The phenomena considered from this viewpoint are rainbows, sparkling reflections on water, mirages, green flashes, earthlight on the moon, glories, daylight, crystals and the squint moon. And the concepts involved include refraction, caustics (focal singularities of ray optics), wave interference, numerical experiments, mathematical asymptotics, dispersion, complex angular momentum (Regge poles), polarisation singularities, Hamilton's conical intersections of eigenvalues ('Dirac points'), geometric phases and visual illusions.

Workshop on Condition Based Maintenance Held in Atlantic Beach, North Carolina on November 15 - 17, 1993

DTIC Science & Technology

1993-11-17

pounds of Torque Over Three Minutes Continuous Operation IYMCO1A 14 DMAE Corporation C-130 Engine Gearbox January 19925 Stress Wave Analysis - I in’. I...FaUi.O The CBM needs associated with surface initiated failure mechanisms can be divided into I singular defects and low (h/a) operation. Singular defec-t...These include nicks, scratches, corrosion pits and dents caused by third’ body particles (hard or soft). These defects cause local stress risers

Topics in General Relativity theory: Gravitational-wave measurements of black-hole parameters; gravitational collapse of a cylindrical body; and classical-particle evolution in the presence of closed, timelike curves

NASA Astrophysics Data System (ADS)

Echeverria, Fernando

I study three different topics in general relativity. The first study investigates the accuracy with which the mass and angular momentum of a black hole can be determined by measurements of gravitational waves from the hole, using a gravitational-wave detector. The black hole is assumed to have been strongly perturbed and the detector measures the waves produced by its resulting vibration and ring-down. The uncertainties in the measured parameters arise from the noise present in the detector. It is found that the faster the hole rotates, the more accurate the measurements will be, with the uncertainty in the angular momentum decreasing rapidly with increasing rotation speed. The second study is an analysis of the gravitational collapse of an infinitely long, cylindrical dust shell, an idealization of more realistic, finite-length bodies. It is found that the collapse evolves into a naked singularity in finite time. Analytical expressions for the variables describing the collapse are found at late times, near the singularity. The collapse is also followed, with a numerical simulation, from the start until very close to the singularity. The singularity is found to be strong, in the sense that an observer riding on the shell will be infinitely stretched in one direction and infinitely compressed in another. The gravitational waves emitted from the collapse are also analyzed. The last study focuses on the consequences of the existence of closed time like curves in a worm hole space time. One might expect that such curves might cause a system with apparently well-posed initial conditions to have no self-consistent evolution. We study the case of a classical particle with a hard-sphere potential, focusing attention on initial conditions for which the evolution, if followed naively, is self-inconsistent: the ball travels to the past through the worm hole colliding with its younger self, preventing itself from entering the worm hole. We find, surprisingly, that for all such 'dangerous' initial conditions, there are an infinite number of self-consistent solutions. We also find that for many non-dangerous initial conditions, there also exist an infinity of possible evolutions.

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.

Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarization-resolved angular patterns

NASA Astrophysics Data System (ADS)

Kiselev, Alexei D.; Chigrinov, Vladimir G.

2014-10-01

In order to explore electric-field-induced transformations of polarization singularities in the polarization-resolved angular (conoscopic) patterns emerging after deformed-helix ferroelectric liquid crystal (DHFLC) cells with subwavelength helix pitch, we combine the transfer matrix formalism with the results for the effective dielectric tensor of biaxial FLCs evaluated using an improved technique of averaging over distorted helical structures. Within the framework of the transfer matrix method, we deduce a number of symmetry relations and show that the symmetry axis of L lines (curves of linear polarization) is directed along the major in-plane optical axis which rotates under the action of the electric field. When the angle between this axis and the polarization plane of incident linearly polarized light is above its critical value, the C points (points of circular polarization) appear in the form of symmetrically arranged chains of densely packed star-monstar pairs. We also emphasize the role of phase singularities of a different kind and discuss the enhanced electro-optic response of DHFLCs near the exceptional point where the condition of zero-field isotropy is fulfilled.

Confined disclinations: exterior versus material constraints in developable thin elastic sheets.

PubMed

Efrati, Efi; Pocivavsek, Luka; Meza, Ruben; Lee, Ka Yee C; Witten, Thomas A

2015-02-01

We examine the shape change of a thin disk with an inserted wedge of material when it is pushed against a plane, using analytical, numerical, and experimental methods. Such sheets occur in packaging, surgery, and nanotechnology. We approximate the sheet as having vanishing strain, so that it takes a conical form in which straight generators converge to a disclination singularity. Then, its shape is that which minimizes elastic bending energy alone. Real sheets are expected to approach this limiting shape as their thickness approaches zero. The planar constraint forces a sector of the sheet to buckle into the third dimension. We find that the unbuckled sector is precisely semicircular, independent of the angle δ of the inserted wedge. We generalize the analysis to include conical as well as planar constraints and thereby establish a law of corresponding states for shallow cones of slope ε and thin wedges. In this regime, the single parameter δ/ε^{2} determines the shape. We discuss the singular limit in which the cone becomes a plane, and the unexpected slow convergence to the semicircular buckling observed in real sheets.

Confined disclinations: Exterior versus material constraints in developable thin elastic sheets

NASA Astrophysics Data System (ADS)

Efrati, Efi; Pocivavsek, Luka; Meza, Ruben; Lee, Ka Yee C.; Witten, Thomas A.

2015-02-01

We examine the shape change of a thin disk with an inserted wedge of material when it is pushed against a plane, using analytical, numerical, and experimental methods. Such sheets occur in packaging, surgery, and nanotechnology. We approximate the sheet as having vanishing strain, so that it takes a conical form in which straight generators converge to a disclination singularity. Then, its shape is that which minimizes elastic bending energy alone. Real sheets are expected to approach this limiting shape as their thickness approaches zero. The planar constraint forces a sector of the sheet to buckle into the third dimension. We find that the unbuckled sector is precisely semicircular, independent of the angle δ of the inserted wedge. We generalize the analysis to include conical as well as planar constraints and thereby establish a law of corresponding states for shallow cones of slope ɛ and thin wedges. In this regime, the single parameter δ /ɛ2 determines the shape. We discuss the singular limit in which the cone becomes a plane, and the unexpected slow convergence to the semicircular buckling observed in real sheets.

Squeezing and de-wetting of a shear thinning fluid drop between plane parallel surfaces: capillary adhesion phenomenon

NASA Astrophysics Data System (ADS)

Ward, Thomas

2017-11-01

The radial squeezing and de-wetting of a thin film of viscous shear thinning fluid filling the gap between parallel plane walls is examined both experimentally and theoretically for gap spacing much smaller than the capillary length. The interaction between motion of fluid in the gap driven by squeezing or de-wetting and surface tension is parameterized by a dimensionless variable, F, that is the ratio of the constant force supplied by the top plate (either positive or negative) to surface tension at the drop's circumference. Furthermore, the dimensionless form of the rate equation for the gap's motion reveals a time scale that is dependent on the drop volume when analyzed for a power law shear thinning fluid. In the de-wetting problem the analytical solution reveals the formation of a singularity, leading to capillary adhesion, as the gap spacing approaches a critical value that depends on F and the contact angle. Experiments are performed to test the analytical predictions for both squeezing, and de-wetting in the vicinity of the singularity.

On Resolutions of Cosmological Singularities in Higher-Spin Gravity

NASA Astrophysics Data System (ADS)

Burrington, Benjamin; Pando Zayas, Leopoldo; Rombes, Nicholas

2014-03-01

Gravity in three dimensions is simpler than in four, due to the lack of gravitational waves, and can be recast as a Chern-Simons theory. In this context, it is straightforward to generalize Einstein's gravity, with or without cosmological constant, by changing the gauge group. Using this, we study the resolution of certain cosmological singularities, and extend the singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big-bang singularity in the case of gravity coupled to a spin-4 field realized as Chern-Simons theory with gauge group SL (4 , C) . We show the existence of gauge transformations that do not change the holonomy of the Chern-Simons gauge potential and lead to metrics without the initial singularity. We argue that such transformations always exist in the context of gravity coupled to a spin-N field when described by Chern-Simons with gauge group SL (N , C) . This work was supported by the DOE under grant DE-FG02-95ER40899, a research grant from Troy University, and the Honors Summer Fellowship at the University of Michigan.

Quantum jump from singularity to outside of black hole

NASA Astrophysics Data System (ADS)

Dündar, Furkan Semih; Hajian, Kamal

2016-02-01

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitarity in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.

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).

On the construction of a direct numerical simulation of a breaking inertia-gravity wave in the upper mesosphere

NASA Astrophysics Data System (ADS)

Fruman, Mark D.; Remmler, Sebastian; Achatz, Ulrich; Hickel, Stefan

2014-10-01

A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and structure of the primary instability and to initialize nonlinear "2.5-D" simulations (with three-dimensional velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave, a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of the wave and generation of turbulence is faster in three dimensions, but the results are otherwise qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the domain and initial condition are chosen properly.

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

Reduced-rank approximations to the far-field transform in the gridded fast multipole method

NASA Astrophysics Data System (ADS)

Hesford, Andrew J.; Waag, Robert C.

2011-05-01

The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.

Reduced-Rank Approximations to the Far-Field Transform in the Gridded Fast Multipole Method.

PubMed

Hesford, Andrew J; Waag, Robert C

2011-05-10

The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.

Reduced-Rank Approximations to the Far-Field Transform in the Gridded Fast Multipole Method

PubMed Central

Hesford, Andrew J.; Waag, Robert C.

2011-01-01

The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly. PMID:21552350

Absolute instabilities of travelling wave solutions in a Keller-Segel model

NASA Astrophysics Data System (ADS)

Davis, P. N.; van Heijster, P.; Marangell, R.

2017-11-01

We investigate the spectral stability of travelling wave solutions in a Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity function and a constant, sublinear, and linear consumption rate. Linearising around the travelling wave solutions, we locate the essential and absolute spectrum of the associated linear operators and find that all travelling wave solutions have parts of the essential spectrum in the right half plane. However, we show that in the case of constant or sublinear consumption there exists a range of parameters such that the absolute spectrum is contained in the open left half plane and the essential spectrum can thus be weighted into the open left half plane. For the constant and sublinear consumption rate models we also determine critical parameter values for which the absolute spectrum crosses into the right half plane, indicating the onset of an absolute instability of the travelling wave solution. We observe that this crossing always occurs off of the real axis.

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.

Regular and chaotic dynamics of non-spherical bodies. Zeldovich's pancakes and emission of very long gravitational waves

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Tsupko, O. Yu.

2015-10-01

> In this paper we review a recently developed approximate method for investigation of dynamics of compressible ellipsoidal figures. Collapse and subsequent behaviour are described by a system of ordinary differential equations for time evolution of semi-axes of a uniformly rotating, three-axis, uniform-density ellipsoid. First, we apply this approach to investigate dynamic stability of non-spherical bodies. We solve the equations that describe, in a simplified way, the Newtonian dynamics of a self-gravitating non-rotating spheroidal body. We find that, after loss of stability, a contraction to a singularity occurs only in a pure spherical collapse, and deviations from spherical symmetry prevent the contraction to the singularity through a stabilizing action of nonlinear non-spherical oscillations. The development of instability leads to the formation of a regularly or chaotically oscillating body, in which dynamical motion prevents the formation of the singularity. We find regions of chaotic and regular pulsations by constructing a Poincaré diagram. A real collapse occurs after damping of the oscillations because of energy losses, shock wave formation or viscosity. We use our approach to investigate approximately the first stages of collapse during the large scale structure formation. The theory of this process started from ideas of Ya. B. Zeldovich, concerning the formation of strongly non-spherical structures during nonlinear stages of the development of gravitational instability, known as `Zeldovich's pancakes'. In this paper the collapse of non-collisional dark matter and the formation of pancake structures are investigated approximately. Violent relaxation, mass and angular momentum losses are taken into account phenomenologically. We estimate an emission of very long gravitational waves during the collapse, and discuss the possibility of gravitational lensing and polarization of the cosmic microwave background by these waves.

Observational signatures of unusual outgoing longwave radiation (OLR) and atmospheric gravity waves (AGW) as precursory effects of May 2015 Nepal earthquakes

NASA Astrophysics Data System (ADS)

Chakraborty, Suman; Sasmal, Sudipta; Chakrabarti, Sandip K.; Bhattacharya, Arnab

2018-01-01

Earthquake preparation processes may start 1-30 days before its actual occurrence. Measurements of outgoing longwave radiation (OLR) and detection of the presence of atmospheric gravity waves (AGW) in very low frequency (VLF) radio signals can be used as tools to identify such processes. We studied these signals monitored prior to a recent major earthquake that occurred in Nepal at southeast of Kodari on May 12, 2015 at 12:50 pm local time (07:05 UTC) with Richter scale magnitude of M = 7.3 and depth 10 km (6.21 miles). It was preceded by another major earthquake on April 25, 2015 with magnitude M = 7.9. First, to study the effects of seismic events on OLR, we used NOAA/IR daily (two degree gridded) data from April 16 to May 30, 2015 and followed the method of Eddy field calculation mean to find pre-seismic anomalies. We found singularities in Eddy field OLR curves around the earthquake epicenter starting 3 days prior to the earthquake days and disappearance of such singularities after the events. Such singularities can be associated with a large amount of energy released by the earthquakes. Second, we analyzed very low frequency (VLF) data recorded at Ionospheric and Earthquake Research Centre (IERC) of Indian Centre for Space Physics transmitted from JJI (22.2 kHz) station of Japan. We looked for the presence of atmospheric gravity waves in the ionosphere which can be considered as an important factor in finding seismo-ionospheric correlations. We performed both fast Fourier transform (FFT) and wavelet analysis on the signal and found significant presence of such waves (periods of almost 1 h) four days before the earthquake.

On the nonlinear three dimensional instability of Stokes layers and other shear layers to pairs of oblique waves

NASA Technical Reports Server (NTRS)

Wu, Xuesong; Lee, Sang Soo; Cowley, Stephen J.

1992-01-01

The nonlinear evolution of a pair of initially oblique waves in a high Reynolds Number Stokes layer is studied. Attention is focused on times when disturbances of amplitude epsilon have O(epsilon(exp 1/3)R) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects. Viscous effects are included by studying the distinguished scaling epsilon = O(R(exp -1)). This leads to a complicated modification of the kernel function in the integro-differential amplitude equation. When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be introduced by nonlinear effects; we suggest that such explosive growth can lead to the bursts observed in experiments. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave vortex approach is identified.

Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

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

Zampeli, Adamantia; Pailas, Theodoros; Terzis, Petros A.

2016-05-01

In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries onmore » the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.« less

In vivo real-time cavitation imaging in moving organs

NASA Astrophysics Data System (ADS)

Arnal, B.; Baranger, J.; Demene, C.; Tanter, M.; Pernot, M.

2017-02-01

The stochastic nature of cavitation implies visualization of the cavitation cloud in real-time and in a discriminative manner for the safe use of focused ultrasound therapy. This visualization is sometimes possible with standard echography, but it strongly depends on the quality of the scanner, and is hindered by difficulty in discriminating from highly reflecting tissue signals in different organs. A specific approach would then permit clear validation of the cavitation position and activity. Detecting signals from a specific source with high sensitivity is a major problem in ultrasound imaging. Based on plane or diverging wave sonications, ultrafast ultrasonic imaging dramatically increases temporal resolution, and the larger amount of acquired data permits increased sensitivity in Doppler imaging. Here, we investigate a spatiotemporal singular value decomposition of ultrafast radiofrequency data to discriminate bubble clouds from tissue based on their different spatiotemporal motion and echogenicity during histotripsy. We introduce an automation to determine the parameters of this filtering. This method clearly outperforms standard temporal filtering techniques with a bubble to tissue contrast of at least 20 dB in vitro in a moving phantom and in vivo in porcine liver.

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.

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.

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.

P T Symmetry and Singularity-Enhanced Sensing Based on Photoexcited Graphene Metasurfaces

NASA Astrophysics Data System (ADS)

Chen, Pai-Yen; Jung, Jeil

2016-06-01

We introduce here a parity-time-(P T ) symmetric system using an optically pumped, active graphene metasurface paired with a resistive metallic filament, realizing a unidirectional reflectionless propagation of terahertz (THz) waves. The amplified THz stimulated emission and tailored plasmon resonances in the graphene metasurface may achieve an equivalent negative-resistance converter at THz frequencies. We theoretically demonstrate that the combination of the spectral singularity in a P T -symmetric system and the chemical sensitivity of graphene may give rise to exotic scattering responses, strongly influenced by the presence of charged impurities in graphene at the spontaneous P T -symmetry-breaking point. This graphene-based P T -symmetric device may have broad relevance beyond the extraordinary manipulation of THz waves, as it may also open exciting prospects for detecting gas, chemical, and biological agents with high sensitivities.

Elastodynamic cloaking and field enhancement for soft spheres

NASA Astrophysics Data System (ADS)

Diatta, Andre; Guenneau, Sebastien

2016-11-01

We propose a spherical cloak described by a non-singular asymmetric elasticity tensor {C} depending upon a small parameter η, that defines the softness of a region one would like to conceal from elastodynamic waves. By varying η, we generate a class of soft spheres dressed by elastodynamic cloaks, which are shown to considerably reduce the scattering of the soft spheres. Importantly, such cloaks also provide some wave protection except for a countable set of frequencies, for which some large elastic field enhancement can be observed within the soft spheres. Through an investigation of trapped modes in elasticity, we supply a good approximation of such Mie-type resonances by some transcendental equation. Our results, unlike previous studies that focused merely on the invisibility aspects, shed light on potential pitfalls of elastodynamic cloaks for earthquake protection designed via geometric transforms: a seismic cloak needs to be designed in such a way that its inner resonances differ from eigenfrequencies of the building one wishes to protect. In order to circumvent this downfall of field enhancement inside the cloaked area, we introduce a novel generation of cloaks, named here, mixed cloaks. Such mixed cloaks consist of a shell that detours incoming waves, hence creating an invisibility region, and of a perfectly matched layer (PML, located at the inner boundary of the cloaks) that absorbs residual wave energy in such a way that aforementioned resonances in the soft sphere are strongly attenuated. The designs of mixed cloaks with a non-singular elasticity tensor combined with an inner PML and non-vanishing density bring seismic cloaks one step closer to a practical implementation. Note in passing that the concept of mixed cloaks also applies in the case of singular cloaks and can be translated in other wave areas for a similar purpose (i.e. to smear down inner resonances within the invisibility region).

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…

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.

Crack problems for a rectangular plate and an infinite strip

NASA Technical Reports Server (NTRS)

Civelek, M. B.; Erdogan, F.

1980-01-01

The general plane problem for an infinite strip containing multiple cracks perpendicular to its boundaries is considered. The problem is reduced to a system of singular integral equations. Two specific problems of practical interest are then studied in detail. The first problem explores the interaction effect of multiple edge cracks in a plate or beam under tension or bending. The second problem is that of a rectangular plate containing an arbitrarily oriented crack in the plane of symmetry. Particular emphasis is placed on the problem of a plate containing an edge crack and subjected to concentrated forces.

Trajectory optimization and guidance law development for national aerospace plane applications

NASA Technical Reports Server (NTRS)

Calise, A. J.; Flandro, G. A.; Corban, J. E.

1988-01-01

The work completed to date is comprised of the following: a simple vehicle model representative of the aerospace plane concept in the hypersonic flight regime, fuel-optimal climb profiles for the unconstrained and dynamic pressure constrained cases generated using a reduced order dynamic model, an analytic switching condition for transition to rocket powered flight as orbital velocity is approached, simple feedback guidance laws for both the unconstrained and dynamic pressure constrained cases derived via singular perturbation theory and a nonlinear transformation technique, and numerical simulation results for ascent to orbit in the dynamic pressure constrained case.

Analysis of a Generally Oriented Crack in a Functionally Graded Strip Sandwiched Between Two Homogeneous Half Planes

NASA Technical Reports Server (NTRS)

Shbeeb, N.; Binienda, W. K.; Kreider, K.

1999-01-01

The driving forces for a generally oriented crack embedded in a Functionally Graded strip sandwiched between two half planes are analyzed using singular integral equations with Cauchy kernels, and integrated using Lobatto-Chebyshev collocation. Mixed-mode Stress Intensity Factors (SIF) and Strain Energy Release Rates (SERR) are calculated. The Stress Intensity Factors are compared for accuracy with previously published results. Parametric studies are conducted for various nonhomogeneity ratios, crack lengths. crack orientation and thickness of the strip. It is shown that the SERR is more complete and should be used for crack propagation analysis.

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.

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.

Intralines of quasi-conical intersections on torsion planes: methylamine as a case study.

PubMed

Levi, C; Halász, G J; Vibók, A; Bar, I; Zeiri, Y; Kosloff, R; Baer, M

2009-06-18

Recently we reported on a novel feature associated with the intersection of the two lowest states (1)A' and (1)A'' of the methylamine (J. Chem. Phys. 2008, 128, 244302). We established the existence of a finite (closed) line of conical intersections (ci), namely, a finite seam, located in the HC-NHH symmetry plane, a line that is formed by moving a single hydrogen on that plane while locking the positions of the (six) other atoms. In the present article, this study is extended to the corresponding torsion planes formed by rotating the methyl group around the CN axis. The torsion planes, in contrast with the HC-NHH symmetry plane, do not satisfy the symmetry feature that enables the seam just mentioned. Nevertheless, the calculated nonadiabatic coupling terms (NACTs) resemble features similar to those encountered in the HC-NHH symmetry plane. Following a tedious numerical study supported by a theoretical model (Section III), it was verified that these NACTs may become similar to those on the symmetry plane, sometimes even to the level of almost no distinction, but lack one basic feature; namely, they are not singular and therefore do not form topological effects.

The Euler-Poisson-Darboux equation for relativists

NASA Astrophysics Data System (ADS)

Stewart, John M.

2009-09-01

The Euler-Poisson-Darboux (EPD) equation is the simplest linear hyperbolic equation in two independent variables whose coefficients exhibit singularities, and as such must be of interest as a paradigm to relativists. Sadly it receives scant treatment in the textbooks. The first half of this review is didactic in nature. It discusses in the simplest terms possible the nature of solutions of the EPD equation for the timelike and spacelike singularity cases. Also covered is the Riemann representation of solutions of the characteristic initial value problem, which is hard to find in the literature. The second half examines a few of the possible applications, ranging from explicit computation of the leading terms in the far-field backscatter from predominantly outgoing radiation in a Schwarzschild space-time, to computing explicitly the leading terms in the matter-induced singularities in plane symmetric space-times. There are of course many other applications and the aim of this article is to encourage relativists to investigate this underrated paradigm.

Nonlinear zero-sum differential game analysis by singular perturbation methods

NASA Technical Reports Server (NTRS)

Sinar, J.; Farber, N.

1982-01-01

A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

Introducing time-dependent molecular fields: a new derivation of the wave equations

NASA Astrophysics Data System (ADS)

Baer, Michael

2018-02-01

This article is part of a series of articles trying to establish the concept molecular field. The theory that induced us to introduce this novel concept is based on the Born-Huang expansion as applied to the Schroedinger equation that describes the interaction of a molecular system with an external electric field. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from a single spatial curl equation, two space-time curl equations and one single space-time divergent equation to a pair of decoupled wave equations usually encountered within the theory of fields. In the present study, just like in the previous study [see Baer et al., Mol. Phys. 114, 227 (2016)] the wave equations are derived for an electric field having two features: (a) its intensity is high enough; (b) its duration is short enough. Although not all the findings are new the derivation, in the present case, is new, straightforward, fluent and much friendlier as compared to the previous one and therefore should be presented again. For this situation the study reveals that the just described interaction creates two fields that coexist within a molecule: one is a novel vectorial field formed via the interaction of the electric field with the Born-Huang non-adiabatic coupling terms (NACTs) and the other is an ordinary, scalar, electric field essentially identical to the original electric field. Section 4 devoted to the visualization of the outcomes via two intersecting Jahn-Teller cones which contain NACTs that become singular at the intersection point of these cones. Finally, the fact that eventually we are facing a kind of a cosmic situation may bring us to speculate that singular NACTs are a result of cosmic phenomena. Thus, if indeed this singularity is somehow connected to reality then, like other singularities in physics, it is formed at (or immediately after) the Big Bang and consequently, guarantees the formation of molecules.

Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem.

PubMed

Gancedo, Francisco; Strain, Robert M

2014-01-14

In this paper, for both the sharp front surface quasi-geostrophic equation and the Muskat problem, we rule out the "splash singularity" blow-up scenario; in other words, we prove that the contours evolving from either of these systems cannot intersect at a single point while the free boundary remains smooth. Splash singularities have been shown to hold for the free boundary incompressible Euler equation in the form of the water waves contour evolution problem. Our result confirms the numerical simulations in earlier work, in which it was shown that the curvature blows up because the contours collapse at a point. Here, we prove that maintaining control of the curvature will remove the possibility of pointwise interphase collapse. Another conclusion that we provide is a better understanding of earlier work in which squirt singularities are ruled out; in this case, a positive volume of fluid between the contours cannot be ejected in finite time.

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…

Nonlinear wave choked inlets

NASA Technical Reports Server (NTRS)

1979-01-01

The quasi-one dimensional flow program was modified in two ways. The Runge-Kutta subroutine was replaced with a subroutine which used a modified divided difference form of the Adams Pece method and the matrix inversion routine was replaced with a pseudo inverse routine. Calculations were run using both the original and modified programs. Comparison of the calculations showed that the original Runge-Kutta routine could not detect singularity near the throat and was integrating across it. The modified version was able to detect the singularity and therefore gave more valid calculations.

Maslov indices, Poisson brackets, and singular differential forms

NASA Astrophysics Data System (ADS)

Esterlis, I.; Haggard, H. M.; Hedeman, A.; Littlejohn, R. G.

2014-06-01

Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the 6j-symbol, which is important in angular-momentum theory and in quantum gravity.

Orbiting naked singularities in large-ω Brans-Dicke gravity

NASA Astrophysics Data System (ADS)

Chauvineau, Bertrand

2017-11-01

Brans-Dicke gravity admits spherical solutions describing naked singularities rather than black holes. Depending on some parameters entering such a solution, stable circular orbits exist for all radii. One shows that, despite the fact a naked singularity is an infinite redshift location, the far observed orbital motion frequency is unbounded for an adiabatically decreasing radius. We then argue that this feature remains true in a wide set of scalar(s)-tensor theories if gravity. This is a salient difference with general relativity, and the repercussion on the gravitational radiation by EMRI systems is stressed. Since this behaviour survives the ω \\longrightarrow ∞ limit, the possibility of such solutions is of utmost interest in the new gravitational wave astronomy context, despite the current constraints on scalar-tensor gravity.

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.

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.

On the stability of lumps and wave collapse in water waves.

PubMed

Akylas, T R; Cho, Yeunwoo

2008-08-13

In the classical water-wave problem, fully localized nonlinear waves of permanent form, commonly referred to as lumps, are possible only if both gravity and surface tension are present. While much attention has been paid to shallow-water lumps, which are generalizations of Korteweg-de Vries solitary waves, the present study is concerned with a distinct class of gravity-capillary lumps recently found on water of finite or infinite depth. In the near linear limit, these lumps resemble locally confined wave packets with envelope and wave crests moving at the same speed, and they can be approximated in terms of a particular steady solution (ground state) of an elliptic equation system of the Benney-Roskes-Davey-Stewartson (BRDS) type, which governs the coupled evolution of the envelope along with the induced mean flow. According to the BRDS equations, however, initial conditions above a certain threshold develop a singularity in finite time, known as wave collapse, due to nonlinear focusing; the ground state, in fact, being exactly at the threshold for collapse suggests that the newly discovered lumps are unstable. In an effort to understand the role of this singularity in the dynamics of lumps, here we consider the fifth-order Kadomtsev-Petviashvili equation, a model for weakly nonlinear gravity-capillary waves on water of finite depth when the Bond number is close to one-third, which also admits lumps of the wave packet type. It is found that an exchange of stability occurs at a certain finite wave steepness, lumps being unstable below but stable above this critical value. As a result, a small-amplitude lump, which is linearly unstable and according to the BRDS equations would be prone to wave collapse, depending on the perturbation, either decays into dispersive waves or evolves into an oscillatory state near a finite-amplitude stable lump.

Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

NASA Astrophysics Data System (ADS)

Elwakil, S. A.; El-Labany, S. K.; Zahran, M. A.; Sabry, R.

2004-04-01

The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D( u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K( u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m>1 is the power of the nonlinear convection term).

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.

Theory and application of equivalent transformation relationships between plane wave and spherical wave

NASA Astrophysics Data System (ADS)

Wang, Yao; Yang, Zailin; Zhang, Jianwei; Yang, Yong

2017-10-01

Based on the governing equations and the equivalent models, we propose an equivalent transformation relationships between a plane wave in a one-dimensional medium and a spherical wave in globular geometry with radially inhomogeneous properties. These equivalent relationships can help us to obtain the analytical solutions of the elastodynamic issues in an inhomogeneous medium. The physical essence of the presented equivalent transformations is the equivalent relationships between the geometry and the material properties. It indicates that the spherical wave problem in globular geometry can be transformed into the plane wave problem in the bar with variable property fields, and its inverse transformation is valid as well. Four different examples of wave motion problems in the inhomogeneous media are solved based on the presented equivalent relationships. We obtain two basic analytical solution forms in Examples I and II, investigate the reflection behavior of inhomogeneous half-space in Example III, and exhibit a special inhomogeneity in Example IV, which can keep the traveling spherical wave in constant amplitude. This study implies that our idea makes solving the associated problem easier.

Stress intensity factors in a cracked infinite elastic wedge loaded by a rigid punch

NASA Technical Reports Server (NTRS)

Erdogan, F.; Civelek, M. B.

1978-01-01

A plane elastic wedge-shaped solid was split through the application of a rigid punch. It was assumed that the coefficient of friction on the the contact area was constant, and the problem had a plane of symmetry with respect to loading and geometry, with the crack in the plane of symmetry. The problem was formulated in terms of a system of integral equations with the contact stress and the derivative of the crack surface displacement as the unknown functions. The solution was obtained for an internal crack and for an edge crack. The results include primarily the stress intensity factors at the crack tips, and the measure of the stress singularity at the wedge apex, and at the end points of the contact area.

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.

Triangle singularities and XYZ quarkonium peaks

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

Szczepaniak, Adam P.

2015-06-01

We discuss analytical properties of partial waves derived from projection of a 4-legged amplitude with crossed-channel exchanges in the kinematic region of the direct channel that corresponds to the XYZ peaks in charmonium and bottomonium. We show that in general partial waves can develop anomalous branch points in the vicinity of the direct channel physical region. In a specific case, when these branch points lie on the opposite side of the unitary cut they pinch the integration contour in a dispersion relation and if the pinch happens close to threshold, the normal threshold cusp is enhanced. We show that this effect only occurs if masses of resonances in the crossed channel are in a specific, narrow range. We estimate the size of threshold enhancements originating from these anomalous singularities in reactions where themore » $$Z_c(3900)$$ and the $$Z_b(10610)$$ peaks have been observed.« less

Pulse wave imaging using coherent compounding in a phantom and in vivo

NASA Astrophysics Data System (ADS)

Zacharias Apostolakis, Iason; McGarry, Matthew D. J.; Bunting, Ethan A.; Konofagou, Elisa E.

2017-03-01

Pulse wave velocity (PWV) is a surrogate marker of arterial stiffness linked to cardiovascular morbidity. Pulse wave imaging (PWI) is a technique developed by our group for imaging the pulse wave propagation in vivo. PWI requires high temporal and spatial resolution, which conventional ultrasonic imaging is unable to simultaneously provide. Coherent compounding is known to address this tradeoff and provides full aperture images at high frame rates. This study aims to implement PWI using coherent compounding within a GPU-accelerated framework. The results of the implemented method were validated using a silicone phantom against static mechanical testing. Reproducibility of the measured PWVs was assessed in the right common carotid of six healthy subjects (n  =  6) approximately 10-15 mm before the bifurcation during two cardiac cycles over the course of 1-3 d. Good agreement of the measured PWVs (3.97  ±  1.21 m s-1, 4.08  ±  1.15 m s-1, p  =  0.74) was obtained. The effects of frame rate, transmission angle and number of compounded plane waves on PWI performance were investigated in the six healthy volunteers. Performance metrics such as the reproducibility of the PWVs, the coefficient of determination (r 2), the SNR of the PWI axial wall velocities (\\text{SN}{{\\text{R}}{{\\text{v}_{\\text{PWI}}}}} ) and the percentage of lateral positions where the pulse wave appears to arrive at the same time-point, indicating inadequacy of the temporal resolution (i.e. temporal resolution misses) were used to evaluate the effect of each parameter. Compounding plane waves transmitted at 1° increments with a linear array yielded optimal performance, generating significantly higher r 2 and \\text{SN}{{\\text{R}}{{\\text{v}_{\\text{PWI}}}}} values (p  ⩽  0.05). Higher frame rates (⩾1667 Hz) produced improvements with significant gains in the r 2 coefficient (p  ⩽  0.05) and significant increase in both r 2 and \\text{SN}{{\\text{R}}{{\\text{v}_{\\text{PWI}}}}} from single plane wave imaging to 3-plane wave compounding (p  ⩽  0.05). Optimal performance was established at 2778 Hz with 3 plane waves and at 1667 Hz with 5 plane waves.

Spread-Spectrum Beamforming and Clutter Filtering for Plane-Wave Color Doppler Imaging.

PubMed

Mansour, Omar; Poepping, Tamie L; Lacefield, James C

2016-07-21

Plane-wave imaging is desirable for its ability to achieve high frame rates, allowing the capture of fast dynamic events and continuous Doppler data. In most implementations of plane-wave imaging, multiple low-resolution images from different plane wave tilt angles are compounded to form a single high-resolution image, thereby reducing the frame rate. Compounding improves the lateral beam profile in the high-resolution image, but it also acts as a low-pass filter in slow time that causes attenuation and aliasing of signals with high Doppler shifts. This paper introduces a spread-spectrum color Doppler imaging method that produces high-resolution images without the use of compounding, thereby eliminating the tradeoff between beam quality, maximum unaliased Doppler frequency, and frame rate. The method uses a long, random sequence of transmit angles rather than a linear sweep of plane wave directions. The random angle sequence randomizes the phase of off-focus (clutter) signals, thereby spreading the clutter power in the Doppler spectrum, while keeping the spectrum of the in-focus signal intact. The ensemble of randomly tilted low-resolution frames also acts as the Doppler ensemble, so it can be much longer than a conventional linear sweep, thereby improving beam formation while also making the slow-time Doppler sampling frequency equal to the pulse repetition frequency. Experiments performed using a carotid artery phantom with constant flow demonstrate that the spread-spectrum method more accurately measures the parabolic flow profile of the vessel and outperforms conventional plane-wave Doppler in both contrast resolution and estimation of high flow velocities. The spread-spectrum method is expected to be valuable for Doppler applications that require measurement of high velocities at high frame rates.

Null geodesics and wave front singularities in the Gödel space-time

NASA Astrophysics Data System (ADS)

Kling, Thomas P.; Roebuck, Kevin; Grotzke, Eric

2018-01-01

We explore wave fronts of null geodesics in the Gödel metric emitted from point sources both at, and away from, the origin. For constant time wave fronts emitted by sources away from the origin, we find cusp ridges as well as blue sky metamorphoses where spatially disconnected portions of the wave front appear, connect to the main wave front, and then later break free and vanish. These blue sky metamorphoses in the constant time wave fronts highlight the non-causal features of the Gödel metric. We introduce a concept of physical distance along the null geodesics, and show that for wave fronts of constant physical distance, the reorganization of the points making up the wave front leads to the removal of cusp ridges.

The January 2001, El Salvador event: a multi-data analysis

NASA Astrophysics Data System (ADS)

Vallee, M.; Bouchon, M.; Schwartz, S. Y.

2001-12-01

On January 13, 2001, a large normal event (Mw=7.6) occured 100 kilometers away from the Salvadorian coast (Central America) with a centroid depth of about 50km. The size of this event is surprising according to the classical idea that such events have to be much weaker than thrust events in subduction zones. We analysed this earthquake with different types of data: because teleseismic waves are the only data which offer a good azimuthal coverage, we first built a kinematic source model with P and SH waves provided by the IRIS-GEOSCOPE networks. The ambiguity between the 30o plane (plunging toward Pacific Ocean) and the 60o degree plane (plunging toward Central America) leaded us to do a parallel analysis of the two possible planes. We used a simple point-source modelling in order to define the main characteristics of the event and then used an extended source to retrieve the kinematic features of the rupture. For the 2 possible planes, this analysis reveals a downdip and northwest rupture propagation but the difference of fit remains subtle even when using the extended source. In a second part we confronted our models for the two planes with other seismological data, which are (1) regional data, (2) surface wave data through an Empirical Green Function given by a similar but much weaker earthquake which occured in July 1996 and lastly (3) nearfield data provided by Universidad Centroamericana (UCA) and Centro de Investigationes Geotecnicas (CIG). Regional data do not allow to discriminate the 2 planes neither but surface waves and especially near field data confirm that the fault plane is the steepest one plunging toward Central America. Moreover, the slight directivity toward North is confirmed by surface waves.

Green's functions for dislocations in bonded strips and related crack problems

NASA Technical Reports Server (NTRS)

Ballarini, R.; Luo, H. A.

1990-01-01

Green's functions are derived for the plane elastostatics problem of a dislocation in a bimaterial strip. Using these fundamental solutions as kernels, various problems involving cracks in a bimaterial strip are analyzed using singular integral equations. For each problem considered, stress intensity factors are calculated for several combinations of the parameters which describe loading, geometry and material mismatch.

Computational approach to compact Riemann surfaces

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Klein, Christian

2017-01-01

A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on collocation points along these contours and by analytically continuing the roots. The collocation points are chosen to correspond to Chebychev collocation points for an ensuing Clenshaw-Curtis integration of the holomorphic differentials which gives the periods of the Riemann surface with spectral accuracy. At the singularities of the algebraic curve, Puiseux expansions computed by contour integration on the circles around the singularities are used to identify the holomorphic differentials. The Abel map is also computed with the Clenshaw-Curtis algorithm and contour integrals. As an application of the code, solutions to the Kadomtsev-Petviashvili equation are computed on non-hyperelliptic Riemann surfaces.

Scattering on plane waves and the double copy

NASA Astrophysics Data System (ADS)

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

2018-01-01

Perturbatively around flat space, the scattering amplitudes of gravity are related to those of Yang–Mills by colour-kinematic duality, under which gravitational amplitudes are obtained as the ‘double copy’ of the corresponding gauge theory amplitudes. We consider the question of how to extend this relationship to curved scattering backgrounds, focusing on certain ‘sandwich’ plane waves. We calculate the 3-point amplitudes on these backgrounds and find that a notion of double copy remains in the presence of background curvature: graviton amplitudes on a gravitational plane wave are the double copy of gluon amplitudes on a gauge field plane wave. This is non-trivial in that it requires a non-local replacement rule for the background fields and the momenta and polarization vectors of the fields scattering on the backgrounds. It must also account for new ‘tail’ terms arising from scattering off the background. These encode a memory effect in the scattering amplitudes, which naturally double copies as well.

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.

Mathematical formulation and numerical simulation of bird flu infection process within a poultry farm

NASA Astrophysics Data System (ADS)

Putri, Arrival Rince; Nova, Tertia Delia; Watanabe, M.

2016-02-01

Bird flu infection processes within a poultry farm are formulated mathematically. A spatial effect is taken into account for the virus concentration with a diffusive term. An infection process is represented in terms of a traveling wave solutions. For a small removal rate, a singular perturbation analysis lead to existence of traveling wave solutions, that correspond to progressive infection in one direction.

Reference Values for Shear Wave Elastography of Neck and Shoulder Muscles in Healthy Individuals.

PubMed

Ewertsen, Caroline; Carlsen, Jonathan; Perveez, Mohammed Aftab; Schytz, Henrik

2018-01-01

to establish reference values for ultrasound shear-wave elastography for pericranial muscles in healthy individuals (m. trapezius, m. splenius capitis, m. semispinalis capitis, m. sternocleidomastoideus and m. masseter). Also to evaluate day-to-day variations in the shear-wave speeds and evaluate the effect of the pennation of the muscle fibers, ie scanning parallel or perpendicularly to the fibers. 10 healthy individuals (5 males and 5 females) had their pericranial muscles examined with shear-wave elastography in two orthogonal planes on two different days for their dominant and non-dominant side. Mean shear wave speeds from 5 ROI's in each muscle, for each scan plane for the dominant and non-dominant side for the two days were calculated. The effect of the different parameters - muscle pennation, gender, dominant vs non-dominant side and day was evaluated. The effect of scan plane in relation to muscle pennation was statistically significant (p<0.0001). The mean shear-wave speed when scanning parallel to the muscle fibers was significantly higher than the mean shear-wave speed when scanning perpendicularly to the fibers. The day-to-day variation was statistically significant (p=0.0258), but not clinically relevant. Shear-wave speeds differed significantly between muscles. Mean shear wave speeds (m/s) for the muscles in the parallel plane were: for masseter 2.45 (SD:+/-0.25), semispinal 3.36 (SD:+/-0.75), splenius 3.04 (SD:+/-0.65), sternocleidomastoid 2.75 (SD:+/-0.23), trapezius 3.20 (SD:+/-0.27) and trapezius lateral 3.87 (SD:+/-3.87). The shear wave speed variation depended on the direction of scanning. Shear wave elastography may be a method to evaluate muscle stiffness in patients suffering from chronic neck pain.

Hysteresis and precession of a swirling jet normal to a wall.

PubMed

Shtern, V; Mi, J

2004-01-01

Interaction of a swirling jet with a no-slip surface has striking features of fundamental and practical interest. Different flow states and transitions among them occur at the same conditions in combustors, vortex tubes, and tornadoes. The jet axis can undergo precession and bending in combustors; this precession enhances large-scale mixing and reduces emissions of NOx. To explore the mechanisms of these phenomena, we address conically similar swirling jets normal to a wall. In addition to the Serrin model of tornadolike flows, a new model is developed where the flow is singularity free on the axis. New analytical and numerical solutions of the Navier-Stokes equations explain occurrence of multiple states and show that hysteresis is a common feature of wall-normal vortices or swirling jets no matter where sources of motion are located. Then we study the jet stability with the aid of a new approach accounting for deceleration and nonparallelism of the base flow. An appropriate transformation of variables reduces the stability problem for this strongly nonparallel flow to a set of ordinary differential equations. A particular flow whose stability is studied in detail is a half-line vortex normal to a rigid plane-a model of a tornado and of a swirling jet issuing from a nozzle in a combustor. Helical counter-rotating disturbances appear to be first growing as Reynolds number increases. Disturbance frequency changes its sign along the neutral curve while the wave number remains positive. Short disturbance waves propagate downstream and long waves propagate upstream. This helical instability causes bending of the vortex axis and its precession-the effects observed in technological flows and in tornadoes.

An efficient 3-dim FFT for plane wave electronic structure calculations on massively parallel machines composed of multiprocessor nodes

NASA Astrophysics Data System (ADS)

Goedecker, Stefan; Boulet, Mireille; Deutsch, Thierry

2003-08-01

Three-dimensional Fast Fourier Transforms (FFTs) are the main computational task in plane wave electronic structure calculations. Obtaining a high performance on a large numbers of processors is non-trivial on the latest generation of parallel computers that consist of nodes made up of a shared memory multiprocessors. A non-dogmatic method for obtaining high performance for such 3-dim FFTs in a combined MPI/OpenMP programming paradigm will be presented. Exploiting the peculiarities of plane wave electronic structure calculations, speedups of up to 160 and speeds of up to 130 Gflops were obtained on 256 processors.

Improvement of both bandwidth and driving voltage of polymer phase modulators using buried in-plane coupled micro-strip driving electrodes

NASA Astrophysics Data System (ADS)

Hadjloum, Massinissa; El Gibari, Mohammed; Li, Hongwu; Daryoush, Afshin S.

2017-06-01

A large performance improvement of polymer phase modulators is reported by using buried in-plane coupled microstrip (CMS) driving electrodes, instead of standard vertical Micro-Strip electrodes. The in-plane CMS driving electrodes have both low radio frequency (RF) losses and high overlap integral between optical and RF waves compared to the vertical designs. Since the optical waveguide and CMS electrodes are located in the same plane, optical injection and microwave driving access cannot be separated perpendicularly without intersection between them. A via-less transition between grounded coplanar waveguide access and CMS driving electrodes is introduced in order to provide broadband excitation of optical phase modulators and avoid the intersection of the optical core and the electrical probe. Simulation and measurement results of the benzocyclobutene polymer as a cladding material and the PMMI-CPO1 polymer as an optical core with an electro-optic coefficient of 70 pm/V demonstrate a broadband operation of 67 GHz using travelling-wave driving electrodes with a half-wave voltage of 4.5 V, while satisfying its low RF losses and high overlap integral between optical and RF waves of in-plane CMS electrodes.

Detection of in-plane displacements of acoustic wave fields using extrinsic Fizeau fiber interferometric sensors

NASA Technical Reports Server (NTRS)

Dhawan, R.; Gunther, M. F.; Claus, R. O.

1991-01-01

Quantitative measurements of the in-plane particle displacement components of ultrasonic surface acoustic wave fields using extrinsic Fizeau fiber interferometric (EFFI) sensors are reported. Wave propagation in materials and the fiber sensor elements are briefly discussed. Calibrated experimental results obtained for simulated acoustic emission events on homogeneous metal test specimens are reported and compared to previous results obtained using piezoelectric transducers.

Solvable model of spiral wave chimeras.

PubMed

Martens, Erik A; Laing, Carlo R; Strogatz, Steven H

2010-01-29

Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to zero. But if the coupling is nonlocal, a new kind of spiral can occur, with a circular core consisting of desynchronized oscillators running at full amplitude. Here, we provide the first analytical description of such a spiral wave chimera and use perturbation theory to calculate its rotation speed and the size of its incoherent core.

A nonlinear wave equation in nonadiabatic flame propagation

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

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

1988-06-01

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

Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams.

PubMed

Hansinger, Peter; Maleshkov, Georgi; Garanovich, Ivan L; Skryabin, Dmitry V; Neshev, Dragomir N; Dreischuh, Alexander; Paulus, Gerhard G

2014-05-05

Experiments performed with different vortex pump beams show for the first time the algebra of the vortex topological charge cascade, that evolves in the process of nonlinear wave mixing of optical vortex beams in Kerr media due to competition of four-wave mixing with self-and cross-phase modulation. This leads to the coherent generation of complex singular beams within a spectral bandwidth larger than 200nm. Our experimental results are in good agreement with frequency-domain numerical calculations that describe the newly generated spectral satellites.

Current induced multi-mode propagating spin waves in a spin transfer torque nano-contact with strong perpendicular magnetic anisotropy

NASA Astrophysics Data System (ADS)

Mohseni, S. Morteza; Yazdi, H. F.; Hamdi, M.; Brächer, T.; Mohseni, S. Majid

2018-03-01

Current induced spin wave excitations in spin transfer torque nano-contacts are known as a promising way to generate exchange-dominated spin waves at the nano-scale. It has been shown that when these systems are magnetized in the film plane, broken spatial symmetry of the field around the nano-contact induced by the Oersted field opens the possibility for spin wave mode co-existence including a non-linear self-localized spin-wave bullet and a propagating mode. By means of micromagnetic simulations, here we show that in systems with strong perpendicular magnetic anisotropy (PMA) in the free layer, two propagating spin wave modes with different frequency and spatial distribution can be excited simultaneously. Our results indicate that in-plane magnetized spin transfer nano-contacts in PMA materials do not host a solitonic self-localized spin-wave bullet, which is different from previous studies for systems with in plane magnetic anisotropy. This feature renders them interesting for nano-scale magnonic waveguides and crystals since magnon transport can be configured by tuning the applied current.

Modern developments in shear flow control with swirl

NASA Technical Reports Server (NTRS)

Farokhi, Saeed; Taghavi, R.

1990-01-01

Passive and active control of swirling turbulent jets is experimentally investigated. Initial swirl distribution is shown to dominate the free jet evolution in the passive mode. Vortex breakdown, a manifestation of high intensity swirl, was achieved at below critical swirl number (S = 0.48) by reducing the vortex core diameter. The response of a swirling turbulent jet to single frequency, plane wave acoustic excitation was shown to depend strongly on the swirl number, excitation Strouhal number, amplitude of the excitation wave, and core turbulence in a low speed cold jet. A 10 percent reduction of the mean centerline velocity at x/D = 9.0 (and a corresponding increase in the shear layer momentum thickness) was achieved by large amplitude internal plane wave acoustic excitation. Helical instability waves of negative azimuthal wave numbers exhibit larger amplification rates than the plane waves in swirling free jets, according to hydrodynamic stability theory. Consequently, an active swirling shear layer control is proposed to include the generation of helical instability waves of arbitrary helicity and the promotion of modal interaction, through multifrequency forcing.

Spectral Properties of Dirac Billiards at the van Hove Singularities.

PubMed

Dietz, B; Klaus, T; Miski-Oglu, M; Richter, A; Wunderle, M; Bouazza, C

2016-01-15

We study distributions of the ratios of level spacings of rectangular and Africa-shaped superconducting microwave resonators containing circular scatterers on a triangular grid, so-called Dirac billiards (DBs). The high-precision measurements allowed the determination of, respectively, all 1651 and 1823 eigenfrequencies in the first two bands. The resonance densities are similar to that of graphene. They exhibit two sharp peaks at the van Hove singularities which separate the band structure into regions with a linear and a quadratic dispersion relation, respectively. In the vicinity of the van Hove singularities we observe rapid changes in, e.g., the wave function structure. Accordingly, we question whether the spectral properties are there still determined by the shapes of the DBs. The commonly used statistical measures are no longer applicable; however, we demonstrate in this Letter that the ratio distributions provide suitable measures.

Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

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

Mitsuda, Eiji; Yoshino, Hirotaka; Tomimatsu, Akira

Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green's function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from 'quasinormal' modes of the self-similar system as well as 'high-frequency' waves are clarified. We find a characteristic power-law time evolution of the outgoingmore » energy flux which appears just before naked singularity formation and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.« less

Asymmetric lasing at spectral singularities

NASA Astrophysics Data System (ADS)

Jin, L.

2018-03-01

Scattering coefficients can diverge at spectral singularities. In such situation, the stationary solution becomes a laser solution with outgoing waves only. We explore a parity-time (PT )-symmetric non-Hermitian two-arm Aharonov-Bohm interferometer consisting of three coupled resonators enclosing synthetic magnetic flux. The synthetic magnetic flux does not break the PT symmetry, which protects the symmetric transmission. The features and conditions of symmetric, asymmetric, and unidirectional lasing at spectral singularities are discussed. We elucidate that lasing affected by the interference is asymmetric; asymmetric lasing is induced by the interplay between the synthetic magnetic flux and the system's non-Hermiticity. The product of the left and right transmissions is equal to that of the reflections. Our findings reveal that the synthetic magnetic flux affects light propagation, and the results can be applied in the design of lasing devices.

Generic short-time propagation of sharp-boundaries wave packets

NASA Astrophysics Data System (ADS)

Granot, E.; Marchewka, A.

2005-11-01

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wave function is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can be written as an expression that depends only on the values of the function (and its derivatives) at the boundaries. In particular, it is shown that at short times (t << 2mx2/hbar, where x is the distance to the boundaries) the wave function propagation depends only on the wave function's values (or its derivatives) at the boundaries of the region. Finally, we generalize these findings to a non-singular wave function (i.e., for wave packets with finite-width boundaries) and suggest an experimental verification.

Several localized waves induced by linear interference between a nonlinear plane wave and bright solitons

NASA Astrophysics Data System (ADS)

Qin, Yan-Hong; Zhao, Li-Chen; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by a pair-transition coupled two-component Bose-Einstein condensate. We demonstrate that the interference effects can induce several localized waves possessing distinctive wave structures, mainly including anti-dark solitons, W-shaped solitons, multi-peak solitons, Kuznetsov-Ma like breathers, and multi-peak breathers. Specifically, the explicit conditions for them are clarified by a phase diagram based on the linear interference properties. Furthermore, the interactions between these localized waves are discussed. The detailed analysis indicates that the soliton-soliton interaction induced phase shift brings the collision between these localized waves which can be inelastic for solitons involving collision and can be elastic for breathers. These characters come from the fact that the profile of solitons depends on the relative phase between bright solitons and a plane wave, and the profile of breathers does not depend on the relative phase. These results would motivate more discussions on linear interference between other nonlinear waves. Specifically, the solitons or breathers obtained here are not related to modulational instability. The underlying reasons are discussed in detail. In addition, possibilities to observe these localized waves are discussed in a two species Bose-Einstein condensate.

Simplification and analysis of models of calcium dynamics based on IP3-sensitive calcium channel kinetics.

PubMed

Tang, Y; Stephenson, J L; Othmer, H G

1996-01-01

We study the models for calcium (Ca) dynamics developed in earlier studies, in each of which the key component is the kinetics of intracellular inositol-1,4,5-trisphosphate-sensitive Ca channels. After rapidly equilibrating steps are eliminated, the channel kinetics in these models are represented by a single differential equation that is linear in the state of the channel. In the reduced kinetic model, the graph of the steady-state fraction of conducting channels as a function of log10(Ca) is a bell-shaped curve. Dynamically, a step increase in inositol-1,4,5-trisphosphate induces an incremental increase in the fraction of conducting channels, whereas a step increase in Ca can either potentiate or inhibit channel activation, depending on the Ca level before and after the increase. The relationships among these models are discussed, and experimental tests to distinguish between them are given. Under certain conditions the models for intracellular calcium dynamics are reduced to the singular perturbed form epsilon dx/d tau = f(x, y, p), dy/d tau = g(x, y, p). Phase-plane analysis is applied to a generic form of these simplified models to show how different types of Ca response, such as excitability, oscillations, and a sustained elevation of Ca, can arise. The generic model can also be used to study frequency encoding of hormonal stimuli, to determine the conditions for stable traveling Ca waves, and to understand the effect of channel properties on the wave speed.

Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions

NASA Astrophysics Data System (ADS)

Yang, Bo; Chen, Yong

2018-05-01

A study of rogue-wave solutions in the reverse-time nonlocal nonlinear Schrödinger (NLS) and nonlocal Davey-Stewartson (DS) equations is presented. By using Darboux transformation (DT) method, several types of rogue-wave solutions are constructed. Dynamics of these rogue-wave solutions are further explored. It is shown that the (1 + 1)-dimensional fundamental rogue-wave solutions in the reverse-time NLS equation can be globally bounded or have finite-time blowing-ups. It is also shown that the (2 + 1)-dimensional line rogue waves in the reverse-time nonlocal DS equations can be bounded for all space and time or develop singularities in critical time. In addition, the multi- and higher-order rogue waves exhibit richer structures, most of which have no counterparts in the corresponding local nonlinear equations.

Singularity formations for a surface wave model

NASA Astrophysics Data System (ADS)

Castro, Angel; Córdoba, Diego; Gancedo, Francisco

2010-11-01

In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex patch (see Biello and Hunter 2010 Commun. Pure Appl. Math. LXIII 0303-36 Marsden and Weinstein 1983 Physica D 7 305-23). We prove blowup in finite time for a large class of initial data with finite energy. Considering a more general nonlocal term, of the form ΛαHu for 0 < α < 1, finite time singularity formation is also shown.

Diffraction of Nondiverging Bessel Beams by Fork-Shaped and Rectilinear Grating

NASA Astrophysics Data System (ADS)

Janicijevic, Ljiljana; Topuzoski, Suzana

2007-04-01

We present an investigation about Fresnel diffraction of Bessel beams, propagating as nondiverging within a distance Ln, with or without phase singularities, by rectilinear and fork-shaped gratings. The common general transmission function of these gratings is defined and specialized for three different cases: binary amplitude gratings, amplitude holograms and their phase versions. Solving the Fresnel diffraction integral in cylindrical coordinates, we obtain analytical expressions for the diffracted wave amplitude for all types of proposed gratings, and make conclusions about the existence of phase singularities and corresponding topological charges in the created by the gratings beams of different diffraction orders.

Compacted dimensions and singular plasmonic surfaces

NASA Astrophysics Data System (ADS)

Pendry, J. B.; Huidobro, Paloma Arroyo; Luo, Yu; Galiffi, Emanuele

2017-11-01

In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer.

An Experimental Study of Droplets Produced by a Plunging Breakers

NASA Astrophysics Data System (ADS)

Erinin, Martin; Wang, Dan; Towle, David; Liu, Xinan; Duncan, James

2016-11-01

In this study, the production of droplets by a mechanically generated plunging breaking water wave is investigated in a wave tank. The breaker, with an amplitude of 0.070 m, is generated repeatedly with a programmable wave maker by using a dispersively focused wave packet (average frequency 1.15 Hz). The profile histories of the breaking wave crests along the center plane of the tank are measured using cinematic laser-induced fluorescence. The droplets are measured using a cinematic digital in-line holographic system positioned at 30 locations along a horizontal plane that is 1 cm above the maximum wave crest height. This measurement plane covers the entire region in the tank where the wave breaks. The holographic system is used to obtain the droplet diameters (d, for d >100 microns) and the three components of the droplet velocities. From these measurements and counting only the droplets that are moving up, the spatio-temporal distribution of droplet generation by the breaking wave is obtained. The main features of the droplet generation are correlated with the features and phases of the breaking process. The support of the National Science Foundation under Grant OCE0751853 from the Division of Ocean Sciences is gratefully acknowledged.

Sensor Modelling for the ’Cyclops’ Focal Plane Detector Array Based Technology Demonstrator

DTIC Science & Technology

1992-12-01

Detector Array IFOV Instantaneous field of view IRFPDA Infrared Focal Plane Detector Array LWIR Long-Wave Infrared 0 MCT Mercury Cadmium Telluride MTF...scale focal plane detector array (FPDA). The sensor system operates in the long-wave infrared ( LWIR ) spectral region. The detector array consists of...charge transfer inefficiencies in the readout circuitry. The performance of the HgCdTe FPDA based sensor is limited by the nonuniformity of the

Third All-Union Symposium on Wave Diffraction.

DTIC Science & Technology

1982-08-02

the Half - Plane of Waves, Formed on the Surface of Liquid and on the Interface in the Laminar Liquid by the Periodically Functioning Source, by...majority of the cases is of basic practical interest. For this way of integration it is displaced into lower half - plane Im xɘ and are computed deductions...and f(x) exponentially decrease, then u(x, p) is continued as meromorphic function for the variable/alternating p into half - plane Re p>-b,

High-frequency sound waves to eliminate a horizon in the mixmaster universe.

NASA Technical Reports Server (NTRS)

Chitre, D. M.

1972-01-01

From the linear wave equation for small-amplitude sound waves in a curved space-time, there is derived a geodesiclike differential equation for sound rays to describe the motion of wave packets. These equations are applied in the generic, nonrotating, homogeneous closed-model universe (the 'mixmaster universe,' Bianchi type IX). As for light rays described by Doroshkevich and Novikov (DN), these sound rays can circumnavigate the universe near the singularity to remove particle horizons only for a small class of these models and in special directions. Although these results parallel those of DN, different Hamiltonian methods are used for treating the Einstein equations.

Reflection and Refraction of Acoustic Waves by a Shock Wave

NASA Technical Reports Server (NTRS)

Brillouin, J.

1957-01-01

The presence of sound waves in one or the other of the fluid regions on either side of a shock wave is made apparent, in the region under superpressure, by acoustic waves (reflected or refracted according to whether the incident waves lie in the region of superpressure or of subpressure) and by thermal waves. The characteristics of these waves are calculated for a plane, progressive, and uniform incident wave. In the case of refraction, the refracted acoustic wave can, according to the incidence, be plane, progressive, and uniform or take the form of an 'accompanying wave' which remains attached to the front of the shock while sliding parallel to it. In all cases, geometrical constructions permit determination of the kinematic characteristics of the reflected or refractive acoustic waves. The dynamic relationships show that the amplitude of the reflected wave is always less than that of the incident wave. The amplitude of the refracted wave, whatever its type, may in certain cases be greater than that of the incident wave.

Optimizing snake locomotion on an inclined plane

NASA Astrophysics Data System (ADS)

Wang, Xiaolin; Osborne, Matthew T.; Alben, Silas

2014-01-01

We develop a model to study the locomotion of snakes on inclined planes. We determine numerically which snake motions are optimal for two retrograde traveling-wave body shapes, triangular and sinusoidal waves, across a wide range of frictional parameters and incline angles. In the regime of large transverse friction coefficients, we find power-law scalings for the optimal wave amplitudes and corresponding costs of locomotion. We give an asymptotic analysis to show that the optimal snake motions are traveling waves with amplitudes given by the same scaling laws found in the numerics.

The crack problem for a nonhomogeneous plane

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

The crack problem for a nonhomogeneous plane

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1983-01-01

The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.

Interface crack in a nonhomogeneous elastic medium

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1988-01-01

The linear elasticity problem for an interface crack between two bonded half planes is reconsidered. It is assumed that one of the half planes is homogeneous and the second is nonhomogeneous in such a way that the elastic properties are continuous throughout the plane and have discontinuous derivatives along the interface. The problem is formulated in terms of a system of integral equations and the asymptotic behavior of the stress state near the crack tip is determined. The results lead to the conclusion that the singular behavior of stresses in the nonhomogeneous medium is identical to that in a homogeneous material provided the spacial distribution of material properties is continuous near and at the crack tip. The problem is solved for various values of the nonhomogeneity parameter and for four different sets of crack surface tractions, and the corresponding stress intensity factors are tabulated.

Propagation of elastic wave in nanoporous material with distributed cylindrical nanoholes

NASA Astrophysics Data System (ADS)

Qiang, FangWei; Wei, PeiJun; Liu, XiQiang

2013-08-01

The effective propagation constants of plane longitudinal and shear waves in nanoporous material with random distributed parallel cylindrical nanoholes are studied. The surface elastic theory is used to consider the surface stress effects and to derive the nontraditional boundary condition on the surface of nanoholes. The plane wave expansion method is used to obtain the scattering waves from the single nanohole. The multiple scattering effects are taken into consideration by summing the scattered waves from all scatterers and performing the configuration averaging of random distributed scatterers. The effective propagation constants of coherent waves along with the associated dynamic effective elastic modulus are numerically evaluated. The influences of surface stress are discussed based on the numerical results.

Oblique superposition of two elliptically polarized lightwaves using geometric algebra: is energy-momentum conserved?

PubMed

Sze, Michelle Wynne C; Sugon, Quirino M; McNamara, Daniel J

2010-11-01

In this paper, we use Clifford (geometric) algebra Cl(3,0) to verify if electromagnetic energy-momentum density is still conserved for oblique superposition of two elliptically polarized plane waves with the same frequency. We show that energy-momentum conservation is valid at any time only for the superposition of two counter-propagating elliptically polarized plane waves. We show that the time-average energy-momentum of the superposition of two circularly polarized waves with opposite handedness is conserved regardless of the propagation directions of the waves. And, we show that the resulting momentum density of the superposed waves generally has a vector component perpendicular to the momentum densities of the individual waves.

Self-energy of an impurity in an ideal Fermi gas to second order in the interaction strength

NASA Astrophysics Data System (ADS)

Trefzger, Christian; Castin, Yvan

2014-09-01

We study in three dimensions the problem of a spatially homogeneous zero-temperature ideal Fermi gas of spin-polarized particles of mass m perturbed by the presence of a single distinguishable impurity of mass M. The interaction between the impurity and the fermions involves only the partial s wave through the scattering length a and has negligible range b compared to the inverse Fermi wave number 1/kF of the gas. Through the interactions with the Fermi gas the impurity gives birth to a quasiparticle, which will be here a Fermi polaron (or more precisely a monomeron). We consider the general case of an impurity moving with wave vector K ≠0: Then the quasiparticle acquires a finite lifetime in its initial momentum channel because it can radiate particle-hole pairs in the Fermi sea. A description of the system using a variational approach, based on a finite number of particle-hole excitations of the Fermi sea, then becomes inappropriate around K =0. We rely thus upon perturbation theory, where the small and negative parameter kFa→0- excludes any branches other than the monomeronic one in the ground state (as, e.g., the dimeronic one), and allows us a systematic study of the system. We calculate the impurity self-energy Σ(2)(K,ω) up to second order included in a. Remarkably, we obtain an analytical explicit expression for Σ(2)(K,ω), allowing us to study its derivatives in the plane (K,ω). These present interesting singularities, which in general appear in the third-order derivatives ∂3Σ(2)(K,ω). In the special case of equal masses, M =m, singularities appear already in the physically more accessible second-order derivatives ∂2Σ(2)(K,ω); using a self-consistent heuristic approach based on Σ(2) we then regularize the divergence of the second-order derivative ∂K2ΔE(K) of the complex energy of the quasiparticle found in Trefzger and Castin [Europhys. Lett. 104, 50005 (2013), 10.1209/0295-5075/104/50005] at K =kF, and we predict an interesting scaling law in the neighborhood of K =kF. As a by product of our theory we have access to all moments of the momentum of the particle-hole pair emitted by the impurity while damping its motion in the Fermi sea at the level of Fermi's golden rule.

Planck's constant and the three waves (TWs) of Einstein's covariant ether

NASA Astrophysics Data System (ADS)

Kostro, L.

1985-11-01

The implications of a three-wave model for elementary particles, satisfying the principles of both quantum mechanics and General Relativity (GR), are discussed. In GR, the ether is the fundamental source of all activity, where particles (waves) arise at singularities. Inertia and gravity are field properties of the ether. In flat regions of the space-time geodesic, wave excitations correspond to the presence of particles. A momentum-carrying excitation which occurs in the ether is a superluminal radiation (phase- or B-waves) which transports neither energy nor mass. Superposition of the B-waves produces soliton-like excitations on the ether to form C-waves, i.e., particles. The particle-waves travel through space-time on D-waves, and experience reflection, refraction and interference only where B-waves have interacted with the ether. The original particles, photons-maximons, existed at the Big Bang and had physical properties which are describable in terms of Planck's quantities.

Investigation of the Dynamics of Low-Tension Cables

DTIC Science & Technology

1992-06-01

chapter 3. An implicit time domain routine is nec- essary as the high propagation speed of elastic waves would require prohibitively small time-step...singularities by ensuring smooth curvature. However, sustained boundary layers are found to develop, demonstrating the importance of the underlying physical...chain and elastic chain, EA* = 4.0 x 103 ............... 124 3.10 Mode shape for tension variation due to elastic waves , using EA* - 4.0 x 103.125 6.11

Discrete mathematical model of wave diffraction on pre-fractal impedance strips. TM mode case

NASA Astrophysics Data System (ADS)

Nesvit, K. V.

2013-10-01

In this paper a transverse magnetic (TM) wave diffraction problem on pre-fractal impedance strips is considered. The overall aim of this work is to develop a discrete mathematical model of the boundary integral equations (IEs) with the help of special quadrature formulas with the nodes in the zeros of Chebyshev polynomials and to perform a numerical experiments with the help of an efficient discrete singularities method (DSM).

The development of a mixing layer under the action of weak streamwise vortices

NASA Technical Reports Server (NTRS)

Goldstein, Marvin E.; Mathew, Joseph

1993-01-01

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds-number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon(sup -1)), where epsilon is much less than 1 is the cross flow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by the appearance of a singularity. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the singular location.

Bonded orthotropic strips with cracks

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1978-01-01

The elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. First, the problem of cracks fully imbedded into the homogeneous strips is considered. Then, the singular behavior of the stresses for two special crack geometries is studied in some detail. The first is the case of a broken laminate in which the crack tips touch the interfaces. The second is the case of cracks crossing the interfaces. A number of numerical examples are worked out in order to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters. Finally, some numerical results are given for the stress intensity factors in certain basic crack geometries and for typical material combinations.

Efficient evaluation of Coulomb integrals in a mixed Gaussian and plane-wave basis using the density fitting and Cholesky decomposition.

PubMed

Čársky, Petr; Čurík, Roman; Varga, Štefan

2012-03-21

The objective of this paper is to show that the density fitting (resolution of the identity approximation) can also be applied to Coulomb integrals of the type (k(1)(1)k(2)(1)|g(1)(2)g(2)(2)), where k and g symbols refer to plane-wave functions and gaussians, respectively. We have shown how to achieve the accuracy of these integrals that is needed in wave-function MO and density functional theory-type calculations using mixed Gaussian and plane-wave basis sets. The crucial issues for achieving such a high accuracy are application of constraints for conservation of the number electrons and components of the dipole moment, optimization of the auxiliary basis set, and elimination of round-off errors in the matrix inversion. © 2012 American Institute of Physics

Photoelectron wave function in photoionization: plane wave or Coulomb wave?

PubMed

Gozem, Samer; Gunina, Anastasia O; Ichino, Takatoshi; Osborn, David L; Stanton, John F; Krylov, Anna I

2015-11-19

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 photoelectron 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. 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.

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.

Free energy and phase transition of the matrix model on a plane wave

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

Hadizadeh, Shirin; Ramadanovic, Bojan; Semenoff, Gordon W.

2005-03-15

It has recently been observed that the weakly coupled plane-wave matrix model has a density of states which grows exponentially at high energy. This implies that the model has a phase transition. The transition appears to be of first order. However, its exact nature is sensitive to interactions. In this paper, we analyze the effect of interactions by computing the relevant parts of the effective potential for the Polyakov loop operator in the finite temperature plane-wave matrix model to three-loop order. We show that the phase transition is indeed of first order. We also compute the correction to the Hagedornmore » temperature to order two loops.« less

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.

Size Reduction of Hamiltonian Matrix for Large-Scale Energy Band Calculations Using Plane Wave Bases

NASA Astrophysics Data System (ADS)

Morifuji, Masato

2018-01-01

We present a method of reducing the size of a Hamiltonian matrix used in calculations of electronic states. In the electronic states calculations using plane wave basis functions, a large number of plane waves are often required to obtain precise results. Even using state-of-the-art techniques, the Hamiltonian matrix often becomes very large. The large computational time and memory necessary for diagonalization limit the widespread use of band calculations. We show a procedure of deriving a reduced Hamiltonian constructed using a small number of low-energy bases by renormalizing high-energy bases. We demonstrate numerically that the significant speedup of eigenstates evaluation is achieved without losing accuracy.

Numerical study of electromagnetic waves generated by a prototype dielectric logging tool

USGS Publications Warehouse

Ellefsen, K.J.; Abraham, J.D.; Wright, D.L.; Mazzella, A.T.

2004-01-01

To understand the electromagnetic waves generated by a prototype dielectric logging tool, a numerical study was conducted using both the finite-difference, time-domain method and a frequency-wavenumber method. When the propagation velocity in the borehole was greater than that in the formation (e.g., an air-filled borehole in the unsaturated zone), only a guided wave propagated along the borehole. As the frequency decreased, both the phase and the group velocities of the guided wave asymptotically approached the phase velocity of a plane wave in the formation. The guided wave radiated electromagnetic energy into the formation, causing its amplitude to decrease. When the propagation velocity in the borehole was less than that in the formation (e.g., a water-filled borehole in the saturated zone), both a refracted wave and a guided wave propagated along the borehole. The velocity of the refracted wave equaled the phase velocity of a plane wave in the formation, and the refracted wave preceded the guided wave. As the frequency decreased, both the phase and the group velocities of the guided wave asymptotically approached the phase velocity of a plane wave in the formation. The guided wave did not radiate electromagnetic energy into the formation. To analyze traces recorded by the prototype tool during laboratory tests, they were compared to traces calculated with the finite-difference method. The first parts of both the recorded and the calculated traces were similar, indicating that guided and refracted waves indeed propagated along the prototype tool. ?? 2004 Society of Exploration Geophysicists. All rights reserved.

Diffraction of a Gaussian laser beam by a straight edge leading to the formation of optical vortices and elliptical diffraction fringes

NASA Astrophysics Data System (ADS)

Zeylikovich, Iosif; Nikitin, Aleksandr

2018-04-01

The diffraction of a Gaussian laser beam by a straight edge has been studied theoretically and experimentally for many years. In this paper, we have experimentally observed for the first time the formation of the cusped caustic (for the Fresnel number F ≈ 100) in the shadow region of the straight edge, with the cusp placed near the center of the circular laser beam(λ = 0 . 65 μm) overlapped with the elliptical diffraction fringes. These fringes are originated at the region near the cusp of the caustic where light intensity is zero and the wave phase is singular (the optical vortex). We interpret observed diffraction fringes as a result of interference between the helical wave created by the optical vortex and cylindrical wave diffracted at the straight edge. We have theoretically revealed that the number of high contrast diffraction fringes observable in a shadow region is determined by the square of the diffracted angles in the range of spatial frequencies of the scattered light field in excellent agreement with experiments. The extra phase singularities with opposite charges are also observed along the shadow boundary as the fork-like diffraction fringes.

On irregular singularity wave functions and superconformal indices

NASA Astrophysics Data System (ADS)

Buican, Matthew; Nishinaka, Takahiro

2017-09-01

We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregular singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU( N). As an application, we give closed-form expressions for the Schur indices of all ( A N - 1 , A N ( n - 1)-1) Argyres-Douglas (AD) superconformal field theories (SCFTs), thus completing the computation of these quantities for the ( A N , A M ) SCFTs. With minimal effort, our wave functions also give new Schur indices of various infinite sets of "Type IV" AD theories. We explore the discrete symmetries of these indices and also show how highly intricate renormalization group (RG) flows from isolated theories and conformal manifolds in the ultraviolet to isolated theories and (products of) conformal manifolds in the infrared are encoded in these indices. We compare our flows with dimensionally reduced flows via a simple "monopole vev RG" formalism. Finally, since our expressions are given in terms of concise Lie algebra data, we speculate on extensions of our results that might be useful for probing the existence of hypothetical SCFTs based on other Lie algebras. We conclude with a discussion of some open problems.

The pattern space factor and quality factor of cylindrical source antennas

NASA Astrophysics Data System (ADS)

Jarem, John M.

1982-09-01

For the first time the quality factor of cylindrical source antennas is derived by a plane wave expansion. The evanescent energy (and therefore the quality factor) as defined by a plane wave expansion is shown to be different from Collin and Rothschild's [IEEE Trans. Antennas Propagation AP-12, 23 (1964)] quality factor.

Determination of plane stress state using terahertz time-domain spectroscopy

PubMed Central

Wang, Zhiyong; Kang, Kai; Wang, Shibin; Li, Lin'an; Xu, Ningning; Han, Jiaguang; He, Mingxia; Wu, Liang; Zhang, Weili

2016-01-01

THz wave has been increasingly applied in engineering practice. One of its outstanding advantages is the penetrability through certain optically opaque materials, whose interior properties could be therefore obtained. In this report, we develop an experimental method to determine the plane stress state of optically opaque materials based on the stress-optical law using terahertz time-domain spectroscopy (THz-TDS). In this method, two polarizers are combined into the conventional THz-TDS system to sense and adjust the polarization state of THz waves and a theoretical model is established to describe the relationship between phase delay of the received THz wave and the plane stress applied on the specimen. Three stress parameters that represent the plane stress state are finally determined through an error function of THz wave phase-delay. Experiments were conducted on polytetrafluoroethylene (PTFE) specimen and a reasonably good agreement was found with measurement using traditional strain gauges. The presented results validate the effectiveness of the proposed method. The proposed method could be further used in nondestructive tests for a wide range of optically opaque materials. PMID:27824112

Determination of plane stress state using terahertz time-domain spectroscopy

NASA Astrophysics Data System (ADS)

Wang, Zhiyong; Kang, Kai; Wang, Shibin; Li, Lin'an; Xu, Ningning; Han, Jiaguang; He, Mingxia; Wu, Liang; Zhang, Weili

2016-11-01

THz wave has been increasingly applied in engineering practice. One of its outstanding advantages is the penetrability through certain optically opaque materials, whose interior properties could be therefore obtained. In this report, we develop an experimental method to determine the plane stress state of optically opaque materials based on the stress-optical law using terahertz time-domain spectroscopy (THz-TDS). In this method, two polarizers are combined into the conventional THz-TDS system to sense and adjust the polarization state of THz waves and a theoretical model is established to describe the relationship between phase delay of the received THz wave and the plane stress applied on the specimen. Three stress parameters that represent the plane stress state are finally determined through an error function of THz wave phase-delay. Experiments were conducted on polytetrafluoroethylene (PTFE) specimen and a reasonably good agreement was found with measurement using traditional strain gauges. The presented results validate the effectiveness of the proposed method. The proposed method could be further used in nondestructive tests for a wide range of optically opaque materials.

Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave.

PubMed

Frisvad, Jeppe Revall

2018-04-01

In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation of the complex hypergeometric function F 1 2 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far-field scattering components, that is, the phase function. I include recurrence formulas for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity is not negligible for light entering an absorbing medium at an oblique angle. The presented theory could thus be useful for predicting scattering behavior in dye-based random lasing and in solar cell absorption enhancement.

System alignment using the Talbot effect

NASA Astrophysics Data System (ADS)

Chevallier, Raymond; Le Falher, Eric; Heggarty, Kevin

1990-08-01

The Talbot effect is utilized to correct an alignment problem related to a neural network used for image recognition, which required the alignment of a spatial light modulator (SLM) with the input module. A mathematical model which employs the Fresnel diffraction theory is presented to describe the method. The calculation of the diffracted amplitude describes the wavefront sphericity and the original object transmittance function in order to qualify the lateral shift of the Talbot image. Another explanation is set forth in terms of plane-wave illumination in the neural network. Using a Fourier series and by describing planes where all the harmonics are in phase, the reconstruction of Talbot images is explained. The alignment is effective when the lenslet array is aligned on the even Talbot images of the SLM pixels and the incident wave is a plane wave. The alignment is evaluated in terms of source and periodicity errors, tilt of the incident plane waves, and finite object dimensions. The effects of the error sources are concluded to be negligible, the lenslet array is shown to be successfully aligned with the SLM, and other alignment applications are shown to be possible.

Electromagnetic absorption in a multilayered slab model of tissue under near-field exposure conditions.

PubMed

Chatterjee, I; Hagmann, M J; Gandhi, O P

1980-01-01

The electromagnetic energy deposited in a semi-infinite slab model consisting of skin, fat, and muscle layers is calculated for both plane-wave and near-field exposures. The plane-wave spectrum (PWS) approach is used to calculate the energy deposited in the model by fields present due to leakage from equipment using electromagnetic energy. This analysis applies to near-field exposures where coupling of the target to the leakage source can be neglected. Calculations were made for 2,450 MHz, at which frequency the layered slab adequately models flat regions of the human body. Resonant absorption due to layering is examined as a function of the skin and fat thicknesses for plane-wave exposure and as a function of the physical extent of the near-field distribution. Calculations show that for fields that are nearly constant over at least a free-space wavelength, the energy deposition (for skin, fat, and muscle combination that gives resonant absorption) is equal to or less than that resulting from plane-wave exposure, but is appreciably greater than that obtained for a homogeneous muscle slab model.

Non-contact measurements of ultrasonic waves on paper webs using a photorefractive interferometer

DOEpatents

Brodeur, Pierre H.; Lafond, Emmanuel F.

2000-01-01

An apparatus and method for non-contact measurement of ultrasonic waves on moving paper webs employs a photorefractive interferometer. The photorefractive interferometer employs an optical head in which the incident beam and reflected beam are coaxial, thus enabling detection of both in-plane and out-of-plane waves with a single apparatus. The incident beam and reference beams are focused into a line enabling greater power to be used without damaging the paper.

High-Resolution Large-Field-of-View Ultrasound Breast Imager

DTIC Science & Technology

2012-06-01

plane waves all having the same wave vector magnitude 0k but propagating in different directions . This observation forms the mathematical basis of the...origin of the object Fourier space and is oriented opposite the propagation direction of the probing plane wave field. Moreover, the 43 radius of...in water. Each element was electrically tuned to match to the 50-Ohm impedance of an RF Amplifier powered by a 4.0 MHz electrical signal from a

Alignment error of mirror modules of advanced telescope for high-energy astrophysics due to wavefront aberrations

NASA Astrophysics Data System (ADS)

Zocchi, Fabio E.

2017-10-01

One of the approaches that is being tested for the integration of the mirror modules of the advanced telescope for high-energy astrophysics x-ray mission of the European Space Agency consists in aligning each module on an optical bench operated at an ultraviolet wavelength. The mirror module is illuminated by a plane wave and, in order to overcome diffraction effects, the centroid of the image produced by the module is used as a reference to assess the accuracy of the optical alignment of the mirror module itself. Among other sources of uncertainty, the wave-front error of the plane wave also introduces an error in the position of the centroid, thus affecting the quality of the mirror module alignment. The power spectral density of the position of the point spread function centroid is here derived from the power spectral density of the wave-front error of the plane wave in the framework of the scalar theory of Fourier diffraction. This allows the defining of a specification on the collimator quality used for generating the plane wave starting from the contribution to the error budget allocated for the uncertainty of the centroid position. The theory generally applies whenever Fourier diffraction is a valid approximation, in which case the obtained result is identical to that derived by geometrical optics considerations.

Wave propagation in piezoelectric layered structures of film bulk acoustic resonators.

PubMed

Zhu, Feng; Qian, Zheng-Hua; Wang, Bin

2016-04-01

In this paper, we studied the wave propagation in a piezoelectric layered plate consisting of a piezoelectric thin film on an electroded elastic substrate with or without a driving electrode. Both plane-strain and anti-plane waves were taken into account for the sake of completeness. Numerical results on dispersion relations, cut-off frequencies and vibration distributions of selected modes were given. The effects of mass ratio of driving electrode layer to film layer on the dispersion curve patterns and cut-off frequencies of the plane-strain waves were discussed in detail. Results show that the mass ratio does not change the trend of dispersion curves but larger mass ratio lowers corresponding frequency at a fixed wave number and may extend the frequency range for energy trapping. Those results are of fundamental importance and can be used as a reference to develop effective two-dimensional plate equations for structural analysis and design of film bulk acoustic resonators. Copyright © 2016 Elsevier B.V. All rights reserved.

A Spherical to Plane Wave Transformation Using a Reflectarray

NASA Technical Reports Server (NTRS)

Zaman, Afroz J.; Lee, Richard Q.

1997-01-01

A reflectarray has generally been used as a replacement for a reflector antenna. Using in this capacity, different configurations (prime focus, offset etc.) and various applications (dual frequency, scanning etc.) have been demonstrated with great success. Another potential application that has not been explored previously is the use of reflectarrays to compensate for phase errors in space power combining applications such as space-fed lens and power combining amplifier. In these applications, it is required to convert a spherical wave to a plane wave with proper phase correction added to each element of the reflectarray. This paper reports an experiment to investigate the feasibility of using a reflectarray as an alternative to a lens in space power combining. The experiment involves transforming a spherical wave from a orthomode horn to a plane wave at the horn aperture. The reflcctarray consists of square patches terminated in open stubs to provide necessary phase compensation. In this paper, preliminary results will be presented and the feasibility of such compensation scheme will be discussed.

Influence of vorticity distribution on singularities in linearized supersonic flow

NASA Astrophysics Data System (ADS)

Gopal, Vijay; Maddalena, Luca

2018-05-01

The linearized steady three-dimensional supersonic flow can be analyzed using a vector potential approach which transforms the governing equation to a standard form of two-dimensional wave equation. Of particular interest are the canonical horseshoe line-vortex distribution and the resulting induced velocity field in supersonic flow. In this case, the singularities are present at the vortex line itself and also at the surface of the cone of influence originating from the vertices of the horseshoe structure. This is a characteristic of the hyperbolic nature of the flow which renders the study of supersonic vortex dynamics a challenging task. It is conjectured in this work that the presence of the singularity at the cone of influence is associated with the step-function nature of the vorticity distribution specified in the canonical case. At the phenomenological level, if one considers the three-dimensional steady supersonic flow, then a sudden appearance of a line-vortex will generate a ripple of singularities in the induced velocity field which convect downstream and laterally spread, at the most, to the surface of the cone of influence. Based on these findings, this work includes an exploration of potential candidates for vorticity distributions that eliminate the singularities at the cone of influence. The analysis of the resulting induced velocity field is then compared with the canonical case, and it is observed that the singularities were successfully eliminated. The manuscript includes an application of the proposed method to study the induced velocity field in a confined supersonic flow.

Electron acceleration and emission in a field of a plane and converging dipole wave of relativistic amplitudes with the radiation reaction force taken into account

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

Bashinov, Aleksei V; Gonoskov, Arkady A; Kim, A V

2013-04-30

A comparative analysis is performed of the electron emission characteristics as the electrons move in laser fields with ultra-relativistic intensity and different configurations corresponding to a plane or tightly focused wave. For a plane travelling wave, analytical expressions are derived for the emission characteristics, and it is shown that the angular distribution of the radiation intensity changes qualitatively even when the wave intensity is much less than that in the case of the radiation-dominated regime. An important conclusion is drawn that the electrons in a travelling wave tend to synchronised motion under the radiation reaction force. The characteristic features ofmore » the motion of electrons are found in a converging dipole wave, associated with the curvature of the phase front and nonuniformity of the field distribution. The values of the maximum achievable longitudinal momenta of electrons accelerated to the centre, as well as their distribution function are determined. The existence of quasi-periodic trajectories near the focal region of the dipole wave is shown, and the characteristics of the emission of both accelerated and oscillating electrons are analysed. (extreme light fields and their applications)« less

Helicon mysteries: fitting a plane wave into a cylinder

NASA Astrophysics Data System (ADS)

Boswell, Rod

2011-10-01

Since the first reports in the 1960s, the dispersion of helicon waves in a plasma cylinder has been difficult to describe theoretically for axial wavelengths that are greater than the plasma radius. About 10 years ago, Breizman and Arefiev showed how radial density gradients make the plasma column similar to a coaxial cable, allowing the helicon waves to propagate below the cut-off frequency. The resulting dispersion relation is similar to that of a plane wave propagating parallel to the magnetic field. A few years later, Degeling et. al. presented experimental evidence demonstrating such a plane wave dispersion for a broad range of axial wave numbers. The reason lies in the decoupling of the Hall and electron inertial terms in the dispersion, the former describing the electromagnetic propagation and the latter the electrostatic propagation. Combining the experimental and theoretical results has recently thrown further light on this phenomenon that is applicable to both space and laboratory situations. Radially Localized Helicon Modes in Nonuniform Plasma, Boris N. Breizman and Alexey V. Arefiev, Phys. Rev. Letts. 84, 3863 (2000). Transitions from electrostatic to electromagnetic whistler wave excitation, A. W. Degeling, G. G. Borg and R. W. Boswell, Phys. Plasmas, 11, 2144, (2004).

Multifractal and Singularity Maps of soil surface moisture distribution derived from 2D image analysis.

NASA Astrophysics Data System (ADS)

Cumbrera, Ramiro; Millán, Humberto; Martín-Sotoca, Juan Jose; Pérez Soto, Luis; Sanchez, Maria Elena; Tarquis, Ana Maria

2016-04-01

Soil moisture distribution usually presents extreme variation at multiple spatial scales. Image analysis could be a useful tool for investigating these spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to describe the local scaling of apparent soil moisture distribution and (ii) to define apparent soil moisture patterns from vertical planes of Vertisol pit images. Two soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. One was excavated in April/2011 and the other pit was established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. For more details see Cumbrera et al. (2012). Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, using the concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012). This method is based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. We have applied it to each soil image. The results show that, in spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used to study the dynamical change of soil moisture sampling in agreement with previous results (Millán et al., 2016). REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Cumbrera, R., Ana M. Tarquis, Gabriel Gascó, Humberto Millán (2012) Fractal scaling of apparent soil moisture estimated from vertical planes of Vertisol pit images. Journal of Hydrology (452-453), 205-212. Martin Sotoca; J.J. Antonio Saa-Requejo, Juan Grau and Ana M. Tarquis (2016). Segmentation of singularity maps in the context of soil porosity. Geophysical Research Abstracts, 18, EGU2016-11402. Millán, H., Cumbrera, R. and Ana M. Tarquis (2016) Multifractal and Levy-stable statistics of soil surface moisture distribution derived from 2D image analysis. Applied Mathematical Modelling, 40(3), 2384-2395.

An Experimental Study Comparing Droplet Production by a Strong Plunging and a Weak Spilling Breaking Water Waves

NASA Astrophysics Data System (ADS)

Erinin, Martin; Wang, Dan; Towle, David; Liu, Xinan; Duncan, James

2017-11-01

In this study, the production of droplets by two mechanically generated breaking water waves is investigated in a wave tank. A strong plunging breaker and weak spilling breaker are generated repeatedly with a programmable wave maker by using two dispersively focused wave packets with the same wave maker motion profile shape (average frequency 1.15 Hz) and two overall amplitude factors. The profile histories of the breaking wave crests along the center plane of the tank are measured using cinematic laser-induced fluorescence. The droplets are measured using a high speed (650 Hz) cinematic digital in-line holographic system positioned at various locations along a horizontal plane that is 1 cm above the maximum wave crest height. The measurement plane covers the entire region in the tank where the wave breaks. The holographic system is used to obtain the droplet diameters (d, for d >100 microns) and the three components of the droplet velocities. From these measurements and counting only the droplets that are moving up, the spatio-temporal distribution of droplet generation by the two breaking waves is obtained. The main features of the droplet generation are correlated with the features and phases of the breaking process. The support of the National Science Foundation under Grant OCE0751853 from the Division of Ocean Sciences is gratefully acknowledged.

An ansatz for solving nonlinear partial differential equations in mathematical physics.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

Peri-Elastodynamic Simulations of Guided Ultrasonic Waves in Plate-Like Structure with Surface Mounted PZT.

PubMed

Patra, Subir; Ahmed, Hossain; Banerjee, Sourav

2018-01-18

Peridynamic based elastodynamic computation tool named Peri-elastodynamics is proposed herein to simulate the three-dimensional (3D) Lamb wave modes in materials for the first time. Peri-elastodynamics is a nonlocal meshless approach which is a scale-independent generalized technique to visualize the acoustic and ultrasonic waves in plate-like structure, micro-electro-mechanical systems (MEMS) and nanodevices for their respective characterization. In this article, the characteristics of the fundamental Lamb wave modes are simulated in a sample plate-like structure. Lamb wave modes are generated using a surface mounted piezoelectric (PZT) transducer which is actuated from the top surface. The proposed generalized Peri-elastodynamics method is not only capable of simulating two dimensional (2D) in plane wave under plane strain condition formulated previously but also capable of accurately simulating the out of plane Symmetric and Antisymmetric Lamb wave modes in plate like structures in 3D. For structural health monitoring (SHM) of plate-like structures and nondestructive evaluation (NDE) of MEMS devices, it is necessary to simulate the 3D wave-damage interaction scenarios and visualize the different wave features due to damages. Hence, in addition, to simulating the guided ultrasonic wave modes in pristine material, Lamb waves were also simulated in a damaged plate. The accuracy of the proposed technique is verified by comparing the modes generated in the plate and the mode shapes across the thickness of the plate with theoretical wave analysis.

Quantum-shutter approach to tunneling time scales with wave packets

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

Yamada, Norifumi; Garcia-Calderon, Gaston; Villavicencio, Jorge

2005-07-15

The quantum-shutter approach to tunneling time scales [G. Garcia-Calderon and A. Rubio, Phys. Rev. A 55, 3361 (1997)], which uses a cutoff plane wave as the initial condition, is extended to consider certain type of wave packet initial conditions. An analytical expression for the time-evolved wave function is derived. The time-domain resonance, the peaked structure of the probability density (as the function of time) at the exit of the barrier, originally found with the cutoff plane wave initial condition, is studied with the wave packet initial conditions. It is found that the time-domain resonance is not very sensitive to themore » width of the packet when the transmission process occurs in the tunneling regime.« less

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

Li Jibin; Qiao Zhijun

This paper deals with the following equation m{sub t}=(1/2)(1/m{sup k}){sub xxx}-(1/2)(1/m{sup k}){sub x}, which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the casesmore » of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.« less

Formulation of the rotational transformation of wave fields and their application to digital holography.

PubMed

Matsushima, Kyoji

2008-07-01

Rotational transformation based on coordinate rotation in Fourier space is a useful technique for simulating wave field propagation between nonparallel planes. This technique is characterized by fast computation because the transformation only requires executing a fast Fourier transform twice and a single interpolation. It is proved that the formula of the rotational transformation mathematically satisfies the Helmholtz equation. Moreover, to verify the formulation and its usefulness in wave optics, it is also demonstrated that the transformation makes it possible to reconstruct an image on arbitrarily tilted planes from a wave field captured experimentally by using digital holography.

Brillouin light scattering on Fe/Cr/Fe thin-film sandwiches

NASA Astrophysics Data System (ADS)

Kabos, P.; Patton, C. E.; Dima, M. O.; Church, D. B.; Stamps, R. L.; Camley, R. E.

1994-04-01

The aim of this work is to perform Brillouin light scattering measurements of the field and wave-vector dependencies of the frequencies of the fundamental magnetic excitations in Fe/Cr/Fe thin film sandwiches with antiferromagnetically coupled magnetic layers, correlate these results with magnetization versus field data on such films, and compare the observed dependencies with theory for low-wave number spin-wave modes in sandwich films. The measurements were made for the in-plane static magnetic field H along the crystallographic and directions, with the in-plane wave vector k always perpendicular to H.

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.

On the finite length-scale of compressible shock-waves formed in free-surface flows of dry granular materials down a slope

NASA Astrophysics Data System (ADS)

Faug, Thierry

2017-04-01

The Rankine-Hugoniot jump conditions traditionally describe the theoretical relationship between the equilibrium state on both sides of a shock-wave. They are based on the crucial assumption that the length-scale needed to adjust the equilibrium state upstream of the shock to downstream of it is too small to be of significance to the problem. They are often used with success to describe the shock-waves in a number of applications found in both fluid and solid mechanics. However, the relations based on jump conditions at singular surfaces may fail to capture some features of the shock-waves formed in complex materials, such as granular matter. This study addresses the particular problem of compressible shock-waves formed in flows of dry granular materials down a slope. This problem is for instance relevant to full-scale geophysical granular flows in interaction with natural obstacles or man-made structures, such as topographical obstacles or mitigation dams respectively. Steady-state jumps formed in granular flows and travelling shock-waves produced at the impact of a granular avalanche-flow with a rigid wall are considered. For both situations, new analytical relations which do not consider that the granular shock-wave shrinks into a singular surface are derived, by using balance equations in their depth-averaged forms for mass and momentum. However, these relations need additional inputs that are closure relations for the size and the shape of the shock-wave, and a relevant constitutive friction law. Small-scale laboratory tests and numerical simulations based on the discrete element method are shortly presented and used to infer crucial information needed for the closure relations. This allows testing some predictive aspects of the simple analytical approach proposed for both steady-state and travelling shock-waves formed in free-surface flows of dry granular materials down a slope.

Hyperasymptotics and quark-hadron duality violations in QCD

NASA Astrophysics Data System (ADS)

Boito, Diogo; Caprini, Irinel; Golterman, Maarten; Maltman, Kim; Peris, Santiago

2018-03-01

We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex q2 plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality-violating contributions. Starting with the assumption that for QCD at Nc=∞ the spectrum approaches a Regge trajectory at large energy, we obtain an expression for quark-hadron duality violations at large, but finite Nc.

Exact solution for an optimal impermeable parachute problem

NASA Astrophysics Data System (ADS)

Lupu, Mircea; Scheiber, Ernest

2002-10-01

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.

Photonic band structures solved by a plane-wave-based transfer-matrix method.

PubMed

Li, Zhi-Yuan; Lin, Lan-Lan

2003-04-01

Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method.

Quantum scattering beyond the plane-wave approximation

NASA Astrophysics Data System (ADS)

Karlovets, Dmitry

2017-12-01

While a plane-wave approximation in high-energy physics works well in a majority of practical cases, it becomes inapplicable for scattering of the vortex particles carrying orbital angular momentum, of Airy beams, of the so-called Schrödinger cat states, and their generalizations. Such quantum states of photons, electrons and neutrons have been generated experimentally in recent years, opening up new perspectives in quantum optics, electron microscopy, particle physics, and so forth. Here we discuss the non-plane-wave effects in scattering brought about by the novel quantum numbers of these wave packets. For the well-focused electrons of intermediate energies, already available at electron microscopes, the corresponding contribution can surpass that of the radiative corrections. Moreover, collisions of the cat-like superpositions of such focused beams with atoms allow one to probe effects of the quantum interference, which have never played any role in particle scattering.

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 singular and highly oscillatory properties of the Green function for ship motions

NASA Astrophysics Data System (ADS)

Chen, Xiao-Bo; Xiong Wu, Guo

2001-10-01

The Green function used for analysing ship motions in waves is the velocity potential due to a point source pulsating and advancing at a uniform forward speed. The behaviour of this function is investigated, in particular for the case when the source is located at or close to the free surface. In the far field, the Green function is represented by a single integral along one closed dispersion curve and two open dispersion curves. The single integral along the open dispersion curves is analysed based on the asymptotic expansion of a complex error function. The singular and highly oscillatory behaviour of the Green function is captured, which shows that the Green function oscillates with indefinitely increasing amplitude and indefinitely decreasing wavelength, when a field point approaches the track of the source point at the free surface. This sheds some light on the nature of the difficulties in the numerical methods used for predicting the motion of a ship advancing in waves.

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.

Revisiting the Plane Electromagnetic Wave Transmission and Reflection Coefficients for the Layer with AN Alternating-Sign Disturbance of Relative Dielectric Permittivity

NASA Astrophysics Data System (ADS)

Milov, V. R.; Kogan, L. P.; Gorev, P. V.; Kuzmichev, P. N.; Egorova, P. A.

2017-01-01

In this paper, we consider the question of the plane electromagnetic wave incidence at the inhomogeneity with an arbitrary profile of the relative permittivity disturbance. Module estimation of Neumann series remainder is carried out for the field of the wave passing through the nonhomogeneous section. Based on that, the number of summands in the series, required to calculate with a given accuracy, the transmission and reflection coefficients have been determined.

Delay-Encoded Harmonic Imaging (DE-HI) in Multiplane-Wave Compounding.

PubMed

Gong, Ping; Song, Pengfei; Chen, Shigao

2017-04-01

The development of ultrafast ultrasound imaging brings great opportunities to improve imaging technologies such as shear wave elastography and ultrafast Doppler imaging. In ultrafast imaging, several tilted plane or diverging wave images are coherently combined to form a compounded image, leading to trade-offs among image signal-to-noise ratio (SNR), resolution, and post-compounded frame rate. Multiplane wave (MW) imaging is proposed to solve this trade-off by encoding multiple plane waves with Hadamard matrix during one transmission event (i.e. pulse-echo event), to improve image SNR without sacrificing the resolution or frame rate. However, it suffers from stronger reverberation artifacts in B-mode images compared to standard plane wave compounding due to longer transmitted pulses. If harmonic imaging can be combined with MW imaging, the reverberation artifacts and other clutter noises such as sidelobes and multipath scattering clutters should be suppressed. The challenge, however, is that the Hadamard codes used in MW imaging cannot encode the 2 nd harmonic component by inversing the pulse polarity. In this paper, we propose a delay-encoded harmonic imaging (DE-HI) technique to encode the 2 nd harmonic with a one quarter period delay calculated at the transmit center frequency, rather than reversing the pulse polarity during multiplane wave emissions. Received DE-HI signals can then be decoded in the frequency domain to recover the signals as in single plane wave emissions, but mainly with improved SNR at the 2 nd harmonic component instead of the fundamental component. DE-HI was tested experimentally with a point target, a B-mode imaging phantom, and in-vivo human liver imaging. Improvements in image contrast-to-noise ratio (CNR), spatial resolution, and lesion-signal-to-noise ratio ( l SNR) have been achieved compared to standard plane wave compounding, MW imaging, and standard harmonic imaging (maximal improvement of 116% on CNR and 115% on l SNR as compared to standard HI around 55 mm depth in the B-mode imaging phantom study). The potential high frame rate and the stability of encoding and decoding processes of DE-HI were also demonstrated, which made DE-HI promising for a wide spectrum of imaging applications.

The synoptic setting and possible energy sources for mesoscale wave disturbances

NASA Technical Reports Server (NTRS)

Uccellini, Louis W.; Koch, Steven E.

1987-01-01

Published data on 13 cases of mesoscale wave disturbances and their environment were examined to isolate common features for these cases and to determine possible energy sources for the waves. These events are characterized by either a singular wave of depression or wave packets with periods of 1-4 h, horizontal wavelengths of 50-500 km, and surface-pressure perturbation amplitudes of 0.2-7.0 mb. These wave events are shown to be associated with a distinct synoptic pattern (including the existence of a strong inversion in the lower troposphere and the propagation of a jet streak toward a ridge axis in the upper troposphere) while displaying little correlation with the presence of convective storm cells. The observed development of the waves is consistent with the hypothesis that the energy source needed to initiate and sustain the wave disturbances may be related to a geostrophic adjustment process associated with upper-tropospheric jet streaks.

Recent Results on Singularity Strengths

NASA Astrophysics Data System (ADS)

Nolan, Brien

2002-12-01

In this contribution, we review some recent results on strengths of singularities. In a space-time (M,g), let γ[τ0, 0) → M be an incomplete, inextendible causal geodesic, affinely parametrised by τ, tangent ěc k. Let Jτ1 :=set of Jacobi fields along γ, orthogonal to γ and vanishing at time τ1 ≥ τ0 i.e. ěc ξ ∈ J{τ 1 } iff D2ξa = -Rbcdakbkdξc, gabξakb = 0, and ěc ξ (τ 1 ) = 0. Vτ1(τ) := volume element defined by full set of independent elements of Jτ1 (2-dim for null geodesies, 3-dim for time-like); Vτ1 := ∥Vτ1∥. Definition (Tipler 1977): γ terminates in a gravitationally strong singularity if for all 0 > τ1 ≥ τ0, lim infτ→0- Vτ1(τ) = 0. γ... gravitationally weak ... lim infτ→0- Vτ1(τ) > 0. The interpretation is that at a strong singularity, an extended body, e.g. a gravitational wave detector, is crushed to zero volume by the singularity. Tipler's definition does not take account of the possibility that (i) V → ∞ or (ii) V → finite, non-zero value, but with infinite stretching/crushing in orthogonal directions ('spaghettifying singularity'). Extended definition (Nolan 1999): strong if either V → 0,∞ or if for every τ1, there is an element ěc ξ of Jτ1 satisfying ||ěc ξ || -> 0. Otherwise weak. (Ori 2000): singularity is 'deformationally strong' if either (i) it is Tipler-strong or (ii) for every τ1, there is an element ěc ξ of Jτ1 satisfying ||ěc ξ || -> ∞ . Otherwise, deformationally weak...

Swinging Atwood's Machine

NASA Astrophysics Data System (ADS)

Tufillaro, Nicholas B.; Abbott, Tyler A.; Griffiths, David J.

1984-10-01

We examine the motion of an Atwood's Machine in which one of the masses is allowed to swing in a plane. Computer studies reveal a rich variety of trajectories. The orbits are classified (bounded, periodic, singular, and terminating), and formulas for the critical mass ratios are developed. Perturbative techniques yield good approximations to the computer-generated trajectories. The model constitutes a simple example of a nonlinear dynamical system with two degrees of freedom.

New fundamental parameters for attitude representation

NASA Astrophysics Data System (ADS)

Patera, Russell P.

2017-08-01

A new attitude parameter set is developed to clarify the geometry of combining finite rotations in a rotational sequence and in combining infinitesimal angular increments generated by angular rate. The resulting parameter set of six Pivot Parameters represents a rotation as a great circle arc on a unit sphere that can be located at any clocking location in the rotation plane. Two rotations are combined by linking their arcs at either of the two intersection points of the respective rotation planes. In a similar fashion, linking rotational increments produced by angular rate is used to derive the associated kinematical equations, which are linear and have no singularities. Included in this paper is the derivation of twelve Pivot Parameter elements that represent all twelve Euler Angle sequences, which enables efficient conversions between Pivot Parameters and any Euler Angle sequence. Applications of this new parameter set include the derivation of quaternions and the quaternion composition rule, as well as, the derivation of the analytical solution to time dependent coning motion. The relationships between Pivot Parameters and traditional parameter sets are included in this work. Pivot Parameters are well suited for a variety of aerospace applications due to their effective composition rule, singularity free kinematic equations, efficient conversion to and from Euler Angle sequences and clarity of their geometrical foundation.

Quantum square-well with logarithmic central spike

NASA Astrophysics Data System (ADS)

Znojil, Miloslav; Semorádová, Iveta

2018-01-01

Singular repulsive barrier V (x) = -gln(|x|) inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction ℒeff(x) = -gln[ψ∗(x)ψ(x)] in nonlinear Schrödinger equation. In the linearized case, Rayleigh-Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small g or after an amendment of the unperturbed Hamiltonian. At any spike strength g, the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables x = expy which interchanges the roles of the asymptotic and central boundary conditions.

Topological transformation of fractional optical vortex beams using computer generated holograms

NASA Astrophysics Data System (ADS)

Maji, Satyajit; Brundavanam, Maruthi M.

2018-04-01

Optical vortex beams with fractional topological charges (TCs) are generated by the diffraction of a Gaussian beam using computer generated holograms embedded with mixed screw-edge dislocations. When the input Gaussian beam has a finite wave-front curvature, the generated fractional vortex beams show distinct topological transformations in comparison to the integer charge optical vortices. The topological transformations at different fractional TCs are investigated through the birth and evolution of the points of phase singularity, the azimuthal momentum transformation, occurrence of critical points in the transverse momentum and the vorticity around the singular points. This study is helpful to achieve better control in optical micro-manipulation applications.

Compacted dimensions and singular plasmonic surfaces.

PubMed

Pendry, J B; Huidobro, Paloma Arroyo; Luo, Yu; Galiffi, Emanuele

2017-11-17

In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer. Copyright © 2017, American Association for the Advancement of Science.

Evaluating the Improvement in Shear Wave Speed Image Quality Using Multidimensional Directional Filters in the Presence of Reflection Artifacts.

PubMed

Lipman, Samantha L; Rouze, Ned C; Palmeri, Mark L; Nightingale, Kathryn R

2016-08-01

Shear waves propagating through interfaces where there is a change in stiffness cause reflected waves that can lead to artifacts in shear wave speed (SWS) reconstructions. Two-dimensional (2-D) directional filters are commonly used to reduce in-plane reflected waves; however, SWS artifacts arise from both in- and out-of-imaging-plane reflected waves. Herein, we introduce 3-D shear wave reconstruction methods as an extension of the previous 2-D estimation methods and quantify the reduction in image artifacts through the use of volumetric SWS monitoring and 4-D-directional filters. A Gaussian acoustic radiation force impulse excitation was simulated in phantoms with Young's modulus ( E ) of 3 kPa and a 5-mm spherical lesion with E = 6, 12, or 18.75 kPa. The 2-D-, 3-D-, and 4-D-directional filters were applied to the displacement profiles to reduce in-and out-of-plane reflected wave artifacts. Contrast-to-noise ratio and SWS bias within the lesion were calculated for each reconstructed SWS image to evaluate the image quality. For 2-D SWS image reconstructions, the 3-D-directional filters showed greater improvements in image quality than the 2-D filters, and the 4-D-directional filters showed marginal improvement over the 3-D filters. Although 4-D-directional filters can further reduce the impact of large magnitude out-of-plane reflection artifacts in SWS images, computational overhead and transducer costs to acquire 3-D data may outweigh the modest improvements in image quality. The 4-D-directional filters have the largest impact in reducing reflection artifacts in 3-D SWS volumes.

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.

Visible and shortwave infrared focal planes for remote sensing instruments

NASA Astrophysics Data System (ADS)

Tower, J. R.; McCarthy, B. M.; Pellon, L. E.; Strong, R. T.; Elabd, H.

1984-01-01

The development of solid-state sensor technology for multispectral linear array (MLA) instruments is described. A buttable four-spectral-band linear-format CCD and a buttable two-spectral band linear-format short-wave IR CCD have been designed, and first samples have been demonstrated. In addition, first-sample four-band interference filters have been fabricated, and hybrid packaging technology is being developed. Based on this development work, the design and construction of focal planes for a Shuttle sortie MLA instrument have begun. This work involves a visible and near-IR focal plane with 2048 pixels x 4 spectral bands and a short-wave IR focal plane with 1024 pixels x 2 spectral bands.

A Cartesian parametrization for the numerical analysis of material instability

DOE PAGES

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.; ...

2016-02-25

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

A Cartesian parametrization for the numerical analysis of material instability

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

Mota, Alejandro; Chen, Qiushi; Foulk, III, James W.

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, themore » performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.« less

Wavelets on the Group SO(3) and the Sphere S3

NASA Astrophysics Data System (ADS)

Bernstein, Swanhild

2007-09-01

The construction of wavelets relies on translations and dilations which are perfectly given in R. On the sphere translations can be considered as rotations but it difficult to say what are dilations. For the 2-dimensional sphere there exist two different approaches to obtain wavelets which are worth to be considered. The first concept goes back to Freeden and collaborators [2] which defines wavelets by means of kernels of spherical singular integrals. The other concept developed by Antoine and Vandergheynst and coworkers [3] is a purely group theoretical approach and defines dilations as dilations in the tangent plane. Surprisingly both concepts coincides for zonal functions. We will define wavelets on the 3-dimensional sphere by means of kernels of singular integrals and demonstrate that wavelets constructed by Antoine and Vandergheynst for zonal functions meet our definition.

Wave-function functionals

NASA Astrophysics Data System (ADS)

Pan, Xiao-Yin; Slamet, Marlina; Sahni, Viraht

2010-04-01

We extend our prior work on the construction of variational wave functions ψ that are functionals of functions χ:ψ=ψ[χ] rather than simply being functions. In this manner, the space of variations is expanded over those of traditional variational wave functions. In this article we perform the constrained search over the functions χ chosen such that the functional ψ[χ] satisfies simultaneously the constraints of normalization and the exact expectation value of an arbitrary single- or two-particle Hermitian operator, while also leading to a rigorous upper bound to the energy. As such the wave function functional is accurate not only in the region of space in which the principal contributions to the energy arise but also in the other region of the space represented by the Hermitian operator. To demonstrate the efficacy of these ideas, we apply such a constrained search to the ground state of the negative ion of atomic hydrogen H-, the helium atom He, and its positive ions Li+ and Be2+. The operators W whose expectations are obtained exactly are the sum of the single-particle operators W=∑irin,n=-2,-1,1,2, W=∑iδ(ri), W=-(1)/(2)∑i∇i2, and the two-particle operators W=∑nun,n=-2,-1,1,2, where u=|ri-rj|. Comparisons with the method of Lagrangian multipliers and of other constructions of wave-function functionals are made. Finally, we present further insights into the construction of wave-function functionals by studying a previously proposed construction of functionals ψ[χ] that lead to the exact expectation of arbitrary Hermitian operators. We discover that analogous to the solutions of the Schrödinger equation, there exist ψ[χ] that are unphysical in that they lead to singular values for the expectations. We also explain the origin of the singularity.

Japanese space gravitational wave antenna DECIGO and DPF

NASA Astrophysics Data System (ADS)

Musha, Mitsuru

2017-11-01

The gravitational wave detection will open a new gravitational wave astronomy, which gives a fruitful insight about early universe or birth and death of stars. In order to detect gravitational wave, we planed a space gravitational wave detector, DECIGO (DECi-heltz Interferometer Gravitational wave Observatory), which consists of three drag-free satellites forming triangle shaped Fabry-Perot laser interferometer with the arm length of 1000 km, and whose strain sensitivity is designed to be 2x10-24 /√Hz around 0.1 Hz. Before launching DECIGO around 2030, a milestone mission named DECIGO pathfinder (DPF) is planed to be launched whose main purpose is the feasibility test of the key technologies for DECIGO. In the present paper, the conceptual design and current status of DECIGO and DPF are reviewed.

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.

Excitation of plane Lamb wave in plate-like structures under applied surface loading

NASA Astrophysics Data System (ADS)

Zhou, Kai; Xu, Xinsheng; Zhao, Zhen; Yang, Zhengyan; Zhou, Zhenhuan; Wu, Zhanjun

2018-02-01

Lamb waves play an important role in structure health monitoring (SHM) systems. The excitation of Lamb waves has been discussed for a long time with absorbing results. However, little effort has been made towards the precise characterization of Lamb wave excitation by various transducer models with mathematical foundation. In this paper, the excitation of plane Lamb waves with plane strain assumption in isotropic plate structures under applied surface loading is solved with the Hamiltonian system. The response of the Lamb modes excited by applied loading is expressed analytically. The effect of applied loading is divided into the product of two parts as the effect of direction and the effect of distribution, which can be changed by selecting different types of transducer and the corresponding transducer configurations. The direction of loading determines the corresponding displacement of each mode. The effect of applied loading on the in-plane and normal directions depends on the in-plane and normal displacements at the surface respectively. The effect of the surface loading distribution on the Lamb mode amplitudes is mainly reflected by amplitude versus frequency or wavenumber. The frequencies at which the maxima and minima of the S0 or A0 mode response occur depend on the distribution of surface loading. The numerical results of simulations conducted on an infinite aluminum plate verify the theoretical prediction of not only the direction but also the distribution of applied loading. A pure S0 or A0 mode can be excited by selecting the appropriate direction and distribution at the corresponding frequency.

Exact soliton of (2 + 1)-dimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rizvi, S. T. R.; Ali, K.; Bashir, S.; Younis, M.; Ashraf, R.; Ahmad, M. O.

2017-07-01

The nonlinear fractional Schrödinger equation is the basic equation of fractional quantum mechanics introduced by Nick Laskin in 2002. We apply three tools to solve this mathematical-physical model. First, we find the solitary wave solutions including the trigonometric traveling wave solutions, bell and kink shape solitons using the F-expansion and Improve F-expansion method. We also obtain the soliton solution, singular soliton solutions, rational function solution and elliptic integral function solutions, with the help of the extended trial equation method.

Visualizing the Vibration of Laryngeal Tissue during Phonation Using Ultrafast Plane Wave Ultrasonography.

PubMed

Jing, Bowen; Tang, Shanshan; Wu, Liang; Wang, Supin; Wan, Mingxi

2016-12-01

Ultrafast plane wave ultrasonography is employed in this study to visualize the vibration of the larynx and quantify the vibration phase as well as the vibration amplitude of the laryngeal tissue. Ultrasonic images were obtained at 5000 to 10,000 frames/s in the coronal plane at the level of the glottis. Although the image quality degraded when the imaging mode was switched from conventional ultrasonography to ultrafast plane wave ultrasonography, certain anatomic structures such as the vocal folds, as well as the sub- and supraglottic structures, including the false vocal folds, can be identified in the ultrafast plane wave ultrasonic image. The periodic vibration of the vocal fold edge could be visualized in the recorded image sequence during phonation. Furthermore, a motion estimation method was used to quantify the displacement of laryngeal tissue from hundreds of frames of ultrasonic data acquired. Vibratory displacement waveforms of the sub- and supraglottic structures were successfully obtained at a high level of ultrasonic signal correlation. Moreover, statistically significant differences in vibration pattern between the sub- and supraglottic structures were found. Variation of vibration amplitude along the subglottic mucosal surface is significantly smaller than that along the supraglottic mucosal surface. Phase delay of vibration along the subglottic mucosal surface is significantly smaller than that along the supraglottic mucosal surface. Copyright © 2016 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Laser backscattered from partially convex targets of large sizes in random media for E-wave polarization.

PubMed

El-Ocla, Hosam

2006-08-01

The characteristics of a radar cross section (RCS) of partially convex targets with large sizes up to five wavelengths in free space and random media are studied. The nature of the incident wave is an important factor in remote sensing and radar detection applications. I investigate the effects of beam wave incidence on the performance of RCS, drawing on the method I used in a previous study on plane-wave incidence. A beam wave can be considered a plane wave if the target size is smaller than the beam width. Therefore, to have a beam wave with a limited spot on the target, the target size should be larger than the beam width (assuming E-wave incidence wave polarization. The effects of the target configuration, random medium parameters, and the beam width on the laser RCS and the enhancement in the radar cross section are numerically analyzed, resulting in the possibility of having some sort of control over radar detection using beam wave incidence.

Emergent geometries and nonlinear-wave dynamics in photon fluids.

PubMed

Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D

2016-03-22

Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.

Emergent geometries and nonlinear-wave dynamics in photon fluids

NASA Astrophysics Data System (ADS)

Marino, F.; Maitland, C.; Vocke, D.; Ortolan, A.; Faccio, D.

2016-03-01

Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.

Gauge theories with time dependent couplings and their cosmological duals

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

Awad, Adel; Center for Theoretical Physics, British University of Egypt, Sherouk City 11837, P.O. Box 43; Das, Sumit R.

2009-02-15

We consider the N=4 super Yang-Mills theory in flat 3+1-dimensional space-time with a time dependent coupling constant which vanishes at t=0, like g{sub YM}{sup 2}=t{sup p}. In an analogous quantum mechanics toy model we find that the response is singular. The energy diverges at t=0, for a generic state. In addition, if p>1 the phase of the wave function has a wildly oscillating behavior, which does not allow it to be continued past t=0. A similar effect would make the gauge theory singular as well, though nontrivial effects of renormalization could tame this singularity and allow a smooth continuation beyondmore » t=0. The gravity dual in some cases is known to be a time dependent cosmology which exhibits a spacelike singularity at t=0. Our results, if applicable in the gauge theory for the case of the vanishing coupling, imply that the singularity is a genuine sickness and does not admit a meaningful continuation. When the coupling remains nonzero and becomes small at t=0, the curvature in the bulk becomes of order string scale. The gauge theory now admits a time evolution beyond this point. In this case, a finite amount of energy is produced which possibly thermalizes and leads to a black hole in the bulk.« less

Nanoscale measurement of Nernst effect in two-dimensional charge density wave material 1T-TaS 2

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

Wu, Stephen M.; Luican-Mayer, Adina; Bhattacharya, Anand

Advances in nanoscale material characterization on two-dimensional van der Waals layered materials primarily involve their optical and electronic properties. The thermal properties of these materials are harder to access due to the difficulty of thermal measurements at the nanoscale. In this work, we create a nanoscale magnetothermal device platform to access the basic out-of-plane magnetothermal transport properties of ultrathin van der Waals materials. Specifically, the Nernst effect in the charge density wave transition metal dichalcogenide 1T-TaS 2 is examined on nano-thin flakes in a patterned device structure. It is revealed that near the commensurate charge density wave (CCDW) to nearlymore » commensurate charge density wave (NCCDW) phase transition, the polarity of the Nernst effect changes. Since the Nernst effect is especially sensitive to changes in the Fermi surface, this suggests that large changes are occurring in the out-of-plane electronic structure of 1T-TaS 2, which are otherwise unresolved in just in-plane electronic transport measurements. This may signal a coherent evolution of out-of-plane stacking in the CCDW! NCCDW transition.« less

Sound pressure distribution within natural and artificial human ear canals: forward stimulation.

PubMed

Ravicz, Michael E; Tao Cheng, Jeffrey; Rosowski, John J

2014-12-01

This work is part of a study of the interaction of sound pressure in the ear canal (EC) with tympanic membrane (TM) surface displacement. Sound pressures were measured with 0.5-2 mm spacing at three locations within the shortened natural EC or an artificial EC in human temporal bones: near the TM surface, within the tympanic ring plane, and in a plane transverse to the long axis of the EC. Sound pressure was also measured at 2-mm intervals along the long EC axis. The sound field is described well by the size and direction of planar sound pressure gradients, the location and orientation of standing-wave nodal lines, and the location of longitudinal standing waves along the EC axis. Standing-wave nodal lines perpendicular to the long EC axis are present on the TM surface >11-16 kHz in the natural or artificial EC. The range of sound pressures was larger in the tympanic ring plane than at the TM surface or in the transverse EC plane. Longitudinal standing-wave patterns were stretched. The tympanic-ring sound field is a useful approximation of the TM sound field, and the artificial EC approximates the natural EC.

Evolution of the frequency chirp of Gaussian pulses and beams when passing through a pulse compressor.

PubMed

Li, Derong; Lv, Xiaohua; Bowlan, Pamela; Du, Rui; Zeng, Shaoqun; Luo, Qingming

2009-09-14

The evolution of the frequency chirp of a laser pulse inside a classical pulse compressor is very different for plane waves and Gaussian beams, although after propagating through the last (4th) dispersive element, the two models give the same results. In this paper, we have analyzed the evolution of the frequency chirp of Gaussian pulses and beams using a method which directly obtains the spectral phase acquired by the compressor. We found the spatiotemporal couplings in the phase to be the fundamental reason for the difference in the frequency chirp acquired by a Gaussian beam and a plane wave. When the Gaussian beam propagates, an additional frequency chirp will be introduced if any spatiotemporal couplings (i.e. angular dispersion, spatial chirp or pulse front tilt) are present. However, if there are no couplings present, the chirp of the Gaussian beam is the same as that of a plane wave. When the Gaussian beam is well collimated, the introduced frequency chirp predicted by the plane wave and Gaussian beam models are in closer agreement. This work improves our understanding of pulse compressors and should be helpful for optimizing dispersion compensation schemes in many applications of femtosecond laser pulses.

Wideband radar cross section reduction using two-dimensional phase gradient metasurfaces

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

Li, Yongfeng; Qu, Shaobo; Wang, Jiafu

2014-06-02

Phase gradient metasurface (PGMs) are artificial surfaces that can provide pre-defined in-plane wave-vectors to manipulate the directions of refracted/reflected waves. In this Letter, we propose to achieve wideband radar cross section (RCS) reduction using two-dimensional (2D) PGMs. A 2D PGM was designed using a square combination of 49 split-ring sub-unit cells. The PGM can provide additional wave-vectors along the two in-plane directions simultaneously, leading to either surface wave conversion, deflected reflection, or diffuse reflection. Both the simulation and experiment results verified the wide-band, polarization-independent, high-efficiency RCS reduction induced by the 2D PGM.

CMS-Wave

DTIC Science & Technology

2015-10-30

Coastal Inlets Research Program CMS -Wave CMS -Wave is a two-dimensional spectral wind-wave generation and transformation model that employs a forward...marching, finite-difference method to solve the wave action conservation equation. Capabilities of CMS -Wave include wave shoaling, refraction... CMS -Wave can be used in either on a half- or full-plane mode, with primary waves propagating from the seaward boundary toward shore. It can

Noise reduction in digital holography based on a filtering algorithm

NASA Astrophysics Data System (ADS)

Zhang, Wenhui; Cao, Liangcai; Zhang, Hua; Jin, Guofan; Brady, David

2018-02-01

Holography is a tool to record the object wavefront by interference. Complex amplitude of the object wave is coded into a two dimensional hologram. Unfortunately, the conjugate wave and background wave would also appear at the object plane during reconstruction, as noise, which blurs the reconstructed object. From the perspective of wave, we propose a filtering algorithm to get a noise-reduced reconstruction. Due to the fact that the hologram is a kind of amplitude grating, three waves would appear when reconstruction, which are object wave, conjugate wave and background wave. The background is easy to eliminate by frequency domain filtering. The object wave and conjugate wave are signals to be dealt with. These two waves, as a whole, propagate in the space. However, when detected at the original object plane, the object wave would diffract into a sparse pattern while the conjugate wave would diffract into a diffused pattern forming the noise. Hence, the noise can be reduced based on these difference with a filtering algorithm. Both amplitude and phase distributions are truthfully retrieved in our simulation and experimental demonstration.

Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio

NASA Astrophysics Data System (ADS)

Hoffman, Aaron; Wright, J. Douglas

2017-11-01

Consider an infinite chain of masses, each connected to its nearest neighbors by a (nonlinear) spring. This is a Fermi-Pasta-Ulam-Tsingou lattice. We prove the existence of traveling waves in the setting where the masses alternate in size. In particular we address the limit where the mass ratio tends to zero. The problem is inherently singular and we find that the traveling waves are not true solitary waves but rather ;nanopterons;, which is to say, waves which are asymptotic at spatial infinity to very small amplitude periodic waves. Moreover, we can only find solutions when the mass ratio lies in a certain open set. The difficulties in the problem all revolve around understanding Jost solutions of a nonlocal Schrödinger operator in its semi-classical limit.

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.

Ultrasonic modeling of an embedded elliptic crack

NASA Astrophysics Data System (ADS)

Fradkin, Larissa Ju.; Zalipaev, Victor

2000-05-01

Experiments indicate that the radiating near zone of a compressional circular transducer directly coupled to a homogeneous and isotropic solid has the following structure: there are geometrical zones where one can distinguish a plane compressional wave and toroidal waves, both compressional and shear, radiated by the transducer rim. As has been shown previously the modern diffraction theory allows to describe these explicitly. It also gives explicit asymptotic description of waves present in the transition zones. In case of a normal incidence of a plane compressional wave the explicit expressions have been obtained by Achenbach and co-authors for the fields diffracted by a penny-shaped crack. We build on the above work by applying the uniform GTD to model an oblique incidence of a plane compressional wave on an elliptical crack. We compare our asymptotic results with numerical results based on the boundary integral code as developed by Glushkovs, Krasnodar University, Russia. The asymptotic formulas form a basis of a code for high-frequency simulation of ultrasonic scattering by elliptical cracks situated in the vicinity of a compressional circular transducer, currently under development at our Center.

Backscattering enhancement with a finite beam width for millimeter-wavelength weather radars

NASA Astrophysics Data System (ADS)

Kobayashi, Satoru; Tanelli, Simone; Iguchi, Toshio; Im, Eastwood

2004-12-01

Backscattering enhancement from random hydrometeors should increase as wavelengths of radars reach millimeter regions. For 95 GHz radars, the reflectivity of backscattering is expected to increase by 2 dB, due to multiple scattering including backscattering enhancement, for water droplets of diameter of 1 mm with a density of 5 x 103 m-3. Previous theoretical studies of backscattering enhancement considered infinitely extending plane waves. In this paper, we expand the theory to spherical waves with a Gaussian antenna pattern, including depolarizing effects. While the differences from the plane wave results are not great when the optical thickness is small, as the latter increases the differences become significant, and essentially depend on the ratio of radar footprint radius to the mean free path of hydrometeors. In this regime, for a radar footprint that is smaller than the mean free path, the backscattering-enhancement reflectivity corresponding to spherical waves is significantly less pronounced than in the case of the plane wave theory. Hence this reduction factor must be taken into account when analyzing radar reflectivity factors for use in remote sensing applications.

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.

Stress waves in transversely isotropic media: The homogeneous problem

NASA Technical Reports Server (NTRS)

Marques, E. R. C.; Williams, J. H., Jr.

1986-01-01

The homogeneous problem of stress wave propagation in unbounded transversely isotropic media is analyzed. By adopting plane wave solutions, the conditions for the existence of the solution are established in terms of phase velocities and directions of particle displacements. Dispersion relations and group velocities are derived from the phase velocity expressions. The deviation angles (e.g., angles between the normals to the adopted plane waves and the actual directions of their propagation) are numerically determined for a specific fiber-glass epoxy composite. A graphical method is introduced for the construction of the wave surfaces using magnitudes of phase velocities and deviation angles. The results for the case of isotropic media are shown to be contained in the solutions for the transversely isotropic media.

Acoustic plane waves incident on an oblique clamped panel in a rectangular duct

NASA Technical Reports Server (NTRS)

Unz, H.; Roskam, J.

1980-01-01

The theory of acoustic plane waves incident on an oblique clamped panel in a rectangular duct was developed from basic theoretical concepts. The coupling theory between the elastic vibrations of the panel (plate) and the oblique incident acoustic plane wave in infinite space was considered in detail, and was used for the oblique clamped panel in the rectangular duct. The partial differential equation which governs the vibrations of the clamped panel (plate) was modified by adding to it stiffness (spring) forces and damping forces. The Transmission Loss coefficient and the Noise Reduction coefficient for oblique incidence were defined and derived in detail. The resonance frequencies excited by the free vibrations of the oblique finite clamped panel (plate) were derived and calculated in detail for the present case.

Comparison of localized basis and plane-wave basis for density-functional calculations of organic molecules on metals

NASA Astrophysics Data System (ADS)

Lee, Kyuho; Yu, Jaejun; Morikawa, Yoshitada

2007-01-01

Localized pseudoatomic orbitals (PAOs) are mainly optimized and tested for the strong chemical bonds within molecules and solids with their proven accuracy and efficiency, but are prone to significant basis set superposition error (BSSE) for weakly interacting systems. Here we test the accuracy of PAO basis in comparison with the BSSE-free plane-wave basis for the physisorption of pentacene molecule on Au (001) by calculating the binding energy, adsorption height, and energy level alignment. We show that both the large cutoff radius for localized PAOs and the counter-poise correction for BSSE are necessary to obtain well-converged physical properties. Thereby obtained results are as accurate as the plane-wave basis results. The comparison with experiment is given as well.

3D DNS and LES of Breaking Inertia-Gravity Waves

NASA Astrophysics Data System (ADS)

Remmler, S.; Fruman, M. D.; Hickel, S.; Achatz, U.

2012-04-01

As inertia-gravity waves we refer to gravity waves that have a sufficiently low frequency and correspondingly large horizontal wavelength to be strongly influenced by the Coriolis force. Inertia-gravity waves are very active in the middle atmosphere and their breaking is potentially an important influence on the circulation in this region. The parametrization of this process requires a good theoretical understanding, which we want to enhance with the present study. Primary linear instabilities of an inertia-gravity wave and "2.5-dimensional" nonlinear simulations (where the spatial dependence is two dimensional but the velocity and vorticity fields are three-dimensional) with the wave perturbed by its leading primary instabilities by Achatz [1] have shown that the breaking differs significantly from that of high-frequency gravity waves due to the strongly sheared component of velocity perpendicular to the plane of wave-propagation. Fruman & Achatz [2] investigated the three-dimensionalization of the breaking by computing the secondary linear instabilities of the same waves using singular vector analysis. These secondary instabilities are variations perpendicular to the direction of the primary perturbation and the wave itself, and their wavelengths are an order of magnitude shorter than both. In continuation of this work, we carried out fully three-dimensional nonlinear simulations of inertia-gravity waves perturbed by their leading primary and secondary instabilities. The direct numerical simulation (DNS) was made tractable by restricting the domain size to the dominant scales selected by the linear analyses. The study includes both convectively stable and unstable waves. To the best of our knowledge, this is the first fully three-dimensional nonlinear direct numerical simulation of inertia-gravity waves at realistic Reynolds numbers with complete resolution of the smallest turbulence scales. Previous simulations either were restricted to high frequency gravity waves (e. g. Fritts et al. [3]), or the ratio N/f was artificially reduced (e. g. Lelong & Dunkerton [4]). The present simulations give us insight into the three-dimensional breaking process as well as the emerging turbulence. We assess the possibility of reducing the computational costs of three-dimensional simulations by using an implicit turbulence subgrid-scale parametrization based on the Adaptive Local Deconvolution Method (ALDM) for stratified turbulence [5]. In addition, we have performed ensembles of nonlinear 2.5-dimensional DNS, like those in Achatz [1] but with a small amount of noise superposed to the initial state, and compared the results with coarse-resolution simulations using either ALDM as well as with standard LES schemes. We found that the results of the models with parametrized turbulence, which are orders of magnitude more computationally economical than the DNS, compare favorably with the DNS in terms of the decay of the wave amplitude with time (the quantity most important for application to gravity-wave drag parametrization) suggesting that they may be trusted in future simulations of gravity wave breaking.

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.

A New Algorithm with Plane Waves and Wavelets for Random Velocity Fields with Many Spatial Scales

NASA Astrophysics Data System (ADS)

Elliott, Frank W.; Majda, Andrew J.

1995-03-01

A new Monte Carlo algorithm for constructing and sampling stationary isotropic Gaussian random fields with power-law energy spectrum, infrared divergence, and fractal self-similar scaling is developed here. The theoretical basis for this algorithm involves the fact that such a random field is well approximated by a superposition of random one-dimensional plane waves involving a fixed finite number of directions. In general each one-dimensional plane wave is the sum of a random shear layer and a random acoustical wave. These one-dimensional random plane waves are then simulated by a wavelet Monte Carlo method for a single space variable developed recently by the authors. The computational results reported in this paper demonstrate remarkable low variance and economical representation of such Gaussian random fields through this new algorithm. In particular, the velocity structure function for an imcorepressible isotropic Gaussian random field in two space dimensions with the Kolmogoroff spectrum can be simulated accurately over 12 decades with only 100 realizations of the algorithm with the scaling exponent accurate to 1.1% and the constant prefactor accurate to 6%; in fact, the exponent of the velocity structure function can be computed over 12 decades within 3.3% with only 10 realizations. Furthermore, only 46,592 active computational elements are utilized in each realization to achieve these results for 12 decades of scaling behavior.

Re-evaluation of ``;The Propagation of Radiation in the Spherical Wave Form''

NASA Astrophysics Data System (ADS)

Joshi, Narahari V.

2012-03-01

It is well accepted that radiation propagates in the free space (without obstacles) in a spherical wave form as well as in a plane wave form. Almost all observed phenomena such as interference, diffraction etc are explained satisfactorily on the basis of spherical wave propagation with a slight alteration in the mathematical treatment. However, one of the fundamental aspects, namely the intensity of the radiation as a function of the distance still remains an unsolved problem as the intensity varies with 1/(distance)2 when one represents the propagation in terms of spherical waves while it is independent of the distance if it is considered as a plane wave. In order to understand this puzzle, the propagation by a spherical wave form is reexamined. It is found that conversion of fields into particle (vice versa), via the field quantization process, explains several dilemma related with the radiation propagation.

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.

Diffraction of Harmonic Flexural Waves in a Cracked Elastic Plate Carrying Electrical Current

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.; Hasanyan, Davresh; Librescu, iviu; Qin, Zhanming

2005-01-01

The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal z-axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

Propagation of Sound at Moderate and High Intensities in Absorbent and Hard-Walled Cylindrical Ducts. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Mcdaniel, Oliver Herbert

1975-01-01

The propagation of plane wave and higher order acoustic modes in both hard-walled and absorbent cylindrical ducts was studied at moderate sound intensities where the linear wave equation is valid, and at high intensities where nonlinear effects can be observed. The experiments were conducted with an anechoically terminated twelve-inch inside-diameter transite pipe. Various types of sound sources were mounted at one end of the duct to generate the desired acoustic fields within the duct. Arrays of conventional loudspeakers were used to generate plane waves and higher order acoustic modes at moderate intensities, and an array of four high intensity electro-pneumatic sound sources was used for the experiments in the nonlinear region. The attenuation of absorbent liners made of several different materials was obtained at moderate intensities for both plane waves and high order modes. It was found that the characteristics of the liners studied did not change appreciably at high intensities.

Anisotropic itinerant magnetism and spin fluctuations in BaFe2As2 : A neutron scattering study

NASA Astrophysics Data System (ADS)

Matan, K.; Morinaga, R.; Iida, K.; Sato, T. J.

2009-02-01

Neutron scattering measurements were performed to investigate magnetic excitations in a single-crystal sample of the ternary iron arsenide BaFe2As2 , a parent compound of a recently discovered family of Fe-based superconductors. In the ordered state, we observe low energy spin-wave excitations with a gap energy Δ=9.8(4)meV . The in-plane spin-wave velocity vab and out-of-plane spin-wave velocity vc measured at 12 meV are 280(150) and 57(7)meVÅ , respectively. At high energy, we observe anisotropic scattering centered at the antiferromagnetic wave vectors. This scattering indicates two-dimensional spin dynamics, which possibly exist inside the Stoner continuum. At TN=136(1)K , the gap closes and quasielastic scattering is observed above TN , indicative of short-range spin fluctuations. In the paramagnetic state, the scattering intensity along the L direction becomes “rodlike,” characteristic of uncorrelated out-of-plane spins, attesting to the two-dimensionality of the system.

Incentive and Architecture of Multi-Band Enabled Small Cell and UE for Up-/Down-Link and Control-/User-Plane Splitting for 5G Mobile Networks

NASA Astrophysics Data System (ADS)

Saha, Rony Kumer; Aswakul, Chaodit

2017-01-01

In this paper, a multi-band enabled femtocell base station (FCBS) and user equipment (UE) architecture is proposed in a multi-tier network that consists of small cells, including femtocells and picocells deployed over the coverage of a macrocell for splitting uplink and downlink (UL/DL) as well as control-plane and user-plane (C-/U-plane) for 5G mobile networks. Since splitting is performed at the same FCBS, we define this architecture as the same base station based split architecture (SBSA). For multiple bands, we consider co-channel (CC) microwave and different frequency (DF) 60 GHz millimeter wave (mmWave) bands for FCBSs and UEs with respect to the microwave band used by their over-laid macrocell base station. All femtocells are assumed to be deployed in a 3-dimensional multi-storage building. For CC microwave band, cross-tier CC interference of femtocells with macrocell is avoided using almost blank subframe based enhanced inter-cell interference coordination techniques. The co-existence of CC microwave and DF mmWave bands for SBSA on the same FCBS and UE is first studied to show their performance disparities in terms of system capacity and spectral efficiency in order to provide incentives for employing multiple bands at the same FCBS and UE and identify a suitable band for routing decoupled UL/DL or C-/U-plane traffic. We then present a number of disruptive architectural design alternatives of multi-band enabled SBSA for 5G mobile networks for UL/DL and C-/U-plane splitting, including a disruptive and complete splitting of UL/DL and C-/U-plane as well as a combined UL/DL and C-/U-plane splitting, by exploiting dual connectivity on CC microwave and DF mmWave bands. The outperformances of SBSA in terms of system level capacity, average spectral efficiency, energy efficiency, and control-plane overhead traffic capacity in comparison with different base stations based split architecture (DBSA) are shown. Finally, a number of technical and business perspectives as well as key research issues of SBSA are discussed.

Quantum transitions through cosmological singularities

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

Bramberger, Sebastian F.; Lehners, Jean-Luc; Hertog, Thomas

2017-07-01

In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddlemore » points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.« less

Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near (1)/(4) doping

NASA Astrophysics Data System (ADS)

Wang, Wan-Sheng; Xiang, Yuan-Yuan; Wang, Qiang-Hua; Wang, Fa; Yang, Fan; Lee, Dung-Hai

2012-01-01

We study the electronic instabilities of near 1/4 electron doped graphene using the singular-mode functional renormalization group, with a self-adaptive k mesh to improve the treatment of the van Hove singularities, and variational Monte Carlo method. At 1/4 doping the system is a chiral spin-density wave state exhibiting the anomalous quantized Hall effect. When the doping deviates from 1/4, the dx2-y2+idxy Cooper pairing becomes the leading instability. Our results suggest that near 1/4 electron or hole doping (away from the neutral point) the graphene is either a Chern insulator or a topoligical superconductor.