Fraunhofer diffraction of the plane wave by a multilevel (quantized) spiral phase plate.
Kotlyar, Victor V; Kovalev, Alexey A
2008-01-15
We obtain an analytical expression in the form of a finite sum of plane waves that describes the paraxial scalar Fraunhofer diffraction of a limited plane wave by a multilevel (quantized) spiral phase plate (SPP) bounded by a polygonal aperture. For several topological charges of the SPP we numerically obtain the minimal number of SPP sectors for which the RMS between the Fraunhofer diffraction patterns for multilevel and continuous SPP does not exceed 2%.
Sound Scattering by a Hard Half-Plane Experimental Evidence of the Edge-Diffracted Wave
NASA Astrophysics Data System (ADS)
OUIS, D.
2002-05-01
In this short note, some experimental results are presented on the diffraction of a spherical way by a hard half-plane. This study was conducted with the aim to give evidence to the existence of the edge-diffracted wave. The sound source used in this experimental study is a condenser microphone operating in a reverse way. The wave emitted by a sound source propagates in space and hits a thin aluminium sheet with a straight edge, considered as an idealization of the hard half-plane. The resulting impulse response includes among others a wave diffracted by the edge of the half-plane, which is compared to its theoretical prediction. This latter is calculated from the exact Biot and Tolstoy solution to the problem of diffraction of a spherical wave by a hard wedge. Relatively satisfactory agreement is found between theory and experiment.
X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity
NASA Astrophysics Data System (ADS)
Balyan, M. K.
2016-12-01
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.
Diffraction of a plane, finite-radius wave by a spiral phase plate.
Kotlyar, V V; Khonina, S N; Kovalev, A A; Soifer, V A; Elfstrom, H; Turunen, J
2006-06-01
We derive analytical expressions containing a hypergeometric function to describe the Fresnel and Fraunhofer diffraction of a plane wave of circular and ringlike cross section by a spiral phase plate (SPP) of an arbitrary integer order. Experimental diffraction patterns generated by an SPP fabricated in resist through direct e-beam writing are in good agreement with the theoretical intensity distribution.
Plane-wave Fresnel diffraction by elliptic apertures: a Fourier-based approach.
Borghi, Riccardo
2014-10-01
A simple theoretical approach to evaluate the scalar wavefield, produced, within paraxial approximation, by the diffraction of monochromatic plane waves impinging on elliptic apertures or obstacles is presented. We find that the diffracted field can be mathematically described in terms of a Fourier series with respect to an angular variable suitably related to the elliptic parametrization of the observation plane. The convergence features of such Fourier series are analyzed, and a priori truncation criterion is also proposed. Two-dimensional maps of the optical intensity diffraction patterns are then numerically generated and compared, at a visual level, with several experimental pictures produced in the past. The last part of this work is devoted to carrying out an analytical investigation of the diffracted field along the ellipse axis. A uniform approximation is derived on applying a method originally developed by Schwarzschild, and an asymptotic estimate, valid in the limit of small eccentricities, is also obtained via the Maggi-Rubinowicz boundary wave theory.
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.
Plane Wave Diffraction by a Finite Plate with Impedance Boundary Conditions
Nawaz, Rab; Ayub, Muhammad; Javaid, Akmal
2014-01-01
In this study we have examined a plane wave diffraction problem by a finite plate having different impedance boundaries. The Fourier transforms were used to reduce the governing problem into simultaneous Wiener-Hopf equations which are then solved using the standard Wiener-Hopf procedure. Afterwards the separated and interacted fields were developed asymptotically by using inverse Fourier transform and the modified stationary phase method. Detailed graphical analysis was also made for various physical parameters we were interested in. PMID:24755624
Scattering and diffraction of plane SH-waves by periodically distributed canyons
NASA Astrophysics Data System (ADS)
Ba, Zhenning; Liang, Jianwen; Zhang, Yanju
2016-06-01
A new method is presented to study the scattering and diffraction of plane SH-waves by periodically distributed canyons in a layered half-space. This method uses the indirect boundary element method combined with Green's functions of uniformly distributed loads acting on periodically distributed inclined lines. The periodicity feature of the canyons is exploited to limit the discretization effort to a single canyon, which avoids errors induced by the truncation of the infinite boundary, and the computational complexity and the demand on memory can be significantly reduced. Furthermore, the total wave fields are decomposed into the free field and scattered field in the process of calculation, which means that the method has definite physical meaning. The implementation of the method is described in detail and its accuracy is verified. Parametric studies are performed in the frequency domain by taking periodically distributed canyons of semi-circular and semi-elliptic cross-sections as examples. Numerical results show that the dynamic responses of periodically distributed canyons can be quite different from those for a single canyon and significant dynamic interactions exist between the canyons.
Takahashi, Yukio; Nishino, Yoshinori; Ishikawa, Tetsuya; Tsutsumi, Ryosuke; Kubo, Hideto; Furukawa, Hayato; Mimura, Hidekazu; Matsuyama, Satoshi; Zettsu, Nobuyuki; Matsubara, Eiichiro; Yamauchi, Kazuto
2009-08-01
X-ray waves in the center of the beam waist of nearly diffraction limited focused x-ray beams can be considered to have amplitude and phase that are both almost uniform, i.e., they are x-ray plane waves. Here we report the results of an experimental demonstration of high-resolution diffraction microscopy using the x-ray plane wave of the synchrotron x-ray beam focused using Kirkpatrik-Baez mirrors. A silver nanocube with an edge length of {approx}100 nm is illuminated with the x-ray beam focused to a {approx}1 {mu}m spot at 12 keV. A high-contrast symmetric diffraction pattern of the nanocube is observed in the forward far field. An image of the nanocube is successfully reconstructed by an iterative phasing method and its half-period resolution is 3.0 nm. This method does not only dramatically improve the spatial resolution of x-ray microscopy but also is a key technology for realizing single-pulse diffractive imaging using x-ray free-electron lasers.
Garcia-Gracia, Hipolito; Gutiérrez-Vega, Julio C
2009-04-01
A detailed analysis of the plane-wave diffraction by a finite-radius circular spiral phase plate (SPP) with integer and fractional topological charge and with variable transmission coefficients inside and outside of the plate edge is presented. We characterize the effect of varying the transmission coefficients and the parameters of the SPP on the propagated field. The vortex structure for integer and fractional phase step of the SPPs with and without phase apodization at the plate edge is also analyzed. The consideration of the interference between the light crossing the SPP and the light that undergoes no phase alteration at the aperture plane reveals new and interesting phenomena associated to this classical problem.
NASA Astrophysics Data System (ADS)
Brandow, Heather P.; Lee, Vincent
2017-07-01
Scattering and Diffraction of elastic in-plane P- and SV- waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong-motion seismologists for over forty years. The case of out-of-plane SH waves on the same elastic canyon that is semi-circular in shape on the half-space surface is the first such problem that was solved by analytic closed form solutions over forty years ago by Trifunac. The corresponding case of in-plane P- and SV-waves on the same circular canyon is a much more complicated problem because, the in-plane P- and SV- scattered waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by the author in the work of Lee and Liu. This paper uses the technique of Lee and Liu of defining these stress-free scattered waves to solve the problem of the scattered and diffraction of these in-plane waves on an almost-circular surface canyon that is arbitrary in shape.
A diffraction-based optical method for the detection of in-plane motion of lamb waves.
Yang, Che-Hua; Tsai, Yua-Ching
2005-08-01
This paper describes a laser optical technique that allows the detection of in-plane motion of Lamb waves. This interference-based laser optical technique includes a tiny square indentation with a width of about 30 micron on the sample surface and a relatively simple optical arrangement. The current technique is applied for the detection of in-plane motions of Lamb waves propagating in a 70-micron thick brass plate. Measurement of So mode dominated by in-plane motion in the low fd (frequency times thickness) regime is successfully demonstrated with the current technique. With the indentation replaced by a microreflector in a microelectromechanical (MEMS) structure, this technique is applicable for the detection of in-plane motion in MEMS structures.
Dossou, Kokou B.; Botten, Lindsay C.
2012-08-15
A three-dimensional finite element method (FEM) for the analysis of plane wave diffraction by a bi-periodic slab is described and implemented. A scattering matrix formalism based on the FEM allows the efficient treatment of light reflection and transmission by multilayer bi-periodic structures, and the computation of Bloch modes of three-dimensional arrays. Numerical simulations, which show the accuracy and flexibility of the FEM, are presented.
Kotlyar, Victor V; Kovalev, Alexey A; Skidanov, Roman V; Moiseev, Oleg Yu; Soifer, Victor A
2007-07-01
We derive what we believe to be new analytical relations to describe the Fraunhofer diffraction of the finite-radius plane wave by a helical axicon (HA) and a spiral phase plate (SPP). The solutions are deduced in the form of a series of the Bessel functions for the HA and a finite sum of the Bessel functions for the SPP. The solution for the HA changes to that for the SPP if the axicon parameter is set equal to zero. We also derive what we believe to be new analytical relations to describe the Fresnel and Fraunhofer diffraction of the Gaussian beam by a HA are derived. The solutions are deduced in the form of a series of the hypergeometric functions. We have fabricated by photolithography a binary diffractive optical element (a HA with number n=10) able to produce in the focal plane of a spherical lens an optical vortex, which was then used to perform rotation of several polystyrene beads of diameter 5 microm.
Fingerprinting ordered diffractions in multiply diffracted waves
NASA Astrophysics Data System (ADS)
Meles, Giovanni Angelo; Curtis, Andrew
2014-09-01
We show how to `fingerprint' individual diffractors inside an acoustic medium using interrogative wave energy from arrays of sources and receivers. For any recorded multiply diffracted wave observed between any source and any receiver, the set of such fingerprints is sufficient information to identify all diffractors involved in the corresponding diffraction path, and the sequential order in which diffractors are encountered. The method herein thus decomposes complex, multiply diffracted wavefields into constituent, single-diffraction interactions.
Tang, Huiqin; Wang, Taofen; Zhu, Kaicheng
2008-08-15
We introduce a multilevel spiral phase plate (SPP) limited by a pseudoring polygonal aperture (PRPA). Such an SPP has the advantages of easier fabrication and greater suppression of the sidelobes of the diffraction field over that generated with a polygonal aperture (PA). The Fraunhofer diffraction fields generated by an SPP with a PRPA or with a PA have the same topological charge features and a similar diffraction pattern. Numerical evaluations show that the maximum bright annular-intensity difference between the diffraction patterns for the SPP with a PRPA and that of a PA does not exceed 3% under optimal design parameters.
Lamb wave diffraction tomography
NASA Astrophysics Data System (ADS)
Malyarenko, Eugene Valentinovich
, fails. Diffraction tomography is a way to incorporate scattering effects into tomographic algorithms in order to improve image quality and resolution. This work describes the iterative reconstruction procedure developed for the Lamb Wave tomography and allowing for ray bending correction for imaging of moderately scattering objects.
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.
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.
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.
Realizing in-plane surface diffraction by x-ray multiple-beam diffraction with large incidence angle
Huang, Xian-Rong Gog, Thomas; Assoufid, Lahsen; Peng, Ru-Wen; Siddons, D. P.
2014-11-03
Based on rigorous dynamical-theory calculations, we demonstrate the principle of an x-ray multiple-beam diffraction (MBD) scheme that overcomes the long-lasting difficulties of high-resolution in-plane diffraction from crystal surfaces. This scheme only utilizes symmetric reflection geometry with large incident angles but activates the out-of-plane and in-plane diffraction processes simultaneously and separately in the continuous MBD planes. The in-plane diffraction is realized by detoured MBD, where the intermediate diffracted waves propagate parallel to the surface, which corresponds to an absolute Bragg surface diffraction configuration that is extremely sensitive to surface structures. A series of MBD diffraction and imaging techniques may be developed from this principle to study surface/interface (misfit) strains, lateral nanostructures, and phase transitions of a wide range of (pseudo)cubic crystal structures, including ultrathin epitaxial films and multilayers, quantum dots, strain-engineered semiconductor or (multi)ferroic materials, etc.
Plasmonic Airy beam generated by in-plane diffraction.
Li, L; Li, T; Wang, S M; Zhang, C; Zhu, S N
2011-09-16
We report an experimental realization of a plasmonic Airy beam, which is generated thoroughly on a silver surface. With a carefully designed nanoarray structure, such Airy beams come into being from an in-plane propagating surface plasmon polariton wave, exhibiting nonspreading, self-bending, and self-healing properties. Besides, a new phase-tuning method based on nonperfectly matched diffraction processes is proposed to generate and modulate the beam almost at will. This unique plasmonic Airy beam as well as the generation method would significantly promote the evolutions in in-plane surface plasmon polariton manipulations and indicate potential applications in lab-on-chip photonic integrations.
Generalization of the Kirchhoff theory to elastic wave diffraction problems
NASA Astrophysics Data System (ADS)
Israilov, M. Sh.; Nosov, S. E.
2017-01-01
The Kirchhoff approximation in the theory of diffraction of acoustic and electromagnetic waves by plane screens assumes that the field and its normal derivative on the part of the plane outside the screen coincides with the incident wave field and its normal derivative, respectively. This assumption reduces the problem of wave diffraction by a plane screen to the Dirichlet or Neumann problems for the half-space (or the half-plane in the two-dimensional case) and permits immediately writing out an approximate analytical solution. The present paper is the first to generalize this approach to elastic wave diffraction. We use the problem of diffraction of a shear SH-wave by a half-plane to show that the Kirchhoff theory gives a good approximation to the exact solution. The discrepancies mainly arise near the screen, i.e., in the region where the influence of the boundary conditions is maximal.
NASA Astrophysics Data System (ADS)
Forgács, Péter; Lukács, Árpád; Romańczukiewicz, Tomasz
2013-12-01
It is shown that in a large class of systems, plane waves act as tractor beams: i.e., an incident plane wave can exert a pulling force on the scatterer. The underlying physical mechanism for the pulling force is due to the sufficiently strong scattering of the incoming wave into another mode carrying more momentum, in which case excess momentum is created behind the scatterer. This tractor beam or negative radiation pressure (NRP) effect, is found to be generic in systems with multiple scattering channels. In a birefringent medium, electromagnetic plane waves incident on a thin plate exert NRP of the same order of magnitude as optical radiation pressure, while in artificial dielectrics (metamaterials), the magnitude of NRP can even be macroscopic. In two dimensions, we study various scattering situations on vortices, and NRP is shown to occur by the scattering of heavy baryons into light leptons off cosmic strings, and by neutron scattering off vortices in the XY model.
Anisotropic diffraction of bulk acoustic wave beams in lithium niobate.
Naumenko, Natalya F; Chizhikov, Sergey I; Molchanov, Vladimir Ya; Yushkov, Konstantin B
2015-12-01
The formalism of planar diffraction tensor was applied to the analysis of anisotropy of bulk acoustic wave diffraction and to build a full map of anisotropic diffractional coefficients for three bulk acoustic wave modes propagating in lithium niobate. For arbitrary propagation direction the diffractional coefficients derived allow estimation of ultrasonic beam divergence in far-field. Analysis of obtained data revealed that the maxima of acousto-optic figure of merit for anisotropic diffraction in the YZ plane correspond to moderate diffractional spreading of the beams exceeding isotropic diffraction 2-3 times.
Electron diffraction by plasmon waves
NASA Astrophysics Data System (ADS)
García de Abajo, F. J.; Barwick, B.; Carbone, F.
2016-07-01
An electron beam traversing a structured plasmonic field is shown to undergo diffraction with characteristic angular patterns of both elastic and inelastic outgoing electron components. In particular, a plasmonic grating (e.g., a standing wave formed by two counterpropagating plasmons in a thin film) produces diffraction orders of the same parity as the net number of exchanged plasmons. Large diffracted beam fractions are predicted to occur for realistic plasmon intensities in attainable geometries due to a combination of phase and amplitude changes locally imprinted on the passing electron wave. Our study opens vistas in the study of multiphoton exchanges between electron beams and evanescent optical fields with unexplored effects related to the transversal component of the electron wave function.
Singularities from colliding plane gravitational waves
NASA Astrophysics Data System (ADS)
Tipler, Frank J.
1980-12-01
A simple geometrical argument is given which shows that a collision between two plane gravitational waves must result in singularities. The argument suggests that these singularities are a peculiar feature of plane waves, because singularities are also a consequence of a collision between self-gravitating plane waves of other fields with arbitrarily small energy density.
NASA Astrophysics Data System (ADS)
Soler, José M.; Williams, Arthur R.
1990-11-01
Results are presented that demonstrate the effectiveness of a calculational method of electronic-structure theory. The method combines the power (tractable basis-set size) and flexibility (transition and first-row elements) of the augmented-plane-wave method with the computational efficiency of the Car-Parrinello method of molecular dynamics and total-energy minimization. Equilibrium geometry and vibrational frequencies in agreement with experiment are presented for Si, to demonstrate agreement with existing methods and for Cu, N2, and H2O to demonstrate the broader applicability of the approach.
Interior impedance wedge diffraction with surface waves
NASA Technical Reports Server (NTRS)
Balanis, Constantine A.; Griesser, Timothy
1988-01-01
The exact impedance wedge solution is evaluated asymptotically using the method of steepest descents for plane wave illumination at normal incidence. Uniform but different impedances on each face are considered for both soft and hard polarizations. The asymptotic solution isolates the incident, singly reflected, multiply reflected, diffracted, and surface wave fields. Multiply reflected fields of any order are permitted. The multiply reflected fields from the exact solution are written as ratios of auxiliary Maliuzhinets functions, whereas a geometrical analysis gives the reflected fields as products of reflection coefficients. These two representations are shown to be identical in magnitude, phase and the angular range over which they exist. The diffracted field includes four Fresnel transition functions as in the perfect conductor case, and the expressions for the appropriate discontinuities at the shadow boundaries are presented. The surface wave exists over a finite angular range and only for certain surface impedances. A surface wave transition field is included to retain continuity. Computations are presented for interior wedge diffractions although the formulation is valid for both exterior and interior wedges.
Complex space monofilar approximation of diffraction currents on a conducting half plane
NASA Technical Reports Server (NTRS)
Lindell, I. V.
1987-01-01
Simple approximation of diffraction surface currents on a conducting half plane, due to an incoming plane wave, is obtained with a line current (monofile) in complex space. When compared to an approximating current at the edge, the diffraction pattern is seen to improve by an order of magnitude for a minimal increase of computation effort. Thus, the inconvient Fresnel integral functions can be avoided for quick calculations of diffracted fields and the accuracy is good in other directions than along the half plane. The method can be applied to general problems involving planar metal edges.
Realizing in-plane surface diffraction by x-ray multiple-beam diffraction with large incidence angle
Huang, Xian-Rong; Peng, Ru-Wen; Gog, Thomas; Siddons, D. P.; Assoufid, Lahsen
2014-11-04
Based on rigorous dynamical-theory calculations, we demonstrate in this paper the principle of an x-ray multiple-beam diffraction (MBD) scheme that overcomes the long-lasting difficulties of high-resolution in-plane diffraction from crystal surfaces. This scheme only utilizes symmetric reflection geometry with large incident angles but activates the out-of-plane and in-plane diffraction processes simultaneously and separately in the continuous MBD planes. The in-plane diffraction is realized by detoured MBD, where the intermediate diffracted waves propagate parallel to the surface, which corresponds to an absolute Bragg surface diffraction configuration that is extremely sensitive to surface structures. Finally, a series of MBD diffraction and imaging techniques may be developed from this principle to study surface/interface (misfit) strains, lateral nanostructures, and phase transitions of a wide range of (pseudo)cubic crystal structures, including ultrathin epitaxial films and multilayers, quantum dots, strain-engineered semiconductor or (multi)ferroic materials, etc.
Realizing in-plane surface diffraction by x-ray multiple-beam diffraction with large incidence angle
Huang, Xian-Rong; Peng, Ru-Wen; Gog, Thomas; ...
2014-11-04
Based on rigorous dynamical-theory calculations, we demonstrate in this paper the principle of an x-ray multiple-beam diffraction (MBD) scheme that overcomes the long-lasting difficulties of high-resolution in-plane diffraction from crystal surfaces. This scheme only utilizes symmetric reflection geometry with large incident angles but activates the out-of-plane and in-plane diffraction processes simultaneously and separately in the continuous MBD planes. The in-plane diffraction is realized by detoured MBD, where the intermediate diffracted waves propagate parallel to the surface, which corresponds to an absolute Bragg surface diffraction configuration that is extremely sensitive to surface structures. Finally, a series of MBD diffraction and imagingmore » techniques may be developed from this principle to study surface/interface (misfit) strains, lateral nanostructures, and phase transitions of a wide range of (pseudo)cubic crystal structures, including ultrathin epitaxial films and multilayers, quantum dots, strain-engineered semiconductor or (multi)ferroic materials, etc.« less
Electromagnetic diffraction efficiencies for plane reflection diffraction gratings
NASA Technical Reports Server (NTRS)
Marathay, A. S.; Shrode, T. E.
1974-01-01
The theory and computer programs, based on electromagnetic theory, for the analysis and design of echelle gratings were developed. The gratings are designed for instruments that operate in the ultraviolet portion of the spectrum. The theory was developed so that the resulting computer programs will be able to analyze deep (up to 30 wavelengths) gratings by including as many as 100 real or homogeneous diffraction orders. The program calculates the complex amplitude coefficient for each of the diffracted orders. A check on the numerical method used to solve the integral equations is provided by a conservation of energy calculation.
Wave diffraction in weak cosmic-ray-modified shocks
NASA Technical Reports Server (NTRS)
Webb, G. M.; Zank, G. P.
1992-01-01
Weakly multidirectional, long-wavelength cosmic-ray-modified shocks are studied via multiple scale perturbation techniques. The effects of diffraction are discussed in terms of Green's function solutions of the linearized 1 + 3D Burgers and 1 + 3D KdVB equations, and also in terms of solutions with singular Dirac delta initial distributions. The solutions show a monotonic decrease of the wave-front curvature with increasing time owing to the effects of wave diffraction. The shape of the wave surface is discussed in terms of solutions S to the wave eikonal equation corresponding to singular initial conditions. For the fast magnetosonic wave propagating in the positive x-direction, the wave phase surface S = 0 has elliptic cross sections with the planes x = constant and has a convex paraboloidal shape. Plane-wave solutions of the 1 + 3D KdVB equation are discussed.
Diffraction optics for terahertz waves
NASA Astrophysics Data System (ADS)
Wiltse, James C.
2004-09-01
Conventional lenses are important components for many terahertz applications, but ordinary lenses are very difficult to fabricate for short-focal lengths. Multi-level phase-corrected zoned lens antennas have been investigated with particular application at terahertz wavelengths. These zoned lenses (or diffractive optics) give better performance than ordinary lenses, and because of their planar construction are easier and cheaper to fabricate. The depths of cut needed for a grooved zone plate are quite small, even when materials with low dielectric constants are used. Zoned lenses have been built and tested at various frequencies from 100 GHz to 1.5 THz, with phase correction levels of half-wave, quarter-wave, or eighth-wavelength. The inherent losses in transparent materials increase monotonically over this frequency range. Typical low-loss materials include polystyrene, polyethylene, Teflon, polycarbonate, polystyrene foam, foamed polyethylene, low density polytetrafluoroethylene (PTFE), TPX, quartz, sapphire, and silicon. Low dielectric-constant materials are normally preferred to reduce reflection and attenuation losses. Techniques for cutting or milling the materials to small dimensions are important, because at 1.0 THz an eighth-wavelength correction for silicon is only 15 μm. Another characteristic of zoned diffraction optics is their frequency behavior. Previous investigations have considered their bandwidth dependence and quasi-periodic extended frequency response for a specified focal length. As frequency changes, the focal point moves along the axis of the zoned lens. An analysis is given to explain this effect.
Imaging scatterer planes by photoelectron diffraction
NASA Astrophysics Data System (ADS)
Seelmann-Eggebert, M.
1997-04-01
A novel direct crystallographic method CHRISDA (combined holographic real-space imaging by superimposed dimer function algorithm) is proposed which permits an assessment of the near-surface structure of a solid sample by analysis of a single core-level photoemission or Auger emission diffraction pattern (XPD or AED) recorded over the hemisphere of electron escape angles. Combining the elements of holography and real-space triangulation, the approach achieves a high spatial resolution (≈0.1 Å) and requires a knowledge of only a few non-structural parameters. To demonstrate the experimental efficacy of CHRISDA, a Sn film deposited on a CdTe(111) substrate is analyzed and yields the diamond structure characteristic of α-Sn.
Near-Field Diffraction Imaging from Multiple Detection Planes
NASA Astrophysics Data System (ADS)
Loetgering, L.; Golembusch, M.; Hammoud, R.; Wilhein, T.
2017-06-01
We present diffraction imaging results obtained from multiple near-field diffraction constraints. An iterative phase retrieval algorithm was implemented that uses data redundancy achieved by measuring near-field diffraction intensities at various sample-detector distances. The procedure allows for reconstructing the exit surface wave of a sample within a multiple constraint satisfaction framework neither making use of a priori knowledge as enforced in coherent diffraction imaging (CDI) nor exact scanning grid knowledge as required in ptychography. We also investigate the potential of the presented technique to deal with polychromatic radiation as important for potential application in diffraction imaging by means of tabletop EUV and X-ray sources.
Aberrations of diffracted wave fields. II. Diffraction gratings.
Mahajan, V N
2000-12-01
The Rayleigh-Sommerfeld theory is applied to diffraction of a spherical wave by a grating. The grating equation is obtained from the aberration-free diffraction pattern, and its aberrations are shown to be the same as the conventional aberrations obtained by using Fermat's principle. These aberrations are shown to be not associated with the diffraction process. Moreover, it is shown that the irradiance distribution of a certain diffraction order is the Fraunhofer diffraction pattern of the grating aperture as a whole aberrated by the aberration of that order.
Carroll symmetry of plane gravitational waves
NASA Astrophysics Data System (ADS)
Duval, C.; Gibbons, G. W.; Horvathy, P. A.; Zhang, P.-M.
2017-09-01
The well-known 5-parameter isometry group of plane gravitational waves in 4 dimensions is identified as Lévy-Leblond’s Carroll group in 2+1 dimensions with no rotations. Our clue is that plane waves are Bargmann spaces into which Carroll manifolds can be embedded. We also comment on the scattering of light by a gravitational wave and calculate its electric permittivity considered as an impedance-matched metamaterial.
Causal inheritence in plane wave quotients
Hubeny, Veronika E.; Rangamani, Mukund; Ross, Simon F.
2003-11-24
We investigate the appearance of closed timelike curves in quotients of plane waves along spacelike isometries. First we formulate a necessary and sufficient condition for a quotient of a general spacetime to preserve stable causality. We explicitly show that the plane waves are stably causal; in passing, we observe that some pp-waves are not even distinguishing. We then consider the classification of all quotients of the maximally supersymmetric ten-dimensional plane wave under a spacelike isometry, and show that the quotient will lead to closed timelike curves iff the isometry involves a translation along the u direction. The appearance of these closed timelike curves is thus connected to the special properties of the light cones in plane wave spacetimes. We show that all other quotients preserve stable causality.
A scattering approach to sea wave diffraction
Corradini, M. L. Garbuglia, M. Maponi, P.; Ruggeri, M.
2016-06-08
This paper intends to show a model for the diffraction of sea waves approaching an OWC device, which converts the sea waves motion into mechanical energy and then electrical energy. This is a preliminary study to the optimisation of the device, in fact the computation of sea waves diffraction around the device allows the estimation of the sea waves energy which enters into the device. The computation of the diffraction phenomenon is the result of a sea waves scattering problem, solved with an integral equation method.
Incidence of plane waves upon a fracture
NASA Astrophysics Data System (ADS)
Gu, Boliang; SuáRez-Rivera, R.; Nihei, Kurt T.; Myer, Larry R.
1996-11-01
This paper investigates the details of reflection, transmission, and conversion of plane waves incident upon a fracture at arbitrary angles. The elastic compliance of fractures that is produced by the presence of a planar collection of void spaces and asperities of contact is modeled as a displacement-discontinuity boundary condition between two elastic half-spaces. Closed-form expressions for the transmission and reflection coefficients on a fracture are derived by replacing the boundary conditions for a welded interface by those for a fracture into the standard procedure for plane wave analysis. The closed-form expressions reveal that a single fracture can produce a variety of potentially diagnostic waves such as transmitted waves, reflected waves, converted waves, head waves, and P interface waves and introduce a finite group time delay to all these waves with respect to the incident wave. The amplitude and group time delay of the fracture-induced waves are controlled by the fracture stiffness, wave frequency, and the Poisson's ratio of the medium. The head wave and inhomogeneous P interface waves are generated when an SV wave is incident upon a fracture, at and beyond a critical angle, respectively, which is determined by Snell's law. For some combinations of the fracture stiffness and the Poisson's ratio of the half-spaces, no reflection or transmission of a P wave or an SV wave occurs.
NASA Technical Reports Server (NTRS)
Rojas, Roberto G.
1985-01-01
A uniform geometrical theory of diffraction (UTD) solution is developed for the problem of the diffraction by a thin dielectric/ferrite half plane when it is excited by a plane, cylindrical, or surface wave field. Both transverse electric and transverse magnetic cases are considered. The solution of this problem is synthesized from the solutions to the related problems of EM diffraction by configurations involving perfectly conducting electric and magnetic walls covered by a dielectric/ferrite half-plane of one half the thickness of the original half-plane.
Aberrations of diffracted wave fields: distortion.
Harvey, James E; Bogunovic, Dijana; Krywonos, Andrey
2003-03-01
Near-field diffraction patterns are merely aberrated Fraunhofer diffraction patterns. These aberrations, inherent to the diffraction process, provide insight and understanding into wide-angle diffraction phenomena. Nonparaxial patterns of diffracted orders produced by a laser beam passing through a grating and projected upon a plane screen exhibit severe distortion (W311). This distortion is an artifact of the configuration chosen to observe diffraction patterns. Grating behavior expressed in terms of the direction cosines of the propagation vectors of the incident and diffracted orders exhibits no distortion. Use of a simple direction cosine diagram provides an elegant way to deal with nonparaxial diffraction patterns, particularly when large obliquely incident beams produce conical diffraction.
Double plane wave reverse time migration with plane wave Green's function
NASA Astrophysics Data System (ADS)
Zhao, Z.; Sen, M. K.; Stoffa, P. L.
2015-12-01
Reverse time migration (RTM) is effective in obtaining complex subsurface structures from seismic data. By solving the two-way wave equation, RTM can use entire wavefield for imaging. Although powerful computer are becoming available, the conventional pre-stack shot gather RTM is still computationally expensive. Solving forward and backward wavefield propagation for each source location and shot gather is extremely time consuming, especially for large seismic datasets. We present an efficient, accurate and flexible plane wave RTM in the frequency domain where we utilize a compressed plane wave dataset, known as the double plane wave (DPW) dataset. Provided with densely sampled seismic dataset, shot gathers can be decomposed into source and receiver plane wave components with minimal artifacts. The DPW RTM is derived under the Born approximation and utilizes frequency domain plane wave Green's function for imaging. Time dips in the shot profiles can help to estimate the range of plane wave components present in shot gathers. Therefore, a limited number of plane wave Green's functions are needed for imaging. Plane wave Green's functions can be used for imaging both source and receiver plane waves. Source and receiver reciprocity can be used for imaging plane wave components at no cost and save half of the computation time. As a result, the computational burden for migration is substantially reduced. Plane wave components can be migrated independently to recover specific targets with given dips, and ray parameter common image gathers (CIGs) can be generated after migration directly. The ray parameter CIGs can be used to justify the correctness of velocity models. Subsurface anisotropy effects can also be included in our imaging condition, provided with plane wave Green's functions in the anisotropic media.
Rayleigh–Bloch waves along elastic diffraction gratings
Colquitt, D. J.; Craster, R. V.; Antonakakis, T.; Guenneau, S.
2015-01-01
Rayleigh–Bloch (RB) waves in elasticity, in contrast to those in scalar wave systems, appear to have had little attention. Despite the importance of RB waves in applications, their connections to trapped modes and the ubiquitous nature of diffraction gratings, there has been no investigation of whether such waves occur within elastic diffraction gratings for the in-plane vector elastic system. We identify boundary conditions that support such waves and numerical simulations confirm their presence. An asymptotic technique is also developed to generate effective medium homogenized equations for the grating that allows us to replace the detailed microstructure by a continuum representation. Further numerical simulations confirm that the asymptotic scheme captures the essential features of these waves. PMID:25568616
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)
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)
Wave diffraction by a cosmic string
NASA Astrophysics Data System (ADS)
Fernández-Núñez, Isabel; Bulashenko, Oleg
2016-08-01
We show that if a cosmic string exists, it may be identified through characteristic diffraction pattern in the energy spectrum of the observed signal. In particular, if the string is on the line of sight, the wave field is shown to fit the Cornu spiral. We suggest a simple procedure, based on Keller's geometrical theory of diffraction, which allows to explain wave effects in conical spacetime of a cosmic string in terms of interference of four characteristic rays. Our results are supposed to be valid for scalar massless waves, including gravitational waves, electromagnetic waves, or even sound in case of condensed matter systems with analogous topological defects.
Coded excitation plane wave imaging for shear wave motion detection.
Song, Pengfei; Urban, Matthew W; Manduca, Armando; Greenleaf, James F; Chen, Shigao
2015-07-01
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 SNR compared with 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 to 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.
NASA Technical Reports Server (NTRS)
Kearns, James A.
1989-01-01
Phenomena associated with long range propagation of sound over irregular topography motivated this work, which was to analyze the diffraction effects which would occur near the tops of hills and ridges. The diffraction of a high frequency plane wave due to its grazing of a two-dimensional curved surface of finite impedance was also studied. Laboratory scale models were constructed and measurements were made of the field on, above, and behind either of two curved surfaces possessing distinctly different impedances; that is, one was soft while the other was hard. The experimental technique consisted of simultaneously measuring the pressure at a reference point and at a field point due to a transient pulse generated by an electric spark. The pressure waveforms were digitized and processed. The ratio of the discrete Fourier transforms of the two waveforms provided an estimate of the insertion loss between them. The results of the measurements were compared with the predictions of a theory which was derived by Pierce using the method of Matched Asymptotic Expansions (MAE). The predictions relied upon the experimental evaluation of the impedance of each surface at grazing angles of incidence. This evaluation was achieved by a fairly standard technique involving empirical models of various generic types of surfaces. An example was shown of the important role that the structural intricacies of a surface play in the determination of an appropriate model. The comparison between the measurements and predictions indicated that the theory gives an excellent description of the field anywhere near a curved surface. Further, with a simple modification, the theory was also shown to give nearly as good of a description of the field surrounding a curved surface even at distances far behind the surface yet near the line of sight.
Spherical-wave effects in photoelectron diffraction
NASA Astrophysics Data System (ADS)
Sagurton, M.; Bullock, E. L.; Saiki, R.; Kaduwela, A.; Brundle, C. R.; Fadley, C. S.; Rehr, J. J.
1986-02-01
The influence of spherical-wave (SW) effects on the analysis of photoelectron diffraction (PD) data is considered by comparing full SW single-scattering calculations with similar calculations based upon the plane-wave (PW) approximation and a new approximation for including SW effects (SW(1)) due to Rehr, Albers, Natoli, and Stern, as well as with experimental data involving both scanned-energy and scanned-angle measurements. In general, SW effects are found to be much more important in forward scattering and to explain prior empirical adjustments of PW x-ray PD scattering amplitudes at higher energies of >~500 eV. The more easily used SW(1) approximation is also seen to allow very well for SW effects. Not all PD data are expected to be equally sensitive to SW corrections. For example, scanned-energy data for S/Ni(001) emphasizing backscattering events are about equally well described by the PW and SW models, whereas higher-energy azimuthal-scan data for O/Ni(001) in which forward scattering is dominant require SW corrections to describe some, but not all, directions of emission quantitatively.
Nonlinear interaction of plane elastic waves
Korneev, V.A.; Nihei, K.T.; Myer, L.R.
1998-06-01
The paper presents basic first order results of nonlinear elastic theory by Murnaghan for elastic wave propagation in isotropic solids. The authors especially address the problem of resonant scattering of two collimated beams and present analytical solutions for amplitudes of all possible types of resonant interactions for elastic plane waves. For estimation of nonlinear scattered waves they use measured elastic parameters for sandstone. The most profound nonlinear effect is expected for interactions of two SH waves generating compressional P wave at sum frequency. Estimations show that nonlinear phenomena is likely to be observed in seismic data. Basic equations of nonlinear five-constant theory by Murnaghan are also presented.
Diffractive waveplates for long wave infrared
NASA Astrophysics Data System (ADS)
Ouskova, Elena; Roberts, David; Tabiryan, Nelson; Steeves, D. M.; Kimball, B. R.
2017-05-01
We report about developing long-wave infrared diffractive optical components based on liquid crystals. The components show high efficiency and high transparency for the 10.6 μm wavelength of CO2 laser beam.
Toward loop quantization of plane gravitational waves
NASA Astrophysics Data System (ADS)
Hinterleitner, Franz; Major, Seth
2012-03-01
The polarized Gowdy model in terms of Ashtekar-Barbero variables is reduced with an additional constraint derived from the Killing equations for plane gravitational waves with parallel rays. The new constraint is formulated in a diffeomorphism invariant manner and, when it is included in the model, the resulting constraint algebra is first class, in contrast to the prior work done in special coordinates. Using an earlier work by Banerjee and Date, the constraints are expressed in terms of classical quantities that have an operator equivalent in loop quantum gravity, making these plane gravitational wave spacetimes accessible to loop quantization techniques.
Nonlinear Fresnel diffraction of weak shock waves.
Coulouvrat, François; Marchiano, Régis
2003-10-01
Fresnel diffraction at a straight edge is revisited for nonlinear acoustics. Considering the penumbra region as a diffraction boundary layer governed by the KZ equation and its associated jump relations for shocks, similarity laws are established for the diffraction of a step shock, an "N" wave, or a periodic sawtooth wave. Compared to the linear case described by the well-known Fresnel functions, it is shown that weak shock waves penetrate more deeply into the shadow zone than linear waves. The thickness of the penumbra increases as a power of the propagation distance, power 1 for a step shock, or 3/4 for an N wave, as opposed to power 1/2 for a periodic sawtooth wave or a linear wave. This is explained considering the frequency spectrum of the waveform and its nonlinear evolution along the propagation, and is confirmed by direct numerical simulations of the KZ equation. New formulas for the Rayleigh/Fresnel distance in the case of nonlinear diffraction of weak shock waves by a large, finite aperture are deduced from the present study.
Coded Excitation Plane Wave Imaging for Shear Wave Motion Detection
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
Antenna arrays for producing plane whistler waves
NASA Astrophysics Data System (ADS)
Stenzel, Reiner; Urrutia, J. Manuel
2014-10-01
Linear whistler modes with ω ~= 0 . 3ωce <<ωpe are excited in a large laboratory plasma with magnetic loop antennas. A single antenna always produces a spatially bounded wave packet whose propagation cannot be directly compared to plane wave theories. By superimposing the fields from spatially separated antennas, the wavenumber along the antenna array can be nearly eliminated. 2D arrays nearly produce plane waves. The angle θ of wave propagation has been varied by a phase shift along the array. The refractive index surface n (θ) has been measured. The parallel phase and group velocities for Gendrin modes has been demonstrated. The interference between two oblique plane whistlers creates a whistler ``waveguide'' mode, i.e. standing waves for k ⊥B0 and propagation for k | |B0 . It also describes the reflection of oblique whistlers from a sharp discontinuity in the refractive index or conductivity. Radial reflections are also a dominant factor in small plasma columns of helicon devices. These results are of interest to space and laboratory plasmas. Work supported by NSF/DOE.
Design of diffractive microlens array integration with focal plane arrays
NASA Astrophysics Data System (ADS)
Chen, Sihai; Yi, Xinjian; Li, Yi; He, Miao; Chen, Sixiang; Kong, Lingbin
2000-10-01
The IR spectrum from 3 to 5micrometers has numerous applications in both military and civil industries. High performance at high operating temperature is often important in these applications. Conventional Focal Plane Arrays (FPAs) without integration with concentrator such as microlens have poor sensitivity and low signal-to-noise ratio because of their lower fill factor. The binary optics microlens arrays reported in this paper are designed for integration with FPAs. Thus, the FPAs' fill factor, sensitivity, and signal- to-noise ratio can be improved while retaining a given image resolution and optical collection area. In the paper, we discussed the 256(Horizontal)x290(Vertical) microlens arrays designed for a center wavelength of 4micrometers , with 50micrometers (Horizontalx33micrometers (Vertical) quadrate pixel dimension and a speed (F number) of F/1.96. PtSi FPAs were fabricated on the front side of a 400-micrometers -thick Si substrate. The designed diffractive microlens arrays will be etched on the back side of the same wafer in a register fashion and it will be reported in other paper. Considering the diffraction efficiency, 8-phase-level approximation is enough. For the diffraction efficiency of 8-phase-level diffractive microlens reaches 95%. The process only need three mask-level, so we designed and fabricated three masks with the same dimension 4'x4'. Also, a set of fine verniers was designed and fabricated on each mask to allow accurate alignment during the fabrication process. Through a computer simulation, the microlens arrays are nearly diffraction limited, with the diffraction efficiency of 93%, a bit lower than the theoretical value of 95%. Introduction of microlens arrays has the ability to increase the FPAs' fill factor to 100%, while it is only about 21.6% without microlens. To our knowledge, this is the first trial of integration large area microlens arrays with FPAs at home.
Plane wave reflection at flow intakes
NASA Astrophysics Data System (ADS)
Davies, P. O. A. L.
1987-06-01
A treatment is presented for prediction of the acoustic field associated with an open duct termination whose inflow is at a mean Mach number, and requires a quantitative description of both the acoustic and flow conditions in the vicinity of the open end. This problem is presently simplified by restricting the acoustic field within the duct to plane wave motion, with component wave amplitudes p(+) and p(-), where p(+) is incident at the termination. A 'vena contracta' develops in the pipe just downstream of the intake, leading to a significant mean pressure loss.
The memory effect for plane gravitational waves
NASA Astrophysics Data System (ADS)
Zhang, P.-M.; Duval, C.; Gibbons, G. W.; Horvathy, P. A.
2017-09-01
We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einstein's vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zel'dovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the "velocity memory effect", considered by Braginsky, Thorne, Grishchuk, and Polnarev.
Boundary diffraction wave integrals for diffraction modeling of external occulters.
Cady, Eric
2012-07-02
An occulter is a large diffracting screen which may be flown in conjunction with a telescope to image extrasolar planets. The edge is shaped to minimize the diffracted light in a region beyond the occulter, and a telescope may be placed in this dark shadow to view an extrasolar system with the starlight removed. Errors in position, orientation, and shape of the occulter will diffract additional light into this region, and a challenge of modeling an occulter system is to accurately and quickly model these effects. We present a fast method for the calculation of electric fields following an occulter, based on the concept of the boundary diffraction wave: the 2D structure of the occulter is reduced to a 1D edge integral which directly incorporates the occulter shape, and which can be easily adjusted to include changes in occulter position and shape, as well as the effects of sources-such as exoplanets-which arrive off-axis to the occulter. The structure of a typical implementation of the algorithm is included.
Diffraction manipulation by four-wave mixing.
Katzir, Itay; Ron, Amiram; Firstenberg, Ofer
2015-03-09
We suggest a scheme to manipulate paraxial diffraction by utilizing the dependency of a four-wave mixing process on the relative angle between the light fields. A microscopic model for four-wave mixing in a Λ-type level structure is introduced and compared to recent experimental data. We show that images with feature size as low as 10 μm can propagate with very little or even negative diffraction. The mechanism is completely different from that conserving the shape of spatial solitons in nonlinear media, as here diffraction is suppressed for arbitrary spatial profiles. At the same time, the gain inherent to the nonlinear process prevents loss and allows for operating at high optical depths. Our scheme does not rely on atomic motion and is thus applicable to both gaseous and solid media.
Fresnel diffraction in the case of an inclined image plane.
Modregger, Peter; Lübbert, Daniel; Schäfer, Peter; Köhler, Rolf; Weitkamp, Timm; Hanke, Michael; Baumbach, Tilo
2008-03-31
An extension of the theoretical formalism of Fresnel diffraction to the case of an inclined image plane is proposed. The resulting numerical algorithm speeds up computation times by typically three orders of magnitude, thus opening the possibility of utilizing previously inapplicable image analysis algorithms for this special type of a non shift-invariant imaging system. This is exemplified by adapting an iterative phase retrieval algorithm developed for electron microscopy to the case of hard x-ray imaging with asymmetric Bragg reflection (the so-called "Bragg Magnifier"). Numerical simulations demonstrate the convergence and feasibility of the iterative phase retrieval algorithm for the case of x-ray imaging with the Bragg Magnifier.
Symmetrically converging plane thermonuclear burn waves
NASA Astrophysics Data System (ADS)
Charakhch'yan, A. A.; Khishchenko, K. V.
2013-10-01
Five variants of a one-dimensional problem on synchronous bilateral action of two identical drivers on opposite surfaces of a plane layer of DT fuel with the normal or five times greater initial density, where the solution includes two thermonuclear burn waves propagating to meet one another at the symmetry plane, are simulated. A laser pulse with total absorption of energy at the critical density (in two variants) and a proton bunch that provides for a nearly isochoric heating (in three variants) are considered as drivers. A wide-range equation of state for the fuel, electron and ion heat conduction, self-radiation of plasma and plasma heating by α-particles are taken into account. In spite of different ways of ignition, various models of α-particle heat, whether the burn wave remains slow or transforms into the detonation wave, and regardless of way of such a transformation, the final value of the burn-up factor depends essentially on the only parameter Hρ0, where H is the half-thickness of the layer and ρ0 is the initial fuel density. This factor is about 0.35 at Hρ0 ≈ 1 g cm-2 and about 0.7 at Hρ0 ≈ 5 g cm-2. The expansion stage of the flow (after reflecting the burn or detonation wave from the symmetry plane) gives the main contribution in forming the final values of the burn-up factor and the gain at Hρ0 ≈ 1 g cm-2 and increases them approximately two times at Hρ0 ≈ 5 g cm-2. In the case of the proton driver, the final value of the gain is about 200 at Hρ0 ≈ 1 g cm-2 and about 2000 at Hρ0 ≈ 5 g cm-2. In the case of the laser driver, the above values are four times less in conformity with the difference between the driver energies.
Inhomogeneous plane waves and cylindrical waves in anisotropic anelastic media
NASA Astrophysics Data System (ADS)
Krebes, E. S.; Le, Lawrence H. T.
1994-12-01
In isotropic anelastic media, the phase velocity of an inhomogeneous plane body wave, which is a function of Q and the degree of inhomogeneity gamma, is significantly less than the corresponding homogeneous wave phase velocity typically only if gamma is very large (unless Q is unusually low). Here we investigate inhomogeneous waves in anisotropic anelastic media, where phase velocities are also functions of the direction of phase propagation theta, and find that (1) the low phase velocities can occur at values of gamma which are substantially less than the isotropic values and that they occur over a limited range of oblique directions theta, and (2) for large positive values of gamma, there are ranges of oblique directions theta in which the inhomogeneous waves cannot propagate at all because there is no physically acceptable solution to the dispersion relation. We show examples of how the waves of case 1 can occur in practice and cause a number of anomalous wave propagation effects. The waves of case 2, though, do not arise in practice (they do not correspond to any points on the horizontal slowness plate). We also show that in the decomposition of a cylindrical wave into plane waves, inhomogeneous plane waves occur whose amplitudes grow in the direction of phase propagation and that this direction is away from the receiver to which they are contributing. The energy in these waves does, however, travel toward the receiver, and their amplitudes decay in the direction of energy propagation. We also show that if the commonly used definition for the quality factor in an isotropic medium, Q = -Re(mu)/Im(mu) where mu is a complex modulus, is applied to an anisotropic anelastic medium in order to study absorption anisotropy, a generally unreliable measure of the anelasticity of inhomogeneous wave propagation in a given arbitrary direction is obtained. The more fundamental definition based on energy loss (i.e., 2pi/Q = Delta E/E) should be used in general, and we present
Diffraction by a Hard Half-Plane Useful Approximations to AN Exact Formulation
NASA Astrophysics Data System (ADS)
OUIS, D.
2002-04-01
In this paper, the problem of diffraction of a spherical wave by a hard half-plane is considered. The starting point is the Biot-Tolstoy theory of diffraction of a spherical wave by a fluid wedge with hard boundaries. In this theory, the field at a point in the fluid is composed eventually of a geometrical part: i.e., a direct component, one or two components due to the reflections on the sides of the hard wedge, and a diffracted component due exclusively to the presence of the edge of the wedge. The mathematical expression of this latter component has originally been given in an explicit closed form for the case of a unit momentum wave incidence, but Medwin has further developed its expression for the more useful case of a Dirac delta point excitation. The expression of this form is given in the time domain, but it is quite difficult to find exactly its Fourier transform for studying the frequency behaviour of the diffracted field. It is thus the aim of this paper to present various useful approximations of the exact expression. Among the approximations treated, three are most accurate for engineering purposes, and one of them is proposed, for its simplicity, as appropriate for most occurring practical situations.
Blackfolds, plane waves and minimal surfaces
NASA Astrophysics Data System (ADS)
Armas, Jay; Blau, Matthias
2015-07-01
Minimal surfaces in Euclidean space provide examples of possible non-compact horizon geometries and topologies in asymptotically flat space-time. On the other hand, the existence of limiting surfaces in the space-time provides a simple mechanism for making these configurations compact. Limiting surfaces appear naturally in a given space-time by making minimal surfaces rotate but they are also inherent to plane wave or de Sitter space-times in which case minimal surfaces can be static and compact. We use the blackfold approach in order to scan for possible black hole horizon geometries and topologies in asymptotically flat, plane wave and de Sitter space-times. In the process we uncover several new configurations, such as black helicoids and catenoids, some of which have an asymptotically flat counterpart. In particular, we find that the ultraspinning regime of singly-spinning Myers-Perry black holes, described in terms of the simplest minimal surface (the plane), can be obtained as a limit of a black helicoid, suggesting that these two families of black holes are connected. We also show that minimal surfaces embedded in spheres rather than Euclidean space can be used to construct static compact horizons in asymptotically de Sitter space-times.
Smoothed half-infinite plane waves: Approaching to their optimum profiles
NASA Astrophysics Data System (ADS)
Sedukhin, Andrey G.
2013-11-01
A concept of homogeneous, smoothed half-infinite plane waves is developed in the framework of a discontinuity-free decomposition of the field of a plane electromagnetic wave diffracted by a perfectly conducting half-infinite screen. It is shown that the entire diffracted field is broken down into the mentioned reflected and transmitted, smoothed half-infinite plane waves and edge quasi-cylindrical waves. In the planes of half-waists, the wavefronts of the smoothed waves are always rigorously plane, whereas their amplitude profiles are odd symmetrical in relation to respective half levels. The smoothed waves possess the phase-conjugate property relative to the planes of their half-waists and, in the first approximation, they are self-similar in the entire space. Also, the amplitude profiles at the half-waists of these waves are well reproduced within certain propagation distances. These and other properties of the smoothed half-infinite plane waves, a procedure for their approximate generation, and two simplest analytic profiles at their half-waists are considered in detail.
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
Effect of distorted illumination waves on coherent diffraction microscopy
Kohmura, Yoshiki; Nishino, Yoshinori; Ishikawa, Tetsuya; Miao Jianwei
2005-12-15
Coherent diffraction microscopy requires a well-defined illumination wave such as a plane wave on a specimen. Experimentally, a small pinhole or a focused beam is often used to reduce the illumination area but they unavoidably distort the waves. The distortion of the illumination wave causes artifacts in the phase retrieval of oversampled diffraction patterns. Using computer simulations, we searched for the conditions where strong artifacts arise by changing the Fresnel number, pinhole size, alignment error and photon statistics. The experimental setup with Fresnel number of around 1 and smaller than 1 realized a small reconstruction error when the pinhole radius is larger than a few times the specimen size. These conditions are suitable for the rotation of specimens for the three-dimensional (3D) observations. Such investigation will have an impact in the design of coherent diffraction microscopes for the 3D characterization of nanoscale materials and biological systems using the third generation synchrotron radiation and future x-ray free-electron lasers.
Correctability limitations imposed by plane-wave scintillation in multiconjugate adaptive optics.
Lee, Lawton H; Baker, Gary J; Benson, Robert S
2006-10-01
Plane-wave scintillation is shown to impose multiconjugate adaptive optics (MCAO) correctability limitations that are independent of wavefront sensing and reconstruction. Residual phase and log-amplitude variances induced by scintillation in weak turbulence are derived using linear (diffraction-based) diffractive MCAO spatial filters or (diffraction-ignorant) geometric MCAO proportional gains as open-loop control parameters. In the case of Kolmogorov turbulence, expressions involving the Rytov variance and/or weighted C(2)(n) integrals apply. Differences in performance between diffractive MCAO and geometric MCAO resemble chromatic errors. Optimal corrections based on least squares imply irreducible performance limits that are validated by wave-optic simulations.
Stolt's f-k migration for plane wave ultrasound imaging.
Garcia, Damien; Le Tarnec, Louis; Muth, Stéphan; Montagnon, Emmanuel; Porée, Jonathan; Cloutier, Guy
2013-09-01
Ultrafast ultrasound is an emerging modality that offers new perspectives and opportunities in medical imaging. Plane wave imaging (PWI) allows one to attain very high frame rates by transmission of planar ultrasound wave-fronts. As a plane wave reaches a given scatterer, the latter becomes a secondary source emitting upward spherical waves and creating a diffraction hyperbola in the received RF signals. To produce an image of the scatterers, all the hyperbolas must be migrated back to their apexes. To perform beamforming of plane wave echo RFs and return high-quality images at high frame rates, we propose a new migration method carried out in the frequency-wavenumber (f-k) domain. The f-k migration for PWI has been adapted from the Stolt migration for seismic imaging. This migration technique is based on the exploding reflector model (ERM), which consists in assuming that all the scatterers explode in concert and become acoustic sources. The classical ERM model, however, is not appropriate for PWI. We showed that the ERM can be made suitable for PWI by a spatial transformation of the hyperbolic traces present in the RF data. In vitro experiments were performed to outline the advantages of PWI with Stolt's f-k migration over the conventional delay-and-sum (DAS) approach. The Stolt's f-k migration was also compared with the Fourier-based method developed by J.-Y. Lu. Our findings show that multi-angle compounded f-k migrated images are of quality similar to those obtained with a stateof- the-art dynamic focusing mode. This remained true even with a very small number of steering angles, thus ensuring a highly competitive frame rate. In addition, the new FFT-based f-k migration provides comparable or better contrast-to-noise ratio and lateral resolution than the Lu's and DAS migration schemes. Matlab codes for the Stolt's f-k migration for PWI are provided.
Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals.
Centeno, E; Felbacq, D
2000-02-01
We present a numerical study of bidimensional photonic crystals with an emphasis on the behavior of the gaps versus the polarization and the conicity of the incident plane wave. We use a rigorous modal theory of diffraction at oblique incidence by a set of arbitrarily shaped parallel fibers. This theory allows the study of the refractive properties of bidimensional photonic crystals. We develop a heuristic method of homogenization that allows us to predict the position of the gaps and their behavior with respect to the polarization and the conicity angle. With this homogenization scheme, we also present some important elements for obtaining full gaps.
NASA Astrophysics Data System (ADS)
Migukin, Artem; Katkovnik, Vladimir; Astola, Jaakko
2010-04-01
The phase retrieval is formulated as an inverse problem, where the forward propagation is defined by Discrete Diffraction Transform (DDT) [1], [2]. This propagation model is precise and aliasing free for pixelwise invariant (pixelated) wave field distributions in the sensor and object planes. Because of finite size of sensors DDT can be ill-conditioned and the regularization is an important component of the inverse. The proposed algorithm is designed for multiple plane observations and can be treated as a generalization of the Gerchberg-Saxton iterative algorithm. The proposed algorithm is studied by numerical experiments produced for phase and amplitude modulated object distributions. Comparison versus the conventional forward propagation models such as the angular spectrum decomposition and the convolutional model used in the algorithm of the same structure shows a clear advantage of DDT enabling better accuracy and better imaging.
Calculating the Fresnel diffraction of light from a shifted and tilted plane.
Yamamoto, Kenji; Ichihashi, Yasuyuki; Senoh, Takanori; Oi, Ryutaro; Kurita, Taiichiro
2012-06-04
We propose a technique for calculating the diffraction of light in the Fresnel region from a plane that is the light source (source plane) to a plane at which the diffracted light is to be calculated (destination plane). When the wavefield of the source plane is described by a group of points on a grid, this technique can be used to calculate the wavefield of the group of points on a grid on the destination plane. The positions of both planes may be shifted, and the plane normal vectors of both planes may have different directions. Since a scaled Fourier transform is used for the calculation, it can be calculated faster than calculating the diffraction by a Fresnel transform at each point. This technique can be used to calculate and generate planar holograms from computer graphics data.
Counterpropagating Rossby waves in confined plane wakes
Biancofiore, L.; Gallaire, F.
2012-01-01
In the present work, we revisit the temporal and the spatio-temporal stability of confined plane wakes under the perspective of the counterpropagating Rossby waves (CRWs). Within the context of broken line velocity profiles, each vorticity discontinuity can be associated to a counterpropagating Rossby wave. In the case of a wake modeled by a broken line profile, the interaction of two CRWs is shown to originate in a shear instability. Following this description, we first recover the stability results obtained by Juniper [J. Fluid Mech. 590, 163–185 (2007)]10.1017/S0022112007007975 and Biancofiore and Gallaire [Phys. Fluids 23, 034103 (2011)]10.1063/1.3554764 by means of the classical normal mode analysis. In this manner, we propose an explanation of the stabilizing influence of the confinement on the temporal stability properties. The CRW description further allows us to propose a new interpretation of the counterintuitive spatio-temporal destabilization in wake flows at moderate confinement noticed by Juniper [J. Fluid Mech. 565, 171–195 (2006)]10.1017/S0022112006001558: it is well predicted by the mean group velocity of the uncoupled CRWs. PMID:22865998
Fresnel diffraction mirror for an atomic wave.
Oberst, Hilmar; Kouznetsov, Dimitrii; Shimizu, Kazuko; Fujita, Jun-Ichi; Shimizu, Fujio
2005-01-14
We have experimentally demonstrated a material-independent mirror for atomic waves that uses the Fresnel diffraction at an array of parallel ridges. He* (2 (3)S(1)) and Ne* (1s(3)) atomic waves were reflected coherently on a silicon plate with a microfabricated grating structure, consisting of narrow wall-like ridges. We measured the reflectivity at grazing incidence as a function of the incident velocity and angle. Our data show that the reflectivity on this type of mirror depends only on the distance between the ridges, the wavelength, and the incident angle, but is insensitive to the material of the grating structure. The reflectivity is observed to increase by 2 orders of magnitude, compared to that of a flat polished silicon surface, where the reflection is caused by the attractive surface potential. For He* atoms, the measured reflectivity exceeds 10% for normal incident velocities below about 25 cm/s.
Plane wave gravitons, curvature singularities and string physics
Brooks, R. . Center for Theoretical Physics)
1991-03-21
This paper discusses bounded (compactifying) potentials arising from a conspiracy between plane wave graviton and dilaton condensates. So are string propagation and supersymmetry in spacetimes with curvature singularities.
The plain truth about forming a plane wave of neutrons
NASA Astrophysics Data System (ADS)
Wagh, Apoorva G.; Abbas, Sohrab; Treimer, Wolfgang
2011-04-01
We have attained the first sub-arcsecond collimation of a monochromatic neutron beam by diffracting neutrons from a Bragg prism, viz. a single crystal prism operating in the vicinity of Bragg incidence. Analytical as well numerical computations based on the dynamical diffraction theory, led to the optimised collimator configuration of a silicon {1 1 1} Bragg prism for 5.26 Å neutrons. We fabricated a Bragg prism to these specifications, tested and operated it at the double diffractometer setup in Helmholtz Zentrum Berlin to produce a 0.58 arcsec wide monochromatic neutron beam. With a similarly optimised Bragg prism analyser of opposite asymmetry, we recorded a 0.62 arcsec wide virgin rocking curve for this ultra-parallel beam. With this nearly plane-wave neutron beam, we have recorded the first ever USANS spectrum in Q˜10-6 Å-1 range with a hydroxyapatite casein protein sample and demonstrated the instrument capability to characterise agglomerates up to 150 μm in size. The super-collimated monochromatic beam has also enabled us to record the first neutron diffraction pattern from a macroscopic grating of 200 μm period. The transverse coherence length of 175 μm (FWHM) of the ultra-parallel beam derived from the analysis of this pattern, is the greatest achieved to date for Å wavelength neutrons.
Physical optics theory for the diffraction of waves by impedance surfaces.
Umul, Yusuf Ziya
2011-02-01
The solution of the scattering problem of waves by a half-screen with equal face impedances, which was introduced by Malyughinetz, is transformed into a physical optics integral by using the inverse edge point method. The obtained integral is applied to the diffraction problem of plane waves by an impedance truncated circular cylinder and the scattered waves are derived asymptotically. The results are examined numerically.
Automatic decomposition of a complex hologram based on the virtual diffraction plane framework
NASA Astrophysics Data System (ADS)
Jiao, A. S. M.; Tsang, P. W. M.; Poon, T.-C.; Liu, J.-P.; Lee, C.-C.; Lam, Y. K.
2014-07-01
Holography is a technique for capturing the hologram of a three-dimensional scene. In many applications, it is often pertinent to retain specific items of interest in the hologram, rather than retaining the full information, which may cause distraction in the analytical process that follows. For a real optical image that is captured with a camera or scanner, this process can be realized by applying image segmentation algorithms to decompose an image into its constituent entities. However, because it is different from an optical image, classic image segmentation methods cannot be applied directly to a hologram, as each pixel in the hologram carries holistic, rather than local, information of the object scene. In this paper, we propose a method to perform automatic decomposition of a complex hologram based on a recently proposed technique called the virtual diffraction plane (VDP) framework. Briefly, a complex hologram is back-propagated to a hypothetical plane known as the VDP. Next, the image on the VDP is automatically decomposed, through the use of the segmentation on the magnitude of the VDP image, into multiple sub-VDP images, each representing the diffracted waves of an isolated entity in the scene. Finally, each sub-VDP image is reverted back to a hologram. As such, a complex hologram can be decomposed into a plurality of subholograms, each representing a discrete object in the scene. We have demonstrated the successful performance of our proposed method by decomposing a complex hologram that is captured through the optical scanning holography (OSH) technique.
Reflections, diffractions, and surface waves for an interior impedance wedge of arbitrary angle
NASA Technical Reports Server (NTRS)
Griesser, Timothy; Balanis, Constantine A.
1989-01-01
The asymptotic-impedance wedge solution for plane-wave illumination at normal incidence is examined for interior wedge diffraction. An efficient method for calculating the diffraction coefficient for arbitrary wedge angle is presented. The asymptotic solution isolates the incident, singly reflected, multiply reflected, diffracted, surface-wave, and associated-surface-wave transition fields. Multiply reflected fields (of any order) from the exact solution arise as ratios of auxiliary Maliuzhinets functions; however, by using properties of these functions, the representation can be reduced to products of reflection coefficients, much more efficient for calculation. A surface-wave transition field is added to the surface wave to retain continuity of the total field at the surface wave boundaries. This formulation is equally valid for both exterior and interior wedges with uniform but different impedances on each face, for both soft and hard polarizations.
Acoustic Propagation and Barrier Diffraction Over an Impedance Plane.
1982-10-13
propagation solution into a barrier model so that ground reflections in addition to edge diffraction could be accounted for. Only the first term in the...model so that ground reflections in addition to edge N diffraction could be accounted for. Only the first term in the asymptotic ground propagation... contemporary research needs-particularly those of underwater acoustics as weil as community and aircraft noise control-a re-evaluation of previous results has
Diffractive wave transmission in dispersive media
NASA Astrophysics Data System (ADS)
Lescarret, Vincent
The aim of this paper is to study the reflection-transmission of diffractive geometrical optic rays described by semi-linear symmetric hyperbolic systems such as the Maxwell-Lorentz equations with the anharmonic model of polarization. The framework is that of P. Donnat's thesis [P. Donnat, Quelques contributions mathématiques en optique non linéaire, chapters 1 and 2, thèse, 1996] and V. Lescarret [V. Lescarret, Wave transmission in dispersive media, M3AS 17 (4) (2007) 485-535]: we consider an infinite WKB expansion of the wave over long times/distances O(1/ɛ) and because of the boundary, we decompose each profile into a hyperbolic (purely oscillating) part and elliptic (evanescent) part as in M. William [M. William, Boundary layers and glancing blow-up in nonlinear geometric optics, Ann. Sci. École Norm. Sup. 33 (2000) 132-209]. Then to get the usual sublinear growth on the hyperbolic part of the profiles, for every corrector, we consider E, the space of bounded functions decomposing into a sum of pure transports and a "quasi compactly" supported part. We make a detailed analysis on the nonlinear interactions on E which leads us to make a restriction on the set of resonant phases. We finally give a convergence result which justifies the use of "quasi compactly" supported profiles.
Spin Wave Diffraction and Perfect Imaging of a Grating
NASA Astrophysics Data System (ADS)
Mansfeld, S.; Topp, J.; Martens, K.; Toedt, J. N.; Hansen, W.; Heitmann, D.; Mendach, S.
2012-01-01
We study the diffraction of Damon-Eshbach-type spin waves incident on a one-dimensional grating realized by microslits in a thin Permalloy film. By means of time-resolved scanning Kerr microscopy, we observe unique diffraction patterns behind the grating which exhibit replications of the spin wave field at the slits. We show that these spin wave images, with details finer than the wavelength of the incident Damon-Eshbach spin wavelength, arise from the strongly anisotropic spin wave dispersion.
Colliding plane waves in F(R)=RN gravity
NASA Astrophysics Data System (ADS)
Tahamtan, T.; Halilsoy, M.; Habib Mazharimousavi, S.
2016-10-01
We identify a region of a specific F( R)= R N gravity solution without external sources which is isometric to the spacetime of colliding plane waves (CPW). The analogy renders construction and collision of plane waves in F( R)= R N gravity possible. The geometry of the interaction region is equivalent to the Reissner-Nordström (RN) one, however there is no Einstein-Maxwell (EM) source --this is made possible by using the model of RN gravity and the parameter N>1 creates the source. For N=1, we naturally recover the plane waves (and their collision) in Einstein's theory.
Zeno dynamics in wave-packet diffraction spreading
Porras, Miguel A.; Luis, Alfredo; Gonzalo, Isabel; Sanz, Angel S.
2011-11-15
We analyze a simple and feasible practical scheme displaying Zeno, anti-Zeno, and inverse-Zeno effects in the observation of wave-packet spreading caused by free evolution. The scheme is valid both in spatial diffraction of classical optical waves and in time diffraction of a quantum wave packet. In the optical realization, diffraction spreading is observed by placing slits between a light source and a light-power detector. We show that the occurrence of Zeno or anti-Zeno effects depends just on the frequency of observations between the source and detector. These effects are seen to be related to the diffraction mode theory in Fabry-Perot resonators.
A new twist on the geometry of gravitational plane waves
NASA Astrophysics Data System (ADS)
Shore, Graham M.
2017-09-01
The geometry of twisted null geodesic congruences in gravitational plane wave spacetimes is explored, with special focus on homogeneous plane waves. The rôle of twist in the relation of the Rosen coordinates adapted to a null congruence with the fundamental Brinkmann coordinates is explained and a generalised form of the Rosen metric describing a gravitational plane wave is derived. The Killing vectors and isometry algebra of homogeneous plane waves (HPWs) are described in both Brinkmann and twisted Rosen form and used to demonstrate the coset space structure of HPWs. The van Vleck-Morette determinant for twisted congruences is evaluated in both Brinkmann and Rosen descriptions. The twisted null congruences of the Ozsváth-Schücking, `anti-Mach' plane wave are investigated in detail. These developments provide the necessary geometric toolkit for future investigations of the rôle of twist in loop effects in quantum field theory in curved spacetime, where gravitational plane waves arise generically as Penrose limits; in string theory, where they are important as string backgrounds; and potentially in the detection of gravitational waves in astronomy.
Plane Waves in a Transparent Isotropic Chiral Medium
NASA Astrophysics Data System (ADS)
Fisanov, V. V.
2015-04-01
A homogeneous isotropic transparent chiral medium supports two normal plane waves with left and right circular polarization and differently valued positive wave numbers. The presence or absence of forward and backward Beltrami waves and their helicity are regulated by the signs of the permittivity and permeability and the strength of the chirality. The ray refractive index is a universal parameter whose sign differentiates the forward and backward waves.
Distorted Plane Waves on Manifolds of Nonpositive Curvature
NASA Astrophysics Data System (ADS)
Ingremeau, Maxime
2017-03-01
We will consider the high frequency behaviour of distorted plane waves on manifolds of nonpositive curvature which are Euclidean or hyperbolic near infinity, under the assumption that the curvature is negative close to the trapped set of the geodesic flow and that the topological pressure associated to half the unstable Jacobian is negative. We obtain a precise expression for distorted plane waves in the high frequency limit, similar to the one in Guillarmou and Naud (Am J Math 136:445-479, 2014) in the case of convex co-compact manifolds. In particular, we will show {L_{loc}^∞} bounds on distorted plane waves that are uniform with frequency. We will also show a small-scale equidistribution result for the real part of distorted plane waves, which implies sharp bounds for the volume of their nodal sets.
Multiple-wave diffraction in high energy resolution back-reflecting x-ray optics.
Stetsko, Yuri P; Keister, J W; Coburn, D S; Kodituwakku, C N; Cunsolo, A; Cai, Y Q
2011-10-07
We have studied the effects of multiple-wave diffraction in a novel optical scheme recently published by Shvyd'ko et al. utilizing Bragg diffraction of x rays in backscattering geometry from asymmetrically cut crystals for achieving energy resolutions beyond the intrinsic width of the Bragg reflection. By numerical simulations based on dynamic x-ray diffraction and by experimentation involving two-dimensional angular scans of the back-reflecting crystal, multiple-wave diffraction was found to contribute up to several tens percent loss of efficiency but can be avoided without degrading the energy resolution of the original scheme by careful choice of azimuthal orientation of the diffracting crystal surface and by tilting of the crystal perpendicular to the dispersion plane.
Continuous-wave terahertz multi-plane in-line digital holography
NASA Astrophysics Data System (ADS)
Huang, Haochong; Wang, Dayong; Li, Weihua; Rong, Lu; Taylor, Zachary D.; Deng, Qinghua; Li, Bin; Wang, Yunxin; Wu, Weidong; Panezai, Spozmai
2017-07-01
Terahertz digital holography is a non-scanning and real time method for reconstructing the absorption and phase distributions of the wave-front diffracted by a given sample simultaneously in the terahertz region. A continuous-wave terahertz in-line digital holographic multi-plane imaging method is presented here for achieving a three-dimensional shape of a specific portion of a sample with the best possible focus. The three enhancement techniques of synthetic aperture, autofocusing and phase retrieval are applied to the single plane recordings for achieving a high resolution, good quality and optimally focused reconstructed image. Later, multi-plane reconstructed images are processed with the threshold mask and a three dimensional profile of the sample is obtained. Experimental verification confirms that the proposed method is a valid tool for acquiring multi-plane information of a target in the terahertz range.
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…
Exact Nonlinear Internal Equatorial Waves in the f-plane
NASA Astrophysics Data System (ADS)
Hsu, Hung-Chu
2016-07-01
We present an explicit exact solution of the nonlinear governing equations for internal geophysical water waves propagating westward above the thermocline in the f-plane approximation near the equator. Moreover, the mass transport velocity induced by this internal equatorial wave is eastward and a westward current occurs in the transition zone between the great depth where the water is still and the thermocline.
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…
Plane wave (curl; Ω) conforming finite elements for Maxwell's equations
NASA Astrophysics Data System (ADS)
Ledger, P. D.; Morgan, K.; Hassan, O.; Weatherill, N. P.
This paper proposes a discretisation of Maxwell's equations which combines the popular edge elements of Nédélec with expansions of plane waves. The method is applied to simple two dimensional electromagnetic wave propagation and scattering simulations and issues of accuracy and matrix conditioning are investigated.
Exact Steady Azimuthal Internal Waves in the f-Plane
NASA Astrophysics Data System (ADS)
Hsu, Hung-Chu
2017-03-01
We present an explicit exact solution of the nonlinear governing equations with Coriolis and centripetal terms in the f-plane approximation for internal geophysical trapped waves with a uniform current near the equator. This solution describes in the Lagrangian framework azimuthal equatorial internal waves propagating westward in a stratified rotational fluid.
Diffraction of three-colour radiation on an acoustic wave
Kotov, V M
2015-07-31
We study acousto-optic Bragg diffraction of three-colour radiation having wavelengths of 488, 514 and 633 nm on a single acoustic wave propagating in a TeO{sub 2} crystal. A technique is developed that allows one to find diffraction regimes with a proportional change in the intensity of all radiations by varying the acoustic power. According to the technique, radiation with a maximum wavelength has to be in strict Bragg synchronism with the acoustic wave, while other radiations diffract during the synchronism detuning. The results obtained using this technique are experimentally confirmed. (diffraction of light)
Soft gravitons and the memory effect for plane gravitational waves
NASA Astrophysics Data System (ADS)
Zhang, P.-M.; Duval, C.; Gibbons, G. W.; Horvathy, P. A.
2017-09-01
The "gravitational memory effect" due to an exact plane wave provides us with an elementary description of the diffeomorphisms associated with the analogue of "soft gravitons for this nonasymptotically flat system. We explain how the presence of the latter may be detected by observing the motion of freely falling particles or other forms of gravitational wave detection. Numerical calculations confirm the relevance of the first, second and third time integrals of the Riemann tensor pointed out earlier. Solutions for various profiles are constructed. It is also shown how to extend our treatment to Einstein-Maxwell plane waves and a midisuperspace quantization is given.
The Plane-Wave/Super Yang-Mills Duality
Sadri, D
2003-10-14
We present a self-contained review of the Plane-wave/super-Yang-Mills duality, which states that strings on a plane-wave background are dual to a particular large R-charge sector of N=4, D=4 superconformal U(N) gauge theory. This duality is a specification of the usual AdS/CFT correspondence in the ''Penrose limit''. The Penrose limit of AdS{sub 5} S{sup 5} leads to the maximally supersymmetric ten dimensional plane-wave (henceforth the plane-wave) and corresponds to restricting to the large R-charge sector, the BMN sector, of the dual superconformal field theory. After assembling the necessary background knowledge, we state the duality and review some of its supporting evidence. We review the suggestion by 't Hooft that Yang-Mills theories with gauge groups of large rank might be dual to string theories and the realization of this conjecture in the form of the AdS/CFT duality. We discuss plane-waves as exact solutions of supergravity and their appearance as Penrose limits of other backgrounds, then present an overview of string theory on the plane-wave background, discussing the symmetries and spectrum. We then make precise the statement of the proposed duality, classify the BMN operators, and mention some extensions of the proposal. We move on to study the gauge theory side of the duality, studying both quantum and non-planar corrections to correlation functions of BMN operators, and their operator product expansion. The important issue of operator mixing and the resultant need for re-diagonalization is stressed. Finally, we study strings on the plane-wave via light-cone string field theory, and demonstrate agreement on the one-loop correction to the string mass spectrum and the corresponding quantity in the gauge theory. A new presentation of the relevant superalgebra is given.
Aperture domain model image reconstruction (ADMIRE) with plane wave synthesis
NASA Astrophysics Data System (ADS)
Dei, Kazuyuki; Tierney, Jaime; Byram, Brett
2017-03-01
In our previous studies, we demonstrated that our aperture domain model-based clutter suppression algorithm improved image quality of in vivo B-mode data obtained from focused transmit beam sequences. Our approach suppresses off-axis clutter and reverberation and tackles limitations of related algorithms because it preserves RF channel signals and speckle statistics. We call the algorithm aperture domain model image reconstruction (ADMIRE). We previously focused on reverberation suppression, but ADMIRE is also effective at suppressing off-axis clutter. We are interested in how ADMIRE performs on plane wave sequences and the impact of AD- MIRE applied before and after synthetic beamforming of steered plane wave sequences. We employed simulated phantoms using Field II and tissue-mimicking phantoms to evaluate ADMIRE applied to plane wave sequencing. We generated images acquired from plane waves with and without synthetic aperture synthesis and measured contrast and contrast-to-noise ratio (CNR). For simulated cyst images formed from single plane waves, the contrast for delay-and-sum (DAS) and ADMIRE are 15.64 dB and 28.34 dB, respectively, while the CNR are 1.76 dB and 3.90 dB, respectively. Based on these findings, ADMIRE improves plane wave image quality. We also applied ADMIRE to resolution phantoms having a point target at 3 cm depth on-axis, simulating the point spread functions from data obtained from 1 and 75 steered plane waves, along with linear scan at focus of 3 and 4 cm depth. We then examined the outcome of applying ADMIRE before and after synthetic aperture processing. Finally, we applied this to an in vivo carotid artery.
On the propagation of plane waves above an impedance surface
NASA Technical Reports Server (NTRS)
Zhong, F. H.; Vanmoorhem, W. K.
1990-01-01
The propagation of grazing incidence plane waves along a finite impedance boundary is investigated. A solution of the semi-infinite problem, where a harmonic motion, parallel to the boundary, is imposed along a line perpendicular to the boundary, is obtained. This solution consists of quasiplane waves, waves moving parallel to the boundary with amplitude and phase variations perpendicular to the boundary. Several approximations to the full solution are considered.
Fan, Quanping; Liu, Yuwei; Yang, Zuhua; Wei, Lai; Zhang, Qiangqiang; Chen, Yong; Hu, Feng; Wang, Chuanke; Gu, Yuqiu; Zhou, Weimin; Jiang, Gang; Cao, Leifeng
2015-06-15
By combining the single-order dispersion properties of quasi-sinusoidal single-order diffraction transmission gratings (QSTG) and the single-foci focusing properties of annulus-sector-shaped-element binary Gabor zone plate (ASZP), we propose a novel focusing single-order diffraction transmission grating (FSDTG). Different from the diffraction patterns of a normal transmission grating (TG), it has a focusing plane perpendicular to the grating surface. Numerical simulations are carried out to verify its diffraction patterns in the framework of Fresnel-Kirchhoff diffraction. Higher-order diffraction components of higher harmonics can be effectively suppressed by the FSDTG we designed. And we find that the focal depth and resolving power are only determined by the structure parameters of our FSDTG by theoretical estimations.
On the direct initiation of a plane detonation wave
NASA Astrophysics Data System (ADS)
Clarke, J. F.; Kassoy, D. R.; Riley, N.
1986-11-01
It is assumed that energy is transferred at a rapid rate through a plane wall into a spatially uniform and initially stagnant combustible gas mixture. This action generates a shock wave, just as it does in an inert mixture, and also switches on a significant rate of chemical reaction. The Navier-Stokes equations for plane unsteady flow are integrated numerically in order to reveal the subsequent history of events. Four principal time domains are identified, namely 'early', 'transitional', 'formation', and 'ZND'. The first contains a conduction-dominated explosion and formation of a shock wave; in the second interval the shock wave is responsible for the acceleration of chemical activity, which becomes intense during the 'formation' period. Finally a wave whose structure is in essence that of a ZND detonation wave emerges.
High-frequency wave diffraction by an impedance segment at oblique incidence
NASA Astrophysics Data System (ADS)
Korol'kov, A. I.; Shanin, A. V.
2016-11-01
The plane problem of high-frequency acoustic wave diffraction by a segment with impedance boundary conditions is considered. The angle of incidence of waves is assumed to be small (oblique). The paper generalizes the method previously developed by the authors for an ideal segment (with Dirichlet or Neumann boundary conditions). An expression for the directional pattern of the scattered field is derived. The optical theorem is proved for the case of the parabolic equation. The surface wave amplitude is calculated, and the results are numerically verified by the integral equation method.
Simple plane wave implementation for photonic crystal calculations.
Guo, Shangping; Albin, Sacharia
2003-01-27
A simple implementation of plane wave method is presented for modeling photonic crystals with arbitrary shaped 'atoms'. The Fourier transform for a single 'atom' is first calculated either by analytical Fourier transform or numerical FFT, then the shift property is used to obtain the Fourier transform for any arbitrary supercell consisting of a finite number of 'atoms'. To ensure accurate results, generally, two iterating processes including the plane wave iteration and grid resolution iteration must converge. Analysis shows that using analytical Fourier transform when available can improve accuracy and avoid the grid resolution iteration. It converges to the accurate results quickly using a small number of plane waves. Coordinate conversion is used to treat non-orthogonal unit cell with non-regular 'atom' and then is treated by standard numerical FFT. MATLAB source code for the implementation requires about less than 150 statements, and is freely available at http://www.lions.odu.edu/~sguox002.
Reflection of a plane shock wave from a slit
NASA Astrophysics Data System (ADS)
Serov, A. O.; Shtemenko, L. S.; Shugaev, F. V.
Laser shadow photography was used in a shock-tube visualization study of a plane shock wave reflected from a slit. The working gases were air and Freon 14, and the Mach number of the incident shock wave was in the 2-3 range. An intense interaction between the reflected wave and the walls of the slit was observed. This interaction could lead to the disappearance of the rectilinear part of this wave, thus reducing the load experienced by the body during this type of reflection.
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).
Adaptive density partitioning technique in the auxiliary plane wave method
NASA Astrophysics Data System (ADS)
Kurashige, Yuki; Nakajima, Takahito; Hirao, Kimihiko
2006-01-01
We have developed the adaptive density partitioning technique (ADPT) in the auxiliary plane wave method, in which a part of the density is expanded to plane waves, for the fast evaluation of Coulomb matrix. Our partitioning is based on the error estimations and allows us to control the accuracy and efficiency. Moreover, we can drastically reduce the core Gaussian products that are left in Gaussian representation (its analytical integrals is the bottleneck in this method). For the taxol molecule with 6-31G** basis, the core Gaussian products accounted only for 5% in submicrohartree error.
Plane-wave analysis of solar acoustic-gravity waves: A (slightly) new approach
NASA Technical Reports Server (NTRS)
Bogart, Richard S.; Sa, L. A. D.; Duvall, Thomas L., Jr.; Haber, Deborah A.; Toomre, Juri; Hill, Frank
1995-01-01
The plane-wave decomposition of the acoustic-gravity wave effects observed in the photosphere provides a computationally efficient technique that probes the structure of the upper convective zone and boundary. In this region, the flat sun approximation is considered as being reasonably accurate. A technique to be used for the systematic plane-wave analysis of Michelson Doppler imager data, as part of the solar oscillations investigation, is described. Estimates of sensitivity are presented, and the effects of using different planar mappings are discussed. The technique is compared with previous approaches to the three dimensional plane-wave problem.
Machikhin, A S; Pozhar, V E
2015-02-28
We consider the problem of determining the spatial and spectral image distortions arising from anisotropic diffraction by ultrasonic waves in crystals with ordinary polarised light (o → e). By neglecting the small-birefringence approximation, we obtain analytical solutions that describe the dependence of the diffraction angles and wave mismatch on the acousto-optic (AO) interaction geometry and crystal parameters. The formulas derived allow one to calculate and analyse the magnitude of diffraction-induced spatial and spectral image distortions and to identify the main types of distortions: chromatic compression and trapezoidal deformation. A comparison of the values of these distortions in the diffraction of ordinary and extraordinary polarised light shows that they are almost equal in magnitude and opposite in signs, so that consistent diffraction (o → e → o or e → o → e) in two identical AO cells rotated through 180° in the plane of diffraction can compensate for these distortions. (diffraction of radiation)
Metaphysics of colliding self-gravitating plane waves
Matzner, R.A.; Tipler, F.J.
1984-04-15
We discuss certain global features of colliding plane-wave solutions to Einstein's equations. In particular, we show that the apparently local curvature singularities both in the Khan-Penrose solution and in the Bell-Szekeres solution are actually global. These global singularities are associated with the breakdown of nondegenerate planar symmetry in the characteristic initial data sets.
Metaphysics of colliding self-gravitating plane waves
NASA Astrophysics Data System (ADS)
Matzner, Richard A.; Tipler, Frank J.
1984-04-01
We discuss certain global features of colliding plane-wave solutions to Einstein's equations. In particular, we show that the apparently local curvature singularities both in the Khan-Penrose solution and in the Bell-Szekeres solution are actually global. These global singularities are associated with the breakdown of nondegenerate planar symmetry in the characteristic initial data sets.
D-branes in Type IIB plane wave background
Lee, Bum-Hoon
2007-01-12
We classify and summarize the intersecting supersymmetric D-branes in the type IIB plane wave background, based on the Green-Schwarz superstring formulation. Many new configurations appears if we turn on the electric or magnetic background fields or boost the D-branes. Applications to the phenomelogical models are left for further study.
Diffraction of dust acoustic waves by a circular cylinder
Kim, S.-H.; Heinrich, J. R.; Merlino, R. L.
2008-09-15
The diffraction of dust acoustic (DA) waves around a long dielectric rod is observed using video imaging methods. The DA waves are spontaneously excited in a dusty plasma produced in a direct current glow discharge plasma. The rod acquires a negative charge that produces a coaxial dust void around it. The diameter of the void is the effective size of the 'obstacle' encountered by the waves. The wavelength of the DA waves is approximately the size of the void. The observations are considered in relation to the classical problem of the diffraction of sound waves from a circular cylinder, a problem first analyzed by Lord Rayleigh [Theory of Sound, 2nd ed. (MacMillan, London, 1896)].
Measuring method of diffraction efficiency for plane grating based on Fourier spectral technology.
Ma, Zhenyu; Qi, Xiangdong; Li, Xiaotian; Zhang, Shanwen; Bayanheshig; Yu, Hongzhu; Yu, Haili; Jiao, Qingbin
2016-01-20
A traditional double monochromatic measurement instrument of diffraction efficiency for a plane grating involves two major problems: one is the differences of output spectrum bandwidths during measurement of a standard reflection mirror and the tested grating; the other is overlapping of diffracted spectra, which influence testing accuracy of diffraction efficiency. In this paper, a new measuring method of diffraction efficiency based on Fourier spectral technology is presented. The mathematical model of diffraction efficiency is first deduced and then verified by ray tracing and Fourier optics simulation. The influences of the moving cube corner's tilt error, lateral shift error, and maximal moving distance error on the measurement accuracy are analyzed in detail. The analyses provide theoretical references for designing diffraction efficiency instruments. Compared with the traditional diffraction efficiency measurement instrument with double monochromator structure, our method not only improves the measurement accuracy of diffraction efficiency but also has the advantage of high luminous flux, high spectral resolution, multiwavelength measurement in mean time, and high wavenumber accuracy.
Jeong, Hyunjo Cho, Sungjong; Zhang, Shuzeng; Li, Xiongbing
2016-04-15
In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave is defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.
Light Diffraction by Large Amplitude Ultrasonic Waves in Liquids
NASA Technical Reports Server (NTRS)
Adler, Laszlo; Cantrell, John H.; Yost, William T.
2016-01-01
Light diffraction from ultrasound, which can be used to investigate nonlinear acoustic phenomena in liquids, is reported for wave amplitudes larger than that typically reported in the literature. Large amplitude waves result in waveform distortion due to the nonlinearity of the medium that generates harmonics and produces asymmetries in the light diffraction pattern. For standing waves with amplitudes above a threshold value, subharmonics are generated in addition to the harmonics and produce additional diffraction orders of the incident light. With increasing drive amplitude above the threshold a cascade of period-doubling subharmonics are generated, terminating in a region characterized by a random, incoherent (chaotic) diffraction pattern. To explain the experimental results a toy model is introduced, which is derived from traveling wave solutions of the nonlinear wave equation corresponding to the fundamental and second harmonic standing waves. The toy model reduces the nonlinear partial differential equation to a mathematically more tractable nonlinear ordinary differential equation. The model predicts the experimentally observed cascade of period-doubling subharmonics terminating in chaos that occurs with increasing drive amplitudes above the threshold value. The calculated threshold amplitude is consistent with the value estimated from the experimental data.
Radiation of Electron in the Field of Plane Light Wave
Zelinsky, A.; Drebot, I.V.; Grigorev, Yu.N.; Zvonareva, O.D.; Tatchyn, R.; /SLAC
2006-02-24
Results of integration of a Lorentz equation for a relativistic electron moving in the field of running, plane, linear polarized electromagnetic wave are presented in the paper. It is shown that electron velocities in the field of the wave are almost periodic functions of time. For calculations of angular spectrum of electron radiation intensity expansion of the electromagnetic field in a wave zone into generalized Fourier series was used. Expressions for the radiation intensity spectrum are presented in the paper. Derived results are illustrated for electron and laser beam parameters of NSC KIPT X-ray generator NESTOR. It is shown that for low intensity of the interacting electromagnetic wave the results of energy and angular spectrum calculations in the frame of classical electrodynamics completely coincide with calculation results produced using quantum electrodynamics. Simultaneously, derived expressions give possibilities to investigate dependence of energy and angular Compton radiation spectrum on phase of interaction and the interacting wave intensity.
Ultrafast vascular strain compounding using plane wave transmission.
Hansen, H H G; Saris, A E C M; Vaka, N R; Nillesen, M M; de Korte, C L
2014-03-03
Deformations of the atherosclerotic vascular wall induced by the pulsating blood can be estimated using ultrasound strain imaging. Because these deformations indirectly provide information on mechanical plaque composition, strain imaging is a promising technique for differentiating between stable and vulnerable atherosclerotic plaques. This paper first explains 1-D radial strain estimation as applied intravascularly in coronary arteries. Next, recent methods for noninvasive vascular strain estimation in a transverse imaging plane are discussed. Finally, a compounding technique that our group recently developed is explained. This technique combines motion estimates of subsequently acquired focused ultrasound images obtained at various insonification angles. However, because the artery moves and deforms during the multi-angle acquisition, errors are introduced when compounding. Recent advances in computational power have enabled plane wave ultrasound acquisition, which allows 100 times faster image acquisition and thus might resolve the motion artifacts. In this paper the performance of strain imaging using plane wave compounding is investigated using simulations of an artery with a vulnerable plaque and experimental data of a two-layered vessel phantom. The results show that plane wave compounding outperforms 0° focused strain imaging. For the simulations, the root mean squared error reduced by 66% and 50% for radial and circumferential strain, respectively. For the experiments, the elastographic signal-to-noise and contrast-to-noise ratio (SNR(e) and CNR(e)) increased with 2.1 dB and 3.7 dB radially, and 5.6 dB and 16.2dB circumferentially. Because of the high frame rate, the plane wave compounding technique can even be further optimized and extended to 3D in future.
Optimization of double patterning split by analyzing diffractive orders in the pupil plane
NASA Astrophysics Data System (ADS)
Zeggaoui, N.; Farys, V.; Trouiller, Y.; Yesilada, E.; Robert, F.; Besacier, M.
2010-09-01
In double patterning technology (DPT), two adjacent features must be assigned opposite colors, corresponding to different exposures if their pitch is less than a predefined minimum coloring pitch. However, certain design orientations for which pattern features separated by more than the minimum coloring pitch cannot be imaged with either of the two exposures. In such cases, there are no aerial images formed because in these directions there are no constructive interferences between diffractive orders in the pupil plane. The 22nm and 16nm nodes require the use of pixelized sources that will be generated using SMO (source mask co-optimization). Such pixelized sources while helpful in improving the contrast for selected configurations can lead to degraded contrast for configurations which have not been set during the SMO process. Therefore, we analyze the diffractive orders interactions in the pupil plane in order to detect limited orientations in the design and thus propose a decomposition to overcome the problem.
Gravitational scattering of zero-rest-mass plane waves
NASA Technical Reports Server (NTRS)
De Logi, W. K.; Kovacs, S. J., Jr.
1977-01-01
The Feyman-diagram technique is used to calculate the differential cross sections for the scattering of zero-rest-mass plane waves of spin 0, 1, and 2 by linearized Schwarzschild and Kerr geometries in the long-wavelength weak-field limit. It is found that the polarization of right (or left) circularly polarized electromagnetic waves is unaffected by the scattering process (i.e., helicity is conserved) and that the two helicity (polarization) states of the photon are scattered differently by the Kerr geometry. This coupling between the photon helicity and the angular momentum of the scatterer also leads to a partial polarization of unpolarized incident light. For gravitational waves, on the other hand, there is neither helicity conservation nor helicity-dependent scattering; the angular momentum of the scatterer has no polarizing effect on incident unpolarized gravitational waves.
Diffractive Focusing of Waves in Time and in Space.
Weisman, Dror; Fu, Shenhe; Gonçalves, Manuel; Shemer, Lev; Zhou, Jianying; Schleich, Wolfgang P; Arie, Ady
2017-04-14
We study the general wave phenomenon of diffractive focusing from a single slit for two types of waves and demonstrate several properties of this effect. Whereas in the first situation, the envelope of a surface gravity water wave is modulated in time by a rectangular function, leading to temporal focusing, in the second example, surface plasmon polariton waves are focused in space by a thin metal slit to a transverse width narrower than the slit itself. The observed evolution of the phase carrier of the water waves is measured for the first time and reveals a nearly flat phase as well as an 80% increase in the intensity at the focal point. We then utilize this flat phase with plasmonic beams in the spatial domain, and study the case of two successive slits, creating a tighter focusing of the waves by putting the second slit at the focal point of the first slit.
Wave diffraction around three-dimensional bodies in a current
Cheung, K.F.; Isaacson, M.; Lee, J.W.
1996-11-01
The effects of a collinear current on the diffraction of regular waves around three-dimensional surface-piercing bodies are examined. With the current speed assumed to be small, the boundary-value problem is separated into a steady current problem with a rigid wall condition applied at the still water level and a linear wave propagation problem in the resulting current field. The boundary conditions of the wave propagation problem are satisfied by a time-stepping procedure and the field solution is obtained by an integral equation method. Free surface profiles, runup, and wave forces are described for a vertical circular cylinder in combined waves and a current. The current is shown to affect significantly the steady drift force and runup predictions. Comparisons of the computed wave forces are made with a previous numerical solution involving a semi-immersed sphere in deep water, and indicate good agreement.
Achieving control of in-plane elastic waves
NASA Astrophysics Data System (ADS)
Brun, M.; Guenneau, S.; Movchan, A. B.
2009-02-01
We derive the elastic properties of a cylindrical cloak for in-plane coupled shear and pressure waves. The cloak is characterized by a rank 4 elasticity tensor with spatially varying entries, which are deduced from a geometric transform. Remarkably, the Navier equations retain their form under this transform, which is generally untrue [G. W. Milton et al., N. J. Phys. 8, 248 (2006)]. The validity of our approach is confirmed by comparison of the analytic Green's function in homogeneous isotropic elastic space against full-wave finite element computations in a heterogeneous anisotropic elastic region surrounded by perfectly matched layers.
Scattering of Plane Guided Waves Obliquely Incident on Straight Features
NASA Astrophysics Data System (ADS)
Wilcox, P. D.; Velichko, A.; Drinkwater, B. W.; Croxford, A. J.; Todd, M. D.
2011-06-01
A semi-analytical finite element model is developed to study the scattering of plane guided waves obliquely incident on a straight geometric feature. The model is first used to investigate the reflection of the S0 mode from a free edge and the results are compared to those of bulk waves reflecting from a free boundary. The model is then used to predict the transmission of the S0 mode past an adhesively-bonded stiffener. The results obtained are in excellent agreement with experimental measurements.
Scattering of plane guided waves obliquely incident on straight features
Wilcox, P. D.; Velichko, A.; Drinkwater, B. W.; Croxford, A. J.; Todd, M. D.
2011-06-23
A semi-analytical finite element model is developed to study the scattering of plane guided waves obliquely incident on a straight geometric feature. The model is first used to investigate the reflection of the S0 mode from a free edge and the results are compared to those of bulk waves reflecting from a free boundary. The model is then used to predict the transmission of the S0 mode past an adhesively-bonded stiffener. The results obtained are in excellent agreement with experimental measurements.
Scattering of a CW plane wave by a pulse
NASA Astrophysics Data System (ADS)
Trivett, D. H.; Rogers, P. H.
1982-05-01
A procedure similar to the CW crossed-beam calculation of Ingard and Pridmore-Brown (1956) is used to calculate the far field scattered sound pressure of a pulse interacting with a plane wave. The scattered sound is found to be at neither the sum nor the difference frequency. It is suggested that this type of interaction is ideal for investigating the scattering of sound by sound, and a numerical solution is used to discuss the general features of the nearfield waveform.
Holography and entropy bounds in the plane wave matrix model
Bousso, Raphael; Mints, Aleksey L.
2006-06-15
As a quantum theory of gravity, matrix theory should provide a realization of the holographic principle, in the sense that a holographic theory should contain one binary degree of freedom per Planck area. We present evidence that Bekenstein's entropy bound, which is related to area differences, is manifest in the plane wave matrix model. If holography is implemented in this way, we predict crossover behavior at strong coupling when the energy exceeds N{sup 2} in units of the mass scale.
Diffracted and head waves associated with waves on nonseparable surfaces
NASA Technical Reports Server (NTRS)
Barger, Raymond L.
1992-01-01
A theory is presented for computing waves radiated from waves on a smooth surface. With the assumption that attention of the surface wave is due only to radiation and not to dissipation in the surface material, the radiation coefficient is derived in terms of the attenuation factor. The excitation coefficient is determined by the reciprocity condition. Formulas for the shape and the spreading of the radiated wave are derived, and some sample calculations are presented. An investigation of resonant phase matching for nonseparable surfaces is presented with a sample calculation. A discussion of how such calculations might be related to resonant frequencies of nonseparable thin shell structures is included. A description is given of nonseparable surfaces that can be modeled in the vector that facilitates use of the appropriate formulas of differential geometry.
Diffraction of Gaussian wave packets by a single slit
NASA Astrophysics Data System (ADS)
Zecca, A.
2011-02-01
A two-dimensional formulation of particle diffraction by a single slit is proposed within Schrödinger QM. The study is done in terms of Gaussian wave packets. A "confinement" assumption is considered together with a previous "truncation" assumption when the wave packet passes the slit. In the limiting situation of entering Gaussian wave packet peaked in the transverse-momentum probability distribution, the diffraction pattern results in an unaltered central maximum with lateral maxima narrower and higher than in the absence of the confinement assumption. For entering wave packets peaked in the transverse position probability distribution, the diffraction pattern consists of a central Gaussian spot with lateral diffraction maxima, not present in the absence of the "confinement" assumption, whose visibility depends on the configuration of the parameters. With a different analysis, a similar effect was obtained also in G. Kalbermann (J. Phys. A: Math. Gen. 35, 4599 (2002)). Its experimental verification seems of interest to discriminate between Schrödinger QM and stochastic electrodynamics with spin.
Transition operators in electromagnetic-wave diffraction theory - General theory
NASA Technical Reports Server (NTRS)
Hahne, G. E.
1992-01-01
A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.
Transition operators in electromagnetic-wave diffraction theory - General theory
NASA Technical Reports Server (NTRS)
Hahne, G. E.
1992-01-01
A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.
Part A: Nonprincipal-plane scattering from flat plates: Second-order and corner diffractions
NASA Technical Reports Server (NTRS)
Balanis, Constantine A.; Polka, Lesley A.
1989-01-01
Two models of a flat plate for nonprincipal-plane scattering are explored. The first is a revised version of the Physical Optics/Physical Theory of Diffraction (PO/PTD) model with second-order PTD equivalent currents included to account for second-order interactions among the plate edges. The second model uses a heurisitcally derived corner diffraction coefficient to account for the corner scattering mechanism. The patterns obtained using the newer models were compared to the data of previously reported models, the Moment Method (MM), and experimental results. Near normal incidence, all the models agreed; however, near grazing incidence a need for higher-order and corner diffraction mechanisms was noted. In many instances the second-order and corner-scattered fields which were formulated improved the results.
Yin, Meng; Rouvière, Olivier; Glaser, Kevin J.; Ehman, Richard L.
2008-01-01
Magnetic Resonance Elastography (MRE) is a technique for quantifying the acoustic response of biological tissues to propagating waves applied at low frequencies in order to evaluate mechanical properties. Application-specific MRE drivers are typically required to effectively deliver shear waves within the tissue of interest. Surface MRE drivers with transversely oriented vibrations have often been used to directly generate shear waves. These drivers may have disadvantages in certain applications, such as poor penetration depth and inflexible orientation. Therefore, surface MRE drivers with longitudinally oriented vibrations are used in some situations. The purpose of this work was to investigate and optimize a longitudinal driver system for MR elastography applications. It is shown that a cone-like hemispherical distribution of shear waves are generated by these drivers and the wave propagation is governed by diffraction in the near field. Using MRE visualization of the vector displacement field, the properties of the shear wave field created by longitudinal MRE drivers of various sizes were studied to identify optimum shear wave imaging planes. The results offer insights and improvements in both experimental design and imaging plane selection for 2-D MRE data acquisition. PMID:18467059
2006-07-01
model M2D . Future technical notes in this series will describe the interface and report additional validation and enhancements of WABED...circulation model M2D (Militello et al. 2004) is operated with WABED for calculation of the wave-induced current. A background flood current was supplied as...input to the wave model. To calculate the wave-induced current, M2D was forced by radiation stresses (Longuet-Higgins and Stewart 1964) computed by
Diffraction correction for precision surface acoustic wave velocity measurements
NASA Astrophysics Data System (ADS)
Ruiz M., Alberto; Nagy, Peter B.
2002-09-01
Surface wave dispersion measurements can be used to nondestructively characterize shot-peened, laser shock-peened, burnished, and otherwise surface-treated specimens. In recent years, there have been numerous efforts to separate the contribution of surface roughness from those of near-surface material variations, such as residual stress, texture, and increased dislocation density. As the accuracy of the dispersion measurements was gradually increased using state-of-the-art laser-ultrasonic scanning and sophisticated digital signal processing methods, it was recognized that a perceivable dispersive effect, similar to the one found on rough shot-peened specimens, is exhibited by untreated smooth surfaces as well. This dispersion effect is on the order of 0.1%, that is significantly higher than the experimental error associated with the measurements and comparable to the expected velocity change produced by near-surface compressive residual stresses in metals below their yield point. This paper demonstrates that the cause of this apparent dispersion is the diffraction of the surface acoustic wave (SAW) as it travels over the surface of the specimen. The results suggest that a diffraction correction may be introduced to increase the accuracy of surface wave dispersion measurements. A simple diffraction correction model was developed for surface waves and this correction was subsequently validated by laser-interferometric velocity measurements on aluminum specimens. copyright 2002 Acoustical Society of America.
Millimeter-wave Bragg diffraction of microfabricated crystal structures
NASA Astrophysics Data System (ADS)
Yuan, C. P.; Lin, S. Y.; Chang, T. H.; Shew, B. Y.
2011-06-01
A compact diffraction apparatus is developed with millimeter-wave propagation between two parallel plates. Two types of microfabricated model crystals are individually mounted on a rotatable structure. In contrast to previous work, the experimental results agree well with Bragg's predictions because multiple scattering is minimized in this configuration. Factors that affect the resolution and signal strength, such as the number of scatterers, cylinder radius, and the distance between the detector and the model crystal, are analyzed. The apparatus offers a visually accessible way to teach students about crystal structure as well as scattering and diffraction.
The Study of Shock Waves and Laser Excited Lattice Dynamics using Ultrafast X-ray Diffraction
NASA Astrophysics Data System (ADS)
Funk, David J.; Hur, N.; Wark, J.
2005-07-01
We have studied the picosecond lattice dynamics of optically pumped hexagonal manganite LuMnO3 using ultrafast x-ray diffraction. The results show a shift and broadening of the diffraction curve due to the stimulated lattice expansion. To understand the transient response of the lattice, the measured time- and angle-resolved diffraction curves are compared with a theoretical calculation based on dynamical diffraction theory modified for the hexagonal crystal structure of LuMnO3. Our simulations reveal that a large coupling coefficient between the a-b plane and the c-axis (c13) is required to the data. We compare this result to our previous coherent phonon studies of LuMnO3 using optical pump-probe spectroscopy. We have also performed preliminary experiments of shock waves traversing thin (approximately one micron) metal single-crystals, characterizing the shock wave using ultrafast spatial interferometry and with ultrafast x-ray diffraction. A summary of our current results will be presented.
NASA Technical Reports Server (NTRS)
Ricoy, M. A.; Volakis, J. L.
1991-01-01
The diffraction problem associated with a multilayer material slab recessed in a perfectly conducting ground plane is formulated and solved via the generalized scattering matrix formulation in conjunction with the dual integral equation approach. The multilayer slab is replaced by a surface obeying a generalized impedance boundary condition to facilitate the computation of the pertinent Wiener Hopf split functions and their zeros. Both Ez and Hz polarizations are considered, and a number of scattering patterns are presented, some of which are compared to exact results available for a homogeneous recessed slab.
Decoding the matrix: Coincident membranes on the plane wave
Bousso, Raphael; Mints, Aleksey L.
2006-03-15
At the core of nonperturbative theories of quantum gravity lies the holographic encoding of bulk data in large matrices. At present this mapping is poorly understood. The plane wave matrix model provides a laboratory for isolating aspects of this problem in a controlled setting. At large boosts, configurations of concentric membranes become superselection sectors, whose exact spectra are known. From the bulk point of view, one expects product states of individual membranes to be contained within the full spectrum. However, for non-BPS states this inclusion relation is obscured by Gauss law constraints. Its validity rests on nontrivial relations in representation theory, which we identify and verify by explicit computation.
Unsteady relativistic shock-wave diffraction by cylinders and spheres.
Tsai, I-Nan; Huang, Juan-Chen; Tsai, Shang-Shi; Yang, J Y
2012-02-01
The unsteady relativistic shock-wave diffraction patterns generated by a relativistic blast wave impinging on a circular cylinder and a sphere are numerically simulated using some high-resolution relativistic kinetic beam schemes in a general coordinate system for solving the relativistic Euler equations of gas dynamics. The diffraction patterns are followed through about 6 radii of travel of the incident shock past the body. The complete diffraction patterns, including regular reflection, transition from regular to Mach reflection, slip lines, and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the body are reported in detail. Computational results of several incident shock Mach numbers covering the near ultrarelativistic limit are studied. Various contours of flow properties including the Lorentz factor and velocity streamline plots are also presented to add a better understanding of the complex diffraction phenomena. The three-dimensional relieving effects of the sphere cases are evident and can be quantitatively evaluated as compared with the corresponding cylinder cases.
Analysis of near-field Cassegrain reflector - Plane wave versus element-by-element approach
NASA Technical Reports Server (NTRS)
Houshmand, Bijan; Lee, Shung-Wu; Rahmat-Samii, Yahya; Lam, Peter T.
1990-01-01
A near-field Cassegrain reflector (NFCR) is an effective way to magnify a small phased array into a much larger-aperture antenna for limited scan applications. Traditionally the pattern analysis of NFCR is based on a plane wave approach, which simplifies the computation tremendously, but fails to provide design information about the most critical component of the whole antenna system, the feed array. Currently available computers make it possible to calculate the pattern of an NFCR by a more exact element-by-element approach. Each element in the feed array is considered individually, and the diffraction pattern from the subreflector is calculated by the geometrical theory of diffraction (including uniform theories at the shadow boundaries). The field contributions from all elements are superimposed at the curved main reflector surface, and a physical-optics integration is performed to obtain the secondary pattern.
Augmented-plane-wave calculations on small molecules
Serena, P.A.; Baratoff, A. ); Soler, J.M. )
1993-07-15
We have performed [ital ab] [ital initio] calculations on a wide range of small molecules, demonstrating the accuracy and flexibility of an alternative method for calculating the electronic structure of molecules, solids, and surfaces. It is based on the local-density approximation (LDA) for exchange and correlation and the nonlinear augmented-plane-wave method. Very accurate atomic forces are obtained directly. This allows for implementation of Car-Parrinello-like techniques to determine simultaneously the self-consistent electron wave functions and the equilibrium atomic positions within an iterative scheme. We find excellent agreement with the best existing LDA-based calculations and remarkable agreement with experiment for the equilibrium geometries, vibrational frequencies, and dipole moments of a wide variety of molecules, including strongly bound homopolar and polar molecules, hydrogen-bound and electron-deficient molecules, and weakly bound alkali and noble-metal dimers, although binding energies are overestimated.
Plane shock wave structure in a dilute granular gas
NASA Astrophysics Data System (ADS)
Reddy, M. H. Lakshminarayana; Alam, Meheboob
2016-11-01
We analyse the early time evolution of the Riemann problem of planar shock wave structures for a dilute granular gas by solving Navier-Stokes equations numerically. The one-dimensional reduced Navier-Stokes equations for plane shock wave problem are solved numerically using a relaxation-type numerical scheme. The results on the shock structures in granular gases are presented for different Mach numbers and restitution coefficients. Based on our analysis on early time shock dynamics we conclude that the density and temperature profiles are "asymmetric"; the density maximum and the temperature maximum occur within the shock layer; the absolute magnitudes of longitudinal stress and heat flux which are initially zero at both end states attain maxima in a very short time and thereafter decrease with time.
Chae, Byung Gyu
2014-05-20
We carry out a comparative analysis on a viewing angle change in Fresnel and Fourier holographic images reconstructed by a tilted plane wave. A tilted plane wave illuminating an on-axis hologram generates a diffractive wave carrying the holographic image in a paraxial region of a new diffraction axis. The reconstructed image in the Fresnel hologram is deformed along the new viewing direction, which is well described as Affine transformation. In the Fourier holographic image, the replica of the image is formed without its deformation when the hologram is placed in the front focal plane of the lens, whereas in the case of a hologram that is located at a distance different from a focal length, image deformation arises. This property is investigated through numerical simulation based on a wide-angle diffraction phenomenon. We also perform a similar interpretation for high-order diffraction images appearing in the sampled Fourier hologram and discuss a method for enlarging the viewing angle of the holographic image.
NASA Astrophysics Data System (ADS)
Fisanov, V. V.
2017-09-01
Analytical expressions for complex values of the wave number, refractive index, and the characteristic wave impedance of homogeneous electromagnetic plane waves propagating in a linear, homogeneous, isotropic medium with losses and gain are derived. Formulas for determining the type of normal wave as a function of the values of the real and imaginary parts of the permittivity and permeability are obtained, and conditions for the appearance of positive and negative refraction at the interface of two isotropic media are indicated. In the approach applied here, the concept of a negative refractive index is not used.
Spin wave modes in out-of-plane magnetized nanorings
NASA Astrophysics Data System (ADS)
Zhou, X.; Tartakovskaya, E. V.; Kakazei, G. N.; Adeyeye, A. O.
2017-07-01
We investigated the spin wave modes in flat circular permalloy rings with a canted external bias field using ferromagnetic resonance spectroscopy. The external magnetic field H was large enough to saturate the samples. For θ =0∘ (perpendicular geometry), three distinct resonance peaks were observed experimentally. In the case of the cylindrical symmetry violation due to H inclination from normal to the ring plane (the angle θ of H inclination was varied in the 0∘-6∘ range), the splitting of all initial peaks appeared. The distance between neighbor split peaks increased with the θ increment. Unexpectedly, the biggest splitting was observed for the mode with the smallest radial wave vector. This special feature of splitting behavior is determined by the topology of the ring shape. Developed analytical theory revealed that in perpendicular geometry, each observed peak is a combination of signals from the set of radially quantized spin wave excitation with almost the same radial wave vectors, radial profiles, and frequencies, but with different azimuthal dependencies. This degeneracy is a consequence of circular symmetry of the system and can be removed by H inclination from the normal. Our findings were further supported by micromagnetic simulations.
The implementation of holography in the plane wave matrix model
NASA Astrophysics Data System (ADS)
Mints, Aleksey Leonidovich
It is expected that at the core of nonperturbative theories of quantum gravity, such as M-theory, lies the realization of the holographic principle, in the sense that a holographic theory should contain one binary degree of freedom per Planck area. Present understanding of such theories requires the holographic encoding of bulk data in large matrices. Currently this mapping is poorly understood. The plane wave matrix model provides a laboratory for isolating aspects of this problem in a controlled setting. At large boosts, configurations of concentric membranes become superselection sectors, whose exact spectra are known. From the bulk point of view one expects product states of individual membranes to be contained within the full spectrum. However, for non-BPS states this inclusion relation is obscured by Gauss law constraints. Its validity rests on nontrivial relations in representation theory, which we identify and verify by explicit computation. Beyond the decoding and partial identification of selected states in large matrices, one would like to get a better understanding of the holographic state counting of these degrees of freedom, i.e., entropy. Contrary to the naive expectation of holography realized in terms of the covariant entropy bound, we present evidence that it is the Bekenstein entropy bound, which is related to area differences, that is manifest in the plane wave matrix model. If holography is implemented in this way, we predict crossover behavior at strong coupling when the energy exceeds N2 in units of the mass scale.
Acoustic plane wave preferential orientation of metal oxide superconducting materials
Tolt, Thomas L.; Poeppel, Roger B.
1991-01-01
A polycrystalline metal oxide such as YBa.sub.2 Cu.sub.3 O.sub.7-X (where 0
Szkudlarek, Krzesimir; Sypek, Maciej; Cywiński, Grzegorz; Suszek, Jarosław; Zagrajek, Przemysław; Feduniewicz-Żmuda, Anna; Yahniuk, Ivan; Yatsunenko, Sergey; Nowakowska-Siwińska, Anna; Coquillat, Dominique; But, Dmytro B; Rachoń, Martyna; Węgrzyńska, Karolina; Skierbiszewski, Czesław; Knap, Wojciech
2016-09-05
We present the concept, the fabrication processes and the experimental results for materials and optics that can be used for terahertz field-effect transistor detector focal plane arrays. More specifically, we propose 3D printed arrays of a new type - diffractive multi-zone lenses of which the performance is superior to that of previously used mono-zone diffractive or refractive elements and evaluate them with GaN/AlGaN field-effect transistor terahertz detectors. Experiments performed in the 300-GHz atmospheric window show that the lens arrays offer both a good efficiency and good uniformity, and may improve the signal-to-noise ratio of the terahertz field-effect transistor detectors by more than one order of magnitude. In practice, we tested 3 × 12 lens linear arrays with printed circuit board THz detector arrays used in postal security scanners and observed significant signal-to-noise improvements. Our results clearly show that the proposed technology provides a way to produce cost-effective, reproducible, flat optics for large-size field-effect transistor THz-detector focal plane arrays.
Improving double patterning flow by analyzing the diffractive orders in the pupil plane
NASA Astrophysics Data System (ADS)
Zeggaoui, N.; Farys, V.; Besacier, M.; Li, Q.; Yesilada, E.; Trouiller, Y.
2011-04-01
To print sub 22nm node features, current lithography technology faces some tool limitations. One possible solution to overcome these problems is to use the double patterning technique (DPT). The principle of the double patterning technique is pitch splitting where two adjacent features must be assigned opposite masks (colors) corresponding to different exposures if their pitch is less than a predefined minimum coloring pitch. However, certain design orientations for which pattern features separated by more than the minimum coloring pitch cannot be imaged with either of the two exposures. In these directions, the contrast and the process window are degraded because constructive interferences between diffractive orders in the pupil plane are not sufficient. The 22nm and 16nm nodes require the use of very coherent sources that will be generated using SMO (source mask cooptimization). Such pixelized sources while helpful in improving the contrast for selected configurations, can lead to degrade it for configurations which have not been counted for during the SMO process. Therefore, we analyze the diffractive orders interactions in the pupil plane in order to detect these limited orientations in the design and thus propose a new double patterning decomposition algorithm to enlarge the process window and the contrast of each mask.
Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.
Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing
2016-10-01
The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.
Quantitative damage imaging using Lamb wave diffraction tomography
NASA Astrophysics Data System (ADS)
Zhang, Hai-Yan; Ruan, Min; Zhu, Wen-Fa; Chai, Xiao-Dong
2016-12-01
In this paper, we investigate the diffraction tomography for quantitative imaging damages of partly through-thickness holes with various shapes in isotropic plates by using converted and non-converted scattered Lamb waves generated numerically. Finite element simulations are carried out to provide the scattered wave data. The validity of the finite element model is confirmed by the comparison of scattering directivity pattern (SDP) of circle blind hole damage between the finite element simulations and the analytical results. The imaging method is based on a theoretical relation between the one-dimensional (1D) Fourier transform of the scattered projection and two-dimensional (2D) spatial Fourier transform of the scattering object. A quantitative image of the damage is obtained by carrying out the 2D inverse Fourier transform of the scattering object. The proposed approach employs a circle transducer network containing forward and backward projections, which lead to so-called transmission mode (TMDT) and reflection mode diffraction tomography (RMDT), respectively. The reconstructed results of the two projections for a non-converted S0 scattered mode are investigated to illuminate the influence of the scattering field data. The results show that Lamb wave diffraction tomography using the combination of TMDT and RMDT improves the imaging effect compared with by using only the TMDT or RMDT. The scattered data of the converted A0 mode are also used to assess the performance of the diffraction tomography method. It is found that the circle and elliptical shaped damages can still be reasonably identified from the reconstructed images while the reconstructed results of other complex shaped damages like crisscross rectangles and racecourse are relatively poor. Project supported by the National Natural Science Foundation of China (Grant Nos. 11474195, 11274226, 11674214, and 51478258).
Space-time analogy for partially coherent plane-wave-type pulses.
Lancis, Jesús; Torres-Company, Víctor; Silvestre, Enrique; Andrés, Pedro
2005-11-15
In this Letter we extend the well-known space-time duality to partially coherent wave fields and, as a limit case, to incoherent sources. We show that there is a general analogy between the paraxial diffraction of quasi-monochromatic beams of limited spatial coherence and the temporal distortion of partially coherent plane-wave pulses in parabolic dispersive media. Next, coherence-dependent effects in the propagation of Gaussian Schell-model pulses are retrieved from that of their spatial counterpart, the Gaussian Schell-model beam. Finally, the last result allows us to present a source linewidth analysis in an optical fiber communication system operating around the 1.55 microm wavelength window.
Ultrafast Dynamics of a Charge Density Wave via Time-Resolved Resonant Diffraction
NASA Astrophysics Data System (ADS)
Moore, R. G.
2012-02-01
Understanding the emergence of collective behavior in correlated electron systems remains at the forefront of modern condensed matter physics. The key to such an understanding is unraveling the contributions from the coupling degrees of freedom in exotic many body states. Density waves, both of charge and spin, have been studied for decades and a wealth of information and insight has been gained. However, there are still open questions that need to be solved for a complete description of the phenomena as there are several existing density wave systems that exhibit prototypical behavior while violating traditional theory. Ultrafast dynamics of such a system, TbTe3, has been investigated via time-resolved resonant diffraction at the SXR endstation at LCLS. Oscillations of the amplitude mode and coherent phonons have been observed previously in time resolved photoemission and reflectivity measurement but, here we reveal a direct observation of the lattice response via resonant diffraction. Watching dynamics of the two dimensional Te plane density wave diffraction peak at a resonant energy of a bystander Tb atom reveals new insights into the coupling responsible for the formation of the state. Results and comparison with previous time resolved measurements will be discussed.
A physical solution for plane SH waves in anelastic media
NASA Astrophysics Data System (ADS)
Ursin, Bjorn; Carcione, José M.; Gei, Davide
2017-05-01
In a lossy medium with complex frequency-dependent wave speed both rays and plane waves at an interface should satisfy the dispersion relation (that is, the wave equation), the radiation condition (the amplitude should go to zero at infinity) and the horizontal complex slowness should be continuous (Snell's law). It is known that this may lead to a transmitted wave which violates the radiation condition and which also causes problems with the phase of the reflection coefficient. In fact, ray-tracing algorithms and analytical evaluations of the reflection and transmission coefficients in anelastic media may lead to non-physical solutions related to the complex square roots of the vertical slowness and polarizations. The steepest-descent approximation with complex horizontal slowness involves non-physical complex horizontal distances, and in some cases also a non-physical vertical slowness that violates the radiation condition. Similarly, the reflection and transmission coefficients and ray-tracing codes obtained with this approach yields wrong results. In order to tackle this problem, we choose the stationary-phase approximation with real horizontal slowness. This gives real horizontal distances, the radiation condition is always satisfied and the reflection and transmission coefficients are correct. This is shown by comparison to full-wave space-time modelling results by computing the reflection and transmission coefficients and respective phase angles from synthetic seismograms. This numerical evaluation is based on a 2-D wavenumber-frequency Fourier transform. The results indicate that the stationary-phase method with a real horizontal slowness provides the correct physical solution.
NASA Astrophysics Data System (ADS)
Yong, Peng; Huang, Jianping; Li, Zhenchun; Liao, Wenyuan; Qu, Luping; Li, Qingyang; Liu, Peijun
2016-12-01
In finite difference (FD) method, numerical dispersion is the dominant factor influencing the accuracy of seismic modeling. Various optimized FD schemes for scalar wave modeling have been proposed to reduce grid dispersion, while the optimized time-space domain FD schemes for elastic wave modeling have not been fully investigated yet. In this paper, an optimized FD scheme with Equivalent Staggered Grid (ESG) for elastic modelling has been developed. We start from the constant P- and S-wave speed elastic wave equations and then deduce analytical plane wave solutions in the wavenumber domain with eigenvalue decomposition method. Based on the elastic plane wave solutions, three new time-space domain dispersion relations of ESG elastic modeling are obtained, which are represented by three equations corresponding to P-, S- and converted wave terms in the elastic equations, respectively. By using these new relations, we can study the dispersion errors of different spatial FD terms independently. The dispersion analysis showed that different spatial FD terms have different errors. It is therefore suggested that different FD coefficients to be used to approximate the three spatial derivative terms. In addition, the relative dispersion error in L2-norm is minimized through optimizing FD coefficients using Newton's method. Synthetic examples have demonstrated that this new optimal FD schemes have superior accuracy for elastic wave modeling compared to Taylor-series expansion and optimized space domain FD schemes.
Plane wave solution for elastic wave scattering by a heterogeneous fracture
NASA Astrophysics Data System (ADS)
Nakagawa, Seiji; Nihei, Kurt T.; Myer, Larry R.
2004-06-01
A plane-wave method for computing the three-dimensional scattering of propagating elastic waves by a planar fracture with heterogeneous fracture compliance distribution is presented. This method is based upon the spatial Fourier transform of the seismic displacement-discontinuity (SDD) boundary conditions (also called linear slip interface conditions), and therefore, called the wave-number-domain SDD method (wd-SDD method). The resulting boundary conditions explicitly show the coupling between plane waves with an incident wave number component (specular component) and scattered waves which do not follow Snell's law (nonspecular components) if the fracture is viewed as a planar boundary. For a spatially periodic fracture compliance distribution, these boundary conditions can be cast into a linear system of equations that can be solved for the amplitudes of individual wave modes and wave numbers. We demonstrate the developed technique for a simulated fracture with a stochastic (correlated) surface compliance distribution. Low- and high-frequency solutions of the method are also compared to the predictions by low-order Born series in the weak and strong scattering limit.
NASA Astrophysics Data System (ADS)
Yong, Peng; Huang, Jianping; Li, Zhenchun; Liao, Wenyuan; Qu, Luping; Li, Qingyang; Liu, Peijun
2017-02-01
In finite-difference (FD) method, numerical dispersion is the dominant factor influencing the accuracy of seismic modelling. Various optimized FD schemes for scalar wave modelling have been proposed to reduce grid dispersion, while the optimized time-space domain FD schemes for elastic wave modelling have not been fully investigated yet. In this paper, an optimized FD scheme with Equivalent Staggered Grid (ESG) for elastic modelling has been developed. We start from the constant P- and S-wave speed elastic wave equations and then deduce analytical plane wave solutions in the wavenumber domain with eigenvalue decomposition method. Based on the elastic plane wave solutions, three new time-space domain dispersion relations of ESG elastic modelling are obtained, which are represented by three equations corresponding to P-, S- and converted-wave terms in the elastic equations, respectively. By using these new relations, we can study the dispersion errors of different spatial FD terms independently. The dispersion analysis showed that different spatial FD terms have different errors. It is therefore suggested that different FD coefficients to be used to approximate the three spatial derivative terms. In addition, the relative dispersion error in L2-norm is minimized through optimizing FD coefficients using Newton's method. Synthetic examples have demonstrated that this new optimal FD schemes have superior accuracy for elastic wave modelling compared to Taylor-series expansion and optimized space domain FD schemes.
Plane wave method for elastic wave scattering by a heterogeneous fracture
Nakagawa, Seiji; Nihei, Kurt T.; Myer, Larry R.
2003-02-21
A plane-wave method for computing the three-dimensional scattering of propagating elastic waves by a planar fracture with heterogeneous fracture compliance distribution is presented. This method is based upon the spatial Fourier transform of the seismic displacement-discontinuity (SDD) boundary conditions (also called linear slip interface conditions), and therefore, called the wave-number-domain SDD method (wd-SDD method). The resulting boundary conditions explicitly show the coupling between plane waves with an incident wave number component (specular component) and scattered waves which do not follow Snell's law (nonspecular components) if the fracture is viewed as a planar boundary. For a spatially periodic fracture compliance distribution, these boundary conditions can be cast into a linear system of equations that can be solved for the amplitudes of individual wave modes and wave numbers. We demonstrate the developed technique for a simulated fracture with a stochastic (correlated) surface compliance distribution. Low- and high-frequency solutions of the method are also compared to the predictions by low-order Born series in the weak and strong scattering limit.
Resonant Enhancement of Charge Density Wave Diffraction in the Rare-Earth Tri-Tellurides
Lee, W.S.; Sorini, A.P.; Yi, M.; Chuang, Y.D.; Moritz, B.; Yang, W.L.; Chu, J.-H.; Kuo, H.H.; Gonzalez, A.G.Cruz; Fisher, I.R.; Hussain, Z.; Devereau, T.P.; Shen, Z.X.
2012-05-15
We performed resonant soft X-ray diffraction on known charge density wave (CDW) compounds, rare earth tri-tellurides. Near the M{sub 5} (3d - 4f) absorption edge of rare earth ions, an intense diffraction peak is detected at a wavevector identical to that of CDW state hosted on Te{sub 2} planes, indicating a CDW-induced modulation on the rare earth ions. Surprisingly, the temperature dependence of the diffraction peak intensity demonstrates an exponential increase at low temperatures, vastly different than that of the CDW order parameter. Assuming 4f multiplet splitting due to the CDW states, we present a model to calculate X-ray absorption spectrum and resonant profile of the diffraction peak, agreeing well with experimental observations. Our results demonstrate a situation where the temperature dependence of resonant X-ray diffraction peak intensity is not directly related to the intrinsic behavior of the order parameter associated with the electronic order, but is dominated by the thermal occupancy of the valence states.
Integrated focal plane arrays for millimeter-wave astronomy
NASA Astrophysics Data System (ADS)
Bock, James J.; Goldin, Alexey; Hunt, Cynthia; Lange, Andrew E.; Leduc, Henry G.; Day, Peter K.; Vayonakis, Anastasios; Zmuidzinas, Jonas
2002-02-01
We are developing focal plane arrays of bolometric detectors for sub-millimeter and millimeter-wave astrophysics. We propose a flexible array architecture using arrays of slot antennae coupled via low-loss superconducting Nb transmission line to microstrip filters and antenna-coupled bolometers. By combining imaging and filtering functions with transmission line, we are able to realize unique structures such as a multi-band polarimeter and a planar, dispersive spectrometer. Micro-strip bolometers have significantly smaller active volume than standard detectors with extended absorbers, and can realize higher sensitivity and speed of response. The integrated array has natural immunity to stray radiation or spectral leaks, and minimizes the suspended mass operating at 0.1-0.3 K. We also discuss future space-borne spectroscopy and polarimetry applications. .
Numerical investigation of diffraction of acoustic waves by phononic crystals
NASA Astrophysics Data System (ADS)
Moiseyenko, Rayisa P.; Declercq, Nico F.; Laude, Vincent
2012-05-01
Diffraction as well as transmission of acoustic waves by two-dimensional phononic crystals (PCs) composed of steel rods in water are investigated in this paper. The finite element simulations were performed in order to compute pressure fields generated by a line source that are incident on a finite size PC. Such field maps are analyzed based on the complex band structure for the infinite periodic PC. Finite size computations indicate that the exponential decrease of the transmission at deaf frequencies is much stronger than that in Bragg band gaps.
Laboratory modeling of edge wave generation over a plane beach by breaking waves
NASA Astrophysics Data System (ADS)
Abcha, Nizar; Ezersky, Alexander; Pelinovsky, Efim
2015-04-01
Edge waves play an important role in coastal hydrodynamics: in sediment transport, in formation of coastline structure and coastal bottom topography. Investigation of physical mechanisms leading to the edge waves generation allows us to determine their effect on the characteristics of spatially periodic patterns like crescent submarine bars and cusps observed in the coastal zone. In the present paper we investigate parametric excitation of edge wave with frequency two times less than the frequency of surface wave propagating perpendicular to the beach. Such mechanism of edge wave generation has been studied previously in a large number of papers using the assumption of non-breaking waves. This assumption was used in theoretical calculations and such conditions were created in laboratory experiments. In the natural conditions, the wave breaking is typical when edge waves are generated at sea beach. We study features of such processes in laboratory experiments. Experiments were performed in the wave flume of the Laboratory of Continental and Coast Morphodynamics (M2C), Caen. The flume is equipment with a wave maker controlled by computer. To model a plane beach, a PVC plate is placed at small angle to the horizontal bottom. Several resistive probes were used to measure characteristics of waves: one of them was used to measure free surface displacement near the wave maker and two probes were glued on the inclined plate. These probes allowed us to measure run-up due to parametrically excited edge waves. Run-up height is determined by processing a movie shot by high-speed camera. Sub-harmonic generation of standing edge waves is observed for definite control parameters: edge waves represent themselves a spatial mode with wavelength equal to double width of the flume; the frequency of edge wave is equal to half of surface wave frequency. Appearance of sub-harmonic mode instability is studied using probes and movie processing. The dependence of edge wave exponential
Diffraction Efficiency Testing of Sinusoidal and Blazed Off-Plane Reflection Gratings
NASA Astrophysics Data System (ADS)
Tutt, James H.; McEntaffer, Randall L.; Marlowe, Hannah; Miles, Drew M.; Peterson, Thomas J.; Deroo, Casey T.; Scholze, Frank; Laubis, Christian
2016-09-01
Reflection gratings in the off-plane mount have the potential to enhance the performance of future high resolution soft X-ray spectrometers. Diffraction efficiency can be optimized through the use of blazed grating facets, achieving high-throughput on one side of zero-order. This paper presents the results from a comparison between a grating with a sinusoidally grooved profile and two gratings that have been blazed. The results show that the blaze does increase throughput to one side of zero-order; however, the total throughput of the sinusoidal gratings is greater than the blazed gratings, suggesting the method of manufacturing the blazed gratings does not produce precise facets. The blazed gratings were also tested in their Littrow and anti-Littrow configurations to quantify diffraction efficiency sensitivity to rotations about the grating normal. Only a small difference in the energy at which efficiency is maximized between the Littrow and anti-Littrow configurations is seen with a small shift in peak efficiency towards higher energies in the anti-Littrow case. This is due to a decrease in the effective blaze angle in the anti-Littrow mounting. This is supported by PCGrate-SX V6.1 modeling carried out for each blazed grating which predicts similar response trends in the Littrow and anti-Littrow orientations.
NASA Astrophysics Data System (ADS)
Rakhmanov, Malik
2014-04-01
Fermi-normal (FN) coordinates provide a standardized way to describe the effects of gravitation from the point of view of an inertial observer. These coordinates have always been introduced via perturbation expansions and were usually limited to distances much less than the characteristic length scale set by the curvature of spacetime. For a plane gravitational wave this scale is given by its wavelength which defines the domain of validity for these coordinates known as the long-wavelength regime. The symmetry of this spacetime, however, allows us to extend FN coordinates far beyond the long-wavelength regime. Here we present an explicit construction for this long-range FN coordinate system based on the unique solution of the boundary-value problem for spacelike geodesics. The resulting formulae amount to summation of the infinite series for FN coordinates previously obtained with perturbation expansions. We also consider two closely related normal-coordinate systems: optical coordinates which are built from null geodesics and wave-synchronous coordinates which are built from spacelike geodesics locked in phase with the propagating gravitational wave. The wave-synchronous coordinates yield the exact solution of Peres and Ehlers-Kundt which is globally defined. In this case, the limitation of the long-wavelength regime is completely overcome, and the system of wave-synchronous coordinates becomes valid for arbitrarily large distances. Comparison of the different coordinate systems is done by considering the motion of an inertial test mass in the field of a plane gravitational wave.
Carretero, Luis; Acebal, Pablo; Blaya, Salvador
2013-04-01
We present a complete electromagnetic study, which includes electric, magnetic, and Poynting vector fields of diffracted convergent spherical waves under all possible polarization states compatible with Maxwell's equations. Exit pupil boundary conditions for these polarizations were obtained by means of Hertz potentials. Using these boundary conditions, two-dimensional Luneburg diffraction integrals for the three components of electric and magnetic fields were formulated, and after some approximations, we showed that the complete electromagnetic description of the inhomogeneous polarization states of spherical waves is reduced to the knowledge of seven one-dimensional integrals. The consistency of the method was tested by comparison with other previously reported methods for linearly polarized (LP), TE, and TM polarizations, while the versatility of the method was showed with the study of nonstandard polarization states, for example, that resulting from the superposition of TE and TM dephased spherical waves, which shows a helicoidal behavior of the Poynting vector at the focalization region, or the inhomogeneous LP state that exhibits a ring structure for the Poynting vector at the focal plane.
Generating Damon-Eshbach Spin Waves in Py using a Conducting Diffraction Grating
NASA Astrophysics Data System (ADS)
Sklenar, J.; Bhat, V. S.; Delong, L.; Ketterson, J. B.
2012-02-01
We have patterned silver hole arrays directly on top of uniform permalloy (Py) films. Typical Py and Ag film thicknesses are 25nm and 40 nm respectively; the holes in the Ag have a 500nm diameter and are patterned on a 1 micron lattice constant. We have measured resonant modes arising from a quasi-uniform microwave excitation field, applied in the plane of the sample, as a function of the in-plane external field and the in-plane field orientation relative to the principal axes of the array. Measurements were done using our broadband meanderline-based ferromagnetic resonance (FMR) spectrometer.ootnotetextC. C. Tsai, J. Choi, S. Cho, B. K. Sarma, C. Thompson, O. Chernyashevskyy, I. Nevirkovets, and J. B Ketterson, Rev. of Sci. Instr. 80, 023904 (2009). In addition to a uniform FMR mode we observe satellite modes that correspond to the Damon-Eshbach spin wavesootnotetextR. W. Damon and J. R. Eshbach J. Phys. Chem. Solids 19, 308 (1961). with wave vectors having Fourier components of the reciprocal lattice of the silver array. Hence, in an otherwise uniform magnetic film the silver array acts as a diffraction grating which excites spin waves with k 0 from the dynamic k 0 microwave magnetic field. The observed spin wave angular dispersion is in excellent agreement with a magnon dispersion relation for spin waves in a uniform film given by Kriesel et al.ootnotetextA. Kreisel, F. Sauli, L. Bartosch, and P. Kopietz, Eur. Phys. J. B 71, 59 (2009).
Concentration gradient limiter designs for incident plane waves and multiple chromophores
NASA Astrophysics Data System (ADS)
McLean, Daniel G.
1998-10-01
A design method for reverse saturable absorbing (RSA) dye concentration gradient limiters, termed here the Absorption Diffraction Balance (ADB) design method, is used to produce designs for multiple chromophores and is extended to allow incident plane waves. The ADB design method is reviewed for Gaussian beams applied to a constant fluence design and a linear fluence design. These two designs are combined to allow different dyes to be used in different portions of the limiter. It is found that this hybrid design significantly enhances performance under some circumstances. It is also shown to reduce the probability of dye photodegradation. The ADB design method is extended to allow for incident plane waves or a top-hat beam profile. The field at the geometric shadow edge, expressed in terms of Lommel functions, is shown to closely match the Gaussian field when the incident irradiance, power, and second moments are the same. Since the irradiance distribution is not monotonically increasing in the focal region, the required concentration distribution has regions of negative concentration, i.e. gain regions. These designs are useful for initiating numerical nonlinear beam propagation studies.
Diffractive pyramid wave-front sensor used for adaptive optics
NASA Astrophysics Data System (ADS)
Zhao, Yuan; Ding, Xiaona; Wang, Kun; Wei, Hongyan; Yang, Huan; Cai, Dongmei
2012-10-01
Wave-front sensor, as the main component of Adaptive optics system, detects light from the astronomic object or reference sources. It aims to improve the utilization of light, especially for AO system work with the faint objects. Compared with Shack-Hartmann sensor, pyramid wave-front sensor is a relatively new one with increased pupil sampling and spatial resolution. Pyramid wave-front sensor uses a refractive element (the pyramid) to produce four images of the entrance pupil. Usually, Single pyramid prototypes are made using the classical figuring and polishing techniques. This approach, however, is not only very time consuming but also does not guarantee a uniform repeatability of the optical characteristics of the pyramids. The loss of low frequency component increases due to the roofs existing on its vertexes. Moreover, stray light is introduced in the four images. We therefore are investigating a modified pyramidal optical components based on the binary optical concept. In this article we describe the diffractive pyramid prototypes using the micro fabrication technique. The parameters of the pyramid are discussed.
Skigin, Diana C; Depine, Ricardo A
2008-05-01
We show that the problem of scattering of an obliquely incident plane wave by a general-shaped groove engraved on a perfectly conducting plane, which was recently studied by Basha et al. [J. Opt. Soc. Am. A24, 1647 (2007)], was solved 11 years ago using the same formulation. This method was further extended to deal with a finite number of grooves and also with complex apertures including several nonlossy and lossy dielectrics, as well as real metals.
Generation of limited-diffraction wave by approximating theoretical X-wave with simple driving
NASA Astrophysics Data System (ADS)
Li, Yaqin; Ding, MingYue; Hua, Shaoyan; Ming, Yuchi
2012-03-01
X-wave is a particular case of limited diffracting waves which has great potential applications in the enlargement of the field depth in acoustic imaging systems. In practice, the generation of real time X-wave ultrasonic fields is a complex technology which involves precise and specific voltage for the excitations for each distinct array element. In order to simplify the X-wave generating process, L. Castellanos proposed an approach to approximate the X-wave excitations with rectangular pulses. The results suggested the possibility of achieving limited-diffraction waves with relatively simple driving waveforms, which could be implemented with a moderate cost in analogical electronics. In this work, we attempt to improve L. Castellanos's method by calculating the approximation driving pulse not only from rectangular but also triangular driving pulse. The differences between theoretical X-wave signals and driving pulses, related to their excitation effects, are minimized by L2 curve criterion. The driving pulses with the minimal optimization result we chosen. A tradeoff is obtained between the cost of implementation of classical 0-order X-wave and the precision of approximation with the simple pulsed electrical driving. The good agreement of the driving pulse and the result resulting field distributions, with those obtained from the classical X-wave excitations can be justified by the filtering effects induced by the transducer elements in frequency domain. From the simulation results, we can see that the new approach improve the precise of the approximation, the difference between theoretical X-wave and the new approach is lower 10 percent than the difference between theoretical X-wave and rectangular as the driving pulse in simulation.
Plane wave discontinuous Galerkin methods for acoustic scattering
NASA Astrophysics Data System (ADS)
Kapita, Shelvean
We apply the Plane Wave Discontinuous Galerkin (PWDG) method to study the direct scattering of acoustic waves from impenetrable obstacles. In the first part of the thesis we consider the full exterior scattering problem with smooth boundaries. This problem is modeled by the Helmholtz equation in the unbounded domain exterior to the scatterer. To compute the scattered field, an artificial boundary is introduced to reduce the infinite domain to a finite computational domain. We then apply Dirichlet-to-Neumann (DtN) and Neumann-to-Dirichlet (NtD) boundary conditions on a circular artificial boundary. By using asymptotic properties of Hankel functions, we are able to prove wavenumber explicit L2-norm error estimates for the DtN-PWDG method on quasi-uniform meshes. Numerical experiments indicate that the accuracy of the PWDG method for the scattering problem is improved by the use of DtN and NtD boundary conditions. The second part of the thesis concerns acoustic scattering from domains with corners. In such domains, quasi-uniform meshes are not efficient so we derive error indicators to drive the selective refinement of the mesh in an adaptive algorithm. We prove a posteriori L2-norm error estimates for the Helmholtz equation with impedance boundary conditions on the artificial boundary. Numerical results demonstrate the efficiency of the proposed indicators. This adaptive strategy is compatible with the DtN and NtD truncation of the infinite domain problem and the combination would significantly improve the accuracy and reliability of PWDG simulations.
Rayleigh-Bloch Wave Expansions for Diffraction Gratings I.
1980-03-01
AD-AO6S 939 UTAH WIIV SALT LAKE CITY DEPT OF MATHEMATICS F /B 20/14 RAYLEIGH-BLOCH WAVE EXPANSIONS FOR DIFFRACTION GRATINGS I. (U) MAR 80 C H WILCOX...a Fr~chet space with family of semi-norms (1.22) P(u) [ f I jD a1D u(X) l2 dX/ KK’ G al+at2<M and L2 (A,G) is a Frechet space with family of semi...or 0D then the classical Plancherel theory can be used to derive an eigenfunction expansion and spectral decomposition for I 14 (1.35) A0 f 0 dO (P
Exact exchange plane-wave-pseudopotential calculations for slabs.
Engel, Eberhard
2014-05-14
The exact exchange of density functional theory is applied to both free-standing graphene and a Si(111) slab, using the plane-wave pseudopotential (PWPP) approach and a periodic repetition of the supercell containing the slab. It is shown that (i) PWPP calculations with exact exchange for slabs in supercell geometry are basically feasible, (ii) the width of the vacuum required for a decoupling of the slabs is only moderately larger than in the case of the local-density approximation, and (iii) the resulting exchange potential vx shows an extended region, both far outside the surface of the slab and far from the middle of the vacuum region between the slabs, in which vx behaves as -e(2)/z, provided the width of the vacuum is chosen sufficiently large. This last result is corroborated by an analytical analysis of periodically repeated jellium slabs. The intermediate -e(2)/z behavior of vx can be used for an absolute normalization of vx and the total Kohn-Sham potential, which, in turn, allows the determination of the work function.
NMR Shielding in Metals Using the Augmented Plane Wave Method
2015-01-01
We present calculations of solid state NMR magnetic shielding in metals, which includes both the orbital and the complete spin response of the system in a consistent way. The latter contains an induced spin-polarization of the core states and needs an all-electron self-consistent treatment. In particular, for transition metals, the spin hyperfine field originates not only from the polarization of the valence s-electrons, but the induced magnetic moment of the d-electrons polarizes the core s-states in opposite direction. The method is based on DFT and the augmented plane wave approach as implemented in the WIEN2k code. A comparison between calculated and measured NMR shifts indicates that first-principle calculations can obtain converged results and are more reliable than initially concluded based on previous publications. Nevertheless large k-meshes (up to 2 000 000 k-points in the full Brillouin-zone) and some Fermi-broadening are necessary. Our results show that, in general, both spin and orbital components of the NMR shielding must be evaluated in order to reproduce experimental shifts, because the orbital part cancels the shift of the usually highly ionic reference compound only for simple sp-elements but not for transition metals. This development paves the way for routine NMR calculations of metallic systems. PMID:26322148
Wave-growth associated with turbulent spot in plane Poiseuille flow
NASA Technical Reports Server (NTRS)
Henningson, D. S.; Landahl, M. T.; Kim, J.
1987-01-01
A kinematic wave theory is used to investigate the cause of the rapid growth of waves observed at the wingtip of turbulent spot in plane Poiseuille flow. It is found that the qualitative behavior of the wave motions is well described by Landahl's breakdown criterion as the wave selection procedure. The predicted wave number, wave angle, and phase velocity are in agreement with those values obtained in a direct simulation.
Diffractive optics based four-wave, six-wave, ..., nu-wave nonlinear spectroscopy.
Miller, R J Dwayne; Paarmann, Alexander; Prokhorenko, Valentyn I
2009-09-15
A detailed understanding of chemical processes requires information about both structure and dynamics. By definition, a reaction involves nonstationary states and is a dynamic process. Structure describes the atomic positions at global minima in the nuclear potential energy surface. Dynamics are related to the anharmonicities in this potential that couple different minima and lead to changes in atomic positions (reactions) and correlations. Studies of molecular dynamics can be configured to directly access information on the anharmonic interactions that lead to chemical reactions and are as central to chemistry as structural information. In this regard, nonlinear spectroscopies have distinct advantages over more conventional linear spectroscopies. Because of this potential, nonlinear spectroscopies could eventually attain a comparable level of importance for studying dynamics on the relevant time scales to barrier crossings and reactive processes as NMR has for determining structure. Despite this potential, nonlinear spectroscopy has not attained the same degree of utility as linear spectroscopy largely because nonlinear studies are more technically challenging. For example, unlike the linear spectrometers that exist in almost all chemistry departments, there are no "black box" four-wave mixing spectrometers. This Account describes recent advances in the application of diffractive optics (DOs) to nonlinear spectroscopy, which reduces the complexity level of this technology to be closer to that of linear spectroscopy. The combination of recent advances in femtosecond laser technology and this single optic approach could bring this form of spectroscopy out of the exclusive realm of specialists and into the general user community. However, the real driving force for this research is the pursuit of higher sensitivity limits, which would enable new forms of nonlinear spectroscopy. This Account chronicles the research that has now extended nonlinear spectroscopy to six-wave
NASA Astrophysics Data System (ADS)
Hooseria, S. J.; Skews, B. W.
2017-01-01
A complex interference flowfield consisting of multiple shocks and expansion waves is produced when high-speed slender bodies are placed in close proximity. The disturbances originating from a generator body impinge onto the adjacent receiver body, modifying the local flow conditions over the receiver. This paper aims to uncover the basic gas dynamics produced by two closely spaced slender bodies in a supersonic freestream. Experiments and numerical simulations were used to interpret the flowfield, where good agreement between the predictions and measurements was observed. The numerical data were then used to characterise the attenuation associated with shock wave diffraction, which was found to be interdependent with the bow shock contact perimeter over the receiver bodies. Shock-induced boundary layer separation was observed over the conical and hemispherical receiver bodies. These strong viscous-shock interactions result in double-reflected, as well as double-diffracted shock wave geometries in the interference region, and the diffracting waves progress over the conical and hemispherical receivers' surfaces in "lambda" type configurations. This gives evidence that viscous effects can have a substantial influence on the local bow shock structure surrounding high-speed slender bodies in close proximity.
Tailored complex 3D vortex lattice structures by perturbed multiples of three-plane waves.
Xavier, Jolly; Vyas, Sunil; Senthilkumaran, Paramasivam; Joseph, Joby
2012-04-20
As three-plane waves are the minimum number required for the formation of vortex-embedded lattice structures by plane wave interference, we present our experimental investigation on the formation of complex 3D photonic vortex lattice structures by a designed superposition of multiples of phase-engineered three-plane waves. The unfolding of the generated complex photonic lattice structures with higher order helical phase is realized by perturbing the superposition of a relatively phase-encoded, axially equidistant multiple of three noncoplanar plane waves. Through a programmable spatial light modulator assisted single step fabrication approach, the unfolded 3D vortex lattice structures are experimentally realized, well matched to our computer simulations. The formation of higher order intertwined helices embedded in these 3D spiraling vortex lattice structures by the superposition of the multiples of phase-engineered three-plane waves interference is also studied.
Uncooled Long-Wave Infrared Small Pixel Focal Plane Array and System Challenges
2013-06-01
Uncooled long-wave infrared small pixel focal plane array and system challenges Dieter Lohrmann Roy Littleton Colin Reese Dan Murphy Jay Vizgaitis...to 00-00-2013 4. TITLE AND SUBTITLE Uncooled long-wave infrared small pixel focal plane array and system challenges 5a. CONTRACT NUMBER 5b... infrared detector ; focal plane arrays; infrared imaging. Paper 121416SS received Oct. 1, 2012; revised manuscript received Dec. 5, 2012;
Multi-frame visualization for detonation wave diffraction
NASA Astrophysics Data System (ADS)
Nagura, Y.; Kasahara, J.; Matsuo, A.
2016-09-01
When a detonation wave emerges from a tube into unconfined space filled with a gas mixture, detonation wave diffraction occurs due to abrupt changes in the cross-sectional area. In the present study, we focused on the local explosion in reinitiation and propagation of a transverse detonation wave by performing comprehensive and direct observation with high time resolution visualization in a two-dimensional rectangular channel. Using the visualization methods of shadowgraph and multi-frame, short-time, open-shutter photography, we determined where the wall reflection point is generated, and also determined where the bright point is originated by the local explosion, and investigated the effects of the deviation angle and initial pressure of the gas mixture. We found that the reinitiation of detonation had two modes that were determined by the deviation angle of the channel. If the deviation angle was less than or equal to 30°, the local explosion of reinitiation might occur in the vicinity of the channel wall, and if the deviation angle was greater than or equal to 60°, the local explosion might originate on the upper side of the tube exit. With a deviation angle greater than 60°, the position of the wall reflection point depended on the cell width, so the radial distance of the wall reflection point from the apex of the tube exit was about 12 times the cell width. Similarly, the bright point (local explosion point) was located a distance of about 11 times the cell width from the apex of the tube exit, with a circumferential angle of 48°.
A vector diffraction model of wave propagation in a coronagraphic terrestrial planet finder
NASA Astrophysics Data System (ADS)
Shiri, Shahram; Lyon, Richard G.; Woodruff, Robert A.; Antosik, Roman
2004-10-01
In this work we study vector electromagnetic wave propagation in a visible-light coronagraph for applications to the design and analysis of Terrestrial Planet Finder (TPF). A visible light coronagraph in TPF requires detection of a terrestrial planet which is ~1010 dimmer than the central stellar source. Consequently, any theory used to design and analyze TPF requires accuracy better than 10-10 in intensity or 10-5 in electric field. Current coronagraphic approaches to TPF have relied on scalar diffraction theory. However, the vector nature of light requires a vector approach to the problem. In this study we employ a time-harmonic vector theory to study the electromagnetic field propagation through metallic focal plane occulting mask on dielectric substrate. We use parallelized edge-based vector finite element model to compute the wave propagation in a three-dimensional tetrahedral grid representing the geometry of the coronagraph. The edge-based finite element method overcomes the problem of modal propagation and rigorously enforces the field divergence to be zero. The reflectivity and transmittivity in the geometry are computed through the gold metal in various shapes using a planar incident beam. Subsequently, the near-field beam diffraction around the mask is investigated.
Plane wave compounding based on a joint transmitting-receiving adaptive beamformer.
Zhao, Jinxin; Wang, Yuanyuan; Zeng, Xing; Yu, Jinhua; Yiu, Billy Y S; Yu, Alfred C H
2015-08-01
Plane wave compounding is a useful mode for ultrasound imaging because it can make a good compromise between imaging quality and frame rate. It is also useful for broad view ultrasound imaging. Traditional coherent plane wave compounding coherently sums the echo data of different steered transmitting waves as the output. The data correlation information of different emissions is not considered. Therefore, some adaptive techniques can be introduced into the compounding procedure. In this paper, we propose a Joint Transmitting-Receiving (JTR) adaptive beamforming scheme for plane wave compounding. Unlike traditional adaptive beamformers, the proposed beamforming scheme is designed for the 2-D data set obtained from multiple plane wave firings. It calculates both the transmitting aperture weights and the receiving aperture weights and then combines them into a 2-D adaptive weight function for compounding. Experiments are conducted on both simulated and phantom data. Results show that the proposed scheme has better performance on both point targets and cysts than the existing plane wave compounding approach. Because of the adaptive process in both apertures for compounding, an improved resolution is observed in both simulation and phantom studies. When the eigenanalysis is introduced, a contrast enhancement is achieved. For the simulated cyst, a contrast ratio (CR) improvement of 48% is achieved compared with the traditional plane wave compounding. For the phantom cyst, this improvement is 213.8%. The proposed scheme also has good robustness against sound velocity errors. Therefore, it is effective in enhancing the coherent plane wave compounding quality.
An Investigation of Wave Impact Duration in High-Speed Planing Craft in Rough Water
2014-04-01
Engineering Department Technical Report AN INVESTIGATION OF WAVE IMPACT DURATION IN HIGH-SPEED PLANING CRAFT IN ROUGH WATER by Michael R. Riley, The...DATES COVERED - 4. TITLE AND SUBTITLE AN INVESTIGATION OF WAVE IMPACT DURATION IN HIGH-SPEED PLANING CRAFT IN ROUGH WATER 5a. CONTRACT NUMBER 5b...The original document contains color images. 14. ABSTRACT This report summarizes the investigation of wave impact duration. Example data plots are
Generating wave vector specific Damon-Eshbach spin waves in Py using a diffraction grating
NASA Astrophysics Data System (ADS)
Sklenar, J.; Bhat, V. S.; Tsai, C. C.; DeLong, L. E.; Ketterson, J. B.
2012-07-01
A patterned square silver antidot lattice on a thin uniform permalloy film facilitates direct coupling of a quasi-uniform microwave field to short wavelength magnetic modes. The resulting modes are studied as a function of both the magnitude and orientation (relative to the symmetry axes of the array) of an in-plane, external DC magnetic field. The observed modes are identified as surface spin waves with wavelengths matching the Fourier components of the silver array.
Stolt’s f-k migration for plane wave ultrasound imaging
Garcia, Damien; Le Tarnec, Louis; Muth, Stéphan; Montagnon, Emmanuel; Porée, Jonathan; Cloutier, Guy
2013-01-01
Ultrafast ultrasound is an emerging modality that offers new perspectives and opportunities in medical imaging. Plane wave imaging (PWI) allows one to attain very high frame rates by transmission of planar ultrasound wavefronts. As a plane wave reaches a given scatterer, the latter becomes a secondary source emitting upward spherical waves and creating a diffraction hyperbola in the received RF (radio-frequency) signals. To produce an image of the scatterers, all the hyperbolas must be migrated back to their apexes. In order to perform beamforming of plane wave echo RFs and return high-quality images at high frame rates, we propose a new migration method carried out in the frequency-wavenumber (f-k) domain. The f-k migration for PWI has been adapted from the Stolt migration for seismic imaging. This migration technique is based on the exploding reflector model (ERM), which consists in assuming that all the scatterers explode in concert and become acoustic sources. The classical ERM model, however, is not appropriate for PWI. We showed that the ERM can be made suitable for PWI by a spatial transformation of the hyperbolic traces present in the RF data. In vitro experiments were performed to sketch the advantages of PWI with Stolt’s f-k migration over the conventional delay-and-sum (DAS) approach. The Stolt’s f-k migration was also compared with the Fourier-based method developed by J-Y Lu. Our findings show that multi-angle compounded f-k migrated images are of quality similar to those obtained with a state-of-the-art dynamic focusing mode. This remained true even with a very small number of steering angles thus ensuring a highly competitive frame rate. In addition, the new FFT-based f-k migration provides comparable or better contrast-to-noise ratio and lateral resolution than the Lu’s and DAS migration schemes. Matlab codes of the Stolt’s f-k migration for PWI are provided. PMID:24626107
Rayleigh-wave diffractions due to a void in the layered half space
Xia, J.; Xu, Y.; Miller, R.D.; Nyquist, J.E.
2006-01-01
Void detection is challenging due to the complexity of near-surface materials and the limited resolution of geophysical methods. Although multichannel, high-frequency, surface-wave techniques can provide reliable shear (S)-wave velocities in different geological settings, they are not suitable for detecting voids directly based on anomalies of the S-wave velocity because of limitations on the resolution of S-wave velocity profiles inverted from surface-wave phase velocities. Xia et al. (2006a) derived a Rayleigh-wave diffraction traveltime equation due to a void in the homogeneous half space. Encouraging results of directly detecting a void from Rayleigh-wave diffractions were presented (Xia et al., 2006a). In this paper we used four two-dimensional square voids in the layered half space to demonstrate the feasibility of detecting a void with Rayleigh-wave diffractions. Rayleigh-wave diffractions were recognizable for all these models after removing direct surface waves by F-K filtering. We evaluate the feasibility of applying the Rayleigh-wave diffraction traveltime equation to a void in the layered earth model. The phase velocity of diffracted Rayleigh waves is predominately determined by surrounding materials of a void. The modeling results demonstrate that the Rayleigh-wave diffraction traveltime equation due to a void in the homogeneous half space can be applied to the case of a void in the layered half space. In practice, only two diffraction times are necessary to define the depth to the top of a void and the average velocity of diffracted Rayleigh waves. ?? 2005 Society of Exploration Geophysicists.
Plane wave holonomies in quantum gravity. II. A sine wave solution
NASA Astrophysics Data System (ADS)
Neville, Donald E.
2015-08-01
This paper constructs an approximate sinusoidal wave packet solution to the equations of canonical gravity. The theory uses holonomy-flux variables with support on a lattice (LHF =lattice-holonomy flux ). There is an SU(2) holonomy on each edge of the LHF simplex, and the goal is to study the behavior of these holonomies under the influence of a passing gravitational wave. The equations are solved in a small sine approximation: holonomies are expanded in powers of sines and terms beyond sin2 are dropped; also, fields vary slowly from vertex to vertex. The wave is unidirectional and linearly polarized. The Hilbert space is spanned by a set of coherent states tailored to the symmetry of the plane wave case. Fixing the spatial diffeomorphisms is equivalent to fixing the spatial interval between vertices of the loop quantum gravity lattice. This spacing can be chosen such that the eigenvalues of the triad operators are large, as required in the small sine limit, even though the holonomies are not large. Appendices compute the energy of the wave, estimate the lifetime of the coherent state packet, discuss circular polarization and coarse-graining, and determine the behavior of the spinors used in the U(N) SHO realization of LQG.
Simulation of elastic wave diffraction by multiple strip-like cracks in a layered periodic composite
NASA Astrophysics Data System (ADS)
Golub, M. V.
2016-12-01
The problem of numerical simulation of the steady-state harmonic vibrations of a layered phononic crystal (elastic periodic composite) with a set of strip-like cracks parallel to the layer boundaries is solved, and the accompanying wave phenomena are considered. The transfer matrix method (propagator matrix method) is used to describe the incident wave field. It allows one not only to construct the wave fields but also to calculate the pass bands and band gaps and to find the localization factor. The wave field scattered by multiple defects is represented by means of an integral approach as a superposition of the fields scattered by all cracks. An integral representation in the form of a convolution of the Fourier symbols of Green's matrices for the corresponding layered structures and a Fourier transform of the crack opening displacement vector is constructed for each of the scattered fields. The crack opening displacements are determined by the boundary integral equation method using the Bubnov-Galerkin scheme, where Chebyshev polynomials of the second kind, which take into account the behavior of the solution near the crack edges, are chosen as the projection and basis systems. The system of linear algebraic equations with a diagonal predominance of components arising when the system of integral equations is discretized has a block structure. The characteristics describing qualitatively and quantitatively the wave processes that take place under the diffraction of plane elastic waves by multiple cracks in a phononic crystal are analyzed. The resonant properties of a system of defects and the influence of the relative positions and sizes of defects in a layered phononic crystal on the resonant properties are studied. To obtain clearer results and to explain them, the energy flux vector is calculated and the energy surfaces and streamlines corresponding to them are constructed.
NASA Technical Reports Server (NTRS)
Balanis, Constantine A.
1989-01-01
Several high-frequency models for nonprincipal-plane scattering from a rectangular, perfectly conducting plate are examined. Two methods, the Method of Equivalent Currents and corner diffraction coefficients, are considered. Formulations for second-order Physical Theory of Diffraction equivalent currents and for corner diffracted fields are presented. Comparisons are made among plate models. Results away from grazing are accurate using only first-order terms. Near grazing, second-order and corner diffraction terms improve the results for many cases. The pattern control of horn antennas using lossy materials to coat the inner walls of the horn is also investigated. Integral Equation and Moment Method techniques are used to formulate the problem. It is clearly demonstrated that side lobe level reduction can be achieved using impedance surfaces on the inner walls of the horn.
Statistics for long irregular wave run-up on a plane beach from direct numerical simulations
NASA Astrophysics Data System (ADS)
Didenkulova, Ira; Senichev, Dmitry; Dutykh, Denys
2017-04-01
Very often for global and transoceanic events, due to the initial wave transformation, refraction, diffraction and multiple reflections from coastal topography and underwater bathymetry, the tsunami approaches the beach as a very long wave train, which can be considered as an irregular wave field. The prediction of possible flooding and properties of the water flow on the coast in this case should be done statistically taking into account the formation of extreme (rogue) tsunami wave on a beach. When it comes to tsunami run-up on a beach, the most used mathematical model is the nonlinear shallow water model. For a beach of constant slope, the nonlinear shallow water equations have rigorous analytical solution, which substantially simplifies the mathematical formulation. In (Didenkulova et al. 2011) we used this solution to study statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. The influence of the wave nonlinearity was approached by considering modifications of probability distribution of the moving shoreline and its horizontal velocity for waves of different amplitudes. It was shown that wave nonlinearity did not affect the probability distribution of the velocity of the moving shoreline, while the vertical displacement of the moving shoreline was affected substantially demonstrating the longer duration of coastal floods with an increase in the wave nonlinearity. However, this analysis did not take into account the actual transformation of irregular wave field offshore to oscillations of the moving shoreline on a slopping beach. In this study we would like to cover this gap by means of extensive numerical simulations. The modeling is performed in the framework of nonlinear shallow water equations, which are solved using a modern shock-capturing finite volume method. Although the shallow water model does not pursue the wave breaking and bore formation in a general sense (including the water surface
Uniform line integral representation of edge-diffracted fields.
Umul, Yusuf Z
2008-01-01
A uniform line integral representation is derived for edge-diffracted fields by using the modified theory of physical optics and uniform asymptotic evaluation methods. The method is applied to the problem of diffraction of plane waves by a semi-infinite edge, which creates tip-diffracted fields with edge-diffracted waves. The uniform diffracted fields are plotted and examined numerically.
Verification of the Uncertainty Principle by Using Diffraction of Light Waves
ERIC Educational Resources Information Center
Nikolic, D.; Nesic, Lj
2011-01-01
We described a simple idea for experimental verification of the uncertainty principle for light waves. We used a single-slit diffraction of a laser beam for measuring the angular width of zero-order diffraction maximum and obtained the corresponding wave number uncertainty. We will assume that the uncertainty in position is the slit width. For the…
Verification of the Uncertainty Principle by Using Diffraction of Light Waves
ERIC Educational Resources Information Center
Nikolic, D.; Nesic, Lj
2011-01-01
We described a simple idea for experimental verification of the uncertainty principle for light waves. We used a single-slit diffraction of a laser beam for measuring the angular width of zero-order diffraction maximum and obtained the corresponding wave number uncertainty. We will assume that the uncertainty in position is the slit width. For the…
Fraunhofer diffraction of coherent and incoherent nuclear matter waves by complementary screens
NASA Astrophysics Data System (ADS)
da Silveira, R.; Leclercq-Willain, Ch.
2013-06-01
The analogy between Fraunhofer diffraction effects observed in nuclear and subnuclear collisions and those observed with light diffracted by complementary screens is revisited. Emphasis will be put on the collision mechanisms playing a role analogous to that of an aperture in light diffraction. These analogies are illustrated with examples involving coherent and incoherent nuclear matter waves.
NASA Astrophysics Data System (ADS)
Li, C. Y.; Lesselier, D.; Zhong, Y.
2015-07-01
The present work aims at building up a full-wave computational model of electromagnetic nondestructive testing of composite materials produced by stacking up dielectric slabs one over the other. In each such dielectric slab, a periodic array of infinite cylindrical fibers is embedded. Electromagnetic scattering of such a multilayered, fiber-based periodic composite is investigated here for an obliquely incident plane wave, the plane of incidence of which differs from the plane orthogonal to the fibers' axes. Full-wave field representations are given first by multipole and plane wave expansions. Mode matching at boundaries between layers then yields the propagating matrices, which are applied to connect reflection and transmission coefficients of the longitudinal field components. Power reflection and transmission coefficients are obtained from time-averaged Poynting vectors. Numerical experiments with comparisons with known results illustrate the accuracy of the model proposed.
Nonlinear diffraction of waves by a submerged shelf in shallow water
Ertekin, R.C.; Becker, J.M.
1996-12-31
The diffraction of water waves by submerged obstacles in shallow water generally requires the use of a nonlinear theory since both dispersive and nonlinear effects are important. In this work, wave diffraction is studied in a numerical wave-tank using the Green-Naghdi (G-N) equations. Cnoidal waves are generated numerically by a wave maker situated at one end of a 2-dimensional numerical wave tank. At the downwave end of the tank, an open-boundary condition is implemented to simulate a wave-absorbing beach and thus to reduce reflections. The G-N equations are solved in the time-domain by employing a finite-difference method. The numerical method is applied to diffraction of cnoidal waves by a submerged shelf, or a sand bar, of considerable height relative to water depth. The predicted results are compared with the available experimental data which indicate the importance of nonlinearity for the shallow-water conditions.
Analysis of a photonic nanojet assuming a focused incident beam instead of a plane wave
NASA Astrophysics Data System (ADS)
Dong, Aotuo; Su, Chin
2014-12-01
The analysis of a photonic nanojet formed by dielectric spheres almost always assumes that the incident field is a plane wave. In this work, using vector spherical harmonics representations, we analyze the case of a more realistic incident field consisting of a focused beam formed by a microscope objective. Also included is the situation in which the sphere is not at the focal plane of the focus beam. We find that the dimension of the nanojet beam waist is less sensitive with respect to the azimuthal angle when compared with the plane wave case. Also, by shifting the particle away from the focal plane, the nanojet beam waist can be positioned outside the particle which otherwise would be inside or at the particle surface. Inherently, no such adjustment is possible with an incident plane wave assumption.
Shear wave in a pre-stressed poroelastic medium diffracted by a rigid strip
NASA Astrophysics Data System (ADS)
Singh, Abhishek Kumar; Yadav, Ram Prasad; Kumar, Santan; Chattopadhyay, Amares
2017-10-01
The investigated work analytically addresses the diffraction of horizontally polarised shear wave by a rigid strip in a pre-stressed transversely isotropic poroelastic infinite medium. The far field solution for the diffracted displacement of shear wave has been established in closed form. The diffraction patterns for displacement in the said medium have been computed numerically and its dependence on wave number has been depicted graphically. Further, the study also delineates the pronounced influence of various affecting parameters viz. anisotropy parameter, porosity parameter, speed of the shear wave, and incident angle on the diffracted displacement of the propagating wave. The effects of horizontal as well as vertical compressive and tensile pre-stresses on diffracted displacement of propagating wave have been examined meticulously in a comparative manner. It can be remarkably quoted that porosity prevailing in the medium disfavors the diffracted displacement of the propagating wave. In addition, some special cases have been deduced from the determined expression of the diffracted displacement of shear wave at a large distance from the strip.
Plane-parallel waves as duals of the flat background II: T-duality with spectators
NASA Astrophysics Data System (ADS)
Petrásek, Filip; Hlavatý, Ladislav; Petr, Ivo
2017-08-01
We give the classification of T-duals of the flat background in four dimensions with respect to one-, two-, and three-dimensional subgroups of the Poincaré group using non-Abelian T-duality with spectators. As duals we find backgrounds for sigma models in the form of plane-parallel waves or diagonalizable curved metrics often with torsion. Among others, we find exactly solvable time-dependent isotropic pp-wave, singular pp-waves, or generalized plane wave (K-model).
Matrix basis for plane and modal waves in a Timoshenko beam.
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.
Matrix basis for plane and modal waves in a Timoshenko beam
NASA Astrophysics Data System (ADS)
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.
Matrix basis for plane and modal waves in a Timoshenko beam
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
On some features of plane waves of thermonuclear burn
NASA Astrophysics Data System (ADS)
Khishchenko, K. V.; Charakhch'yan, A. A.
2015-01-01
The behavior of a slow burn wave propagating over a precompressed thermonuclear fuel heated by several shock waves generated by a laser pulse is studied. It is shown that such a burn wave can rapidly increase the fuel density ahead of the wave front and transform to a pair of detonation waves moving in the opposite directions. Hydrodynamic equations with a linear velocity profile are solved. It is found that the proton beam intensity necessary for ignition increases with the initial fuel density in accordance with the known formula generalizing results of two-dimensional simulations. A possibility of using results of one-dimensional simulations for determining the energy of ignition of a cylindrical target is discussed.
Kanagawa, Tetsuya
2015-05-01
This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.
Diffraction analysis for digital micromirror device scene projectors in the long-wave infrared
NASA Astrophysics Data System (ADS)
Han, Qing; Wang, Jian; Zhang, Jianzhong; Sun, Qiang
2016-08-01
Diffraction effects play a significant role in scene projectors by digital micromirror devices (DMDs) in the long-wave infrared (IR) band (8 to 12 μm). The contrast provided by these projector systems can become noticeably worse because of the diffraction characteristics of the DMD. The actual diffraction characteristics of the DMD deviate significantly from the predictions of scalar diffraction theory in the long-wave IR. To address this issue, we built a vector diffraction-grating model of the DMD; the diffraction grating model is simulated with MATLAB. Furthermore, we analyze the effect of incident angle and polarization, which are the main factors that decrease the contrast of DMD-based scene projectors in the long-wave IR. Finally, an effective method to improve the contrast of the scene projector system is given, and the maximum contrast of the scene projector system is ˜0.7.
Feasibility of detecting near-surface feature with Rayleigh-wave diffraction
Xia, J.; Nyquist, J.E.; Xu, Y.; Roth, M.J.S.; Miller, R.D.
2007-01-01
Detection of near-surfaces features such as voids and faults is challenging due to the complexity of near-surface materials and the limited resolution of geophysical methods. Although multichannel, high-frequency, surface-wave techniques can provide reliable shear (S)-wave velocities in different geological settings, they are not suitable for detecting voids directly based on anomalies of the S-wave velocity because of limitations on the resolution of S-wave velocity profiles inverted from surface-wave phase velocities. Therefore, we studied the feasibility of directly detecting near-surfaces features with surface-wave diffractions. Based on the properties of surface waves, we have derived a Rayleigh-wave diffraction traveltime equation. We also have solved the equation for the depth to the top of a void and an average velocity of Rayleigh waves. Using these equations, the depth to the top of a void/fault can be determined based on traveltime data from a diffraction curve. In practice, only two diffraction times are necessary to define the depth to the top of a void/fault and the average Rayleigh-wave velocity that generates the diffraction curve. We used four two-dimensional square voids to demonstrate the feasibility of detecting a void with Rayleigh-wave diffractions: a 2??m by 2??m with a depth to the top of the void of 2??m, 4??m by 4??m with a depth to the top of the void of 7??m, and 6??m by 6??m with depths to the top of the void 12??m and 17??m. We also modeled surface waves due to a vertical fault. Rayleigh-wave diffractions were recognizable for all these models after FK filtering was applied to the synthetic data. The Rayleigh-wave diffraction traveltime equation was verified by the modeled data. Modeling results suggested that FK filtering is critical to enhance diffracted surface waves. A real-world example is presented to show how to utilize the derived equation of surface-wave diffractions. ?? 2006 Elsevier B.V. All rights reserved.
Run-up of long solitary waves of different polarities on a plane beach
NASA Astrophysics Data System (ADS)
Didenkulova, Ira; Pelinovsky, Efim; Didenkulov, Oleg; Rodin, Artem
2015-04-01
We study the run-up of long solitary waves of different polarities on a beach in the case of composite bottom topography: a plane sloping beach transforms into a region of constant depth. We confirm that nonlinear wave deformation of positive polarity (wave crest) resulting in an increase in the wave steepness leads to a significant increase in the run-up height. It is shown that nonlinear effects are most strongly pronounced for the run-up of a wave with negative polarity (wave trough). In the latter case, the run-up height of such waves increases with their steepness and can exceed the amplitude of the incident wave. This study is extended to the case of long breaking solitary waves, simulated numerically in the nonlinear shallow-water theory framework using CLAWPACK-software. For small-amplitude incident waves regardless their polarity, the results of numerical computations usually coincide with predictions of the nonlinear shallow water theory for non-breaking waves. Nonlinear effects start to be important when incident wave is located far from the shoreline even for initially small-amplitude waves. With further increase in incident wave amplitude, the wave transforms into the shock wave (bore) before approaching the beach. Run-up characteristics of waves of different polarities are compared. Nonlinear effects and induced energy dissipation caused by wave breaking during its run-up on a beach are more prominent for negative pulses rather than for positive ones.
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.
Nonlinear Cylindrical Waves on a Plane Plasma Surface
NASA Astrophysics Data System (ADS)
Gradov, O. M.
2004-01-01
By means of the cold electron plasma equations, it is shown that surface soliton solutions can exist in the azimuthally symmetric case at the boundary of semi-infinite plasmas for both standing and running waves.
Response of a Doppler canceling system to plane gravitational waves
NASA Technical Reports Server (NTRS)
Caporali, A.
1982-01-01
This paper discusses the interaction of long periodic gravitational waves with a three-link microwave system known as the Doppler canceling system. This system, which was developed for a gravitational red-shift experiment, uses one-way and two-way Doppler information to construct the beat signal of two reference oscillators moving with respect to each other. The geometric-optics approximation is used to derive the frequency shift produced on a light signal propagating in a gravitational-wave space-time. The signature left on the Doppler-cancelled beat by bursts and continuous gravitational waves is analyzed. A comparison is made between the response to gravitational waves of the Doppler canceling system and that of a (NASA) Doppler tracking system which employs two-way, round-trip radio waves. A threefold repetition of the gravitational wave form is found to be a common feature of the response functions of both systems. These two functions otherwise exhibit interesting differences.
Response of a Doppler canceling system to plane gravitational waves
NASA Technical Reports Server (NTRS)
Caporali, A.
1982-01-01
This paper discusses the interaction of long periodic gravitational waves with a three-link microwave system known as the Doppler canceling system. This system, which was developed for a gravitational red-shift experiment, uses one-way and two-way Doppler information to construct the beat signal of two reference oscillators moving with respect to each other. The geometric-optics approximation is used to derive the frequency shift produced on a light signal propagating in a gravitational-wave space-time. The signature left on the Doppler-cancelled beat by bursts and continuous gravitational waves is analyzed. A comparison is made between the response to gravitational waves of the Doppler canceling system and that of a (NASA) Doppler tracking system which employs two-way, round-trip radio waves. A threefold repetition of the gravitational wave form is found to be a common feature of the response functions of both systems. These two functions otherwise exhibit interesting differences.
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…
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…
An Exact Solution for Geophysical Edge Waves in the {β}-Plane Approximation
NASA Astrophysics Data System (ADS)
Ionescu-Kruse, Delia
2015-12-01
By taking into account the {β}-plane effects, we provide an exact nonlinear solution to the geophysical edge-wave problem within the Lagrangian framework. This solution describes trapped waves propagating eastward or westward along a sloping beach with the shoreline parallel to the Equator.
A phase-plane analysis of localized frictional waves
NASA Astrophysics Data System (ADS)
Putelat, T.; Dawes, J. H. P.; Champneys, A. R.
2017-07-01
Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick-slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.
Travelling wave modes of a plane layered anelastic earth
NASA Astrophysics Data System (ADS)
Odom, Robert I.
2016-08-01
Incorporation of attenuation into the normal mode sum representations of seismic signals is commonly effected by applying perturbation theory. This is fine for weak attenuation, but problematic for stronger attenuation. In this work, modes of the anelastic medium are represented as complex superpositions of elastic eigenfunctions. For the P-SV system, a generalized eigenvalue equation for the complex eigenwavenumbers and complex coefficients used to construct the anelastic eigenfunctions is derived. The generalized eigenvalue problem for the P-SV problem is exactly linear in the eigenwavenumber at the expense of doubling the dimension. The SH problem is exactly linear in the square of the eigenwavenumber. This is in contrast to a similar standing wave problem for the earth free oscillations. Attenuation is commonly incorporated into synthetic seismogram calculations by introduction of complex frequency-dependent elastic moduli. The moduli depend nonlinearly on the frequency. The independent variable in the standing wave free oscillation problem is the frequency, which makes the eigenvalue problem nonlinear. The choice of the wavenumber as the independent variable for the travelling wave problem leads to a linear problem. The Earth model may be transversely isotropic. Compressional waves and both polarizations of shear waves (SV, SH) are treated.
Wave field reconstruction from multiple plane intensity-only data: augmented lagrangian algorithm.
Migukin, Artem; Katkovnik, Vladimir; Astola, Jaakko
2011-06-01
A complex-valued wave field is reconstructed from intensity-only measurements given at multiple observation planes parallel to the object plane. The phase-retrieval algorithm is obtained from the constrained maximum likelihood approach provided that the additive noise is gaussian. The forward propagation from the object plane to the measurement plane is treated as a constraint in the proposed variational setting of reconstruction. The developed iterative algorithm is based on an augmented lagrangian technique. An advanced performance of the algorithm is demonstrated by numerical simulations.
NASA Astrophysics Data System (ADS)
Shamaev, A. S.; Shumilova, V. V.
2017-01-01
The problem of plane wave propagation through a plane composite layer of thickness h is considered. The composite consists of periodically repeated elastic and Kelvin-Voigt viscoelastic material layers, and all layers are either parallel or perpendicular to the incident wave front. Moreover, it is assumed that the thickness of each separate layer of the composite is much less than the acoustic wave length and the thickness h of the entire composite. We study the problem by using a homogenized model of the composite, which allows us to find the reflection and transmission factors and the variation in the sound intensity level as it propagates though the composite layer of thickness h.
On the motion of a charged particle in a plane monochromatic electromagnetic wave
Andreev, Stepan N; Makarov, Vyacheslav P; Rukhadze, Anri A
2009-01-31
The motion of a charged particle in the external specified field of a plane electromagnetic wave of large amplitude, when the relativistic consideration is required, is analysed in detail. The cases of different initial conditions for the motion of the charged particle and different polarisations of the wave are studied. It is shown that the expression for the kinetic energy of an electron oscillating in the transverse field of the wave, proposed in [1], is valid only in the nonrelativistic limit. (superstrong fields)
Generalized plane waves in Poincaré gauge theory of gravity
NASA Astrophysics Data System (ADS)
Blagojević, Milutin; Cvetković, Branislav; Obukhov, Yuri N.
2017-09-01
A family of exact vacuum solutions, representing generalized plane waves propagating on the (anti-)de Sitter background, is constructed in the framework of Poincaré gauge theory. The wave dynamics is defined by the general Lagrangian that includes all parity even and parity odd invariants up to the second order in the gauge field strength. The structure of the solution shows that the wave metric significantly depends on the spacetime torsion.
Theoretical calculation of plane wave speeds for alkali metals under pressure.
NASA Technical Reports Server (NTRS)
Eftis, J.; Macdonald, D. E.; Arkilic, G. M.
1971-01-01
Theoretical calculations of the variation with pressure of small amplitude plane wave speeds are performed for sodium and potassium at zero temperature. The results obtained for wave speeds associated with volume dependent second-order elastic coefficients show better agreement with experimental data than for wave speeds associated with shear dependent coefficients. This result is believed to be due to omission of the band structure correction to the strain energy density.
NASA Astrophysics Data System (ADS)
Gauthier, Robert C.; Alzahrani, Mohammed A.; Jafari, Seyed Hamed
2015-02-01
The plane wave expansion (PWM) technique applied to Maxwell's wave equations provides researchers with a supply of information regarding the optical properties of dielectric structures. The technique is well suited for structures that display a linear periodicity. When the focus is directed towards optical resonators and structures that lack linear periodicity the eigen-process can easily exceed computational resources and time constraints. In the case of dielectric structures which display cylindrical or spherical symmetry, a coordinate system specific set of basis functions have been employed to cast Maxwell's wave equations into an eigen-matrix formulation from which the resonator states associated with the dielectric profile can be obtained. As for PWM, the inverse of the dielectric and field components are expanded in the basis functions (Fourier-Fourier-Bessel, FFB, in cylindrical and Fourier- Bessel-Legendre, BLF, in spherical) and orthogonality is employed to form the matrix expressions. The theoretical development details will be presented indicating how certain mathematical complications in the process have been overcome and how the eigen-matrix can be tuned to a specific mode type. The similarities and differences in PWM, FFB and BLF are presented. In the case of structures possessing axial cylindrical symmetry, the inclusion of the z axis component of propagation constant makes the technique applicable to photonic crystal fibers and other waveguide structures. Computational results will be presented for a number of different dielectric geometries including Bragg ring resonators, cylindrical space slot channel waveguides and bottle resonators. Steps to further enhance the computation process will be reported.
Anti-plane transverse waves propagation in nanoscale periodic layered piezoelectric structures.
Chen, A-Li; Yan, Dong-Jia; Wang, Yue-Sheng; Zhang, Chuanzeng
2016-02-01
In this paper, anti-plane transverse wave propagation in nanoscale periodic layered piezoelectric structures is studied. The localization factor is introduced to characterize the wave propagation behavior. The transfer matrix method based on the nonlocal piezoelectricity continuum theory is used to calculate the localization factor. Additionally, the stiffness matrix method is applied to compute the wave transmission spectra. A cut-off frequency is found, beyond which the elastic waves cannot propagate through the periodic structure. The size effect or the influence of the ratio of the internal to external characteristic lengths on the cut-off frequency and the wave propagation behavior are investigated and discussed.
Jin Shi Yin Dongsheng
2008-06-01
We construct a class of numerical schemes for the Liouville equation of geometric optics coupled with the Geometric Theory of Diffractions to simulate the high frequency linear waves with a discontinuous index of refraction. In this work [S. Jin, X. Wen, A Hamiltonian-preserving scheme for the Liouville equation of geometric optics with partial transmissions and reflections, SIAM J. Numer. Anal. 44 (2006) 1801-1828], a Hamiltonian-preserving scheme for the Liouville equation was constructed to capture partial transmissions and reflections at the interfaces. This scheme is extended by incorporating diffraction terms derived from Geometric Theory of Diffraction into the numerical flux in order to capture diffraction at the interface. We give such a scheme for curved interfaces. This scheme is proved to be positive under a suitable time step constraint. Numerical experiments show that it can capture diffraction phenomena without fully resolving the wave length of the original wave equation.
Diffraction analysis for DMD-based scene projectors in the long-wave infrared.
Han, Qing; Zhang, Jianzhong; Wang, Jian; Sun, Qiang
2016-10-01
Diffraction effects play a significant role in the digital micromirror device (DMD)-based scene projectors in the long-wave infrared (IR) band (8-12 μm). The contrast provided by these projector systems can become noticeably worse because of the diffraction characteristics of the DMD. We apply a diffraction grating model of the DMD based on the scalar diffraction theory and the Fourier transform to address this issue. In addition, a simulation calculation is conducted with MATLAB. Finally, the simulation result is verified with an experiment. The simulation and experimental results indicate that, when the incident azimuth angle is 0° and the zenith angle is between 42°and 46°, the scene projectors will have a good imaging contrast in the long-wave IR. The diffraction grating model proposed in this study provides a method to improve the contrast of DMD-based scene projectors in the long-wave IR.
Traveling Wave Modes of a Plane Layered Anelastic Earth
2016-05-20
Theo- retical seismology , Wave propagation 1 Distribution Statement A: Approved for public release; distribution is unlimited Accepted for publication...Quantitative Seismology , Theory and Methods, Vol I San Fran- cisco: W.H. Freeman and Company. Apsel, R.J. and J.E. Luco, 1983. On the Green’s function for a
NASA Astrophysics Data System (ADS)
Matula, Thomas John
Electromagnetic acoustic wave transducers (EMATs) are described for generating low-frequency tone bursts on metalized membranes in air and elastic plates in water. Bursts on the membrane have phase velocities much less than the speed of sound in the surrounding air and are accompanied by plane evanescent waves. The frequency and time-domain responses of the EMAT and the dependence on gap spacing between the coupling coil and the membrane were studied. Wave -number selective optical and capacitive probes were used to measure the wave properties. Versions of these transducers are insensitive to long wavelength motion of the membrane. Diffraction of the burst by a sharp edge in air was observed as a function of the gap between the membrane and a razor edge. The scattered pressure decreases exponentially with increasing gap as expected from an approximate analysis of edge diffraction of evanescent waves. In related work an EMAT is used to generate 28 kHz tone bursts of bending waves on an aluminum plate. The bursts propagate down into water where the surrounding wavefield is probed. Observations described indicate that there occurs a branching of energy as the wave crosses the air-water interface. Radiation from subsonic flexural plate waves due to the discontinuity in fluid -loading is observed. It is partially analogous to the transition radiation of fast charged particles crossing a dielectric interface. The angular radiation pattern resembles that of a line quadrupole. Near the interface there exists an interference between the two energy branches in water that produces a series of pressure nulls. The pressure nulls are associated with a pi phase change in the wavefield and are indicators of wavefront dislocations. A computation of the wavefield in an unbounded fluid due to a line-moment excitation of a plate is comparable with the null pattern observed but differs in certain details.
Polarization factors in the symmetrical case of three-wave diffraction.
Sheludko, Sergey
2004-05-01
Particular results of an unconventional approach to the geometry of multiple diffraction are presented. The scalar relations between polarization components of three waves in the symmetrical case, i.e. when the triplet of diffraction vectors forms an isosceles triangle, are considered. The polarization factors are given in simple trigonometric form as functions of the Bragg angle of principal reflection and of a crystallographic parameter, which unambiguously describes such a three-wave configuration.
Wave-front sensing from subdivision of the focal plane with a lenslet array.
Clare, Richard M; Lane, Richard G
2005-01-01
A wave-front sensing scheme based on placing a lenslet array at the focal plane of the telescope with each lenslet reimaging the aperture is analyzed. This wave-front sensing arrangement is the dual of the Shack-Hartmann sensor, with the wave front partitioned in the focal plane rather than in the aperture plane. This arrangement can be viewed as the generalization of the pyramid sensor and allows direct comparisons of this sensor with the Shack-Hartmann sensor. We show that, as with the Shack-Hartmann sensor, when subdividing in the focal plane, the quality of the wave-front estimate is a trade-off between the quality of the slope measurements over each region in the aperture and the resolution to which the slope measurements are obtained. Open-loop simulation results demonstrate that the performance of the lenslet array at the focal plane is equivalent to that of the Shack-Hartmann sensor when no modulation is applied to the lenslet array. However, when the array is modulated in a manner akin to that of the pyramid sensor, subdivision at the focal plane provides advantages when compared with the Shack-Hartmann sensor.
NASA Astrophysics Data System (ADS)
Miles, Drew; McEntaffer, Randall; McCoy, Jake; Tutt, James; DeRoo, Casey
2017-01-01
Future soft X-ray spectroscopy missions have science requirements that demand higher instrument throughput and higher resolution than currently available technology. A key element in such spectrometers are dispersive elements such as diffraction gratings. Our group at Penn State University develops and fabricates off-plane reflection gratings in an effort to achieve the level of performance required by future missions. We present here efficiency measurements made in the 0.3 - 1.5 keV energy band at the Advanced Light Source (ALS) synchrotron at Lawrence Berkley National Laboratory for one such grating, which was replicated using UV-nanoimprint techniques from a grating master fabricated using electron-beam lithography, plasma etching, and potassium hydroxide etching. These results represent the first successful demonstration of off-plane grating replicas produced via these fabrication techniques and provide baseline efficiency measurements for flight-like replicated gratings.
Refinement of a discontinuity-free edge-diffraction model describing focused wave fields.
Sedukhin, Andrey G
2010-03-01
Two equivalent forms of a refined discontinuity-free edge-diffraction model describing the structure of a stationary focused wave field are presented that are valid in the framework of the scalar Debye integral representation for a diffracted rotationally symmetric converging spherical wave of a limited yet not-too-low angular opening. The first form describes the field as the sum of a direct quasi-spherical wave and a plurality of edge quasi-conical waves of different orders, the optimum discontinuity-free angular spectrum functions of all the waves being dependent on the polar angle only. According to the second form, the focused field is fully characterized by only three components--the same quasi-spherical wave and two edge quasi-conical waves of the zero and first order, of which the optimum discontinuity-free angular spectrum functions are dependent on both the polar angle and the polar radius counted from the geometrical focus.
NASA Astrophysics Data System (ADS)
Olson, Erik R.; Knuteson, Robert O.; Revercomb, Hank E.; Li, Jun; Huang, Hung-Lung A.
2004-10-01
The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) and the Hyperspectral Environmental Suite (HES) instruments are geostationary infrared spectrometers. Geostationary orbit provides observations with very good time resolution, but also increases the effect of diffraction. There can be significant differences in emitted radiances due to clouds and changes in surface characteristics. High, thick clouds in particular are much cooler than clear areas. Diffraction causes radiation that originates from cloudy areas outside of the detector field of view to contaminate the clear pixels. GIFTS will also have two detector arrays on different focal planes, which may not be perfectly aligned. This can cause spatial misalignment between the data for the two spectral regions. High spatial resolution numerical models run at the University of Wisconsin - Cooperative Institute for Meteorological Satellite Studies (UW-CIMSS) provide data for examining the diffraction and misalignment effects. The model data represents a variable cloud case during the IHOP field experiment at 1.3-km resolution. This paper outlines the production of high spatial resolution simulated data, characterization of the far field diffraction effects on radiances, and analysis of misalignment effects on temperature and moisture profile retrievals.
The existence and behavior of viscous structure for plane detonation waves
NASA Astrophysics Data System (ADS)
Wagner, David H.
1989-09-01
A necessary condition and a sufficient condition are proved for the existence of steady plane wave solutions to the Navier-Stokes equations for a reacting gas. These solutions represent plane detonation waves, and converge to ZND detonation waves as the viscosity, heat conductivity, and species diffusion rates tend to zero. It is assumed that the Prandtl number is 3/4, but arbitrary Lewis numbers are permitted. No assumption is made concerning the activation energy. It is shown that the stagnation enthalpy and the entropy flux are always monotone for such solutions, and that the mass density and pressure are nearly always not monotone, as predicted by the ZND theory. In certain parameter ranges, typically that of large diffusion, many of these waves have the appearance of a weak detonation followed by an inert shock wave. This confirms a phenomenon observed in numerical calculations and in a model system by Colella, Majda, and Roytburd (1986).
Well-posedness and generalized plane waves simulations of a 2D mode conversion model
Imbert-Gérard, Lise-Marie
2015-12-15
Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the plasma, since it permits to transfer the heat at or near the plasma center. This work focuses on a mathematical model of wave propagation around the mode conversion region, from both theoretical and numerical points of view. It aims at developing, for a well-posed equation, specific basis functions to study a wave mode conversion process. These basis functions, called generalized plane waves, are intrinsically based on variable coefficients. As such, they are particularly adapted to the mode conversion problem. The design of generalized plane waves for the proposed model is described in detail. Their implementation within a discontinuous Galerkin method then provides numerical simulations of the process. These first 2D simulations for this model agree with qualitative aspects studied in previous works.
Propagation of in-plane wave in viscoelastic monolayer graphene via nonlocal strain gradient theory
NASA Astrophysics Data System (ADS)
Xiao, Weiwei; Li, Li; Wang, Meng
2017-06-01
The behaviors of monolayer graphene sheet have attracted increasing attention of many scientists and researchers. In this study, the propagation behaviors of in-plane wave in viscoelastic monolayer graphene are investigated. The constitutive equation and governing equation for in-plane wave propagation is developed by employing Hamilton's principle and nonlocal strain gradient theory. By solving the governing equation of motion, the closed-form dispersion relation between phase velocity and wave number is derived and an asymptotic phase velocity can be acquired. The effects of wave number, material length scale parameter, nonlocal parameter and damping coefficient on in-plane wave propagation behaviors are discussed in the numerical studies. It is found that, when exciting wavelengths or structural dimensions become comparable to the material length scale parameters and nonlocal parameters, the scaling effects on wave propagation behaviors are significant. For nanoscaled graphene sheet, the effects of nonlocal parameter, material length scale parameter and damping coefficient on phase velocity are tiny at low wave numbers while significant at high wave numbers. The phase velocity would increase with the increase of material length scale parameter or the decrease of nonlocal parameter and damping coefficient. Furthermore, results indicate that the asymptotic phase velocity can be increase by increasing material length scale parameter or decreasing nonlocal parameter.
Three-wave diffraction in damaged epitaxial layers with a wurtzite structure
NASA Astrophysics Data System (ADS)
Kyutt, R. N.
2011-05-01
Three-wave diffraction of X-rays is measured using the Renninger scheme for a series of GaN epitaxial layers of various thicknesses and degrees of structural perfection. In each 30°-angular interval of azimuthal rotation, all ten three-wave peaks determined by the geometry of diffraction with the 0001 first forbidden reflection and Cu K α radiation are observed. The φ- and θ-scanned diffraction curves are measured for each three-wave combination. The angular FWHM of the diffraction peaks formed in experiments and its relation with the parameters of the two-wave diffraction pattern and the dislocation structure of the layers are analyzed. It is shown that the φ-scan peaks are less sensitive to the degree of structural perfection than the γ-mode peaks. The strongest dependence on the dislocation density for the latter peaks is observed for the (1bar 100)/(bar 1101) and (3bar 2bar 10)/(bar 3211) three-wave combinations with a pure Laue component of secondary radiation, while the (01bar 13)/(0bar 11bar 2) combination with a large Bragg component exhibits the weakest dependence. Splitting of three-wave Renninger peaks associated with the coarse-block structure of some of the layers with rotations of the blocks about the normal to the surface is detected. The total integrated intensity of all three-wave combinations is determined and their ratios are in qualitative agreement with the theory.
Santarossa, Gianluca; Vargas, Angelo; Iannuzzi, Marcella; Pignedoli, Carlo A; Passerone, Daniele; Baiker, Alfons
2008-12-21
We present a study on structural and electronic properties of bulk platinum and the two surfaces (111) and (100) comparing the Gaussian and plane wave method to standard plane wave schemes, normally employed for density functional theory calculations on metallic systems. The aim of this investigation is the assessment of methods based on the expansion of the Kohn-Sham orbitals into localized basis sets and on the supercell approach, in the description of the metallicity of Pt. Electronic structure calculations performed at Gamma-point only on supercells of different sizes, from 108 up to 864 atoms, are compared to the results obtained for the unit cell of four Pt atoms where the k-point expansion of the wave function over Monkhorst-Pack grids up to (10x10x10) has been employed. The evaluation of the two approaches with respect to bulk properties is done through the calculation of the equilibrium lattice constant, the bulk modulus, and the total and the d-projected density of states. For the Pt(111) and Pt(100) surfaces, we consider the relaxation of the first layers, the surface energies, the work function, the total density of states, as well as the center and filling of the d bands. Our results confirm that the accuracy of two approaches in the description of electronic and structural properties of Pt is equivalent, providing that consistent supercells and k-point meshes are used. Moreover, we estimate the supercell size that can be safely adopted in the Gaussian and plane wave method in order to obtain the same reliability of previous theoretical studies based on well converged plane wave calculations available in literature. The latter studies, in turn, set the level of agreement with experimental data. In particular, we obtain excellent agreement in the evaluation of the density of states for either bulk and surface systems, and our data are also in good agreement with previous works on Pt reported in literature. We conclude that Gaussian and plane wave
Omote, Kazuhiko
2010-12-01
We have measured the strain of a thin Si layer deposited on a SiGe layer using a high resolution x-ray diffraction system. The Si layer was deposited on the SiGe layer in order to introduce a tensile strain to the Si layer. To measure the in-plane lattice constant accurately, we have employed so-called grazing-incidence in-plane diffraction. For this measurement, we have made a new five-axis x-ray goniometer which has four ordinal circles (ω, 2θ, χ, φ) plus a counter-χ-axis for selecting the exit angle of the diffracted x-rays. In grazing-incidence geometry, an incident x-ray is focused on the sample surface in order to obtain good diffraction intensity even though the layer thickness is less than 5 nm. Because diffracted x-rays are detected through analyzer crystals, the diffraction angle can be determined with an accuracy of ± 0.0003°. This indicates that the strain sensitivity is about 10( - 5) when we measure in-plane Si 220 diffraction. Use of x-ray diffraction could be the best standard metrology method for determining strain in thin layers. Furthermore, we have demonstrated that incident/exit angle selected in-plane diffraction is very useful for height/depth selective strain determination.
Transverse spin and transverse momentum in scattering of plane waves.
Saha, Sudipta; Singh, Ankit K; Ray, Subir K; Banerjee, Ayan; Gupta, Subhasish Dutta; Ghosh, Nirmalya
2016-10-01
We study the near field to the far field evolution of spin angular momentum (SAM) density and the Poynting vector of the scattered waves from spherical scatterers. The results show that at the near field, the SAM density and the Poynting vector are dominated by their transverse components. While the former (transverse SAM) is independent of the helicity of the incident circular polarization state, the latter (transverse Poynting vector) depends upon the polarization state. It is further demonstrated that the interference of the transverse electric and transverse magnetic scattering modes enhances both the magnitudes and the spatial extent of the transverse SAM and the transverse momentum components.
X-ray Bragg diffraction from langasite crystal modulated by surface acoustic wave
NASA Astrophysics Data System (ADS)
Roshchupkin, D. V.; Irzhak, D. V.; Tucoulou, R.; Buzanov, O. A.
2003-11-01
X-ray diffraction on the X cut of a langasite crystal (La3Ga5SiO14) modulated by a Λ=12 μm Rayleigh surface acoustic wave (SAW) has been studied at the ESRF synchrotron radiation source. Due to the sinusoidal modulation of the crystal lattice involved by the SAW diffraction satellites appear on the rocking curve, with their number, angular positions, and intensities depending on the amplitude and wavelength of the ultrasonic superlattice. Full extinction of a specific satellite could be performed by adjusting the acoustic amplitude. It is shown that x-ray diffraction can be used to study surface acoustic wave field distributions in crystals.
ERIC Educational Resources Information Center
Maurines, Laurence
2010-01-01
This particular study is part of a research programme on the difficulties encountered by students when learning about wave phenomena in a three-dimensional medium in the absence or presence of obstacles. It focuses on how students reason in situations in which wave optics need to be used: diffraction of light by an aperture, imaging in the…
ERIC Educational Resources Information Center
Maurines, Laurence
2010-01-01
This particular study is part of a research programme on the difficulties encountered by students when learning about wave phenomena in a three-dimensional medium in the absence or presence of obstacles. It focuses on how students reason in situations in which wave optics need to be used: diffraction of light by an aperture, imaging in the…
1978-08-01
The diffraction of shock waves (2 or = M sub s or = 8) in perfect and imperfect nitrogen and argon by sharp compressive corners (2 deg or = Theta...in argon in the ranges 1 or = M subs or = 10 and 0 deg or = Theta sub w or = 90 deg. The domains consist of the four well-known shock wave
On-chip near-wavelength diffraction gratings for surface electromagnetic waves
NASA Astrophysics Data System (ADS)
Bezus, Evgeni A.; Podlipnov, Vladimir V.; Morozov, Andrey A.; Doskolovich, Leonid L.
2017-05-01
In the present work, on-chip dielectric diffraction gratings for steering the propagation of surface plasmon polaritons (SPP) are theoretically, numerically and experimentally studied. The investigated plasmonic gratings consist of dielectric ridges located on the SPP propagation surface (on the metal surface). In contrast to Bragg gratings, at normal incidence the periodicity direction of the grating is perpendicular to the SPP propagation direction. The studied gratings are designed using a simple plane-wave grating model and rigorously simulated using the aperiodic Fourier modal method for numerical solution of Maxwell's equations. In particular, plasmonic grating-based beam splitter with subwavelength footprint in the propagation direction is presented. Along with the theoretical and numerical results, proof-of-concept experimental results are presented. The investigated grating-based plasmonic gratings were fabricated from resist on a silver film using electron beam lithography and characterized using the leakage radiation microscopy technique. The obtained experimental results are in good agreement with the performed numerical simulations. The proposed on-chip gratings may find application in the design of systems for optical information transmission and processing at the nanoscale.
Source extension of chorus waves in the equatorial plane
NASA Astrophysics Data System (ADS)
Hayosh, M.; Santolik, O.; Parrot, M.
2009-04-01
We use measurements of the Cluster spacecraft and a ray tracing simulation to estimate the location and size of the global source of whistler-mode chorus emissions. In this study we use the data provided simultaneously by the STAFF-SA instruments on the four Cluster spacecraft on 19 August, 2003. To determine the direction of propagation of chorus we calculate Poynting vector whereas a ray-tracing method is used to estimate the chorus source extension. For the first time this analysis has been made along whole particular Cluster orbit in both hemispheres. Our study shows that minimum size of the global chorus source region in the equatorial plane is between 1-3 Earth's radii. The resulting location of the chorus source region is at radial distances between 3 and 8 Earth radii. This result is in agreement with previous analysis of Cluster data by Parrot et al., 2003, 2004 and with the study of Santolik et al., 2005 who analyzed data from the Double Star TC-1 spacecraft.
Observation of sagittal X-ray diffraction by surface acoustic waves in Bragg geometry.
Vadilonga, Simone; Zizak, Ivo; Roshchupkin, Dmitry; Evgenii, Emelin; Petsiuk, Andrei; Leitenberger, Wolfram; Erko, Alexei
2017-04-01
X-ray Bragg diffraction in sagittal geometry on a Y-cut langasite crystal (La3Ga5SiO14) modulated by Λ = 3 µm Rayleigh surface acoustic waves was studied at the BESSY II synchrotron radiation facility. Owing to the crystal lattice modulation by the surface acoustic wave diffraction, satellites appear. Their intensity and angular separation depend on the amplitude and wavelength of the ultrasonic superlattice. Experimental results are compared with the corresponding theoretical model that exploits the kinematical diffraction theory. This experiment shows that the propagation of the surface acoustic waves creates a dynamical diffraction grating on the crystal surface, and this can be used for space-time modulation of an X-ray beam.
Observation of sagittal X-ray diffraction by surface acoustic waves in Bragg geometry1
Vadilonga, Simone; Zizak, Ivo; Roshchupkin, Dmitry; Evgenii, Emelin; Petsiuk, Andrei; Leitenberger, Wolfram; Erko, Alexei
2017-01-01
X-ray Bragg diffraction in sagittal geometry on a Y-cut langasite crystal (La3Ga5SiO14) modulated by Λ = 3 µm Rayleigh surface acoustic waves was studied at the BESSY II synchrotron radiation facility. Owing to the crystal lattice modulation by the surface acoustic wave diffraction, satellites appear. Their intensity and angular separation depend on the amplitude and wavelength of the ultrasonic superlattice. Experimental results are compared with the corresponding theoretical model that exploits the kinematical diffraction theory. This experiment shows that the propagation of the surface acoustic waves creates a dynamical diffraction grating on the crystal surface, and this can be used for space–time modulation of an X-ray beam. PMID:28381976
Plane-wave decomposition by spherical-convolution microphone array
NASA Astrophysics Data System (ADS)
Rafaely, Boaz; Park, Munhum
2004-05-01
Reverberant sound fields are widely studied, as they have a significant influence on the acoustic performance of enclosures in a variety of applications. For example, the intelligibility of speech in lecture rooms, the quality of music in auditoria, the noise level in offices, and the production of 3D sound in living rooms are all affected by the enclosed sound field. These sound fields are typically studied through frequency response measurements or statistical measures such as reverberation time, which do not provide detailed spatial information. The aim of the work presented in this seminar is the detailed analysis of reverberant sound fields. A measurement and analysis system based on acoustic theory and signal processing, designed around a spherical microphone array, is presented. Detailed analysis is achieved by decomposition of the sound field into waves, using spherical Fourier transform and spherical convolution. The presentation will include theoretical review, simulation studies, and initial experimental results.
Woods, Daniel C; Bolton, J Stuart; Rhoads, Jeffrey F
2015-10-01
The transmission of airborne sound into high-impedance media is of interest in several applications. For example, sonic booms in the atmosphere may impact marine life when incident on the ocean surface, or affect the integrity of existing structures when incident on the ground. Transmission across high impedance-difference interfaces is generally limited by reflection and refraction at the surface, and by the critical angle criterion. However, spatially decaying incident waves, i.e., inhomogeneous or evanescent plane waves, may transmit energy above the critical angle, unlike homogeneous plane waves. The introduction of a decaying component to the incident trace wavenumber creates a nonzero propagating component of the transmitted normal wavenumber, so energy can be transmitted across the interface. A model of evanescent plane waves and their transmission across fluid-fluid and fluid-solid interfaces is developed here. Results are presented for both air-water and air-solid interfaces. The effects of the incident wave parameters (including the frequency, decay rate, and incidence angle) and the interfacial properties are investigated. Conditions for which there is no reflection at the air-solid interface, due to impedance matching between the incident and transmitted waves, are also considered and are found to yield substantial transmission increases over homogeneous incident waves.
Diffraction from sharply peaked waves as an ocean surface scattering mechanism
NASA Technical Reports Server (NTRS)
Jensen, Glenn A.; Vesecky, John F.; Glazman, Roman E.
1992-01-01
The role of sharply peaked waves as a major ocean scattering mechanism for radar is investigated. A prototype three-dimensional wedgelike wave shape was constructed, and its scattering properties were analyzed. Using results from the theory of the statistical geometry of the ocean surface, it is estimated how many such wedges there are per unit area, as a function of sea conditions. Taking into account a directional distribution of the wedges, the total radar cross section due to wedge diffraction effects is estimated. At large incidence angles, wedge diffraction appears to account for a significant amount of the radar cross section on the ocean surface. The wedgelike wave shape used is a more realistic representation of sharplypeaked waves. The scale-size and spatial density of the wedgelike waves are computed directly from the wave-height spectrum.
Solid explosive plane-wave lenses pressed-to-shape with dies
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.
Probing the smearing effect by a pointlike graviton in the plane-wave matrix model
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.
Population analysis of plane-wave electronic structure calculations of bulk materials
Segall, M.D.; Shah, R.; Pickard, C.J.; Payne, M.C.
1996-12-01
{ital Ab} {ital initio} plane-wave electronic structure calculations are widely used in the study of bulk materials. A technique for the projection of plane-wave states onto a localized basis set is used to calculate atomic charges and bond populations by means of Mulliken analysis. We analyze a number of simple bulk crystals and find correlations of overlap population with covalency of bonding and bond strength, and effective valence charge with ionicity of bonding. Thus, we show that the techniques described in this paper may be usefully applied in the field of solid state physics. {copyright}{ital 1996 The American Physical Society.}
Statistics of nodal points of in-plane random waves in elastic media.
Maksimov, Dmitrii N; Sadreev, Almas F
2008-05-01
We consider the nodal points (NPs) u=0 and v=0 of the in-plane vectorial displacements u=(u,v) which obey the Navier-Cauchy equation. Similar to the Berry conjecture of quantum chaos, we present the in-plane eigenstates of chaotic billiards as the real part of the superposition of longitudinal and transverse plane waves with random phases. By an average over random phases we derive the mean density and correlation function of NPs. Consequently we consider the distribution of the nearest distances between NPs.
NASA Astrophysics Data System (ADS)
Castellanos, L.; Calás, H.; Ramos, A.
2010-01-01
In this paper, an approach for simplifying the experimental arrangement, needed to generate limited diffracting waves through annular ultrasonic arrays, is analyzed in terms mainly of the subsequent acoustic field. The main idea is to approximate the theoretical X-wave electrical excitations to rectangular driving signals in each array annulus, by means of the L2 curve criterion. The differences between theoretical X-wave signals and these approximate signals, related to real excitation effects, were minimized by using the transition times and amplitudes of the rectangular signals as fitting parameters. Acoustic field simulations, based on the impulse response technique, are applied for evaluating the agreement degree between both emitted ultrasonic fields, whit the calculated classical X wave and with the new approximation method proposed here for low-cost limited-diffraction wave generation. In addition, source vibration and ultrasonic field simulated signals were compared with those of the classic x wave under an exact driving, with the purpose of validating the method. The good agreement between the two vibration signals and resulting field distributions, obtained from the classical X wave excitations and those provided by the drastic simplification presented here, can be justified by the filtering effects induced by the transducer elements bands in frequency domain. These results suggest the possibility of achieving limited diffraction waves with relatively simple driving waveforms, which can be implemented with a moderate cost in analogical electronics.
Vectorial approach to Huygens's principle for plane waves: circular aperture and zone plates.
Romero, Julio A; Hernández, Luis
2006-05-01
A vectorial equation that describes the Huygens principle was reported, and an expression for the secondary-spherical-wave energy density was found. With a vectorial formulation, we performed an exact calculation for the relative axial intensity of the wave diffracted by an illuminated circular aperture. The off-axis intensity in Fresnel's and Fraunhofer's approximations was calculated. The zone plate was also studied by vectorial formulation. We showed that with increasing number of rings, the intensity maxima magnify as (2n + 2)(2), their full widths decrease, their positions remain unchanged, and secondary maxima appear, in a behavior similar to that for diffraction gratings.
A time domain energy theorem for scattering of plane electromagnetic waves
NASA Astrophysics Data System (ADS)
de Hoop, A. T.
1984-10-01
A time domain analysis of the scattering problem reveals the more general conditions under which the relevant theorems in the theory of the scattering of electromagnetic waves by an obstacle of bounded extent may also hold in the time domain. The present investigation is concerned with the energy theorem for plane wave scattering. Three different kinds of time behavior are considered, taking into account transient fields, time-periodic fields, and perpetuating fields. The derived energy theorem relates the energy which is both absorbed and scattered by the object to the spherical-wave amplitude of the scattered field in the far-field region, when observed in the direction of propagation of the incident plane wave.
Active control of fan-generated plane wave noise
NASA Technical Reports Server (NTRS)
Gerhold, Carl H.; Nuckolls, William E.; Santamaria, Odillyn L.; Martinson, Scott D.
1993-01-01
Subsonic propulsion systems for future aircraft may incorporate ultra-high bypass ratio ducted fan engines whose dominant noise source is the fan with blade passage frequency less than 1000 Hz. This low frequency combines with the requirement of a short nacelle to diminish the effectiveness of passive duct liners. Active noise control is seen as a viable method to augment the conventional passive treatments. An experiment to control ducted fan noise using a time domain active adaptive system is reported. The control sound source consists of loudspeakers arrayed around the fan duct. The error sensor location is in the fan duct. The purpose of this experiment is to demonstrate that the in-duct error sensor reduces the mode spillover in the far field, thereby increasing the efficiency of the control system. In this first series of tests, the fan is configured so that predominantly zero order circumferential waves are generated. The control system is found to reduce the blade passage frequency tone significantly in the acoustic far field when the mode orders of the noise source and of the control source are the same. The noise reduction is not as great when the mode orders are not the same even though the noise source modes are evanescent, but the control system converges stably and global noise reduction is demonstrated in the far field. Further experimentation is planned in which the performance of the system will be evaluated when higher order radial and spinning modes are generated.
Active control of fan-generated plane wave noise
NASA Astrophysics Data System (ADS)
Gerhold, Carl H.; Nuckolls, William E.; Santamaria, Odillyn L.; Martinson, Scott D.
1993-08-01
Subsonic propulsion systems for future aircraft may incorporate ultra-high bypass ratio ducted fan engines whose dominant noise source is the fan with blade passage frequency less than 1000 Hz. This low frequency combines with the requirement of a short nacelle to diminish the effectiveness of passive duct liners. Active noise control is seen as a viable method to augment the conventional passive treatments. An experiment to control ducted fan noise using a time domain active adaptive system is reported. The control sound source consists of loudspeakers arrayed around the fan duct. The error sensor location is in the fan duct. The purpose of this experiment is to demonstrate that the in-duct error sensor reduces the mode spillover in the far field, thereby increasing the efficiency of the control system. In this first series of tests, the fan is configured so that predominantly zero order circumferential waves are generated. The control system is found to reduce the blade passage frequency tone significantly in the acoustic far field when the mode orders of the noise source and of the control source are the same. The noise reduction is not as great when the mode orders are not the same even though the noise source modes are evanescent, but the control system converges stably and global noise reduction is demonstrated in the far field. Further experimentation is planned in which the performance of the system will be evaluated when higher order radial and spinning modes are generated.
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.
From plane waves to local Gaussians for the simulation of correlated periodic systems
NASA Astrophysics Data System (ADS)
Booth, George H.; Tsatsoulis, Theodoros; Chan, Garnet Kin-Lic; Grüneis, Andreas
2016-08-01
We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller-Plesset perturbation theory.
Transient analysis of wave propagation problems by half-plane BEM
NASA Astrophysics Data System (ADS)
Panji, M.; Kamalian, M.; Marnani, J. Asgari; Jafari, M. K.
2013-09-01
In this paper, a half-plane time-domain boundary element method (BEM) was presented for analysing the 2-D scalar wave problems in a homogenous isotropic linear elastic medium. Using the existing transient full-plane fundamental solution and asking for the assistance of method of source image to satisfy the stress-free boundary conditions, first, a half-plane time-domain fundamental solution was obtained for displacement and traction fields. Then, the condensed closed-form of half-plane time-convoluted kernels were extracted analytically by applying the time-convolution integral on the determined half-plane fundamental solutions. After implementing the half-plane time-domain BEM in computer codes, its applicability and efficiency were verified and compared with those of the published works by analysing several practical examples. The studies showed that the proposed method had good agreement with the existing solutions. Compared to the full-plane time-domain BEM, half-plane time-domain BEM had more capability and better accuracy as well as much shorter run time. It is obvious that this method can be practically used to analyse the site response in substituting the old-style time-domain BEM formulation as well.
Guided torsional wave generation of a linear in-plane shear piezoelectric array in metallic pipes.
Zhou, Wensong; Yuan, Fuh-Gwo; Shi, Tonglu
2016-02-01
Cylindrical guided waves based techniques are effective and promising tools for damage detection in long pipes. The essential operations are generation and reception of guided waves in the structures utilizing transducers. A novel in-plane shear (d36 type) PMNT wafer is proposed to generate and receive the guided wave, especially the torsional waves, in metallic pipes. In contrast to the traditional wafer, this wafer will directly introduce in-plane shear deformation when electrical field is conveniently applied through its thickness direction. A single square d36 PMNT wafer is bonded on the surface of the pipe positioned collinearly with its axis, when actuated can predominantly generate torsional (T) waves along the axial direction, circumferential shear horizontal (C-SH) waves along circumferential direction, and other complex cylindrical Lamb-like wave modes along other helical directions simultaneously. While a linear array of finite square size d36 PMNT wafers was equally spaced circumferentially, when actuated simultaneously can nearly uniform axisymmetric torsional waves generate in pipes and non-symmetric wave modes can be suppressed greatly if the number of the d36 PMNT wafer is sufficiently large. This paper first presents the working mechanism of the linear d36 PMNT array from finite element analysis (FEA) by examining the constructive and destructive displacement wavefield phenomena in metallic pipes. Furthermore, since the amplitude of the received fundamental torsional wave signal strongly depends on frequency, a series of experiments are conducted to determine the frequency tuning curve for the torsional wave mode. All results indicate the linear d36 PMNT array has potential for efficiently generating uniform torsional wavefield of the fundamental torsional wave mode, which is more effective in monitoring structural health in metallic pipes. Copyright © 2015 Elsevier B.V. All rights reserved.
Geometry of magnetosonic shocks and plane-polarized waves: Coplanarity Variance Analysis (CVA)
NASA Astrophysics Data System (ADS)
Scudder, J. D.
2005-02-01
Minimum Variance Analysis (MVA) is frequently used for the geometrical organization of a time series of vectors. The Coplanarity Variance Analysis (CVA) developed in this paper reproduces the layer geometry involving coplanar magnetosonic shocks or plane-polarized wave trains (including normals and coplanarity directions) 300 times more precisely (<0.1°) than MVA using the same input data. The CVA technique exploits the eigenvalue degeneracy of the covariance matrix present at planar structures to find a consistent normal to the coplanarity plane of the fluctuations. Although Tangential Discontinuities (TDs) have a coplanarity plane, the eigenvalues of their covariance matrix are usually not degenerate; accordingly, CVA does not misdiagnose TDs as shocks or plane-polarized waves. Together CVA and MVA may be used to sort between the hypotheses that the time series is caused by a one-dimensional current layer that has magnetic disturbances that are (1) coplanar, linearly polarized (shocks/plane waves), (2) intrinsically helical (rotational/tangential discontinuities), or (3) neither 1 nor 2.
NASA Astrophysics Data System (ADS)
Yuasa, Tetsuya; Hashimoto, Eiko; Maksimenko, Anton; Sugiyama, Hiroshi; Arai, Yoshinori; Shimao, Daisuke; Ichihara, Shu; Ando, Masami
2008-07-01
We discuss the recently proposed computed tomography (CT) technique based on refractive effects for biomedical use, which reconstructs the in-plane refractive-index gradient vector field in a cross-sectional plane of interest by detecting the angular deviation of the beam, refracted by a sample, from the incident beam, using the diffraction-enhanced imaging (DEI) method. The CT has advantages for delineating biological weakly absorbing soft tissues over the conventional absorption-contrast CT because of the use of phase sensitive detection. The paper aims to define the imaging scheme rigidly and to demonstrate its efficacy for non-destructive measurement of biomedical soft-tissue samples without imaging agent. We first describe the imaging principle of in-plane DEI-CT from the physico-mathematical viewpoints in detail, and investigate what physical quantities are extracted from the reconstructed images. Then, we introduce the imaging system using the synchrotron radiation as a light source, constructed at beamline BL-14B in KEK, Japan. Finally, we demonstrate the advantage of the refraction-based image for non-destructive analysis of biological sample by investigating the image of human breast cancer tumors obtained using the imaging system. Here, the refraction- and the apparent absorption-based images obtained simultaneously by the in-plane DEI-CT are compared. Also, the conventional absorption-based image obtained using micro-computed tomography (μCT) imaging system is compared with them. Thereby, it is shown that the refraction contrast much more sensitively delineates the soft tissues than the absorption contrast. In addition, the radiologic-histologic correlation study not only validates the efficacy for imaging soft tissues, but also produces the potential that the pathological inspection for the breast cancer tumors may be feasible non-destructively.
Mid-Wave and Long-Wave Infrared Dualband Megapixel QWIP Focal Plane Array
NASA Technical Reports Server (NTRS)
Gunapala, S. D.; Bandara, S. V.; Liu, J. K.; Mumolo, J. M.; Hill, C. J.; Ting, D. Z.; Kurth, E.; Woolaway, J.; LeVan, P. D.; Tidrow, M. Z.
2008-01-01
Mid-wavelength infrared (MWIR) and long-wavelength infrared (LWIR) 1024x1024 pixel InGaAs/GaAs/AlGaAs based quantum well infrared photodetector (QWIP) focal planes and a 320x256 pixel dual-band pixel co-registered simultaneous QWIP focal plane array have been demonstrated as pathfinders. In this paper, we discuss the development of 1024x1024 MWIR/LWIR dual-band pixel co-registered simultaneous QWIP focal plane array.
Ultrasound plane-wave imaging with delay multiply and sum beamforming and coherent compounding.
Matrone, Giulia; Savoia, Alessandro S; Caliano, Giosue; Magenes, Giovanni
2016-08-01
Improving the frame rate is an important aspect in medical ultrasound imaging, particularly in 3D/4D cardiac applications. However, an accurate trade-off between the higher frame rate and image contrast and resolution should be performed. Plane-Wave Imaging (PWI) can potentially achieve frame rates in the order of 10 kHz, as it uses a single unfocused plane wave (and thus a single transmit event) to acquire the image of the entire region of interest. The lack of transmit focusing however causes a significant drop of image quality, which can be restored by coherently compounding several tilted plane-wave frames, at the expense of the frame rate. PWI together with the use of a beamforming algorithm able to achieve a higher image contrast resolution, such as the Delay Multiply And Sum (DMAS), could thus allow to improve image quality achieving a high frame rate at the same time. This paper presents the first simulation results obtained by employing DMAS beamforming and PWI with different transmission angles and coherent compounding. The simulated Point Spread Function (PSF) and cyst-phantom images show that DMAS makes it possible to achieve a high image quality with a reduced number of compounded frames compared to standard Delay And Sum (DAS), and hence it can be used to improve the contrast and resolution of plane-wave images still achieving a very high frame rate.
Calculation of atomic forces using the linearized-augmented-plane-wave method
NASA Astrophysics Data System (ADS)
Krimmel, H. G.; Ehmann, J.; Elsässer, C.; Fähnle, M.; Soler, J. M.
1994-09-01
The force formula of Soler and Williams is implemented in the full-potential linearized-augmented-plane-wave program wien93. The feasibility and accuracy of the method is demonstrated by calculations for the H-point phonon in Mo and Li and for the Γ-point phonon in Si and diamond.
Transverse plane wave analysis of short elliptical chamber mufflers: An analytical approach
NASA Astrophysics Data System (ADS)
Mimani, A.; Munjal, M. L.
2011-03-01
Short elliptical chamber mufflers are used often in the modern day automotive exhaust systems. The acoustic analysis of such short chamber mufflers is facilitated by considering a transverse plane wave propagation model along the major axis up to the low frequency limit. The one dimensional differential equation governing the transverse plane wave propagation in such short chambers is solved using the segmentation approaches which are inherently numerical schemes, wherein the transfer matrix relating the upstream state variables to the downstream variables is obtained. Analytical solution of the transverse plane wave model used to analyze such short chambers has not been reported in the literature so far. This present work is thus an attempt to fill up this lacuna, whereby Frobenius solution of the differential equation governing the transverse plane wave propagation is obtained. By taking a sufficient number of terms of the infinite series, an approximate analytical solution so obtained shows good convergence up to about 1300 Hz and also covers most of the range of muffler dimensions used in practice. The transmission loss (TL) performance of the muffler configurations computed by this analytical approach agrees excellently with that computed by the Matrizant approach used earlier by the authors, thereby offering a faster and more elegant alternate method to analyze short elliptical muffler configurations.
Ultra-low velocity zone heterogeneities at the core-mantle boundary from diffracted PKKPab waves
NASA Astrophysics Data System (ADS)
Ma, Xiaolong; Sun, Xinlei
2017-08-01
Diffracted waves around Earth's core could provide important information of the lowermost mantle that other seismic waves may not. We examined PKKPab diffraction waves from 52 earthquakes occurring at the western Pacific region and recorded by USArray to probe the velocity structure along the core-mantle boundary (CMB). These diffracted waves emerge at distances up to 10° past the theoretical cutoff epicentral distance and show comparable amplitudes. We measured the ray parameters of PKKPab diffraction waves by Radon transform analysis that is suitable for large-aperture arrays. These ray parameters show a wide range of values from 4.250 to 4.840 s/deg, suggesting strong lateral heterogeneities in sampling regions at the base of the mantle. We further estimated the P-wave velocity variations by converting these ray parameters and found the CMB regions beneath the northwestern edge of African Anomaly (Ritsma et al. in Science 286:1925-1928, 1999) and southern Sumatra Islands exhibit velocity reductions up to 8.5% relative to PREM. We suggest that these low velocity regions are Ultra-low velocity zones, which may be related to partial melt or iron-enriched solids.[Figure not available: see fulltext.
Collision between variably polarized plane gravitational wave and a shell of null matter
NASA Astrophysics Data System (ADS)
Feinstein, Alexander; Senovilla, Josém. M.
1989-06-01
We construct a solution to the Einstein field equations which describes the collision between a variably polarized gravitational wave and a shell of null dust. Depending on the choice of the parameters the variably polarized wave can have an arbitrarily smooth wavefront. The shell of null dust is followed by a constantly polarized plane gravitational wave. Also Grupo de Física Teórica, Departamento de Física, Ingeniería y Radiología Médica, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, Spain.
High-frequency plane waves in the ear canal: application of a simple asymptotic theory.
Rabbitt, R D
1988-12-01
An asymptotic theory describing the propagation of plane waves in a variable cross-section ear canal is combined with pressure measurements in order to determine the energy reflection coefficient at the eardrum and the standing wave patterns along the length of the canal. The relative phase of the reflected wave, and the cross-sectional area function of the ear canal, are also determined from the noninvasive pressure measurements. The theory is based on a high-frequency multiscale solution of the one-dimensional horn equation and is shown to agree well with the phase and amplitude of experimental measurements in human replica ear canals.
Focal shifts in diffracted converging electromagnetic waves. I. Kirchhoff theory.
Li, Yajun
2005-01-01
Starting with the vector formulation of the Kirchhoff diffraction theory, expressions for the total energy density distribution along the axis are presented without using any of the usual assumptions except the assumption made by Kirchhoff for the boundary conditions of a black screen. To make the Kirchhoff integral compatible with Maxwell's equations, a line integral around the edge of the aperture is added in the analysis. The consequence of ignoring the contribution of this line integral to the axial field distribution is examined numerically. The focal shift effect is investigated for both aplanatic systems and parabolic mirrors having an arbitrary numerical aperture (NA) and finite value of the Fresnel number. The combined effects of the Fresnel number and NA on the focal shift are evaluated, and the validity of the results is carefully checked by comparing the wavelength with the system dimensions.
NASA Astrophysics Data System (ADS)
Usuki, Tsuneo
2013-09-01
The moduli of conventional elastic structural materials are extended to one of the viscoelastic materials through a modification whereby the dynamic moduli converge to the static moduli of elasticity as the fractional order approaches zero. By plotting phase velocity curves and group velocity curves of plane waves and Rayleigh surface wave for a viscoelastic material (polyvinyl chloride foam), the influence of the fractional order of viscoelasticity is examined. The phase and group velocity curves in the high frequency range were derived for longitudinal, transverse, and Rayleigh waves inherent to the viscoelastic material. In addition, the equation for the phase velocity was mathematically derived on the complex plane, too, and graphically illustrated. A phenomenon was found that, at the moment when the fractional order of the time derivative reaches an integer value 1, the curve on the complex plane becomes completely different, exhibiting snap-through behavior. We examined the mechanism of the snap-through mathematically. Numerical calculation examples were solved, and good agreement was confirmed between the numerical calculation and the analytical expression mentioned above. From the results of the numerical example, regularities were derived for the absolute value of the complex phase and group velocities on the complex plane.
Spectral Solution of the Helmholtz and Paraxial Wave Equations and Classical Diffraction Formulae
2004-03-01
Traité de la lumière (completed in 1678, published in Leyden, 1690). 7. Kirchoff, G. “Zur Theorie der Lichtstrahlen ,” Wiedemann Ann. 1896, 18(2...4 3. A Précis of Classical Scalar Diffraction Theory 5 3.1 History...derivation of the paraxial wave equation. Section 3 briefly reviews the salient results of classical scalar diffraction theory . In sections 4 and 5
Numerical evolution of plane gravitational waves in the Friedrich-Nagy gauge
NASA Astrophysics Data System (ADS)
Frauendiener, Jörg; Stevens, Chris
2014-05-01
The first proof of well posedness of an initial boundary value problem for the Einstein equations was given in 1999 by Friedrich and Nagy. They used a frame formalism with a particular gauge for formulating the equations. This "Friedrich-Nagy" gauge has never been implemented for use in numerical simulations before because it was deemed too complicated. In this paper we present an implementation of the Friedrich-Nagy gauge for systems with two commuting spacelike Killing vectors. We investigate the numerical performance of this formulation for plane wave space-times, reproducing the well-known Khan-Penrose solution for colliding impulsive plane waves and exhibiting a gravitational wave "ping-pong."
Non-linear Interactions of Rossby waves in shallow water magnetohydrodynamics on a beta-plane
NASA Astrophysics Data System (ADS)
Klimachkov, Dmitry; Petrosyan, Arakel
2017-04-01
Rotating magnetohydrodynamic shallow water equations are obtained from conventional magnetohydrodynamic equations for incompressible inviscid heavy plasma layer with free surface in a external vertical magnetic field. The pressure is assumed to be hydrostatic, and the water layer height is considered to be much smaller than horizontal scales. The MHD shallow water equations with an external vertical magnetic field are revised by supplementing them with the equations that are consequences of the magnetic field divergence-free conditions and reveal the existence of third component of the magnetic field in such approximation providing its relation with the horizontal magnetic field. It is shown that the presence of a vertical magnetic field significantly changes the dynamics of the wave processes in astrophysical plasma compared to the neutral fluid and plasma layer in a horizontal magnetic field. We have investigated the interaction of wave packets in the magnetohydrodynamic shallow water flows in external vertical magnetic field and in horizontal (toroidal and poloidal) magnetic field on a β-plane. Linear analysis leads to magneto-Rossby waves in β-plane approximation. In the absence of the horizontal magnetic field the dynamics of plasma appears to be similar to the neutral fluid dynamics. Using the asymptotic multiscale method we obtained the non-linear interaction equations for the waves amplitudes. The analysis of the amplitudes equations shows that on β-plane there are two types of instabilities: one magneto-Rossby wave decays into two magneto-Rossby waves and magneto-Rossby wave amplifies in field of two magneto-Rossby waves. These instabilities occur in both cases: in the external vertical magnetic field and in the horizontal (toroidal and poloidal) magnetic field. For all types of instabilities the growth rates are found.
Experimental demonstration of broadband reflectionless diffraction-free electromagnetic wave routing
NASA Astrophysics Data System (ADS)
Zhang, Youming; Gao, Zhen; Gao, Fei; Shi, Xihang; Xu, Hongyi; Luo, Yu; Zhang, Baile
2016-12-01
Wave diffraction is fundamentally difficult to overcome in the routing and interconnection of photonic signals. Although the phenomenon of reflectionless transport through sharp corners in a routing path has been realized in many previous demonstrations, wave diffraction does not allow them to transport deep-subwavelength information or sub-diffraction-limited images. Recent advances in ɛ -near-zero and anisotropic ɛ -near-infinity metamaterials have provided unique possibilities of achieving reflectionless diffraction-free electromagnetic wave routing, but their designs are fundamentally limited to narrow bandwidths, and they have not been demonstrated in reality. Here we experimentally demonstrate broadband reflectionless diffraction-free routing of electromagnetic waves through two right-angled sharp corners in a bent microwave rectangular waveguide. An image with deep-subwavelength information is transported through the bent waveguide in a broad bandwidth. This Rapid Communication supplements and extends the current studies of metamaterials with extreme permittivities and can be useful for routing and interconnection of subwavelength photonic information.
Schwab, Hans-Martin; Beckmann, Martin F.; Schmitz, Georg
2016-01-01
Photoacoustic imaging aims to visualize light absorption properties of biological tissue by receiving a sound wave that is generated inside the observed object as a result of the photoacoustic effect. In clinical applications, the strong light absorption in human skin is a major problem. When high amplitude photoacoustic waves that originate from skin absorption propagate into the tissue, they are reflected back by acoustical scatterers and the reflections contribute to the received signal. The artifacts associated with these reflected waves are referred to as clutter or skin echo and limit the applicability of photoacoustic imaging for medical applications severely. This study seeks to exploit the acoustic tissue information gained by plane wave ultrasound measurements with a linear array in order to correct for reflections in the photoacoustic image. By deriving a theory for clutter waves in k-space and a matching inversion approach, photoacoustic measurements compensated for clutter are shown to be recovered. PMID:27446669
Schwab, Hans-Martin; Beckmann, Martin F; Schmitz, Georg
2016-04-01
Photoacoustic imaging aims to visualize light absorption properties of biological tissue by receiving a sound wave that is generated inside the observed object as a result of the photoacoustic effect. In clinical applications, the strong light absorption in human skin is a major problem. When high amplitude photoacoustic waves that originate from skin absorption propagate into the tissue, they are reflected back by acoustical scatterers and the reflections contribute to the received signal. The artifacts associated with these reflected waves are referred to as clutter or skin echo and limit the applicability of photoacoustic imaging for medical applications severely. This study seeks to exploit the acoustic tissue information gained by plane wave ultrasound measurements with a linear array in order to correct for reflections in the photoacoustic image. By deriving a theory for clutter waves in k-space and a matching inversion approach, photoacoustic measurements compensated for clutter are shown to be recovered.
Finite Frequency Measurements of Conventional and Core-diffracted P-waves (P and Pdiff)
NASA Astrophysics Data System (ADS)
Hosseini, K.; Sigloch, K.; Stähler, S. C.
2014-12-01
Core-diffracted waves are body waves that dive deep enough to sense the core, and by interaction with this wave guide become dispersive. They sample the core-mantle boundary and the lower third of the mantle extensively. In ray theoretical modeling, the deepest part of the ray starts to graze the core at around 97 degrees distance, but ray theory is a very poor approximation to propagation of core-diffracted waves. In reality, finite-frequency waves with their spatially extend sensitivity regions start to sense the core at significantly smaller distances already. The actual, non-ray-like sensitivities have been difficult to model, as have been the associated synthetic seismograms. Core-diffracted waves have therefore not been used in tomography, despite abundant observations of these phases on modern broadband seismograms. Hence current global body-wave tomographies illuminate the lower third of the mantle much less well than the upper and especially the middle third. This study aims for broadband, global waveform tomography that seamlessly incorporates core-diffracted phases alongside conventional, teleseismic waves as well as regional body-waves. Here, we investigate the properties of P-diffracted waves in terms of waveform characteristics and travel-time measurements as compared to teleseismic P-wave measured by the same methods. Travel time anomalies, the primary data for tomography, are measured by waveform cross-correlation of data with synthetics, where the synthetics are calculated from fully numerical wave propagation in a spherically symmetric background model. These same numerical tools will be used to calculate the associated sensitivity kernels for tomography (figure, top). Demonstrating the extent to which waveform modeling can fit real data, we assemble and discuss a global data set of 851,905 Pdiff and 2,368,452 P-wave multi-frequency cross-correlation travel times. Findings are summarized in the Pdiff travel time map (figure, bottom) in which most
NASA Astrophysics Data System (ADS)
Deng, Kai; Zhou, Ying
2015-06-01
The structure of seismic discontinuities in the mantle transition zone at depths of about 400 and 670 km provides important constraints on mantle convection as the associated mineral phase transformations are sensitive to thermal perturbations. Teleseismic P-to-S receiver functions have been widely used to map the depths of the two discontinuities. In this study, we investigate the resolution of receiver functions in imaging topographic variations of the 400-km and 670-km discontinuities based on wave propagation simulations using a Spectral Element Method (SEM). We investigate wave diffraction effects on direct P waves as well as P-to-S converted waves by varying the length scale of topography of the two discontinuities. We observe strong wave diffractional effects in both P waves and teleseismic receiver functions at periods of ˜10 to 20 s. Ray theory overpredicts traveltime anomalies by a factor of 2-5 when the topography length scale is about 400 km. In addition, ray-theoretical predictions are out of phase with measurements which indicates that locations of small-scale topographic variations can not be resolved using ray theory. The observed traveltime anomalies further reduce to 10-20 per cent of ray-theoretical predictions when the topography length scale reduces to about 200 km. We calculate 2-D boundary sensitivity kernels for direct P waves as well as receiver functions. In general, calculations based Born sensitivity kernels fit the `ground-truth' SEM measurements very well. They account for wave diffraction effects as well as phase interactions such as P and pP waves arriving in P-wave coda. 3-D wavespeed structure in the upper mantle beneath seismic stations may introduce significant traveltime anomalies on P waves and transition zone receiver functions. We show that traveltime corrections at periods of about 10 to 20 s are frequency dependent when the size of the anomalies becomes less than 500 km.
CMS-Wave Model: Part 5. Full-plane Wave Transformation and Grid Nesting
2012-04-01
directional Buoy 42040 (165-m depth), located 90 km offshore Dauphin Island , AL. The CMS-Wave PG extended from the 15-m depth contour to the shoreline (41 km... islands , semi-enclosed bays and lakes, where incident waves can come from different directions and local wind generation effects are important and...situations would occur when calculating waves around an island or islands . The HP and FP mode of CMS-Wave is controlled by the model parameter IVIEW
Three-dimensional shock wave diffraction off a discontinuous edge
NASA Astrophysics Data System (ADS)
Cooppan, S.; Skews, B.
2017-03-01
The interaction of three-dimensional vortex flows was investigated through vortex shedding off a discontinuous edge. Two wedges of 14.5° wedge angle (up and downstream edges) were separated by an offset. The size of the offset (5, 10, and 20 mm) and the Mach number (Mach 1.32, 1.42, and 1.6) were the key parameters investigated. Experimental images were taken and computational simulations were run; a close relation was found between the two. This enabled the three-dimensional effects of the flow to be studied and analysed. It was found, as the offset increased in size, the vortices shed off the up and downstream edges took a longer time to merge and the strength of the interaction was weaker. The vortex topology changed with a larger offset; the downstream vortex was thinner (in terms of cross-sectional diameter) adjacent to the offset, which is an indication of a change in density, than the rest of the vortex along the downstream diffraction edge. This particular feature was more prevalent at lower Mach numbers. The effect of a higher Mach number was to increase the rate of dissipation of the vortices, lengthen the shear layer due to the higher upstream velocity, and make the vortex profile elliptical.
Korobkin, Dmitriy; Neuner, Burton; Fietz, Chris; Jegenyes, Nikoletta; Ferro, Gabriel; Shvets, Gennady
2010-10-25
An indefinite permittivity medium (IPM) has been fabricated and optically characterized in mid-infrared spectral range (10.7 µm-11.3 µm). Phase and amplitude transmission measurements reveal two remarkable properties of IPMs: (i) transmission of sub-diffraction waves (as short as λ/4) can exceed those of diffraction-limited ones, and (ii) sub-diffraction waves can propagate with negative refractive index. We describe a novel double-detector optical technique relying on the interference between sub-diffraction and diffraction-limited waves for accurate measurement of the transmission amplitude and phase of the former.
Sum, K S; Pan, J
2007-07-01
Distributions of sound pressure and intensity on the surface of a flat impedance strip flush-mounted on a rigid baffle are studied for a grazing incident plane wave. The distributions are obtained by superimposing the unperturbed wave (the specularly reflected wave as if the strip is rigid plus the incident wave) with the radiated wave from the surface vibration of the strip excited by the unperturbed pressure. The radiated pressure interferes with the unperturbed pressure and distorts the propagating plane wave. When the plane wave propagates in the baffle-strip-baffle direction, it encounters discontinuities in acoustical impedance at the baffle-strip and strip-baffle interfaces. The radiated pressure is highest around the baffle-strip interface, but decreases toward the strip-baffle interface where the plane wave distortion reduces accordingly. As the unperturbed and radiated waves have different magnitudes and superimpose out of phase, the surface pressure and intensity increase across the strip in the plane wave propagation direction. Therefore, the surface absorption of the strip is nonzero and nonuniform. This paper provides an understanding of the surface pressure and intensity behaviors of a finite impedance strip for a grazing incident plane wave, and of how the distributed intensity determines the sound absorption coefficient of the strip.
Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices
Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; ...
2016-01-25
We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. Formore » weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.« less
Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices
Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; Ma, Yi-Ping
2016-01-25
We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. For weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.
Theory of steady-state plane tunneling-assisted impact ionization waves
Kyuregyan, A. S.
2013-07-15
The effect of band-to-band and trap-assisted tunneling on the properties of steady-state plane ionization waves in p{sup +}-n-n{sup +} structures is theoretically analyzed. It is shown that such tunneling-assisted impact ionization waves do not differ in a qualitative sense from ordinary impact ionization waves propagating due to the avalanche multiplication of uniformly distributed seed electrons and holes. The quantitative differences of tunneling-assisted impact ionization waves from impact ionization waves are reduced to a slightly different relation between the wave velocity u and the maximum field strength E{sub M} at the front. It is shown that disregarding impact ionization does not exclude the possibility of the existence of tunneling-assisted ionization waves; however, their structure radically changes, and their velocity strongly decreases for the same E{sub M}. A comparison of the dependences u(E{sub M}) for various ionization-wave types makes it possible to determine the conditions under which one of them is dominant. In conclusion, unresolved problems concerning the theory of tunneling-assisted impact ionization waves are discussed and the directions of further studies are outlined.
Electromagnetic scattering of a polarized plane wave from an ellipsoidal particle in the near field
NASA Astrophysics Data System (ADS)
Chen, Feinan; Li, Jia
2017-06-01
Within the validity of the first-order Born approximation, we study the near-zone evanescent wave properties for a polarized plane wave scattering upon an ellipsoidal particle. Integral expressions are obtained for the three-dimensional electromagnetic field of the near-zone scattered evanescent wave, and the dependences of the scattered intensity distributions on the degree of polarization of the incident wave and the scattering potential profile of the particle are presented. The scattered intensity from the particle can exhibit a focused pattern concentrated around the central scattering region, but the scattered intensity generated from a circularly polarized wave shows a smooth distribution for different scattering angles. Moreover, the scattered intensity also enhances when either the summation index or the effective radius of the particle increases. Our results can be utilized to generate near-field focused scattered patterns that can be tuned flexibly by controlling the degree of the polarization of the plane wave and the scattering potential parameters of the ellipsoidal particle.
NASA Astrophysics Data System (ADS)
Yoshida, Shuhei; Mori, Jun; Yamamoto, Manabu
2015-05-01
Many kinds of recording techniques have been proposed for holographic data storages (HDS). Multiplexing recording technique is a primary contributor to determining the recording density in HDS. The method that utilizes spherical reference waves is characterized by the ability to enable multiplexing recording only by displacing (shifting or rotating) the recording medium. In this study, we propose a theoretical diffraction model of peristrophic multiplexing with spherical reference wave for HDS.
Plane wave transport method for low symmetry lattices and its application
Srivastava, Manoj K; Wang, Yan; Zhang, Xiaoguang; Nicholson, Don M; Cheng, Hai-Ping
2012-01-01
The existing first-principles plane wave transport method implementation \\cite{,choi-1,qe} has the limitation that it only allows transport directions along lattice vectors perpendicular to the basal plane formed by two other lattice vectors. We generalize the algorithm to low symmetry, nonorthogonal lattices thus allowing solution to problems in which the transport direction is not along any lattice vectors. As an application, we calculate the transmission and reflection coefficients, and determine interface resistance of various grain boundaries in crystalline copper.
A modified equatorial β-plane approximation modelling nonlinear wave-current interactions
NASA Astrophysics Data System (ADS)
Henry, David
2017-09-01
A modification of the standard geophysical equatorial β-plane model equations, incorporating a gravitational-correction term in the tangent plane approximation, is derived. We present an exact solution satisfying the modified equations, whose form is explicit in the Lagrangian framework, and which represents three-dimensional, nonlinear oceanic wave-current interactions. It is rigorously established, by way of analytical and degree-theoretical considerations, that the solution is dynamically possible, in the sense that the mapping it prescribes from Lagrangian to Eulerian coordinates is a global diffeomorphism.
In-plane spin wave modes in permalloy antidot arrays observation and analysis
NASA Astrophysics Data System (ADS)
Yu, Chengtao; Mankey, Gary
2005-03-01
Previously, we have reported demagnetization field induced localized modes[1] in-plane at 35 GHz ferromagnetic resonance, and dipolar-exchange governed lateral standing spin waves out-of-plane at 9.7 GHz in permalloy antidots. Here we present in-plane investigations at 9.7 GHz on various hole arrays (hole diameter 1.5μm; hole lattice 3μm x 3, 4, 5, and 7μm). In addition to the two main localized modes, which arise from regions confined by holes along the long axis and short axis (region A and B, respectively), spin wave manifolds pertinent to each peak are identified. Owing to the confinement imposed by the holes as well as the demagnetization field, region A and B exhibit distinct resonance geometry. For instance, for field along short axis, region A and B are in Damon-Esbach and magnetostatic backward volume mode geometry respectively, with the spin wave vectors determined by hole separations along long and short axis. This is reversed with field along long axis. The dispersion of the observed spin waves is analyzed accordingly. Supported by US DOE FG02-86ER45281 (MU) and NSF DMR-0213985 (UA). ^1Chengtao Yu, Michael J. Pechan, G. J. Mankey, Appl. Phys. Lett. 83, 3948 (2003).
Domain overlap matrices from plane-wave-based methods of electronic structure calculation
NASA Astrophysics Data System (ADS)
Golub, Pavlo; Baranov, Alexey I.
2016-10-01
Plane waves are one of the most popular and efficient basis sets for electronic structure calculations of solids; however, their delocalized nature makes it difficult to employ for them classical orbital-based methods of chemical bonding analysis. The quantum chemical topology approach, introducing chemical concepts via partitioning of real space into chemically meaningful domains, has no difficulties with plane-wave-based basis sets. Many popular tools employed within this approach, for instance delocalization indices, need overlap integrals over these domains—the elements of the so called domain overlap matrices. This article reports an efficient algorithm for evaluation of domain overlap matrix elements for plane-wave-based calculations as well as evaluation of its implementation for one of the most popular projector augmented wave (PAW) methods on the small set of simple and complex solids. The stability of the obtained results with respect to PAW calculation parameters has been investigated, and the comparison of the results with the results from other calculation methods has also been made.
Traveling Internal Plane-wave Synthesis (TIPS) for uniform B1 in high field MRI.
Anderson, Adam W
2017-02-01
A new target-field approach to generating uniform radio frequency (RF) fields within the human body for high field MRI is described. The method involves producing a set of external fields which, after interaction with a dielectric object, superimpose to produce a traveling plane wave, exposing all spins to the same RF amplitude (B1) over a cycle of the harmonic field. Conceptually this is similar to conventional RF shimming, but uses a different RF source design, input data, and objective function. The method requires a detailed knowledge of the coupling between exterior field modes, produced by an array of RF sources, and field modes within the body. Given an estimate of the coupling matrix, the linear superposition of external modes that produces a desired internal target field can be determined. The new method is termed Traveling Internal Plane-wave Synthesis (TIPS). A simple design of a coil array is described that can, in principle, generate the required field modes. Simulations demonstrate that radio frequency magnetic fields of nearly uniform (<1% variation) magnitude can be produced within dielectric objects larger than a wavelength in size. If the dielectric medium has non-zero conductivity, traveling waves are attenuated as they traverse the object, but field uniformity within planar slices is preserved. For general 3D imaging, a superposition of plane waves can provide field focusing to balance conductive losses, thereby achieving nearly uniform-magnitude B1+ magnetic fields over a volume of interest.
Multi-view horizon-driven sea plane estimation for stereo wave imaging on moving vessels
NASA Astrophysics Data System (ADS)
Bergamasco, Filippo; Benetazzo, Alvise; Barbariol, Francesco; Carniel, Sandro; Sclavo, Mauro
2016-10-01
In the last few years we faced an increased popularity of stereo imaging as an effective tool to investigate wind sea waves at short and medium scales. Given the advances of computer vision techniques, the recovery of a scattered point-cloud from a sea surface area is nowadays a well consolidated technique producing excellent results both in terms of wave data resolution and accuracy. Nevertheless, almost all the subsequent analyses tasks, from the recovery of directional wave spectra to the estimation of significant wave height, are bound to two limiting conditions. First, wave data are required to be aligned to the mean sea plane. Second, a uniform distribution of 3D point samples is assumed. Since the stereo-camera rig is placed tilted with respect to the sea surface, perspective distortion do not allow these conditions to be met. Errors due to this problem are even more challenging if the optical instrumentation is mounted on a moving vessel, so that the mean sea plane cannot be simply obtained by averaging data from multiple subsequent frames. We address the first problem with two main contributions. First, we propose a novel horizon estimation technique to recover the attitude of a moving stereo rig with respect to the sea plane. Second, an effective weighting scheme is described to account for the non-uniform sampling of the scattered data in the estimation of the sea-plane distance. The interplay of the two allows us to provide a precise point cloud alignment without any external positioning sensor or rig viewpoint pre-calibration. The advantages of the proposed technique are evaluated throughout an experimental section spanning both synthetic and real-world scenarios.
Ultrafast Kikuchi diffraction: nanoscale stress-strain dynamics of wave-guiding structures.
Yurtsever, Aycan; Schaefer, Sascha; Zewail, Ahmed H
2012-07-11
Complex structural dynamics at the nanoscale requires sufficiently small probes to be visualized. In conventional imaging using electron microscopy, the dimension of the probe is large enough to cause averaging over the structures present. However, by converging ultrafast electron bunches, it is possible to select a single nanoscale structure and study the dynamics, either in the image or using electron diffraction. Moreover, the span of incident wave vectors in a convergent beam enables sensitivity levels and information contents beyond those of parallel-beam illumination with a single wave vector Bragg diffraction. Here, we report the observation of propagating strain waves using ultrafast Kikuchi diffraction from nanoscale volumes within a wedge-shaped silicon single crystal. It is found that the heterogeneity of the strain in the lateral direction is only 100 nm. The transient elastic wave gives rise to a coherent oscillation with a period of 30 ps and with an envelope that has a width of 140 ps. The origin of this elastic deformation is theoretically examined using finite element analysis; it is identified as propagating shear waves. The wedge-shaped structure, unlike parallel-plate structure, is the key behind the traveling nature of the waves as its angle permits "transverse" propagation; the parallel-plate structure only exhibits the "longitudinal" motion. The studies reported suggest extension to a range of applications for nanostructures of different shapes and for exploring their ultrafast eigen-modes of stress-strain profiles.
Ring-plane traveling-wave tube slow-wave circuit design simulations at V-Band frequencies
Kory, C.L.; Wilson, J.D.
1995-06-01
The V-Band frequency range of 59-64 GHz is a region of the millimeter-wave spectrum that has been designated for intersatellite communications. As a first effort to develop a high-efficiency V-band 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 the high-power capabilities of the ring-plane TWT, disadvantages of low bandwidth and high voltage requirements have until now prevented its acceptance outside the laboratory. In this paper, the authors use the three-dimensional electromagnetic simulation code MAFIA to investigate methods of increasing the bandwidth and lowering the operating voltage. Dispersion, impedance, and attenuation calculations for various geometric variations and loading distributions were performed. Based on the results of the variations, a circuit termed the finned-ladder TWT slowwave circuit was designed and is compared here to the scaled ring-plane prototype and the conventional ferruled coupled-cavity TWT circuit over the V-band frequency range.
Ring-plane traveling-wave tube slow-wave circuit design simulations at V-Band frequencies
NASA Technical Reports Server (NTRS)
Kory, Carol L.; Wilson, Jeffrey D.
1995-01-01
The V-Band frequency range of 59-64 GHz is a region of the millimeter-wave spectrum that has been designated for intersatellite communications. As a first effort to develop a high-efficiency V-band 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 the high-power capabilities of the ring-plane TWT, disadvantages of low bandwidth and high voltage requirements have until now prevented its acceptance outside the laboratory. In this paper, we use the three-dimensional electromagnetic simulation code MAFIA to investigate methods of increasing the bandwidth and lowering the operating voltage. Dispersion, impedance, and attenuation calculations for various geometric variations and loading distributions were performed. Based on the results of the variations, a circuit termed the finned-ladder TWT slowwave circuit was designed and is compared here to the scaled ring-plane prototype and the conventional ferruled coupled-cavity TWT circuit over the V-band frequency range.
Shock wave diffraction in the presence of a supersonic co-flow jet
NASA Astrophysics Data System (ADS)
Gnani, F.; Lo, K. H.; Zare-Behtash, H.; Kontis, K.
2016-05-01
The interaction between a diffracting shock wave and a uniform jet is a case that so far has only been partially investigated. This interaction is extremely important for the control of noise generation and improvement of combustor performance. To fill this knowledge gap, three geometries of the diffracting corner, namely a straight ramp, a serrated ramp, and a rounded corner, have been tested experimentally to study the interaction of shock diffraction with a supersonic co-flow jet at incident Mach numbers of 1.31 and 1.59, with Reynolds numbers of 1.08× 106 and 1.68× 106, respectively. Schlieren photography was employed to analyse the evolution of the flow phenomena. The aim is to provide a qualitative understanding of the interaction between the diffracting shock wave and the uniform jet relevant to future high-speed transport. The results show that the flow field evolves more rapidly and develops stronger structures for a higher shock Mach number. The diffraction around a rounded splitter develops a periodical vortical structure which continues after the disturbance introduced by the passage of the shock wave is removed.
NASA Astrophysics Data System (ADS)
Woods, D. C.; Bolton, J. S.; Rhoads, J. F.
2016-09-01
A number of applications, for instance ultrasonic imaging and nondestructive testing, involve the transmission of acoustic energy across fluid-solid interfaces into dissipative solids. However, such transmission is generally hindered by the large impedance mismatch at the interface. In order to address this problem, inhomogeneous plane waves were investigated in this work for the purpose of improving the acoustic energy transmission. To this end, under the assumption of linear hysteretic damping, models for fluid-structure interaction were developed that allow for both homogeneous and inhomogeneous incident waves. For low-loss solids, the results reveal that, at the Rayleigh angle, a unique value of the wave inhomogeneity can be found which minimizes the reflection coefficient, and consequently maximizes the transmission. The results also reveal that with sufficient dissipation levels in the solid material, homogeneous incident waves yield lower reflection values than inhomogeneous waves, due to the large degrees of inhomogeneity inherent in the transmitted waves. Analytical conditions have also been derived which predict the dependence of the optimal incident wave type on the dissipation level and wave speeds in the solid medium. Finally, implications related to the use of acoustic beams of limited spatial extent are discussed.
NASA Astrophysics Data System (ADS)
Fan, Xiaofeng; Baek, Yonggeun; Ha, Kanglyeol; Kim, Moojoon; Kim, Jungsoon; Kim, Duckjong; Kang, Hyun Wook; Oh, Junghwan
2017-07-01
An optoacoustic transducer made of light-absorbing and elastomeric materials can generate high-pressure wide-band ultrasound waves in water when it is illuminated by a pulse laser. To generate such waves with high efficiency, carbon nanotubes (CNTs) and poly(dimethylsiloxane) (PDMS) are widely used as the light-absorbing and elastomeric materials, respectively. It was previously reported that an optoacoustic concave transducer made of these materials can produce strong shock waves, namely, blast waves, within its focal zone. In this study, we have shown that these waves can also be generated by a plane optoacoustic transducer fabricated by coating CNTs-PDMS on a poly(methyl methacrylate) (PMMA) plate. Some propagation characteristics of the blast wave generated were measured and compared with the calculated results. It was found that the propagation speed and attenuation of the wave are different from those of usual sounds. From the comparison of the measured and the calculated acoustic fields, it is assumed that every point on the transducer surface produces almost the same blast wave.
Evidence of Doppler-shifted Bragg scattering in the vertical plane by ocean surface waves.
Lynch, Stephen D; D'Spain, Gerald L
2012-03-01
A set of narrowband tones (280, 370, 535, and 695 Hz) were transmitted by an acoustic source mounted on the ocean floor in 10 m deep water and received by a 64-element hydrophone line array lying on the ocean bottom 1.25 km away. Beamformer output in the vertical plane for the received acoustic tones shows evidence of Doppler-shifted Bragg scattering of the transmitted acoustic signals by the ocean surface waves. The received, scattered signals show dependence on the ocean surface wave frequencies and wavenumber vectors, as well as on acoustic frequencies and acoustic mode wavenumbers. Sidebands in the beamformer output are offset in frequency by amounts corresponding to ocean surface wave frequencies. Deviations in vertical arrival angle from specular reflection agree with those predicted by the Bragg condition through first-order perturbation theory using measured directional surface wave spectra and acoustic modes measured by the horizontal hydrophone array.
Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow
NASA Astrophysics Data System (ADS)
Rawat, Subhandu; Cossu, Carlo; Rincon, François
2016-06-01
Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite-period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi-streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size Lz of the domain in which they are computed is increased. On the contrary, the upper branch of travelling-wave solutions develops multiple streaks when Lz is increased. Upper-branch travelling-wave solutions can be continued into coherent solutions to the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.
Cavity-based linear polarizer immune to the polarization direction of an incident plane wave.
Wang, Jiang; Shen, Zhongxiang; Gao, Xiang; Wu, Wen
2016-01-15
We herein report a linear polarizer based on a 2D array of substrate integrated waveguide cavities, which can convert an arbitrary linearly polarized (LP) incident wave into an outgoing LP wave in a specified polarization direction with constant transmittance. Two orthogonal slots etched on the front surface of the cavity are utilized to couple a wave of arbitrary polarization into the cavity, while another slot on the back side helps to couple the field out along a desired polarization direction. Microwave experiments are performed as a proof of concept. The proposed polarizer exhibits very good performance with stable transmittance as 50% and a polarization extinction ratio over 45 dB. The new polarizer is potentially useful in novel polarization-selective devices that are immune to the polarization direction of an incident plane wave.
NASA Astrophysics Data System (ADS)
Abramov, Arnold; Kostikov, Alexander
2017-03-01
We report the effect of scattering of electromagnetic plane waves by two cylinders on whispering gallery mode (WGM) formation in a cylinder. WGM can occur because of the presence of additional cylinder scatterers at specific location, while WGMs can only form in a single cylinder for specific cylinder radius and/or wavelength values, the matching accuracy required would be much greater than that required in our model for the additional cylinders locations. Analysis of the general solution to the problem showed that the effect can be explained by the interference of waves scattered by additional cylinders and incident on the main cylinder.
Plane Tidal Waves Generated by an Array of Simultaneous Underwater Explosions.
1981-03-01
shallow water theory verify the formation of a plane tidal wave. The wave energy resulting from the underwater explosion was approximated with an initial...thle fol lowing ajiproxi mt ion- and calculations. The energy reu ’rd to ior thle hemi spheri cal bubble i s approxiniat ed by the energy requ ired to...form an eql voIlme spherical bubble with coinciding cent roids. Approximately half of the explosion’s energy is absorbed by thle ocean floor (Ref 5
S-Wave Dispersion Relations: Exact Left Hand E-Plane Discontinuity from the Born Series
NASA Technical Reports Server (NTRS)
Bessis, D.; Temkin, A.
1999-01-01
We show, for a superposition of Yukawa potentials, that the left hand cut discontinuity in the complex E plane of the (S-wave) scattering amplitude is given exactly, in an interval depending on n, by the discontinuity of the Born series stopped at order n. This also establishes an inverse and unexpected correspondence of the Born series at positive high energies and negative low energies. We can thus construct a viable dispersion relation (DR) for the partial (S-) wave amplitude. The high numerical precision achievable by the DR is demonstrated for the exponential potential at zero scattering energy. We also briefly discuss the extension of our results to Field Theory.
S-Wave Dispersion Relations: Exact Left Hand E-Plane Discontinuity from the Born Series
NASA Technical Reports Server (NTRS)
Bessis, D.; Temkin, A.
1999-01-01
We show, for a superposition of Yukawa potentials, that the left hand cut discontinuity in the complex E plane of the (S-wave) scattering amplitude is given exactly, in an interval depending on n, by the discontinuity of the Born series stopped at order n. This also establishes an inverse and unexpected correspondence of the Born series at positive high energies and negative low energies. We can thus construct a viable dispersion relation (DR) for the partial (S-) wave amplitude. The high numerical precision achievable by the DR is demonstrated for the exponential potential at zero scattering energy. We also briefly discuss the extension of our results to Field Theory.
Density functional calculations of Pd nanoparticles using a plane-wave method.
Viñes, Francesc; Illas, Francesc; Neyman, Konstantin M
2008-09-25
We deal with usage of plane-wave density functional calculations of crystallites formed of 100-200 transition metal atoms to mimic larger experimentally treated particles. A series of model Pd clusters containing up to 225 atoms is chosen as an example. We focused on the description of size-dependent geometric parameters and binding energies of these clusters as compared with previous benchmark calculations; evolution of the particle electronic structure with increasing size has also been addressed. The high performance of the plane-wave calculations for transition-metal nanoparticles has been documented. Implications of this work on broadening opportunities to design and study realistic models of catalytic systems are outlined.
A solution for TM-mode plane waves incident on a two-dimensional inhomogeneity
Lee, K. H.; Morrison, H. F.
1985-07-01
A solution for the electromagnetic fields scattered from a two-dimensional inhomogeneity in a conducting half space has been obtained for an incident TM mode plane wave; the magnetic field is polarized parallel to the strike of the inhomogeneity. The approach has been to determine the scattering currents within the inhomogeneity using an integral equation for the electric fields. This solution is similar in concept to earlier studies of TE mode scattering from two-dimensional inhomogeneities, and it completes the analysis of the scattering of arbitrary plane waves using the integral equation approach. For simple bodies in the earth integral equation solution offers significant computational advantages over alternate finite element or finite difference methods of solution.
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.
A standing wave linear ultrasonic motor operating in in-plane expanding and bending modes.
Chen, Zhijiang; Li, Xiaotian; Ci, Penghong; Liu, Guoxi; Dong, Shuxiang
2015-03-01
A novel standing wave linear ultrasonic motor operating in in-plane expanding and bending modes was proposed in this study. The stator (or actuator) of the linear motor was made of a simple single Lead Zirconate Titanate (PZT) ceramic square plate (15 × 15 × 2 mm(3)) with a circular hole (D = 6.7 mm) in the center. The geometric parameters of the stator were computed with the finite element analysis to produce in-plane bi-mode standing wave vibration. The calculated results predicted that a driving tip attached at midpoint of one edge of the stator can produce two orthogonal, approximate straight-line trajectories, which can be used to move a slider in linear motion via frictional forces in forward or reverse direction. The investigations showed that the proposed linear motor can produce a six times higher power density than that of a previously reported square plate motor.
A standing wave linear ultrasonic motor operating in in-plane expanding and bending modes
NASA Astrophysics Data System (ADS)
Chen, Zhijiang; Li, Xiaotian; Ci, Penghong; Liu, Guoxi; Dong, Shuxiang
2015-03-01
A novel standing wave linear ultrasonic motor operating in in-plane expanding and bending modes was proposed in this study. The stator (or actuator) of the linear motor was made of a simple single Lead Zirconate Titanate (PZT) ceramic square plate (15 × 15 × 2 mm3) with a circular hole (D = 6.7 mm) in the center. The geometric parameters of the stator were computed with the finite element analysis to produce in-plane bi-mode standing wave vibration. The calculated results predicted that a driving tip attached at midpoint of one edge of the stator can produce two orthogonal, approximate straight-line trajectories, which can be used to move a slider in linear motion via frictional forces in forward or reverse direction. The investigations showed that the proposed linear motor can produce a six times higher power density than that of a previously reported square plate motor.
Comparison of finite source and plane wave scattering from corrugated surfaces
NASA Technical Reports Server (NTRS)
Levine, D. M.
1977-01-01
The choice of a plane wave to represent incident radiation in the analysis of scatter from corrugated surfaces was examined. The physical optics solution obtained for the scattered fields due to an incident plane wave was compared with the solution obtained when the incident radiation is produced by a source of finite size and finite distance from the surface. The two solutions are equivalent if the observer is in the far field of the scatterer and the distance from observer to scatterer is large compared to the radius of curvature at the scatter points, condition not easily satisfied with extended scatterers such as rough surfaces. In general, the two solutions have essential differences such as in the location of the scatter points and the dependence of the scattered fields on the surface properties. The implication of these differences to the definition of a meaningful radar cross section was examined.
In situ technique for measuring the orthogonality of a plane wave to a substrate.
Châteauneuf, Marc; Ayliffe, Michael H; Kirk, Andrew G
2003-05-01
A new compact in situ method of measuring the perpendicularity of a plane wave to a substrate is proposed. Off-axis cylindrical Fresnel lenses are used to focus a portion of the incident plane wave onto target lines. The displacement of the focal line from the targets is determined by the degree of angular misalignment. The proposed design has been incorporated into a 10-mm-thick fused-silica module, which enables us to obtain an alignment precision of better than 0.0083 degrees. This method is designed for use in optical assembly procedures that require an incident collimated beam that is normal to the alignment features. Experimental results are presented.
A nonperturbative definition of N = 4 Super Yang-Mills by the plane wave matrix model
Shimasaki, Shinji
2008-11-23
We propose a nonperturbative definition of N = 4 Super Yang-Mills(SYM). We realize N = 4 SYM on RxS{sup 3} as the theory around a vacuum of the plane wave matrix model. Our regularization preserves 16 supersymmetries and the gauge symmetry. We perform the one-loop calculation to give evidence that in the continuum limit the superconformal symmetry is restored.
NASA Astrophysics Data System (ADS)
Pickard, Chris J.; Winkler, Björn; Chen, Roger K.; Payne, M. C.; Lee, M. H.; Lin, J. S.; White, J. A.; Milman, V.; Vanderbilt, David
2000-12-01
We show that plane wave ultrasoft pseudopotential methods readily extend to the calculation of the structural properties of lanthanide and actinide containing compounds. This is demonstrated through a series of calculations performed on UO, UO2, UO3, U3O8, UC2, α-CeC2, CeB6, CeSe, CeO2, NdB6, TmOI, LaBi, LaTiO3, YbO, and elemental Lu.
Pickard; Winkler; Chen; Payne; Lee; Lin; White; Milman; Vanderbilt
2000-12-11
We show that plane wave ultrasoft pseudopotential methods readily extend to the calculation of the structural properties of lanthanide and actinide containing compounds. This is demonstrated through a series of calculations performed on UO, UO2, UO3, U3O8, UC2, alpha-CeC2, CeB6, CeSe, CeO2, NdB6, TmOI, LaBi, LaTiO3, YbO, and elemental Lu.
Multiple-scattering corrections in diluted magnetic semiconductors: A plane-wave expansion
NASA Astrophysics Data System (ADS)
Scalbert, D.; Ghazali, A.; Benoit à la Guillaume, C.
1993-12-01
Energy levels of band edges in diluted magnetic semiconductors are calculated in the effective-mass approximation, retaining off-diagonal terms in the exchange interaction and using a plane-wave expansion. This model accounts qualitatively for the observed asymmetry in the splitting of the A exciton in a magnetic field in Cd1-xMnxS for which multiple-scattering corrections are expected to be important.
Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C
2011-06-01
The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.
Castaings; Hosten
2000-03-01
Electrostatic, air-coupled, ultrasonic transducers are used to generate and detect plane waves in viscoelastic, isotropic or anisotropic solid plates. The through-transmitted field is measured and compared to numerical predictions. An inversion scheme is then applied for identifying the values of the complex Cij which are representative of the viscoelasticity properties of the materials. The issue of this work is a contact-free, ultrasonic technique for material characterisation.
Lectures on the plane-wave string/gauge theory duality
NASA Astrophysics Data System (ADS)
Plefka, J. C.
2004-02-01
These lectures give an introduction to the novel duality relating type IIB string theory in a maximally supersymmetric plane-wave background to = 4, d = 4, U(N) super Yang-Mills theory in a particular large N and large R-charge limit due to Berenstein, Maldacena and Nastase. In the first part of these lectures the duality is derived from the AdS/CFT correspondence by taking a Penrose limit of the AdS5 × S5 geometry and studying the corresponding double-scaling limit on the gauge theory side. The resulting free plane-wave superstring is then quantized in light-cone gauge. On the gauge theory side of the correspondence the composite super Yang-Mills operators dual to string excitations are identified, and it is shown how the string spectrum can be mapped to the planar scaling dimensions of these operators. In the second part of these lectures we study the correspondence at the interacting respectively non-planar level. On the gauge theory side it is demonstrated that the large N large R-charge limit in question preserves contributions from Feynman graphs of all genera through the emergence of a new genus counting parameter - in agreement with the string genus expansion for non-zero gs. Effective quantum mechanical tools to compute higher genus contributions to the scaling dimensions of composite operators are developed and explicitly applied in a genus one computation. We then turn to the interacting string theory side and give an elementary introduction into light-cone superstring field theory in a plane-wave background and point out how the genus one prediction from gauge theory can be reproduced. Finally, we summarize the present status of the plane-wave string/gauge theory duality.
On the convergence of the coupled-wave approach for lamellar diffraction gratings
NASA Technical Reports Server (NTRS)
Li, Lifeng; Haggans, Charles W.
1992-01-01
Among the many existing rigorous methods for analyzing diffraction of electromagnetic waves by diffraction gratings, the coupled-wave approach stands out because of its versatility and simplicity. It can be applied to volume gratings and surface relief gratings, and its numerical implementation is much simpler than others. In addition, its predictions were experimentally validated in several cases. These facts explain the popularity of the coupled-wave approach among many optical engineers in the field of diffractive optics. However, a comprehensive analysis of the convergence of the model predictions has never been presented, although several authors have recently reported convergence difficulties with the model when it is used for metallic gratings in TM polarization. Herein, three points are made: (1) in the TM case, the coupled-wave approach converges much slower than the modal approach of Botten et al; (2) the slow convergence is caused by the use of Fourier expansions for the permittivity and the fields in the grating region; and (3) is manifested by the slow convergence of the eigenvalues and the associated modal fields. The reader is assumed to be familiar with the mathematical formulations of the coupled-wave approach and the modal approach.
Triple Bragg diffraction in paratellurite crystal
NASA Astrophysics Data System (ADS)
Kotov, V. M.; Averin, S. V.; Voronko, A. I.; Kotov, E. V.; Tikhomirov, S. A.
2017-07-01
Triple Bragg diffraction in a paratellurite crystal has been considered for the case when the plane of diffraction is oblique to the optical axis of the crystal. It has been shown that effective photoelastic constants for isotropic and anisotropic diffraction depend on the inclination of the plane of diffraction insignificantly. Triple Bragg diffraction of 0.63-μm coherent radiation in paratellurite at a 47.3-MHz slow acoustic wave has been experimentally demonstrated. For an optical power of 0.69 W delivered to a piezoconverter, the relative intensities of diffraction orders equal 0.4, 0.4, 0.1, and 0.1, respectively.
Kwiek, Piotr
2015-03-01
The phenomenon of collinear correlated photon pairs diffraction by an ultrasonic wave is investigated within Raman-Nath and intermediate region. The numbers of single photons and photon pairs counts in discrete diffraction orders were measured as functions of the Raman-Nath parameter. Similarly, the number of coincidence photon counts in separate diffraction orders was also investigated. It was shown experimentally that the phenomenon of photon pairs diffraction by an ultrasonic wave happens at angles identical to those corresponding to single photons diffraction. It was also demonstrated that in case of Raman-Nath diffraction the number of photon pairs in a selected, n(th), diffraction order varies with the Raman-Nath parameter changes as an n(th) order Bessel function of the first kind, raised to the fourth power. Whilst in the so-called intermediate diffraction zone, the number of diffracted photon pairs varies as squared intensity of a diffracted light beam consisting of single photons. Moreover, it was revealed that correlations between photons in selected diffraction orders change with the Raman-Nath parameter variation as products of relevant intensities of light in the considered diffraction orders. Finally, it should be emphasized that the presented formulae describing diffraction of collinear correlated proton pairs by an ultrasonic wave are in a very good agreement with corresponding experimental data, for both Raman-Nath and intermediate diffraction.
3D resolution tests of two-plane wave approach using synthetic seismograms
NASA Astrophysics Data System (ADS)
Ceylan, S.; Larmat, C. S.; Sandvol, E. A.
2012-12-01
Two-plane wave tomography (TPWT) is becoming a standard approach to obtain fundamental mode Rayleigh wave phase velocities for a variety of tectonic settings. A recent study by Ceylan et al. (2012) has applied this method to eastern Tibet, using data from INDEPTH-IV and Namche-Barwa seismic experiments. The TPWT assumes that distortion of wavefronts at each station can be expressed as the sum of two plane waves. However, there is currently no robust or complete resolution test for TPWT, to address its limitations such as wavefront healing. In this study, we test the capabilities of TPWT and resolution of INDEPTH-IV seismic experiment, by performing 3D resolution tests using synthetic seismograms. Utilizing SPECFEM3D software, we compute synthetic data sets resolving periods down to ~30 s. We implement a checkerboard upper mantle (for depths between 50 and 650 km) with variable cell sizes, superimposed to PREM as the background model. We then calculate fundamental mode surface wave phase velocities using TPWT for periods between 33-143 seconds, using synthetic seismograms computed from our three dimensional hypothetical model. Assuming a constant Poisson's ratio, we use partial derivatives from Saito (1988) to invert for shear wave velocities. We show that the combination of TPWT and Saito (1988) methods is capable of retrieving anomalies down to depths of ~200 km for Rayleigh waves. Below these depths, we observe evidence of both lateral and vertical smearing. We also find that the traditional method for estimating the resolution of TPWT consistently overestimates phase velocity resolutions. Love waves exhibit adequate resolution down to depths of ~100 km. At depths greater than 100 km, smearing is more evident in SH wave results than those of SV waves. Increased smearing of SH waves is most probably due to propagation characteristics and shallower sensitivity of Love waves. Our results imply that TPWT can be applied to Love waves, making future investigations of
Ground-coupled air waves and diffracted infrasound from the Arequipa earthquake of June 23, 2001
NASA Astrophysics Data System (ADS)
Le Pichon, A.; Guilbert, J.; Vega, A.; Garcés, M.; Brachet, N.
2002-09-01
On June 23, 2001, a strong earthquake measuring Mw 8.4 occurred along the coast of south-central Peru. Coherent infrasonic waves were detected over a period of one hour by the IS08 infrasound station in Bolivia. Analysis of the ground-coupled air waves shows that the rupture propagated from the northwestern to the southeastern part of the fault with a rupture velocity of 3.3 km/s. The azimuth variation of the infrasonic waves is attributed to a distribution of secondary sources along the highest mountain ranges, which excite infrasonic waves that are diffracted to the ground. The predominant source of infrasound is likely distributed along the Andean Cordillera. Using the azimuth and arrival time determination, the horizontal scale size of the distant source regions of infrasonic waves is reconstructed over distances greater than 400 km.
NASA Astrophysics Data System (ADS)
Hayner, Mark; Hynynen, Kullervo
2001-12-01
Ultrasonic transmission and absorption of oblique plane waves through the human skull are analyzed numerically for frequencies ranging from 1/2 to 1 MHz. These frequencies are optimum for noninvasive ultrasound therapy of brain disorders where numerical predictions of skull transmission are used to set the phase and amplitude of source elements in the phased array focusing system. The idealized model of the skull is a three-layer solid with ivory outer and inner layers and a middle marrow layer. Each layer is modeled as a flat, homogeneous, isotropic, linear solid with effective complex wave speeds to account for focused energy losses due to material damping and scattering. The model is used to predict the amplitude and phase of the transmitted wave and volumetric absorption. Results are reported for three different skull thicknesses: 3 mm, 6 mm, and 9 mm. Thickness resonances are observed in the transmitted wave for 3 mm skulls at all frequencies and for the 6 mm skulls below 0.75 MHz. Otherwise, the transmission is dominated by the direct wave. Skull phase errors due to shear waves are shown to minimally degrade the power at the focus for angles of incidence up to 20° from normal even for low material damping. The location of the peak volumetric absorption occurs either in the outer ivory or middle marrow layer and shown to vary due to wave interference.
Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave
Chen, Gang; Wu, Zhi-xiang; Yu, An-ping; Zhang, Zhi-hai; Wen, Zhong-quan; Zhang, Kun; Dai, Lu-ru; Jiang, Sen-lin; Li, Yu-yan; Chen, Li; Wang, Chang-tao; Luo, Xian-gang
2016-01-01
The generation of a sub-diffraction optical hollow ring is of great interest in various applications, such as optical microscopy, optical tweezers, and nanolithography. Azimuthally polarized light is a good candidate for creating an optical hollow ring structure. Various of methods have been proposed theoretically for generation of sub-wavelength hollow ring by focusing azimuthally polarized light, but without experimental demonstrations, especially for sub-diffraction focusing. Super-oscillation is a promising approach for shaping sub-diffraction optical focusing. In this paper, a planar sub-diffraction diffractive lens is proposed, which has an ultra-long focal length of 600 λ and small numerical aperture of 0.64. A sub-diffraction hollow ring is experimentally created by shaping an azimuthally polarized wave. The full-width-at-half-maximum of the hollow ring is 0.61 λ, which is smaller than the lens diffraction limit 0.78 λ, and the observed largest sidelobe intensity is only 10% of the peak intensity. PMID:27876885
Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave
NASA Astrophysics Data System (ADS)
Chen, Gang; Wu, Zhi-Xiang; Yu, An-Ping; Zhang, Zhi-Hai; Wen, Zhong-Quan; Zhang, Kun; Dai, Lu-Ru; Jiang, Sen-Lin; Li, Yu-Yan; Chen, Li; Wang, Chang-Tao; Luo, Xian-Gang
2016-11-01
The generation of a sub-diffraction optical hollow ring is of great interest in various applications, such as optical microscopy, optical tweezers, and nanolithography. Azimuthally polarized light is a good candidate for creating an optical hollow ring structure. Various of methods have been proposed theoretically for generation of sub-wavelength hollow ring by focusing azimuthally polarized light, but without experimental demonstrations, especially for sub-diffraction focusing. Super-oscillation is a promising approach for shaping sub-diffraction optical focusing. In this paper, a planar sub-diffraction diffractive lens is proposed, which has an ultra-long focal length of 600 λ and small numerical aperture of 0.64. A sub-diffraction hollow ring is experimentally created by shaping an azimuthally polarized wave. The full-width-at-half-maximum of the hollow ring is 0.61 λ, which is smaller than the lens diffraction limit 0.78 λ, and the observed largest sidelobe intensity is only 10% of the peak intensity.
Generation of a sub-diffraction hollow ring by shaping an azimuthally polarized wave.
Chen, Gang; Wu, Zhi-Xiang; Yu, An-Ping; Zhang, Zhi-Hai; Wen, Zhong-Quan; Zhang, Kun; Dai, Lu-Ru; Jiang, Sen-Lin; Li, Yu-Yan; Chen, Li; Wang, Chang-Tao; Luo, Xian-Gang
2016-11-23
The generation of a sub-diffraction optical hollow ring is of great interest in various applications, such as optical microscopy, optical tweezers, and nanolithography. Azimuthally polarized light is a good candidate for creating an optical hollow ring structure. Various of methods have been proposed theoretically for generation of sub-wavelength hollow ring by focusing azimuthally polarized light, but without experimental demonstrations, especially for sub-diffraction focusing. Super-oscillation is a promising approach for shaping sub-diffraction optical focusing. In this paper, a planar sub-diffraction diffractive lens is proposed, which has an ultra-long focal length of 600 λ and small numerical aperture of 0.64. A sub-diffraction hollow ring is experimentally created by shaping an azimuthally polarized wave. The full-width-at-half-maximum of the hollow ring is 0.61 λ, which is smaller than the lens diffraction limit 0.78 λ, and the observed largest sidelobe intensity is only 10% of the peak intensity.
NASA Astrophysics Data System (ADS)
Serenelli, Roberto
2004-12-01
This paper analyzes simple imaging configurations to scan a human body, suitable as passive or active millimetre-wave imaging systems for concealed weapon detection (CWD). The first cylindrical configuration allows a 360 degrees scan: N unphased diffraction-limited antennas each of size L are placed on a circular support surrounding the subject (allowing scanning in the horizontal plane with N non-overlapping independent beams), and this circle is mechanically displaced over the whole body height. An analytical formula gives the maximum obtainable spatial resolution for different dimensions of the circular scanning device and operating frequencies, and the number of receivers achieving this optimal resolution. Constraints to be taken into account are diffraction, the usable total length of the circle, and the full coverage by the N beams over the subject, which is modelled as a cylinder with variable radius, coaxial with the scanning circle. Numerical calculations of system resolution are shown for different operating microwave (MW) and millimetre-wave (MMW) frequencies; in order to study off-axis performances, situations where the subject is not coaxial with the scanning device are also considered. For the case of a parallelepiped to be imaged instead of a cylinder, a linear array configuration is analyzed similarly to the circular one. A theoretical study is carried out to design other curved arrays, filled with unphased diffraction-limited antennas, for the imaging of linear subjects with finer resolution. Finally, the application of such configurations is considered for the design of active imaging systems, and different system architectures are discussed.
Mitri, F G
2016-03-01
This work proposes a formal analytical theory using the partial-wave series expansion (PWSE) method in cylindrical coordinates, to calculate the acoustic backscattering form function as well as the radiation force-per-length on an infinitely long elliptical (non-circular) cylinder in plane progressive waves. The major (or minor) semi-axis of the ellipse coincides with the direction of the incident waves. The scattering coefficients for the rigid elliptical cylinder are determined by imposing the Neumann boundary condition for an immovable surface and solving a resulting system of linear equations by matrix inversion. The present method, which utilizes standard cylindrical (Bessel and Hankel) wave functions, presents an advantage over the solution for the scattering that is ordinarily expressed in a basis of elliptical Mathieu functions (which are generally non-orthogonal). Furthermore, an integral equation showing the direct connection of the radiation force function with the square of the scattering form function in the far-field from the scatterer (applicable for plane waves only), is noted and discussed. An important application of this integral equation is the adequate evaluation of the radiation force function from a bistatic measurement (i.e., in the polar plane) of the far-field scattering from any 2D object of arbitrary shape. Numerical predictions are evaluated for the acoustic backscattering form function and the radiation force function, which is the radiation force per unit length, per characteristic energy density, and per unit cross-sectional surface of the ellipse, with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes, as well as the dimensionless size parameter kb, without the restriction to a particular range of frequencies. The results are particularly relevant in acoustic levitation, acousto-fluidics and particle dynamics applications. Copyright © 2015 Elsevier B.V. All rights reserved.
Numerical Investigation of Sediment Suspension Above Plane Bed Under Skewed Grouping Waves
NASA Astrophysics Data System (ADS)
Finn, J.; Li, M.; Apte, S.
2016-12-01
Sediment suspension above a plane bed under oscillatory flow is of particular importance to coastal engineering in terms of understanding the influence of surface waves on beach and estuary transport processes. Existing studies, however, largely focus a on single representative wave condition and the randomness of natural waves are not taken into account. The present study aims to investigate wave grouping effects together with wave skewness on near bed boundary layer processes and sediment suspension using a newly developed three dimensional, multiphase, Euler-Lagrange point-particle model, e.g. Finn et al (2016). The sediment in the model is treated as a collection of Lagrangian particles that respond to both hydrodynamic and inter-particle forces, and particle motion is coupled to the near-bed hydrodynamics through the volume filtered Navier Stokes equations, which are solved in a finite volume LES framework at near-particle scale. The experiment by Bhawanin et al (2014) was used to validate the model's prediction on hydrodynamics and turbulence characteristics above boundary layer. Figure 1 shows the computed streamwise flow velocity within the wave group under a velocity-skewed signal in comparison with the measured values at different levels above the bed. The corresponding turbulence kinetic energy distribution under the wave group show similar level of agreement. The signature of waves with different strength within the group is clearly seen in the TKE distribution close to the bed. Subsequently, the Euler-Lagrange point-particle model was activated to investigate sediment suspension under the complex grouped waves. The particle size was chosen as 0.46mm sand. Initial examination of the model results reveals the immediate resuspension of sediment under large waves within the group and rapid drop of concentration under smaller waves, largely due to the coarse grain size and short wave period used in the test. However, the signature of near-bed turbulence on
Johnston, Jessica C.; Iuliucci, Robbie J.; Facelli, Julio C.; Fitzgerald, George; Mueller, Karl T.
2009-01-01
In order to predict accurately the chemical shift of NMR-active nuclei in solid phase systems, magnetic shielding calculations must be capable of considering the complete lattice structure. Here we assess the accuracy of the density functional theory gauge-including projector augmented wave method, which uses pseudopotentials to approximate the nodal structure of the core electrons, to determine the magnetic properties of crystals by predicting the full chemical-shift tensors of all 13C nuclides in 14 organic single crystals from which experimental tensors have previously been reported. Plane-wave methods use periodic boundary conditions to incorporate the lattice structure, providing a substantial improvement for modeling the chemical shifts in hydrogen-bonded systems. Principal tensor components can now be predicted to an accuracy that approaches the typical experimental uncertainty. Moreover, methods that include the full solid-phase structure enable geometry optimizations to be performed on the input structures prior to calculation of the shielding. Improvement after optimization is noted here even when neutron diffraction data are used for determining the initial structures. After geometry optimization, the isotropic shift can be predicted to within 1 ppm. PMID:19831448
Optical Measurement of In-plane Waves in Mechanical Metamaterials Through Digital Image Correlation
Schaeffer, Marshall; Trainiti, Giuseppe; Ruzzene, Massimo
2017-01-01
We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behaviour, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centring image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subse- quent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing of a field of view that is sufficiently large for subsequent processing. The transient response is recorded in the form of the full wavefields, which are processed to unveil features of wave motion in a hexagonal lattice. Time snapshots and frequency contours in the spatial Fourier domain are compared with numerical predictions to illustrate the accuracy of the recorded wavefields. PMID:28205589
Optical Measurement of In-plane Waves in Mechanical Metamaterials Through Digital Image Correlation.
Schaeffer, Marshall; Trainiti, Giuseppe; Ruzzene, Massimo
2017-02-13
We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behaviour, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centring image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subse- quent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing of a field of view that is sufficiently large for subsequent processing. The transient response is recorded in the form of the full wavefields, which are processed to unveil features of wave motion in a hexagonal lattice. Time snapshots and frequency contours in the spatial Fourier domain are compared with numerical predictions to illustrate the accuracy of the recorded wavefields.
Optical Measurement of In-plane Waves in Mechanical Metamaterials Through Digital Image Correlation
NASA Astrophysics Data System (ADS)
Schaeffer, Marshall; Trainiti, Giuseppe; Ruzzene, Massimo
2017-02-01
We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behaviour, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centring image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subse- quent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing of a field of view that is sufficiently large for subsequent processing. The transient response is recorded in the form of the full wavefields, which are processed to unveil features of wave motion in a hexagonal lattice. Time snapshots and frequency contours in the spatial Fourier domain are compared with numerical predictions to illustrate the accuracy of the recorded wavefields.
Automatic identification of multiply diffracted waves and their ordered scattering paths.
Löer, Katrin; Meles, Giovanni A; Curtis, Andrew
2015-04-01
An automated algorithm uses recordings of acoustic energy across a spatially-distributed array to derive information about multiply scattered acoustic waves in heterogeneous media. The arrival time and scattering-order of each recorded diffracted acoustic wave, and the exact sequence of diffractors encountered by that wave, are estimated without requiring an explicit model of the medium through which the wave propagated. Individual diffractors are identified on the basis of their unique single-scattering relative travel-time curves (move-outs) across the array, and secondary (twice-scattered) waves are detected using semblance analysis along temporally offset primary move-outs. This information is sufficient to estimate travel times and scattering paths of all multiply diffracted waves of any order, and for these events to be identified in recorded data. The algorithm is applied to synthetic acoustic data sets from a variety of media, including different numbers of point-diffractors and a medium with strong heterogeneity and non-hyperbolic move-outs.
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.
A continuous Riemann–Hilbert problem for colliding plane gravitational waves
NASA Astrophysics Data System (ADS)
Palenta, Stefan; Meinel, Reinhard
2017-10-01
We present the foundations of a new solution technique for the characteristic initial value problem (IVP) of colliding plane gravitational waves. It has extensive similarities to the approach of Alekseev and Griffiths in 2001, but we use an inverse scattering method with a Riemann–Hilbert problem (RHP), which allows for a transformation to a continuous RHP with a solution given in terms of integral equations for non-singular functions. Ambiguities in this procedure lead to the construction of a family of spacetimes containing the solution to the IVP. Therefore the described technique also serves as an interesting solution generating method. The procedure is exemplified by extending the Szekeres class of colliding wave spacetimes with 2 additional real parameters. The obtained solution seems to feature a limiting case of a new type of impulsive waves, which are circularly polarised.
Acoustic multipath arrivals in the horizontal plane due to approaching nonlinear internal waves.
Badiey, Mohsen; Katsnelson, Boris G; Lin, Ying-Tsong; Lynch, James F
2011-04-01
Simultaneous measurements of acoustic wave transmissions and a nonlinear internal wave packet approaching an along-shelf acoustic path during the Shallow Water 2006 experiment are reported. The incoming internal wave packet acts as a moving frontal layer reflecting (or refracting) sound in the horizontal plane. Received acoustic signals are filtered into acoustic normal mode arrivals. It is shown that a horizontal multipath interference is produced. This has previously been called a horizontal Lloyd's mirror. The interference between the direct path and the refracted path depends on the mode number and frequency of the acoustic signal. A mechanism for the multipath interference is shown. Preliminary modeling results of this dynamic interaction using vertical modes and horizontal parabolic equation models are in good agreement with the observed data.
Nonlinear dynamics and band transport in a superlattice driven by a plane wave
NASA Astrophysics Data System (ADS)
Apostolakis, A.; Awodele, M. K.; Alekseev, K. N.; Kusmartsev, F. V.; Balanov, A. G.
2017-06-01
A quantum particle transport induced in a spatially periodic potential by a propagating plane wave has a number of important implications in a range of topical physical systems. Examples include acoustically driven semiconductor superlattices and cold atoms in an optical crystal. Here we apply a kinetic description of the directed transport in a superlattice beyond standard linear approximation, and utilize exact path-integral solutions of the semiclassical transport equation. We show that the particle drift and average velocities have nonmonotonic dependence on the wave amplitude with several prominent extrema. Such nontrivial kinetic behavior is related to global bifurcations developing with an increase of the wave amplitude. They cause dramatic transformations of the system phase space and lead to changes of the transport regime. We describe different types of phase trajectories contributing to the directed transport and analyze their spectral content.
The relativistic transformation for an electromagnetic plane wave with general time dependence
NASA Astrophysics Data System (ADS)
Smith, Glenn S.
2012-03-01
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 the time dependence of the field is general; for example, it could be a Gaussian pulse in time. The changes that occur on transformation in the quantities that describe the wave are obtained and discussed. These changes include the temporal behaviour, direction of propagation, electromagnetic field, energy, and linear momentum. The derivation uses only elementary principles from special relativity, so it is suitable for an introductory course on the subject or a course on electrodynamics.
Time-resolved coherent X-ray diffraction imaging of surface acoustic waves.
Nicolas, Jan-David; Reusch, Tobias; Osterhoff, Markus; Sprung, Michael; Schülein, Florian J R; Krenner, Hubert J; Wixforth, Achim; Salditt, Tim
2014-10-01
Time-resolved coherent X-ray diffraction experiments of standing surface acoustic waves, illuminated under grazing incidence by a nanofocused synchrotron beam, are reported. The data have been recorded in stroboscopic mode at controlled and varied phase between the acoustic frequency generator and the synchrotron bunch train. At each time delay (phase angle), the coherent far-field diffraction pattern in the small-angle regime is inverted by an iterative algorithm to yield the local instantaneous surface height profile along the optical axis. The results show that periodic nanoscale dynamics can be imaged at high temporal resolution in the range of 50 ps (pulse length).
Liquid-Crystal Point-Diffraction Interferometer for Wave-Front Measurements
NASA Technical Reports Server (NTRS)
Mercer, Carolyn R.; Creath, Katherine
1996-01-01
A new instrument, the liquid-crystal point-diffraction interferometer (LCPDI), is developed for the measurement of phase objects. This instrument maintains the compact, robust design of Linnik's point-diffraction interferometer and adds to it a phase-stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave fronts with very high data density and with automated data reduction. We describe the theory and design of the LCPDI. A focus shift was measured with the LCPDI, and the results are compared with theoretical results,
Numerical simulation of THz-wave-assisted electron diffraction for ultrafast molecular imaging
NASA Astrophysics Data System (ADS)
Kanya, Reika; Yamanouchi, Kaoru
2017-03-01
A scheme for achieving high temporal resolution in gas electron diffraction is proposed, in which time-dependent electron diffraction patterns can be obtained from energy-resolved angular distributions of electrons scattered by molecules in dynamical processes under the presence of a single-cycle THz-wave pulse. Derived formulae of the differential cross section and numerical simulations of electron signals scattered by Ar atoms and C l2 molecules show that the temporal resolution of the proposed method can be <10 fs in the pump-probe measurement without scanning the time delay.
Formation of circular fringes by interference of two boundary diffraction waves using holography.
Kumar, Raj; Chhachhia, D P
2013-08-01
The theory of boundary diffraction waves (BDWs) is gaining importance due to its simplicity and physically appealing nature. The present work reports formation of circular fringes far away from the geometrically illuminated region by interference of two BDWs. One BDW is reconstructed from the hologram while the second is coming directly from the knife-edge. The uniqueness of the fringes is that their position can be controlled on the screen at will and fringes can be produced with bright as well as dark central fringe. These results could play an important role in understanding the nature of diffraction of light.
Time-resolved coherent X-ray diffraction imaging of surface acoustic waves
Nicolas, Jan-David; Reusch, Tobias; Osterhoff, Markus; Sprung, Michael; Schülein, Florian J. R.; Krenner, Hubert J.; Wixforth, Achim; Salditt, Tim
2014-01-01
Time-resolved coherent X-ray diffraction experiments of standing surface acoustic waves, illuminated under grazing incidence by a nanofocused synchrotron beam, are reported. The data have been recorded in stroboscopic mode at controlled and varied phase between the acoustic frequency generator and the synchrotron bunch train. At each time delay (phase angle), the coherent far-field diffraction pattern in the small-angle regime is inverted by an iterative algorithm to yield the local instantaneous surface height profile along the optical axis. The results show that periodic nanoscale dynamics can be imaged at high temporal resolution in the range of 50 ps (pulse length). PMID:25294979
Scattering of S waves diffracted at the core-mantle boundary: forward modelling
NASA Astrophysics Data System (ADS)
Emery, Valérie; Maupin, Valérie; Nataf, Henri-Claude
1999-11-01
The lowermost 200-300 km of the Earth's mantle, known as the D'' layer, is an extremely complex and heterogeneous region where transfer processes between the core and the mantle take place. Diffracted S waves propagate over large distances and are very sensitive to the velocity structure of this region. Strong variations of ampli-tudes and waveforms are observed on recordings from networks of broad-band seismic stations. We perform forward modelling of diffracted S waves in laterally heterogeneous structures in order to analyse whether or not these observations can be related to lateral inhomogeneities in D''. We combine the diffraction due to the core and the scattering due to small-scale volumetric heterogeneities (10-100 km) by coupling single scattering (Born approximation) with the Langer approximation, which describes Sdiff wave propagation. The influence on the direct as well as on the scattered wavefields of the CMB as well as of possible tunnelling in the core or in D'' is fully accounted for. The SH and the SV components of the diffracted waves are analysed, as well as their coupling. The modelling is applied in heterogeneous models with different geometries: isolated heterogeneities, vertical cylinders, horizontal inhomogeneities and random media. Amplitudes of scattered waves are weak and only velocity perturbations of the order of 10 per cent over a volume of 240 x 240 x 300 km3 produce visible effects on seismograms. The two polarizations of Sdiff have different radial sensitivities, the SH components being more sensitive to heterogeneities closer to the CMB. However, we do not observe significant time-shifts between the two components similar to those produced by anisotropy. The long-period Sdiff have a poor lateral resolution and average the velocity perturbations in their Fresnel zone. Random small-scale heterogeneities with +/- 10 per cent velocity contrast in the layer therefore have little effect on Sdiff, in contrast to their effect on PKIKP.
Transient axial solution for plane and axisymmetric waves focused by a paraboloidal reflector.
Tsai, Yi-Te; Zhu, Jinying; Haberman, Michael R
2013-04-01
A time domain analytical solution is presented to calculate the pressure response along the axis of a paraboloidal reflector for a normally incident plane wave. This work is inspired by Hamilton's axial solution for an ellipsoidal mirror and the same methodology is employed in this paper. Behavior of the reflected waves along reflector axis is studied, and special interest is placed on focusing gain obtained at the focal point. This analytical solution indicates that the focusing gain is affected by reflector geometry and the time derivative of the input signal. In addition, focused pressure response in the focal zone given by various reflector geometries and input frequencies are also investigated. This information is useful for selecting appropriate reflector geometry in a specific working environment to achieve the best signal enhancement. Numerical simulation employing the finite element method is used to validate the analytical solution, and visualize the wave field to provide a better understanding of the propagation of reflected waves. This analytical solution can be modified to apply to non-planar incident waves with axisymmetric wavefront and non-uniform pressure distribution. An example of incident waves with conical-shaped wavefront is presented.
Rossby wave radiation by an eddy on a beta-plane: Experiments with laboratory altimetry
Zhang, Y.; Afanasyev, Y. D.
2015-07-15
Results from the laboratory experiments on the evolution of vortices (eddies) generated in a rotating tank with topographic β-effect are presented. The focus of the experiments is on the far-field flow which contains Rossby waves emitted by travelling vortices. The surface elevation and velocity fields are measured by the altimetric imaging velocimetry. The experiments are supplemented by shallow water numerical simulations as well as a linear theory which describes the Rossby wave radiation by travelling vortices. The cyclonic vortices observed in the experiments travel to the northwest and continuously radiate Rossby waves. Measurements show that initially axisymmetric vortices develop a dipolar component which enables them to perform translational motion. A pattern of alternating zonal jets to the west of the vortex is created by Rossby waves with approximately zonal crests. Energy spectra of the flows in the wavenumber space indicate that a wavenumber similar to that introduced by Rhines for turbulent flows on the β-plane can be introduced here. The wavenumber is based on the translational speed of a vortex rather than on the root-mean-square velocity of a turbulent flow. The comparison between the experiments and numerical simulations demonstrates that evolving vortices also emit inertial waves. While these essentially three-dimensional non-hydrostatic waves can be observed in the altimetric data, they are not accounted for in the shallow water simulations.
Projection operators for the Rossby and Poincare waves in a beta-plane approximation
NASA Astrophysics Data System (ADS)
Lebedkina, Anastasia; Ivan, Karpov; Sergej, Leble
2013-04-01
. The idea to use the polarization relations for the classification of waves originated in radio physics in the works of A. A. Novikov. In the theory of the electromagnetic field polarization relations is traditionally included in the analysis of wave phenomena. In the theory of acoustic-gravity waves, projection operators were introduced in a works of S. B. Leble. The object of study is a four-dimentional vector (components of the velocity, pressure and temperature). Based on these assumptions, we can construct the projection operators for superposition state on the linear basis, corresponding to the well-known type of waves. In this paper we consider procedure for construction of a projection operators for planetary Rossby and Poincare waves in the Earth's atmosphere in the approximation of the "beta-plane". In a result of work we constructed projection operators in this approximation for Poincare and Rossby waves. The tests for operators shown, that separation of the contribution of corresponding waves from source of the wave field is possible. Estimation accuracy of the operators and results of applying operators to the data TEC presented.
NASA Technical Reports Server (NTRS)
Kuriyama, Masao; Steiner, Bruce; Dobbyn, Ronald C.; Laor, Uri; Larson, David; Brown, Margaret
1988-01-01
Streaking images restricted to the direction of the diffraction (scattering) vector have been observed on transmission through undoped GaAs. These disruption images (caused by the reduction of diffraction in the direction of observation) appear both in the forward and in Bragg diffracted directions in monochromatic synchrontron radiation diffraction imaging. This previously unobserved phenomenon can be explained in terms of planar defects (interfaces) or platelets which affects the absorption coefficient in anomalous transmission. Such regions of the crystal look perfect despite the presence of imperfections when the scattering vector is not perpendicular to the normal of the platelets. The observed crystallographic orientation of these interfaces strongly indicates that they are antiphase boundaries.
Plane Wave Electromagnetic Reflection and Transmission from a Thin Geologic Layer
NASA Astrophysics Data System (ADS)
Aldridge, D. F.; Weiss, C. J.
2016-12-01
In seismic reflection exploration, a thin geologic layer is defined as one with thickness less than about one-fourth wavelength of an incident plane wave. In this case, distinct reflection arrivals from top and bottom bed boundaries are difficult to recognize. Information regarding layer thickness and material properties is encoded in the amplitude of the composite (reflected and/or transmitted) response. Due to the significantly larger wavelength of an electromagnetic (EM) wave of identical frequency, virtually all geologic layers are considered extremely thin via this definition. This is especially true for a single hydraulic fracture ( 1 cm width) or even a fracture zone ( meters width). In this investigation, we restrict consideration to a normally-incident plane EM wave, and calculate reflection and transmission responses of a uniform-thickness layer embedded between two (possibly dissimilar) homogeneous and isotropic halfspaces. Exact frequency-domain expressions for electric vector E and magnetic vector B are obtained via two equivalent methodologies: 1) summing primaries and all intrabed multiples (the SEIS way), and 2) solving a boundary value problem by imposing wavefield continuity at interfaces (the EM way). Time-domain responses are obtained by inverse numerical Fourier transformation. We predict observable E and B responses, in both reflection and transmission, from layers that are several orders of magnitude smaller than the incident dominant wavelength. Large conductivity or permeability contrast enhances response amplitude, whereas permittivity contrast exerts negligible influence at low frequency. However, responses are relatively insensitive to fixed (parameter × thickness) product, a result that agrees with exact and First Born Approximation scattering theory. An obvious extension involves a non-normal incident plane wave, which offers the intriguing possibility of EM Amplitude vs. Offset (EMAVO) analysis.
The Effects Of Finite Electron Temperature And Diffraction On Lowere Hybrid Wave Propagation
White, J. C.; Bertelli, M.
2014-02-24
In this paper we show that the commonly used cold plasma dispersion relation for plasma waves in the lower hybrid range of frequencies (LHRF) produces a wave trajectory that is notably different than when thermal corrections to the Hermitian part of the dielectric tensor are retained. This is in contrast to the common implementation in LH simulation codes in which thermal effects are retained only for the anti-Hermitian part of the dielectric tensor used for damping calculations. We show which term is the critical one to retain in the dielectric tensor and discuss implications for modeling of LHRF waves in present day and future devices. We conclude with some observations on the effects of diffraction that may be isolated once thermal effects are retained in both ray tracing and full-wave approaches.
On plane-wave relativistic electrodynamics in plasmas and in vacuum
NASA Astrophysics Data System (ADS)
Fiore, Gaetano
2014-06-01
We revisit the exact microscopic equations (in differential, and equivalent integral form) ruling a relativistic cold plasma after the plane-wave Ansatz, without customary approximations. We show that in the Eulerian description the motion of a very diluted plasma initially at rest and excited by an arbitrary transverse plane electromagnetic travelling-wave has a very simple and explicit dependence on the transverse electromagnetic potential; for a non-zero density plasma the above motion is a good approximation of the real one as long as the back-reaction of the charges on the electromagnetic field can be neglected, i.e. for a time lapse decreasing with the plasma density, and can be used as initial step in an iterative resolution scheme. As one of many possible applications, we use these results to describe how the ponderomotive force of a very intense and short plane laser pulse hitting normally the surface of a plasma boosts the surface electrons into the ion background. In response to this penetration, the electrons are pulled back by the electric force exerted by the ions and the other displaced electrons and may leave the plasma with high energy in the direction opposite to that of propagation of the pulse ‘slingshot effect’ (Fiore G et al 2013 arXiv:1309.1400).
Observation of diffraction multifocal radiation focusing
Letfullin, R R; Zayakin, O A
2001-04-30
It is shown experimentally that by placing a flat screen with an axial hole in a diffraction field formed by the first open Fresnel zone upon diffraction of a plane electromagnetic wave from a parallel screen with a hole of a larger diameter, one can observe diffraction multifocal focusing of radiation in the near-field zone of the first screen. The diffraction pattern in the near-field zone of the first screen in focal planes represents circular nonlocalised Fresnel bands with a bright narrow peak at the centre, whose intensity is 6 - 10 greater than that of the incident wave. (nonlinear optical phenomena)
Deciphering Lower Mantle Structure With the Dispersion of Core-Diffracted Waves
NASA Astrophysics Data System (ADS)
Euler, G. G.; Wysession, M. E.; Aleqabi, G. I.; Shore, P. J.
2005-12-01
We investigate lateral variations of the D'' region beneath the West Coast of North America using the dispersion signatures of Pdiff and Sdiff waves originating from the Western Pacific Rim. Data come from large earthquakes recorded by over 50 3-component broadband seismic stations stretched across North America as part of seismic networks including the IRIS Global Seismograph Network, U.S. National Seismic Network, Canadian National Seismic Network, and the IRIS PASSCAL Florida-to-Edmonton Seismic Experiment. All data were obtained from the IRIS DMC, resampled at a constant sample rate (20 sps), converted to displacements, and had the instrument responses removed. When the seismic energy of core-diffracted waves occupies a wide frequency band, the structure at the base of the mantle is sampled differently by the energy at various frequencies. The higher-frequency waves stay closer to the core-mantle boundary, while the longer-frequency waves sample more of the lower mantle. This creates dispersion because of the differences in mantle velocities as a function of depth. Using dispersion slowness curves derived from diffracted body waves sampling the thermal and chemical boundary layer region at the base of the mantle, lateral structural variations can not only be resolved but also their nature may be inferred through comparison with synthetic seismic modeling. For this study, the determination of slownesses of incoming diffracted body waves at periods ranging from 150 to 5 seconds was facilitated by an iterative multiple cross-correlation algorithm. Typical results in our calculation of slownesses show r-squared correlations between arrival times and distances above 0.999. We find that dispersion overall causes the slowness to decrease with shorter periods (also found in the synthetic models) and that the dispersion curves we found for different paths resemble the dispersion curves from several different synthetic structural models of D'', thus quantifying the
Three-wave X-ray diffraction in distorted epitaxial structures.
Kyutt, Reginald; Scheglov, Mikhail
2013-08-01
Three-wave diffraction has been measured for a set of GaN, AlN, AlGaN and ZnO epitaxial layers grown on c-sapphire. A Renninger scan for the primary forbidden 0001 reflection was used. For each of the three-wave combinations, θ-scan curves were measured. The intensity and angular width of both ϕ- and θ-scan three-wave peaks were analyzed. The experimental data were used to determine properties of the multiple diffraction pattern in highly distorted layers. It is shown that the FWHM of θ scans is highly sensitive to the structural perfection and strongly depends on the type of three-wave combination. The narrowest peaks are observed for multiple combinations with the largest l index of the secondary hkl reflection. An influence of the type of the dislocation structure on the θ-scan broadening was revealed. These experimental facts are interpreted by considering the scanning geometry in the reciprocal space and taking into account the disc-shaped reciprocal-lattice points. The total integrated intensities of all the three-wave combinations were determined and their ratios were found to be in only a qualitative agreement with the theory. For AlGaN layers, the presence of the nonzero 0001 reflection was revealed, in contrast to AlN and GaN films.
NASA Astrophysics Data System (ADS)
Gao, Yuanmei; Wen, Zengrun; Zheng, Liren; Zhao, Lina
2017-04-01
A method has been proposed to generate complex periodic discrete non-diffracting beams (PDNBs) via superposition of two identical simple PDNBs at a particular angle. As for special cases, we studied the superposition of the two identical squares (;4+4;) and two hexagonal (;6+6;) periodic wave fields at specific angles, respectively, and obtained a series of interesting complex PDNBs. New PDNBs were also obtained by modulating the initial phase difference between adjacent interfering beams. In the experiment, a 4 f Fourier filter system and a phase-only spatial light modulator imprinting synthesis phase patterns of these PDNBs were used to produce desired wave fields.
MnO spin-wave dispersion curves from neutron powder diffraction
Goodwin, Andrew L.; Dove, Martin T.; Tucker, Matthew G.; Keen, David A.
2007-02-15
We describe a model-independent approach for the extraction of spin-wave dispersion curves from powder neutron total scattering data. Our approach is based on a statistical analysis of real-space spin configurations to calculate spin-dynamical quantities. The RMCPROFILE implementation of the reverse Monte Carlo refinement process is used to generate a large ensemble of supercell spin configurations from MnO powder diffraction data collected at 100 K. Our analysis of these configurations gives spin-wave dispersion curves for MnO that agree well with those determined independently using neutron triple-axis spectroscopic techniques.
A numerical study of shock wave diffraction by a circular cylinder
NASA Technical Reports Server (NTRS)
Yang, J.-Y.; Liu, Y.; Lomax, H.
1986-01-01
The nonstationary shock wave diffraction patterns generated by a blast wave impinging on a circular cylinder are numerically simulated using a second-order hybrid upwind method for solving the two-dimensional inviscid compressible Euler equations of gasdynamics. The complete diffraction patterns, including the transition from regular to Mach reflection, trajectory of the Mach triple point and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the cylinder are reported in detail. Pressure-time history and various contour plots are also included. Comparison between the work of Bryson and Gross (1961) which included both experimental schlieren pictures and theoretical calculations using Whitham's ray-shock theory and results of the present finite difference computation indicate good agreement in every aspect except for some nonideal gas and viscous effects which are not accounted for by the Euler equations.
A numerical study of shock wave diffraction by a circular cylinder
NASA Technical Reports Server (NTRS)
Yang, J.-Y.; Liu, Y.; Lomax, H.
1986-01-01
The nonstationary shock wave diffraction patterns generated by a blast wave impinging on a circular cylinder are numerically simulated using a second-order hybrid upwind method for solving the two-dimensional inviscid compressible Euler equations of gasdynamics. The complete diffraction patterns, including the transition from regular to Mach reflection, trajectory of the Mach triple point and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the cylinder are reported in detail. Pressure-time history and various contour plots are also included. Comparison between the work of Bryson and Gross (1961) which included both experimental schlieren pictures and theoretical calculations using Whitham's ray-shock theory and results of the present finite difference computation indicate good agreement in every aspect except for some nonideal gas and viscous effects which are not accounted for by the Euler equations.
Energy dispersive x-ray diffraction of charge density waves via chemical filtering
Feng Yejun; Somayazulu, M. S.; Jaramillo, R.; Rosenbaum, T.F.; Isaacs, E.D.; Hu Jingzhu; Mao Hokwang
2005-06-15
Pressure tuning of phase transitions is a powerful tool in condensed matter physics, permitting high-resolution studies while preserving fundamental symmetries. At the highest pressures, energy dispersive x-ray diffraction (EDXD) has been a critical method for geometrically confined diamond anvil cell experiments. We develop a chemical filter technique complementary to EDXD that permits the study of satellite peaks as weak as 10{sup -4} of the crystal Bragg diffraction. In particular, we map out the temperature dependence of the incommensurate charge density wave diffraction from single-crystal, elemental chromium. This technique provides the potential for future GPa pressure studies of many-body effects in a broad range of solid state systems.
Demonstration of 1Kx1K long-wave and mid-wave superlattice infrared focal plane arrays
NASA Astrophysics Data System (ADS)
Gunapala, S. D.; Ting, D. Z.; Hill, C. J.; Nguyen, J.; Soibel, A.; Rafol, S. B.; Keo, S. A.; Mumolo, J. M.; Lee, M. C.; Liu, J. K.; Yang, B.; Liao, A.
2010-09-01
Jet Propulsion Laboratory is actively developing the III-V based infrared detector and focal plane arrays (FPAs) for remote sensing and imaging applications. Currently, we are working on Superlattice detectors, multi-band Quantum Well Infrared Photodetectors (QWIPs), and Quantum Dot Infrared Photodetector (QDIPs) technologies suitable for high pixel-pixel uniformity and high pixel operability large area imaging arrays. In this paper, we will discuss the demonstration of long-wavelength 1Kx1K QDIP FPA, 1Kx1K QWIP FPA, the first demonstration of the megapixelsimultaneously- readable and pixel-co-registered dual-band QWIP FPA, and demonstration of the first mid-wave and long-wave 1Kx1K superlattice FPA. In addition, we will discuss the advantages of III-V material system in the context of large format infrared FPAs.
The radiation of sound by the instability waves of a compressible plane turbulent shear layer
NASA Technical Reports Server (NTRS)
Tam, C. K. W.; Morris, P. J.
1980-01-01
The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near- and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.
Hydrodynamic Simulation of Frontal Collision of Two Identical Plane Thermonuclear Burning Waves
NASA Astrophysics Data System (ADS)
Khishchenko, Konstantin V.; Charakhch'yan, Alexander A.
2013-10-01
A one-dimensional problem on synchronous bilateral action of two identical drivers on opposite surfaces of a plane layer of DT fuel with the normal or five times greater initial density is simulated numerically. The solution of the problem includes two thermonuclear burn waves propagating to collide with each other at the symmetry plane. A laser pulse with total absorption of energy at the critical density and a proton bunch that provides for a nearly isochoric heating are considered as drivers. A wide-range equation of state for the fuel, electron and ion heat conduction, self-radiation of plasma and plasma heating by α-particles are taken into account. In spite of different ways of ignition, various models of α-particle heat, whether the burning wave remains slow or transforms into the detonation wave, and regardless of way of such a transformation, the final value of the burn-up factor depends essentially on the only parameter Hρ0 , where H is the half-thickness of the layer and ρ0 is the initial fuel density. This factor is about 0.35 at Hρ0 ~ 1 g/cm2 and about 0.7 at Hρ0 ~ 5 g/cm2.
Simulation of guided wave interaction with in-plane fiber waviness
NASA Astrophysics Data System (ADS)
Leckey, Cara A. C.; Juarez, Peter D.
2017-02-01
Reducing the timeline for certification of composite materials and enabling the expanded use of advanced composite materials for aerospace applications are two primary goals of NASA's Advanced Composites Project (ACP). A key a technical challenge area for accomplishing these goals is the development of rapid composite inspection methods with improved defect characterization capabilities. Ongoing work at NASA Langley is focused on expanding ultrasonic simulation capabilities for composite materials. Simulation tools can be used to guide the development of optimal inspection methods. Custom code based on elastodynamic finite integration technique is currently being developed and implemented to study ultrasonic wave interaction with manufacturing defects, such as in-plane fiber waviness (marcelling). This paper describes details of validation comparisons performed to enable simulation of guided wave propagation in composites containing fiber waviness. Simulation results for guided wave interaction with in-plane fiber waviness are also discussed. The results show that the wavefield is affected by the presence of waviness on both the surface containing fiber waviness, as well as the opposite surface to the location of waviness.
Simulation of Guided Wave Interaction with In-Plane Fiber Waviness
NASA Technical Reports Server (NTRS)
Leckey, Cara A. C.; Juarez, Peter D.
2016-01-01
Reducing the timeline for certification of composite materials and enabling the expanded use of advanced composite materials for aerospace applications are two primary goals of NASA's Advanced Composites Project (ACP). A key a technical challenge area for accomplishing these goals is the development of rapid composite inspection methods with improved defect characterization capabilities. Ongoing work at NASA Langley is focused on expanding ultrasonic simulation capabilities for composite materials. Simulation tools can be used to guide the development of optimal inspection methods. Custom code based on elastodynamic finite integration technique is currently being developed and implemented to study ultrasonic wave interaction with manufacturing defects, such as in-plane fiber waviness (marcelling). This paper describes details of validation comparisons performed to enable simulation of guided wave propagation in composites containing fiber waviness. Simulation results for guided wave interaction with in-plane fiber waviness are also discussed. The results show that the wavefield is affected by the presence of waviness on both the surface containing fiber waviness, as well as the opposite surface to the location of waviness.
Trail-Needs pseudopotentials in quantum Monte Carlo calculations with plane-wave/blip basis sets
NASA Astrophysics Data System (ADS)
Drummond, N. D.; Trail, J. R.; Needs, R. J.
2016-10-01
We report a systematic analysis of the performance of a widely used set of Dirac-Fock pseudopotentials for quantum Monte Carlo (QMC) calculations. We study each atom in the periodic table from hydrogen (Z =1 ) to mercury (Z =80 ), with the exception of the 4 f elements (57 ≤Z ≤70 ). We demonstrate that ghost states are a potentially serious problem when plane-wave basis sets are used in density functional theory (DFT) orbital-generation calculations, but that this problem can be almost entirely eliminated by choosing the s channel to be local in the DFT calculation; the d channel can then be chosen to be local in subsequent QMC calculations, which generally leads to more accurate results. We investigate the achievable energy variance per electron with different levels of trial wave function and we determine appropriate plane-wave cutoff energies for DFT calculations for each pseudopotential. We demonstrate that the so-called "T-move" scheme in diffusion Monte Carlo is essential for many elements. We investigate the optimal choice of spherical integration rule for pseudopotential projectors in QMC calculations. The information reported here will prove crucial in the planning and execution of QMC projects involving beyond-first-row elements.
Lamb waves in phononic crystal slabs: truncated plane parallels to the axis of periodicity.
Chen, Jiujiu; Xia, Yunjia; Han, Xu; Zhang, Hongbo
2012-09-01
A theoretical study is presented on the propagation properties of Lamb wave modes in phononic crystal slabs consisting of a row or more of parallel square cylinders placed periodically in the host material. The surfaces of the slabs are parallel to the axis of periodicity. The dispersion curves of Lamb wave modes are calculated based on the supercell method. The finite element method is employed to calculate the band structures and the transmission power spectra, which are in good agreement with the results by the supercell method. We also have found that the dispersion curves of Lamb waves are strongly dependent on the crystal termination, which is the position of the cut plane through the square cylinders. There exist complete or incomplete (truncated) layers of square cylinders with the change of the crystal termination. The influence of the crystal termination on the band gaps of Lamb wave modes is analyzed by numerical simulations. The variation of the crystal termination leads to obvious changes in the dispersion curves of the Lamb waves and the widths of the band gaps. Copyright © 2012 Elsevier B.V. All rights reserved.
Inertial effects on thin-film wave structures with imposed surface shear on an inclined plane
NASA Astrophysics Data System (ADS)
Sivapuratharasu, M.; Hibberd, S.; Hubbard, M. E.; Power, H.
2016-06-01
This study provides an extended approach to the mathematical simulation of thin-film flow on a flat inclined plane relevant to flows subject to high surface shear. Motivated by modelling thin-film structures within an industrial context, wave structures are investigated for flows with moderate inertial effects and small film depth aspect ratio ε. Approximations are made assuming a Reynolds number, Re ∼ O(ε-1) and depth-averaging used to simplify the governing Navier-Stokes equations. A parallel Stokes flow is expected in the absence of any wave disturbance and a generalisation for the flow is based on a local quadratic profile. This approach provides a more general system which includes inertial effects and is solved numerically. Flow structures are compared with studies for Stokes flow in the limit of negligible inertial effects. Both two-tier and three-tier wave disturbances are used to study film profile evolution. A parametric study is provided for wave disturbances with increasing film Reynolds number. An evaluation of standing wave and transient film profiles is undertaken and identifies new profiles not previously predicted when inertial effects are neglected.
Stamnes, J J; Sithambaranathan, G S
2001-12-01
Exact solutions are obtained for the reflected and transmitted fields resulting when an arbitrary electromagnetic field is incident on a plane interface separating an isotropic medium and a biaxially anisotropic medium in which one of the principal axes is along the interface normal. From our exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component. This gives a change in polarization that can be utilized to determine the properties of the biaxial medium. The time-harmonic solution for the reflected field is in the form of two quadruple integrals, one of which is a superposition of plane waves polarized perpendicular to the plane of incidence and the other a superposition of plane waves polarized parallel to the plane of incidence. The time-harmonic solution for the transmitted field is also in the form of two quadruple integrals. Each of these is a superposition of extraordinary plane waves with displacement vectors that are perpendicular to the direction of phase propagation.
Aircraft noise propagation. [sound diffraction by wings
NASA Technical Reports Server (NTRS)
Hadden, W. J.; Pierce, A. D.
1978-01-01
Sound diffraction experiments conducted at NASA Langley Research Center to study the acoustical implications of the engine over wing configuration (noise-shielding by wing) and to provide a data base for assessing various theoretical approaches to the problem of aircraft noise reduction are described. Topics explored include the theory of sound diffraction around screens and wedges; the scattering of spherical waves by rectangular patches; plane wave diffraction by a wedge with finite impedence; and the effects of ambient flow and distribution sources.
Ding, Chaoliang; Cai, Yangjian; Zhang, Yongtao; Pan, Liuzhan
2012-06-01
The scattering of a stochastic electromagnetic plane-wave pulse on a deterministic spherical medium is investigated. An analytical formula for the degree of polarization (DOP) of the scattered field in the far zone is derived. Letting pulse duration T(0) → ∞, our formula can be applied to study the scattering of a stationary stochastic electromagnetic light wave. Numerical results show that the DOP of the far zone field is closely determined by the size of the spherical medium when the incident field is a stochastic electromagnetic plane-wave pulse. This is much different from the case when the incident field is a stationary stochastic electromagnetic light wave, where the DOP of the far zone field is independent of the size of the medium. One may obtain the information of the spherical medium by measuring the scattering-induced changes in the DOP of a stochastic electromagnetic plane-wave pulse.
Diffraction and Dissipation of Atmospheric Waves in the Vicinity of Caustics
NASA Astrophysics Data System (ADS)
Godin, O. A.
2015-12-01
A large and increasing number of ground-based and satellite-borne instruments has been demonstrated to reliably reveal ionospheric manifestations of natural hazards such as large earthquakes, strong tsunamis, and powerful tornadoes. To transition from detection of ionospheric manifestations of natural hazards to characterization of the hazards for the purposes of improving early warning systems and contributing to disaster recovery, it is necessary to relate quantitatively characteristics of the observed ionospheric disturbances and the underlying natural hazard and, in particular, accurately model propagation of atmospheric waves from the ground or ocean surface to the ionosphere. The ray theory has been used extensively to model propagation of atmospheric waves and proved to be very efficient in elucidating the effects of atmospheric variability on ionospheric signatures of natural hazards. However, the ray theory predicts unphysical, divergent values of the wave amplitude and needs to be modified in the vicinity of caustics. This paper presents an asymptotic theory that describes diffraction, focusing and increased dissipation of acoustic-gravity waves in the vicinity of caustics and turning points. Air temperature, viscosity, thermal conductivity, and wind velocity are assumed to vary gradually with height and horizontal coordinates, and slowness of these variations determines the large parameter of the problem. Uniform asymptotics of the wave field are expressed in terms of Airy functions and their derivatives. The geometrical, or Berry, phase, which arises in the consistent WKB approximation for acoustic-gravity waves, plays an important role in the caustic asymptotics. In addition to the wave field in the vicinity of the caustic, these asymptotics describe wave reflection from the caustic and the evanescent wave field beyond the caustic. The evanescent wave field is found to play an important role in ionospheric manifestations of tsunamis.
NASA Technical Reports Server (NTRS)
Pathak, P. H.; Kouyoumjian, R. G.
1974-01-01
The diffraction of a TM sub o surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation, the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained by a combination of the generalized scattering matrix technique and function theoretic methods.
Exact soliton-on-plane-wave solutions for two-component Bose-Einstein condensates.
Li, Lu; Malomed, Boris A; Mihalache, Dumitru; Liu, W M
2006-06-01
By means of the Darboux transformation, we obtain analytical solutions for a soliton set on top of a plane-wave background in coupled Gross-Pitaevskii equations describing a binary Bose-Einstein condensate. We consider basic properties of the solutions with and without the cross interaction [cross phase modulation (XPM)] between the two components of the background. In the absence of the XPM, this solutions maintain properties of one-component condensates, such as the modulation instability (MI); in the presence of the cross interaction, the solutions exhibit different properties, such as restriction of the MI and soliton splitting.
Exact soliton-on-plane-wave solutions for two-component Bose-Einstein condensates
Li Lu; Malomed, Boris A.; Mihalache, Dumitru; Liu, W. M.
2006-06-15
By means of the Darboux transformation, we obtain analytical solutions for a soliton set on top of a plane-wave background in coupled Gross-Pitaevskii equations describing a binary Bose-Einstein condensate. We consider basic properties of the solutions with and without the cross interaction [cross phase modulation (XPM)] between the two components of the background. In the absence of the XPM, this solutions maintain properties of one-component condensates, such as the modulation instability (MI); in the presence of the cross interaction, the solutions exhibit different properties, such as restriction of the MI and soliton splitting.
Dynamic soil-tunnel interaction in layered half-space for incident plane SH waves
NASA Astrophysics Data System (ADS)
Fu, Jia; Liang, Jianwen; Qin, Lin
2016-12-01
The dynamic soil-tunnel interaction is studied by indirect boundary element method (IBEM), using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.
Electromagnetic plane-wave pulse transmission into a Lorentz half-space.
Cartwright, Natalie A
2011-12-01
The propagation of an electromagnetic plane-wave signal obliquely incident upon a Lorentz half-space is studied analytically. Time-domain asymptotic expressions that increase in accuracy with propagation distance are derived by application of uniform saddle point methods on the Fourier-Laplace integral representation of the transmitted field. The results are shown to be continuous in time and comparable with numerical calculations of the field. Arrival times and angles of refraction are given for prominent transient pulse features and the steady-state signal.
String interactions in a plane-fronted parallel-wave spacetime.
Gopakumar, Rajesh
2002-10-21
We argue that string interactions in a plane-fronted parallel-wave spacetime are governed by an effective coupling g(eff)=g(s)(micro p(+)alpha('))f(micro p(+)alpha(')) where f(microp(+)alpha(')) is proportional to the light-cone energy of the string states involved in the interaction. This simply follows from generalities of a matrix string description of this background. g(eff) nicely interpolates between the expected result (g(s)) for flat space (small micro p(+)alpha(')) and a recently conjectured expression from the perturbative gauge theory side (large micro p(+)alpha(')).
Viscous effects on the attenuation of a plane wave by an acoustic lining in shear flow.
Khamis, Doran; Brambley, Edward James
2017-04-01
The attenuation of a plane acoustic wave incident on a flat impedance surface in a sheared and viscous fluid is investigated numerically and asymptotically. Predictions of various boundary models of impedance surfaces in shear flow are tested by comparing their predicted reflection coefficient. It is found that viscosity has a significant effect, reducing the reflection of upstream propagating sound while increasing the reflection of cross-stream propagating sound. The classical Ingard-Myers boundary condition is shown to incorrectly predict the damping rate of sound in many cases, and in some cases viscous effects are shown to be comparable to shear effects.
Yang, Chao
2009-07-17
We present a practical approach to calculate the complex band structure of an electrode for quantum transport calculations. This method is designed for plane wave based Hamiltonian with nonlocal pseudopotentials and the auxiliary periodic boundary condition transport calculation approach. Currently there is no direct method to calculate all the evanescent states for a given energy for systems with nonlocal pseudopotentials. On the other hand, in the auxiliary periodic boundary condition transport calculation, there is no need for all the evanescent states at a given energy. The current method fills this niche. The method has been used to study copper and gold nanowires and bulk electrodes.
On the scattering of an acoustic plane wave by a soft prolate spheroid
NASA Astrophysics Data System (ADS)
Borromeo, Joseph Michael
This thesis solves the scattering problem in which an acoustic plane wave of propagation number K1 is scattered by a soft prolate spheroid. The interior field of the scatterer is characterized by a propagation number K2, while the field radiated by the scatterer is characterized by the propagation number K3. The three fields and their normal derivatives satisfy boundary conditions at the surface of the scatterer. These boundary conditions involve six complex parameters depending on the propagation numbers. The scattered wave also satisfies the Sommerfeld radiation condition at infinity. Through analytical methods, series representations are constructed for the interior field and scattered field for an arbitrary sphere and a prolate spheroid. In addition, results for the reciprocity relations and Energy theorem are derived. Application to detection of whales and submarines are discussed, as well as classification of fish, squid and zoo plankton. In general Ref[ ] is used for reference and the work is done in three dimensions.
NASA Astrophysics Data System (ADS)
Theobald, Dominik; Egel, Amos; Gomard, Guillaume; Lemmer, Uli
2017-09-01
The computation of light scattering by the superposition T -matrix scheme has been restricted thus far to systems made of particles that are either sparsely distributed or of near-spherical shape. In this work, we extend the range of applicability of the T -matrix method by accounting for the coupling of scattered fields between highly nonspherical particles in close vicinity. This is achieved using an alternative formulation of the translation operator for spherical vector wave functions, based on a plane-wave expansion of the particle's scattered electromagnetic field. The accuracy and versatility of the present approach is demonstrated by simulating arbitrarily oriented and densely packed spheroids, for both dielectric and metallic particles.
PARTICLE DISPLACEMENTS ON THE WALL OF A BOREHOLE FROM INCIDENT PLANE WAVES.
Lee, M.W.
1987-01-01
Particle displacements from incident plane waves at the wall of a fluid-filled borehole are formulated by applying the seismic reciprocity theorem to far-field displacement fields. Such displacement fields are due to point forces acting on a fluid-filled borehole under the assumption of long wavelengths. The displacement fields are analyzed to examine the effect of the borehole on seismic wave propagation, particularly for vertical seismic profiling (VSP) measurements. When the shortest wavelength of interest is approximately 25 times longer than the borehole's diameter, the scattered displacements are proportional to the first power of incident frequency and borehole diameter. When the shortest wavelength of interest is about 40 times longer than the borehole's diameter, borehole effects on VSP measurements using a wall-locking geophone are negligible.
The scattering of obliquely incident plane waves from a corrugated conducting surface
NASA Technical Reports Server (NTRS)
Le Vine, D. M.
1976-01-01
A physical optics solution is presented for the scattering of plane waves from a perfectly conducting corrugated surface in the case of waves incident from an arbitrary direction and for an observer far from the surface. This solution is used to compute the radar cross section of the surface in the case of backscatter from irregular (i.e., stochastic) corrugations. An interesting feature of the solution is the occurrence of singularities in the scattered fields. These singularities appear to be a manifestation of focusing by the surface at its 'stationary' points. Whether or not the singularities occur in the solution depends on the manner in which one restricts the analysis to the far-field.
An efficient algorithm for time propagation as applied to linearized augmented plane wave method
NASA Astrophysics Data System (ADS)
Dewhurst, J. K.; Krieger, K.; Sharma, S.; Gross, E. K. U.
2016-12-01
An algorithm for time propagation of the time-dependent Kohn-Sham equations is presented. The algorithm is based on dividing the Hamiltonian into small time steps and assuming that it is constant over these steps. This allows for the time-propagating Kohn-Sham wave function to be expanded in the instantaneous eigenstates of the Hamiltonian. The method is particularly efficient for basis sets which allow for a full diagonalization of the Hamiltonian matrix. One such basis is the linearized augmented plane waves. In this case we find it is sufficient to perform the evolution as a second-variational step alone, so long as sufficient number of first variational states are used. The algorithm is tested not just for non-magnetic but also for fully non-collinear magnetic systems. We show that even for delicate properties, like the magnetization density, fairly large time-step sizes can be used demonstrating the stability and efficiency of the algorithm.
Lytle, R. Jeffrey; Lager, Darrel L.; Laine, Edwin F.; Davis, Donald T.
1979-01-01
Underground anomalies or discontinuities, such as holes, tunnels, and caverns, are located by lowering an electromagnetic signal transmitting antenna down one borehole and a receiving antenna down another, the ground to be surveyed for anomalies being situated between the boreholes. Electronic transmitting and receiving equipment associated with the antennas is activated and the antennas are lowered in unison at the same rate down their respective boreholes a plurality of times, each time with the receiving antenna at a different level with respect to the transmitting antenna. The transmitted electromagnetic waves diffract at each edge of an anomaly. This causes minimal signal reception at the receiving antenna. Triangulation of the straight lines between the antennas for the depths at which the signal minimums are detected precisely locates the anomaly. Alternatively, phase shifts of the transmitted waves may be detected to locate an anomaly, the phase shift being distinctive for the waves directed at the anomaly.
Non-diffraction propagation of acoustic waves in a rapidly modulated stratified medium.
Zhu, Xing-Feng; Wei, Qi; Cheng, Ying; Wu, Da-Jian; Liu, Xiao-Jun
2017-08-15
A rapidly modulated stratified medium with a large mass density modulation depth (LMMD) is proposed to achieve non-diffraction propagation (NDP) of acoustic waves. It is found that the NDP in LMMD medium is independent of the incident angle and can be operated in a broad-band manner. Such an NDP is robust and is unhampered by medium losses. An effective medium theory (EMT) is developed for acoustic waves propagating in the LMMD medium based on the first-principles method. The LMMD EMT is verified by using the transfer-matrix method (TMM) for both propagating and evanescent waves. Furthermore, we discuss the influence of the geometry on NDP, and finite element simulations are conducted to verify the NDP in the LMMD medium.
Exploring Earth's Lowermost Mantle With Core-Diffracted Waves From Linear Arrays
NASA Astrophysics Data System (ADS)
Wysession, M. E.; Euler, G. G.; Fischer, K. M.
2008-12-01
We investigate lowermost mantle structure using the slowness and decay-rate frequency dependence of core diffracted waves from large earthquakes (mb>5.5) recorded by two broadband seismometer arrays, MOMA and FLED, to provide insights on processes occurring at the base of the mantle. MOMA (Missouri to Massachusetts) and FLED (Florida to Edmonton) were linear transects deployed in 1995-96 and 2001-02, respectively, with the common goal of obtaining seismic images of the Earth's deep interior. Exploiting core diffracted wave observables with the geometry of these arrays aids in establishing strong constraints on the radial velocity structure above the core-mantle interface in a manner analogous to surface wave observables constraining uppermost mantle structure. To estimate the frequency dependence of the slowness and decay rate caused by the diffraction process, we measure the relative arrival time and amplitude of both Pdiff and Sdiff arrivals for a series of frequency bands between 0.017 and 0.17 Hz and make corrections for bias introduced by ellipticity and velocity structure above the lowermost mantle. We present a new semi- automated technique using cluster analysis to remove low-quality waveforms and to accurately determine the slowness values. Comparison with 1D reflectivity and 3D SEM synthetics facilitates quantitative interpretation. Preliminary results confirm that there is measurable frequency dependence in the slowness and decay rate caused by diffraction for both Pdiff and Sdiff, indicative of significant radial velocity gradients. Variations in the frequency dependence are also observed with both geographic location and between Pdiff and Sdiff along the same azimuth suggesting lateral changes in Vp, Vs and Vp/Vs ratio and thus the physical state at the lowermost mantle.
Behavior of plane waves propagating through a temperature-inhomogeneous region
NASA Astrophysics Data System (ADS)
Bednarik, M.; Cervenka, M.; Lotton, P.; Penelet, G.
2016-02-01
Description and analysis of acoustic waves in ducts with a region containing temperature-inhomogeneous fluid represent a significant problem of scientific and practical interest. This interest is induced by the need of understanding how temperature fields affect acoustic processes which would lead to a more efficient design and control of systems involving thermoacoustic interactions. Most of the works addressing these problems limit themselves to the assumption of weak temperature profile gradients or to temperature profiles which do not connect neighboring temperature-homogeneous regions smoothly. In our work we investigate the behavior of plane acoustic waves that enter a region with an arbitrary temperature gradient. A polynomial character of the used temperature profile ensures smooth connection with constant-temperature regions. The one-dimensional wave equation for ducts with an axial mean temperature gradient is solved analytically. The derived solutions based on Heun functions extend the class of published exact analytical solutions of model wave equations taking into account the medium temperature gradient. Due to the property that our proposed polynomial temperature function has derivatives equal to zero at points which are connected with the surrounding temperature-homogeneous regions we can form more complex smooth temperature profiles for which it is possible to use the transfer matrix method.
Full waveform inversion of marine reflection data in the plane-wave domain
Minkoff, S.E.; Symes, W.W.
1997-03-01
Full waveform inversion of a p-{tau} marine data set from the Gulf of Mexico provides estimates of the long-wavelength P-wave background velocity, anisotropic seismic source, and three high-frequency elastic parameter reflectivities that explain 70% of the total seismic data and 90% of the data in an interval around the gas sand target. The forward simulator is based on a plane-wave viscoelastic model for P-wave propagation and primary reflections in a layered earth. Differential semblance optimization, a variant of output least-squares inversion, successfully estimates the nonlinear P-wave background velocity and linear reflectivities. Once an accurate velocity is estimated, output least-squares inversion reestimates the reflectivities and an anisotropic seismic source simultaneously. The viscoelastic model predicts the amplitude-versus-angle trend in the data more accurately than does an elastic model. Simultaneous inversion for reflectivities and source explains substantially more of the actual data than does inversion for reflectivities with fixed source from an air-gun modeler. The best reflectivity estimates conform to widely accepted lithologic relationships and closely match the filtered well logs.
Nonlinear Wave Radiation and Diffraction by a Near-Surface Body
NASA Astrophysics Data System (ADS)
Ananthakrishnan, P.
1997-11-01
Physics of surface-wave and rigid-body interactions is of importance in naval architecture, in that a good understanding of wave-body interactions is necessary for the design of hulls with minimum ship-motion and resistance characteristics. Particular topics of contemporary research such as generation of spray and breaking waves by a surface ship and control of ship motion in high seas are however highly nonlinear, rendering analysis a challenging task. Using a robust numerical algorithm developed for analyzing fully nonlinear free-surface flow in a viscous fluid (see P. Ananthakrishnan, Three-dimensional wave-body interactions in a viscous fluid, Proc. of ISOPE'97 Conference, Hawaii), we have investigated diffraction and radiation of waves by floating and submerged rigid bodies. In the numerical model, the Navier-Stokes equations subject to exact free-surface and body boundary conditions are solved in primitive variables using a fractional-step finite-difference method which is implemented using curvilinear coordinates. Approximate conditions are however used to model the open boundary and the movement of the contact line. Results presented shed light to a better understanding of generation and ensuing spatial-temporal evolution of vortices under the influence of a free surface, vortical and potential components of hydrodynamics forces, symmetry-breaking in the case of large-amplitude oscillations, generation and damping of super-harmonic waves, and parameter ranges in which effect of viscosity is significant.
Ground-coupled air waves and diffracted infrasounds from the Arequipa earthquake of June 23, 2001
NASA Astrophysics Data System (ADS)
Lepichon, A.; Guilbert, J.; Van de Walle, M.
2001-12-01
On June 23, 2001, a strong earthquake measuring Ms 8.2 occurred along the coast of south-central Peru. This event was detected by the IS08 infrasound station of Bolivia operating for the CTBTO(Comprehensive Test Ban Treaty Organization). Coherent infrasonic waves have been detected over a period of one hour. In the first part of the signals, the analysis of the seismic coupled-air waves shows clearly that the rupture propagates from the northwertern to the southeastern part of the fault. The Doppler effect allows us to fixe the velocity of the rupture equal to 3.4 +/- 0.5 km.s-1. In the second part of the signals, the azimuth variation is interpreted as a distribution of secondary sources along the highest mountain ranges generating distant air-coupled waves in the atmosphere. The predominant source mechanism of the earthquake and two main aftershocks is likely diffracted pressure waves radiated along the Eastern Andean Cordillera from the southwest of the station to the coastline near Pamana. From the wave azimuth and arrival time determination, the horizontal scale size of the distant source regions remote from the epicenters is reconstructed over distances greater than 400 km. The generation of pressure waves associated with offshore source regions is also considered.
NASA Astrophysics Data System (ADS)
Stotts, S. A.; Knobles, D. P.; Koch, R. A.; Grant, D. E.; Focke, K. C.; Cook, A. J.
2004-03-01
A new, efficient, versatile ray-based model is presented that performs geoacoustic inversions in range-dependent ocean waveguides faster than alternative forward models for which the computation time becomes extremely long, especially for broadband inversions. The water propagation is approximately separated from the seabed interaction using predetermined bathymetry and a possibly range-dependent water sound speed profile. The geometrical optics approximation is used to calculate eigenrays between sources and receivers, including bottom reflecting paths. Modeled broadband pressure fields are obtained by computing the plane wave reflection coefficient at specific angles and frequencies and by then linking this result with the bottom reflected eigenrays. Each perturbation of the seabed requires a recalculation of the plane wave reflection coefficient, but not a recalculation of the eigenrays, resulting in a highly efficient method. Range-independent problems are treated as a limiting case of the approach. The method is first described and then demonstrated with a few simple range-independent theoretical models. The versatility of addressing range-dependence in the bottom seabed is demonstrated with a simulated data set. Finally, the new model is applied to inversion from a measured data set, taken with impulsive sources, for both range-independent and range-dependent continental shelf environments.
Scaling of plane-wave functions in statistically optimized near-field acoustic holography.
Hald, Jørgen
2014-11-01
Statistically Optimized Near-field Acoustic Holography (SONAH) is a Patch Holography method, meaning that it can be applied in cases where the measurement area covers only part of the source surface. The method performs projections directly in the spatial domain, avoiding the use of spatial discrete Fourier transforms and the associated errors. First, an inverse problem is solved using regularization. For each calculation point a multiplication must then be performed with two transfer vectors--one to get the sound pressure and the other to get the particle velocity. Considering SONAH based on sound pressure measurements, existing derivations consider only pressure reconstruction when setting up the inverse problem, so the evanescent wave amplification associated with the calculation of particle velocity is not taken into account in the regularized solution of the inverse problem. The present paper introduces a scaling of the applied plane wave functions that takes the amplification into account, and it is shown that the previously published virtual source-plane retraction has almost the same effect. The effectiveness of the different solutions is verified through a set of simulated measurements.
Iterative diagonalization in augmented plane wave based methods in electronic structure calculations
Blaha, P.; Laskowski, R.; Schwarz, K.
2010-01-20
Due to the increased computer power and advanced algorithms, quantum mechanical calculations based on Density Functional Theory are more and more widely used to solve real materials science problems. In this context large nonlinear generalized eigenvalue problems must be solved repeatedly to calculate the electronic ground state of a solid or molecule. Due to the nonlinear nature of this problem, an iterative solution of the eigenvalue problem can be more efficient provided it does not disturb the convergence of the self-consistent-field problem. The blocked Davidson method is one of the widely used and efficient schemes for that purpose, but its performance depends critically on the preconditioning, i.e. the procedure to improve the search space for an accurate solution. For more diagonally dominated problems, which appear typically for plane wave based pseudopotential calculations, the inverse of the diagonal of (H - ES) is used. However, for the more efficient 'augmented plane wave + local-orbitals' basis set this preconditioning is not sufficient due to large off-diagonal terms caused by the local orbitals. We propose a new preconditioner based on the inverse of (H - {lambda}S) and demonstrate its efficiency for real applications using both, a sequential and a parallel implementation of this algorithm into our WIEN2k code.
Plane Wave Imaging for ultrasonic non-destructive testing: Generalization to multimodal imaging.
Le Jeune, Léonard; Robert, Sébastien; Lopez Villaverde, Eduardo; Prada, Claire
2016-01-01
This paper describes a new ultrasonic array imaging method for Non-Destructive Testing (NDT) which is derived from the medical Plane Wave Imaging (PWI) technique. The objective is to perform fast ultrasound imaging with high image quality. The approach is to transmit plane waves at several angles and to record the back-scattered signals with all the array elements. Focusing in receive is then achieved by coherent summations of the signals in every point of a region of interest. The medical PWI is generalized to immersion setups where water acts as a coupling medium and to multimodal (direct, half-skip modes) imaging in order to detect different types of defects (inclusions, porosities, cracks). This method is compared to the Total Focusing Method (TFM) which is the reference imaging technique in NDT. First, the two post-processing algorithms are described. Then experimental results with the array probe either in contact or in immersion are presented. A good agreement between the TFM and the PWI is observed, with three to ten times less transmissions required for the PWI. Copyright © 2015 Elsevier B.V. All rights reserved.
Implementation of linear-scaling plane wave density functional theory on parallel computers
NASA Astrophysics Data System (ADS)
Skylaris, Chris-Kriton; Haynes, Peter D.; Mostofi, Arash A.; Payne, Mike C.
We describe the algorithms we have developed for linear-scaling plane wave density functional calculations on parallel computers as implemented in the onetep program. We outline how onetep achieves plane wave accuracy with a computational cost which increases only linearly with the number of atoms by optimising directly the single-particle density matrix expressed in a psinc basis set. We describe in detail the novel algorithms we have developed for computing with the psinc basis set the quantities needed in the evaluation and optimisation of the total energy within our approach. For our parallel computations we use the general Message Passing Interface (MPI) library of subroutines to exchange data between processors. Accordingly, we have developed efficient schemes for distributing data and computational load to processors in a balanced manner. We describe these schemes in detail and in relation to our algorithms for computations with a psinc basis. Results of tests on different materials show that onetep is an efficient parallel code that should be able to take advantage of a wide range of parallel computer architectures.
Whole body exposure at 2100 MHz induced by plane wave of random incidences in a population
NASA Astrophysics Data System (ADS)
Conil, Emmanuelle; Hadjem, Abdelhamid; El Habachi, Aimad; Wiart, J.
2010-11-01
In this article, the whole body exposure induced by plane wave coming from a random direction of arrival is analyzed at 2100 MHz. This work completes previous studies on the influence of different parameters on the whole body exposure (such as morphology, frequency or usage in near field). The Visible Human phantom has been used to build a surrogate model to predict the whole body exposure depending on the highlighted surface of the phantom and on the direction of arrival of the incident plane wave. For the Visible Human, the error on the whole body averaged Specific Absorption Rate (SAR) is on average 4%. The surrogate model is applied to other 3D anthropomorphic phantoms for a frontal incidence with an averaged error of 10%. The great interest of the surrogate model is the possibility to apply a Monte Carlo process to assess probability distribution function of a population. A recent French anthropometric database of more than 3500 adults is used to build the probability distribution function of the whole body SAR for a random direction of arrival.
Scaled plane-wave Born cross sections for atoms and molecules
NASA Astrophysics Data System (ADS)
Tanaka, H.; Brunger, M. J.; Campbell, L.; Kato, H.; Hoshino, M.; Rau, A. R. P.
2016-04-01
Integral cross sections for optically allowed electronic-state excitations of atoms and molecules by electron impact, by applying scaled plane-wave Born models, are reviewed. Over 40 years ago, Inokuti presented an influential review of charged-particle scattering, based on the theory pioneered by Bethe forty years earlier, which emphasized the importance of reliable cross-section data from low eV energies to high keV energies that are needed in many areas of radiation science with applications to astronomy, plasmas, and medicine. Yet, with a couple of possible exceptions, most computational methods in electron-atom scattering do not, in general, overlap each other's validity range in the region from threshold up to 300 eV and, in particular, in the intermediate region from 30 to 300 eV. This is even more so for electron-molecule scattering. In fact this entire energy range is of great importance and, to bridge the gap between the two regions of low and high energy, scaled plane-wave Born models were developed to provide reliable, comprehensive, and absolute integral cross sections, first for ionization by Kim and Rudd and then extended to optically allowed electronic-state excitation by Kim. These and other scaling models in a broad, general application to electron scattering from atoms and molecules, their theoretical basis, and their results for cross sections along with comparison to experimental measurements are reviewed. Where possible, these data are also compared to results from other computational approaches.
Optimization of exit-plane waves restored from HRTEM through-focal series.
Erni, Rolf; Rossell, Marta D; Nakashima, Philip N H
2010-01-01
Atomic-resolution transmission electron microscopy has largely benefited from the implementation of aberration correctors in the imaging part of the microscope. Though the dominant geometrical axial aberrations can in principle be corrected or suitably adjusted, the impact of higher-order aberrations, which are mainly due to the implementation of non-round electron optical elements, on the imaging process remains unclear. Based on a semi-empirical criterion, we analyze the impact of residual aperture aberrations on the quality of exit-plane waves that are retrieved from through-focal series recorded using an aberration-corrected and monochromated instrument which was operated at 300kV and enabled for an information transfer of approximately 0.05nm. We show that the impact of some of the higher-order aberrations in retrieved exit-plane waves can be balanced by a suitable adjustment of symmetry equivalent lower-order aberrations. We find that proper compensation and correction of 1st and 2nd order aberrations is critical, and that the required accuracy is difficult to achieve. This results in an apparent insensitivity towards residual higher-order aberrations. We also investigate the influence of the detector characteristics on the image contrast. We find that correction for the modulation transfer function results in a contrast gain of up to 40%.
Fast solution of elliptic partial differential equations using linear combinations of plane waves
NASA Astrophysics Data System (ADS)
Pérez-Jordá, José M.
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations A x =b , where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O (N logN ) memory and executing an iteration in O (N log2N ) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.
Fast solution of elliptic partial differential equations using linear combinations of plane waves.
Pérez-Jordá, José M
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.
Concepts and Tradeoffs in Velocity Estimation With Plane-Wave Contrast-Enhanced Doppler.
Tremblay-Darveau, Charles; Williams, Ross; Sheeran, Paul S; Milot, Laurent; Bruce, Matthew; Burns, Peter N
2016-11-01
While long Doppler ensembles are, in principle, beneficial for velocity estimates, short acoustic pulses must be used in microbubble contrast-enhanced (CE) Doppler to mitigate microbubble destruction. This introduces inherent tradeoffs in velocity estimates with autocorrelators, which are studied here. A model of the autocorrelation function adapted to the microbubble Doppler signal accounting for transit time, the echo frequency uncertainty, and contrast-agent destruction is derived and validated in vitro. It is further demonstrated that a local measurement of the center frequency of the microbubble echo is essential in order to avoid significant bias in velocity estimates arising from the linear and nonlinear frequency-dependent scattering of microbubbles and compensate for the inherent speckle nature of the received echo frequency. For these reasons, broadband Doppler estimators (2-D autocorrelator and Radon projection) are better suited than simpler narrow-band estimators (1-D autocorrelator and 1-D Fourier transform) for CE flow assessment. A case study of perfusion in a VX-2 carcinoma using CE plane-wave Doppler is also shown. We demonstrate that even when considering all uncertainties associated with microbubble-related decorrelation (destruction, pulse bandwidth, transit time, and flow gradient) and the need for real-time imaging, a coefficient of variation of 4% on the axial velocity is achievable with plane-wave imaging.
Zhang, Xiao-Zheng; Thomas, Jean-Hugh; Bi, Chuan-Xing; Pascal, Jean-Claude
2012-10-01
A time-domain plane wave superposition method is proposed to reconstruct nonstationary sound fields. In this method, the sound field is expressed as a superposition of time convolutions between the estimated time-wavenumber spectrum of the sound pressure on a virtual source plane and the time-domain propagation kernel at each wavenumber. By discretizing the time convolutions directly, the reconstruction can be carried out iteratively in the time domain, thus providing the advantage of continuously reconstructing time-dependent pressure signals. In the reconstruction process, the Tikhonov regularization is introduced at each time step to obtain a relevant estimate of the time-wavenumber spectrum on the virtual source plane. Because the double infinite integral of the two-dimensional spatial Fourier transform is discretized directly in the wavenumber domain in the proposed method, it does not need to perform the two-dimensional spatial fast Fourier transform that is generally used in time domain holography and real-time near-field acoustic holography, and therefore it avoids some errors associated with the two-dimensional spatial fast Fourier transform in theory and makes possible to use an irregular microphone array. The feasibility of the proposed method is demonstrated by numerical simulations and an experiment with two speakers.
Development of a standing-wave fluorescence microscope with high nodal plane flatness.
Freimann, R; Pentz, S; Hörler, H
1997-09-01
This article reports about the development and application of a standing-wave fluorescence microscope (SWFM) with high nodal plane flatness. As opposed to the uniform excitation field in conventional fluorescence microscopes as SWFM uses a standing-wave pattern of laser light. This pattern consists of alternating planar nodes and antinodes. By shifting it along the axis of the microscope a set of different fluorescent structures can be distinguished. Their axial separation may just be a fraction of a wavelength so that an SWFM allows distinction of structures which would appear axially unresolved in a conventional or confocal fluorescence microscope. An SWFM is most powerful when the axial extension of the specimen is comparable to the wavelength of light. Otherwise several planes are illuminated simultaneously and their separation is hardly feasible. The objective of this work was to develop a new SWFM instrument which allows standing-wave fluorescence microscopy with controlled high nodal plane flatness. Earlier SWFMs did not allow such a controlled flatness, which impeded image interpretation and processing. Another design goal was to build a compact, easy-to-use instrument to foster a more widespread use of this new technique. The instrument developed uses a green-emitting helium-neon laser as the light source, a piezoelectric movable beamsplitter to generate two mutually coherent laser beams of variable relative phase and two single-mode fibres to transmit these beams to the microscope. Each beam is passed on to the specimen by a planoconvex lens and an objective lens. The only reflective surface whose residual curvature could cause wavefront deformations is a dichroic beamsplitter. Nodal plane flatness is controlled via interference fringes by a procedure which is similar to the interferometric test of optical surfaces. The performance of the instrument was tested using dried and fluorescently labelled cardiac muscle cells of rats. The SWFM enabled the
NASA Technical Reports Server (NTRS)
Mcaninch, G. L.; Myers, M. K.
1980-01-01
The parabolic approximation for the acoustic equations of motion is applied to the study of the sound field generated by a plane wave at or near grazing incidence to a finite impedance boundary. It is shown how this approximation accounts for effects neglected in the usual plane wave reflection analysis which, at grazing incidence, erroneously predicts complete cancellation of the incident field by the reflected field. Examples are presented which illustrate that the solution obtained by the parabolic approximation contains several of the physical phenomena known to occur in wave propagation near an absorbing boundary.
NASA Technical Reports Server (NTRS)
Mcaninch, G. L.; Myers, M. K.
1980-01-01
The parabolic approximation for the acoustic equations of motion is applied to the study of the sound field generated by a plane wave at or near grazing incidence to a finite impedance boundary. It is shown how this approximation accounts for effects neglected in the usual plane wave reflection analysis which, at grazing incidence, erroneously predicts complete cancellation of the incident field by the reflected field. Examples are presented which illustrate that the solution obtained by the parabolic approximation contains several of the physical phenomena known to occur in wave propagation near an absorbing boundary.
NASA Astrophysics Data System (ADS)
Zhao, Haixia; Gao, Jinghuai; Peng, Jigen
2017-01-01
The frequency-dependent seismic anomalies related to hydrocarbon reservoirs have lately attracted wide interest. The diffusive-viscous model was proposed to explain these anomalies. When an incident diffusive-viscous wave strikes a boundary between two different media, it is reflected and transmitted. The equation for the reflection coefficient is quite complex and laborious, so it does not provide an intuitive understanding of how different amplitude relates to the parameters of the media and how variation of a particular parameter affects the reflection coefficient. In this paper, we firstly derive a two-term (intercept-gradient) and three-term (intercept-gradient-curvature) approximation to the reflection coefficient of the plane diffusive-viscous wave without any assumptions. Then, we study the limitations of the obtained approximations by comparing the approximate value of the reflection coefficient with its exact value. Our results show that the two approximations match well with the exact solutions within the incident angle of 35°. Finally, we analyze the effects of diffusive and viscous attenuation parameters, velocity and density in the diffusive-viscous wave equation on the intercept, gradient and curvature terms in the approximations. The results show that the diffusive attenuation parameter has a big impact on them, while the viscous attenuation parameter is insensitive to them; the velocity and density have a significant influence on the normal reflections and they distinctly affect the intercept, gradient and curvature term at lower acoustic impedance.
[A new method to orthodontically correct dental occlusal plane canting: wave-shaped arch].
Zheng, X; Hu, X X; Ma, N; Chen, X H
2017-02-18
To introduce a technique of second order wave-shaped arch wire to orthodontically treat dental occlusal plane canting (DOPC) with left-right interactive anchorage, and to test its clinical efficacy. Among the permanent dentition malocclusion patients who showed no obvious facial asymmetry, we screened for patients who showed anterior occlusal plane canting (AOPC) after routine orthodontic examination, treatment planning, MBT fixed appliance installation and serial arch wires alignment. Each patient had been clinically appraised in frontal view by 2 orthodontists and the patient him/herself; if all 3 agreed that the AOPC was obvious, the patient was included. By this means, we included 37 patients, including 10 males and 27 females; the average age was (21.9±5.2) years. To correct AOPC, opposite direction equal curvature second order rocking-chair curve was bent on each side of 0.46 mm×0.56 mm stainless steel edgewise wire. With reference to normal occlusal plane, a curve toward the occlusal surface was made to extrude under-erupted teeth on one side while a curve toward the gingiva was made to intrude over-erupted teeth on the other side, so that the arch wire was made into a wave shape in vertical dimension. Before and after application of wave-shaped arch wire, frontal facial photographs were taken when the patient's mouth was open slightly with lips retracted to show anterior occlusal plane (AOP) clearly. An AOP was constructed by connecting the center of the slot in the medial edge of canine bracket on each side in the photograph. The angles between the bipupillary plane(BPP) and the constructed AOP were measured in ImageJ1-48v software and the angle differences before and after treatment were compared with paired Wilcoxon test in SPSS 10.0 software. The wave-shaped arch could correct AOPC effectively in 3 to 10 months time with an average of 5.5±1.7 months; the angles between AOP and BBP before treatment ranged from 2.90° to 6.12° with a median of 4.01
NASA Astrophysics Data System (ADS)
Ravikiran, Y. T.; Vijaya Kumari, S. C.
2013-06-01
To innovate the properties of Polypyrrole/Titanium dioxide (PPy/TiO2) nanocomposite further, it has been synthesized by chemical polymerization technique. The nanostructure and monoclinic phase of the prepared composite have been confirmed by simulating the X-ray diffraction pattern (XRD). Also, complex plane impedance plot of the composite has been simulated to find equivalent resistance capacitance circuit (RC circuit) and numerical values of R and C have been predicted.
Jeong, Hyunjo; Zhang, Shuzeng; Li, Xiongbing; Barnard, Dan
2015-09-15
The accurate measurement of acoustic nonlinearity parameter β for fluids or solids generally requires making corrections for diffraction effects due to finite size geometry of transmitter and receiver. These effects are well known in linear acoustics, while those for second harmonic waves have not been well addressed and therefore not properly considered in previous studies. In this work, we explicitly define the attenuation and diffraction corrections using the multi-Gaussian beam (MGB) equations which were developed from the quasilinear solutions of the KZK equation. The effects of making these corrections are examined through the simulation of β determination in water. Diffraction corrections are found to have more significant effects than attenuation corrections, and the β values of water can be estimated experimentally with less than 5% errors when the exact second harmonic diffraction corrections are used together with the negligible attenuation correction effects on the basis of linear frequency dependence between attenuation coefficients, α{sub 2} ≃ 2α{sub 1}.
Zero-order filter for diffractive focusing of de Broglie matter waves
NASA Astrophysics Data System (ADS)
Eder, S. D.; Ravn, A. K.; Samelin, B.; Bracco, G.; Palau, A. Salvador; Reisinger, T.; Knudsen, E. B.; Lefmann, K.; Holst, B.
2017-02-01
The manipulation of neutral atoms and molecules via their de Broglie wave properties, also referred to as de Broglie matter wave optics, is relevant for several fields ranging from fundamental quantum mechanics tests and quantum metrology to measurements of interaction potentials and new imaging techniques. However, there are several challenges. For example, for diffractive focusing elements, the zero-order beam provides a challenge because it decreases the signal contrast. Here we present the experimental realization of a zero-order filter, also referred to as an order-sorting aperture for de Broglie matter wave diffractive focusing elements. The zero-order filter makes it possible to measure even at low beam intensities. We present measurements of zero-order filtered, focused, neutral helium beams generated at source stagnation pressures between 11 and 81 bars. We show that for certain conditions the atom focusing at lower source stagnation pressures (broader velocity distributions) is better than what has previously been predicted. We present simulations with the software ray-tracing simulation package mcstas using a realistic helium source configuration, which gives very good agreement with our measurements.
Role of long waves in the stability of the plane wake.
Scarsoglio, Stefania; Tordella, Daniela; Criminale, William O
2010-03-01
This work is directed toward investigating the fate of three-dimensional long perturbation waves in a plane incompressible wake. The analysis is posed as an initial-value problem in space. More specifically, input is made at an initial location in the downstream direction and then tracing the resulting behavior further downstream subject to the restriction of finite kinetic energy. This presentation follows the outline given by Criminale and Drazin [W. O. Criminale and P. G. Drazin, Stud. Appl. Math. 83, 123 (1990)] that describes the system in terms of perturbation vorticity and velocity. The analysis is based on large scale waves and expansions using multiscales and multitimes for the partial differential equations. The multiscaling is based on an approach where the small parameter is linked to the perturbation property independently from the flow control parameter. Solutions of the perturbative equations are determined numerically after the introduction of a regular perturbation scheme analytically deduced up to the second order. Numerically, the complete linear system is also integrated. Since the results relevant to the complete problem are in very good agreement with the results of the first-order analysis, the numerical solution at the second order was deemed not necessary. The use for an arbitrary initial-value problem will be shown to contain a wealth of information for the different transient behaviors associated to the symmetry, angle of obliquity, and spatial decay of the long waves. The amplification factor of transversal perturbations never presents the trend--a growth followed by a long damping--usually seen in waves with wave number of order one or less. Asymptotical instability is always observed.
Role of long waves in the stability of the plane wake
NASA Astrophysics Data System (ADS)
Scarsoglio, Stefania; Tordella, Daniela; Criminale, William O.
2010-03-01
This work is directed toward investigating the fate of three-dimensional long perturbation waves in a plane incompressible wake. The analysis is posed as an initial-value problem in space. More specifically, input is made at an initial location in the downstream direction and then tracing the resulting behavior further downstream subject to the restriction of finite kinetic energy. This presentation follows the outline given by Criminale and Drazin [W. O. Criminale and P. G. Drazin, Stud. Appl. Math. 83, 123 (1990)] that describes the system in terms of perturbation vorticity and velocity. The analysis is based on large scale waves and expansions using multiscales and multitimes for the partial differential equations. The multiscaling is based on an approach where the small parameter is linked to the perturbation property independently from the flow control parameter. Solutions of the perturbative equations are determined numerically after the introduction of a regular perturbation scheme analytically deduced up to the second order. Numerically, the complete linear system is also integrated. Since the results relevant to the complete problem are in very good agreement with the results of the first-order analysis, the numerical solution at the second order was deemed not necessary. The use for an arbitrary initial-value problem will be shown to contain a wealth of information for the different transient behaviors associated to the symmetry, angle of obliquity, and spatial decay of the long waves. The amplification factor of transversal perturbations never presents the trend—a growth followed by a long damping—usually seen in waves with wave number of order one or less. Asymptotical instability is always observed.
NASA Technical Reports Server (NTRS)
Heedy, D. J.; Burnside, W. D.
1984-01-01
The moment method and the uniform geometrical theory of diffraction are utilized to obtain two separate solutions for the E-plane field pattern of an aperture-matched horn antenna. This particular horn antenna consists of a standard pyramidal horn with the following modifications: a rolled edge section attached to the aperture edges and a curved throat section. The resulting geometry provides significantly better performance in terms of the pattern, impedance, and frequency characteristics than normally obtainable. The moment method is used to calculate the E-plane pattern and BSWR of the antenna. However, at higher frequencies, large amounts of computation time are required. The uniform geometrical theory of diffraction provides a quick and efficient high frequency solution for the E-plane field pattern. In fact, the uniform geometrical theory of diffraction may be used to initially design the antenna; then, the moment method may be applied to fine tune the design. This procedure has been successfully applied to a compact range feed design.
The strain in the array is mainly in the plane (waves below ~1 Hz)
Gomberg, J.; Pavlis, G.; Bodin, P.
1999-01-01
We compare geodetic and single-station methods of measuring dynamic deformations and characterize their causes in the frequency bands 0.5-1.0 Hz and 4.0-8.0 Hz. The geodetic approach utilizes data from small-aperture seismic arrays, applying techniques from geodesy. It requires relatively few assumptions and a priori information. The single-station method uses ground velocities recorded at isolated or single stations and assumes all the deformation is due to plane-wave propagation. It also requires knowledge of the azimuth and horizontal velocity of waves arriving at the recording station. Data employed come from a small-aperture, dense seismic array deployed in Geyokcha, Turkmenistan, and include seismograms recorded by broadband STS2 and short-period L28 sensors. Poor agreement between geodetic and single-station estimates in the 4.0-8.0 Hz passband indicates that the displacement field may vary nonlinearly with distance over distances of ~50 m. STS2 geodetic estimates provide a robust standard in the 0.5-1.0 Hz passband because they appear to be computationally stable and require fewer assumptions than single-station estimates. The agreement between STS2 geodetic estimates and single-station L28 estimates is surprisingly good for the S-wave and early surface waves, suggesting that the single-station analysis should be useful with commonly available data. These results indicate that, in the 0.5 to 1.0 Hz passband, the primary source of dynamic deformation is plane-wave propagation along great-circle source-receiver paths. For later arriving energy, the effects of scattering become important. The local structure beneath the array exerts a strong control on the geometry of the dynamic deformation, implying that it may be difficult to infer source characteristics of modern or paleoearthquakes from indicators of dynamic deformations. However, strong site control also suggests that the dynamic deformations may be predictable, which would be useful for engineering
Shen Yuandeng; Liu Yu; Zhao Ruijuan; Tian Zhanjun; Su Jiangtao; Li Hui; Ichimoto, Kiyoshi; Shibata, Kazunari
2013-08-20
We present observations of the diffraction, refraction, and reflection of a global extreme-ultraviolet (EUV) wave propagating in the solar corona. These intriguing phenomena are observed when the wave interacts with two remote active regions, and together they exhibit properties of an EUV wave. When the wave approached AR11465, it became weaker and finally disappeared in the active region, but a few minutes later a new wavefront appeared behind the active region, and it was not concentric with the incoming wave. In addition, a reflected wave was also simultaneously observed on the wave incoming side. When the wave approached AR11459, it transmitted through the active region directly and without reflection. The formation of the new wavefront and the transmission could be explained with diffraction and refraction effects, respectively. We propose that the different behaviors observed during the interactions may be caused by different speed gradients at the boundaries of the two active regions. We find that the EUV wave formed ahead of a group of expanding loops a few minutes after the start of the loops' expansion, which represents the initiation of the associated coronal mass ejection (CME). Based on these results, we conclude that the EUV wave should be a nonlinear magnetosonic wave or shock driven by the associated CME, which propagated faster than the ambient fast mode speed and gradually slowed down to an ordinary linear wave. Our observations support the hybrid model that includes both fast wave and slow non-wave components.
NASA Astrophysics Data System (ADS)
Majhi, S.; Pal, P. C.; Kumar, S.
2017-01-01
This study investigates the reflection and transmission of plane SH-waves in two semi-infinite anisotropic magnetoelastic media. The lower half-space is considered as initially stressed and inhomogeneous. The density of lower half-space is taken exponentially varying with depth. The solutions for half-spaces are obtained analytically. The expressions for reflection and transmission coefficient are obtained in the closed form subject to continuity conditions at the interfaces of anisotropic magnetoelastic half-spaces and the Snell's law. It is found that these coefficients depend on the initial stress, inhomogeneity parameter, the magnetoelastic coupling parameter, and the angle at which wave crosses the magnetic field of the half-spaces. Numerical computations are performed for these coefficients for a specific model of two different anisotropic magnetoelastic half-spaces. The numerical results are illustrated by the graph of reflection and transmission coefficient versus the angle of incidence. In general, as the initial stress increases the reflection and transmission coefficient increases, the affect is more prominent for more than 10 GPa. Inhomogeneity in the density of the material also increases the reflection and transmission coefficient. The anisotropic magnetoelastic parameter and the angle at which the wave crosses the magnetic field for both the half-spaces have a quite significant effect on the reflection and transmission coefficient.
Dietrich, F S
2006-09-25
This document is intended to facilitate calculation of inelastic scattering and charge-exchange cross sections in a variety of reaction models, including the plane-wave and distorted-wave approximations and the full coupled-channels treatments. Expressions are given for the coupling potentials between the relevant channels in both coordinate and momentum space. In particular, it is expected that the plane-wave calculations should be useful as a check on the correctness of coupled-channels calculations. The Fourier transform methods used to calculate the plane-wave approximation cross sections are also intended to be used to generate the transition potentials for coupled-channels codes, using a folding model with local effective interactions. Specific expressions are given for calculating transition densities for the folding model in the random phase approximation (RPA).
Huang, Yuanshen; Li, Ting; Xu, Banglian; Hong, Ruijin; Tao, Chunxian; Ling, Jinzhong; Li, Baicheng; Zhang, Dawei; Ni, Zhengji; Zhuang, Songlin
2013-02-10
Fraunhofer diffraction formula cannot be applied to calculate the diffraction wave energy distribution of concave gratings like plane gratings because their grooves are distributed on a concave spherical surface. In this paper, a method based on the Kirchhoff diffraction theory is proposed to calculate the diffraction efficiency on concave gratings by considering the curvature of the whole concave spherical surface. According to this approach, each groove surface is divided into several limited small planes, on which the Kirchhoff diffraction field distribution is calculated, and then the diffraction field of whole concave grating can be obtained by superimposition. Formulas to calculate the diffraction efficiency of Rowland-type and flat-field concave gratings are deduced from practical applications. Experimental results showed strong agreement with theoretical computations. With the proposed method, light energy can be optimized to the expected diffraction wave range while implementing aberration-corrected design of concave gratings, particularly for the concave blazed gratings.
A unique solvable higher order BEM for wave diffraction and radiation
Teng, B.; Li, Y.C.
1995-12-31
For the discretization of higher order elements, the paper presents a modifying integral domain method to remove the irregular frequencies inherited in the integral equation of wave diffraction and radiation from a surface-piercing body. The set of over-determined linear equations obtained from the method is modified into a normal set of linear equations by superposing a set of linear equations with zero solutions. Numerical experiments have also been carried out to find the optimum choice of the size of the auxiliary domain and the discretization on it.
Observation of two-wave coupling during the formation of POLICRYPS diffraction gratings.
Caputo, Roberto; De Sio, Luciano; Veltri, Alessandro; Umeton, Cesare; Sukhov, Andrey V
2005-07-15
We report on the experimental observation of two-wave mixing that occurs inside a sample between the beams used for the fabrication of polymer-liquid-crystal-polymer slices (POLICRYPS) diffraction gratings. The effect depends on the phase shift between the curing interference pattern and the grating being cured. This shift can be mechanically induced by accidental vibrations of the experimental setup; thus a high setup stability is needed. We devised a mechanism that enables us to control setup vibrations in situ and used it to monitor the experiment. When the mechanically induced shift was significantly small, wave mixing was observed only if the initial intensities of the two curing beams were different from each other.
Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water
NASA Astrophysics Data System (ADS)
Jiménez, N.; Romero-García, V.; Picó, R.; Garcia-Raffi, L. M.; Staliunas, K.
2015-11-01
We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10-4). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.
Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water
Jiménez, N.; Picó, R.; Romero-García, V.; Garcia-Raffi, L. M.
2015-11-16
We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10{sup −4}). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.
NASA Astrophysics Data System (ADS)
Grinspan, G. A.; Aguiar, S.; Benech, N.
2016-04-01
Soft biological tissue elasticity is a parameter whose reliable measure is relevant to many applications in fields as diverse as medicine and the agrifood industry. The ultrasonic elastography methods are often unviable to be applied to provide such solutions. In this way, the surface wave elastography (SWE) appears as a viable alternative, due its low cost, easy to use, non-invasive-destructive character as well as its ability to provide in vivo estimates. Previous studies have described a good correlation between the overall behavior of ultrasonic elastography and SWE, although the latter overestimates the elasticity values compared to the first. It has been suggested that this is due to the influence of certain physical effects related to the exclusive use of low frequency waves, as well as by characteristics of the experimental setup and/or medium. In this work we confirm the influence of such effects and discuss different strategies to make independent the estimations thereof. This allows achieving a good agreement between the ultrasonic reference method and SWE. Thus, SWE becomes a reliable method to estimate soft biological tissue elasticity.
Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2015-12-01
The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb < 1). The results are particularly relevant in acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.
Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves
Mitri, F. G.
2015-12-07
The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb < 1). The results are particularly relevant in acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.
Collision of plane thermonuclear detonation waves in a preliminarily compressed DT mixture
NASA Astrophysics Data System (ADS)
Khishchenko, K. V.; Charakhch'yan, A. A.
2015-03-01
The paper deals with a one-dimensional problem on symmetric irradiation of a plane DT fuel layer with a thickness 2 H and density ρ0 ⩽ 100ρ s (where ρ s is the density of the DT fuel in the solid state at atmospheric pressure and a temperature of 4 K) by two identical monoenergetic proton beams with a kinetic energy of 1 MeV, an intensity of 1019 W/cm2, and a duration of 50 ps. The problem is solved in the framework of one-fluid two-temperature hydrodynamic model that takes into account the equation of state for hydrogen, electron and ion heat conductivities, kinetics of the DT reaction, plasma self-radiation, and plasma heating by α-particles. The irradiation of the fuel results in the appearance of two counterpropagating detonation waves to the fronts of which rarefaction waves are adjacent. The efficiency of the DT reaction after the collision (reflection from the plane of symmetry) of the detonation waves depends on the spatial homogeneity of thermodynamic functions between the fronts of the reflected detonation waves. At Hρ0 ≈ 1 g/cm2, the gain factor is G ≈ 200, whereas at Hρ0 ≈ 5 g/cm2, it is G > 2000. As applied to a cylindrical target that is ignited from ends and in which the cylinder with the fuel is surrounded by a heavy magnetized shell, the obtained values of the burn-up and gain factors are maximum possible. To estimate the ignition energy E ig of a cylindrical target by using solutions to the one-dimensional problem, a quasi-one-dimensional model is developed. The model assumes that the main mechanism of target ignition is fuel heating by α-particles. The trajectories of α-particles are limited by a cylindrical surface with a given radius, which is a parameter of the model and is identified with the fuel radius in the target and the radii of the irradiating proton beams. This model reproduces the well-known theoretical dependence E ig ˜ ρ{0/-2} and yields E ig = 160 kJ as a lower estimate of the ignition energy for ρ0 = 100ρ s
Collision of plane thermonuclear detonation waves in a preliminarily compressed DT mixture
Khishchenko, K. V.; Charakhch’yan, A. A.
2015-03-15
The paper deals with a one-dimensional problem on symmetric irradiation of a plane DT fuel layer with a thickness 2H and density ρ{sub 0} ⩽ 100ρ{sub s} (where ρ{sub s} is the density of the DT fuel in the solid state at atmospheric pressure and a temperature of 4 K) by two identical monoenergetic proton beams with a kinetic energy of 1 MeV, an intensity of 10{sup 19} W/cm{sup 2}, and a duration of 50 ps. The problem is solved in the framework of one-fluid two-temperature hydrodynamic model that takes into account the equation of state for hydrogen, electron and ion heat conductivities, kinetics of the DT reaction, plasma self-radiation, and plasma heating by α-particles. The irradiation of the fuel results in the appearance of two counterpropagating detonation waves to the fronts of which rarefaction waves are adjacent. The efficiency of the DT reaction after the collision (reflection from the plane of symmetry) of the detonation waves depends on the spatial homogeneity of thermodynamic functions between the fronts of the reflected detonation waves. At Hρ{sub 0} ≈ 1 g/cm{sup 2}, the gain factor is G ≈ 200, whereas at Hρ{sub 0} ≈ 5 g/cm{sup 2}, it is G > 2000. As applied to a cylindrical target that is ignited from ends and in which the cylinder with the fuel is surrounded by a heavy magnetized shell, the obtained values of the burn-up and gain factors are maximum possible. To estimate the ignition energy E{sub ig} of a cylindrical target by using solutions to the one-dimensional problem, a quasi-one-dimensional model is developed. The model assumes that the main mechanism of target ignition is fuel heating by α-particles. The trajectories of α-particles are limited by a cylindrical surface with a given radius, which is a parameter of the model and is identified with the fuel radius in the target and the radii of the irradiating proton beams. This model reproduces the well-known theoretical dependence E{sub ig} ∼ ρ{sub 0}{sup −2} and yields E
On the Propagation of Plane Acoustic Waves in a Duct With Flexible and Impedance Walls
NASA Technical Reports Server (NTRS)
Frendi, Abdelkader; Vu, Bruce
2003-01-01
This Technical Memorandum (TM) discusses the harmonic and random plane acoustic waves propagating from inside a duct to its surroundings. Various duct surfaces are considered, such as rigid, flexible, and impedance. In addition, the effects of a mean flow are studied when the duct alone is considered. Results show a significant reduction in overall sound pressure levels downstream of the impedance wall for both mean flow and no mean flow cases and for a narrow duct. When a wider duct is used, the overall sound pressure level (OSPL) reduction downstream of the impedance wall is much smaller. In the far field, the directivity is such that the overall sound pressure level is reduced by about 5 decibels (dB) on the side of the impedance wall. When a flexible surface is used, the far field directivity becomes asymmetric with an increase in the OSPL on the side of the flexible surface of about 7 dB.
Plane-wave theory of a Michelson laser coupler with a dielectric slab beam splitter
NASA Astrophysics Data System (ADS)
Cooper, Steven J.; Heckenberg, Norman R.
1996-03-01
The plane-wave theory for the transmittance and absorbtance of a perfectly aligned Michelson coupler with a dielectric slab beam splitter is presented. It is shown that the transmittance and absorbtance vary sinusoidally and in quadrature. As a result of this quadrature relationship, the maximum transmittance occurs at a setting of the translatable coupler mirror at which the absorbtance is not at an extremum, and so the curve of output power as a function of coupler setting is asymmetrical with respect to the setting yielding maximum transmittance. Experimental measurements of the output power of a far-infrared HCN laser as a function of the coupler setting confirm this asymmetry, which seems to have been overlooked or ignored in previous studies.
NASA Astrophysics Data System (ADS)
Cheng, Qiang; Cui, Tie Jun
2006-12-01
We have investigated the reflection and refraction properties of plane waves incident from free space into a uniaxially anisotropic chiral medium, where the chirality appears only in one direction and the host medium can be either an isotropic dielectric or an anisotropic electric plasma. We show that the reflection and refraction properties are closely related to the dispersion relation of the chiral medium and that negative phase refractions and/or negative group refractions may occur. We further demonstrate that the two eigenwaves within the uniaxially anisotropic chiral medium behave differently with respect to the incident angle, and in some cases only one of them can be supported and transmitted. We have studied the critical angle and Brewster's angle with some special properties. We have also discussed the potential application of the uniaxially anisotropic chiral medium for the polarization beam splitter. Numerical results are given to validate our analysis.
Cheng, Qiang; Cui, Tie Jun
2006-12-01
We have investigated the reflection and refraction properties of plane waves incident from free space into a uniaxially anisotropic chiral medium, where the chirality appears only in one direction and the host medium can be either an isotropic dielectric or an anisotropic electric plasma. We show that the reflection and refraction properties are closely related to the dispersion relation of the chiral medium and that negative phase refractions and/or negative group refractions may occur. We further demonstrate that the two eigenwaves within the uniaxially anisotropic chiral medium behave differently with respect to the incident angle, and in some cases only one of them can be supported and transmitted. We have studied the critical angle and Brewster's angle with some special properties. We have also discussed the potential application of the uniaxially anisotropic chiral medium for the polarization beam splitter. Numerical results are given to validate our analysis.
Fast plane wave density functional theory molecular dynamics calculations on multi-GPU machines
Jia, Weile; Fu, Jiyun; Cao, Zongyan; Wang, Long; Chi, Xuebin; Gao, Weiguo; Wang, Lin-Wang
2013-10-15
Plane wave pseudopotential (PWP) density functional theory (DFT) calculation is the most widely used method for material simulations, but its absolute speed stagnated due to the inability to use large scale CPU based computers. By a drastic redesign of the algorithm, and moving all the major computation parts into GPU, we have reached a speed of 12 s per molecular dynamics (MD) step for a 512 atom system using 256 GPU cards. This is about 20 times faster than the CPU version of the code regardless of the number of CPU cores used. Our tests and analysis on different GPU platforms and configurations shed lights on the optimal GPU deployments for PWP-DFT calculations. An 1800 step MD simulation is used to study the liquid phase properties of GaInP.
NASA Astrophysics Data System (ADS)
Zhang, Shenwei; Qiu, Chunyin; Wang, Mudi; Ke, Manzhu; Liu, Zhengyou
2016-11-01
In this work, we study the acoustically mediated interaction forces among multiple well-separated spherical particles trapped in the same node or antinode plane of a standing wave. An analytical expression of the acoustic interaction force is derived, which is accurate even for the particles beyond the Rayleigh limit. Interestingly, the multi-particle system can be decomposed into a series of independent two-particle systems described by pairwise interactions. Each pairwise interaction is a long-range interaction, as characterized by a soft oscillatory attenuation (at the power exponent of n = -1 or -2). The vector additivity of the acoustic interaction force, which is not well expected considering the nonlinear nature of the acoustic radiation force, is greatly useful for exploring a system consisting of a large number of particles. The capability of self-organizing a big particle cluster can be anticipated through such acoustically controllable long-range interaction.
LOBSTER: A tool to extract chemical bonding from plane-wave based DFT.
Maintz, Stefan; Deringer, Volker L; Tchougréeff, Andrei L; Dronskowski, Richard
2016-04-30
The computer program LOBSTER (Local Orbital Basis Suite Towards Electronic-Structure Reconstruction) enables chemical-bonding analysis based on periodic plane-wave (PAW) density-functional theory (DFT) output and is applicable to a wide range of first-principles simulations in solid-state and materials chemistry. LOBSTER incorporates analytic projection routines described previously in this very journal [J. Comput. Chem. 2013, 34, 2557] and offers improved functionality. It calculates, among others, atom-projected densities of states (pDOS), projected crystal orbital Hamilton population (pCOHP) curves, and the recently introduced bond-weighted distribution function (BWDF). The software is offered free-of-charge for non-commercial research. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.
TM Plane Wave Reflection and Transmission from a One-Dimensional Random Slab
NASA Astrophysics Data System (ADS)
Tamura, Yasuhiko
This paper deals with a TM plane wave reflection and transmission from a one-dimensional random slab with stratified fluctuation by means of the stochastic functional approach. Based on a previous manner [IEICE Trans. Electron. E88-C, 4, pp. 713-720, 2005], an explicit form of the random wavefield is obtained in terms of a Wiener-Hermite expansion with approximate expansion coefficients (Wiener kernels) under small fluctuation. The optical theorem and coherent reflection coefficient are illustrated in figures for several physical parameters. It is then found that the optical theorem by use of the first two or three order Wiener kernels holds with good accuracy and a shift of Brewster's angle appears in the coherent reflection.
Evidence of iridescence in TiO2 nanostructures: An approximation in plane wave expansion method
NASA Astrophysics Data System (ADS)
Quiroz, Heiddy P.; Barrera-Patiño, C. P.; Rey-González, R. R.; Dussan, A.
2016-11-01
Titanium dioxide nanotubes, TiO2 NTs, can be obtained by electrochemical anodization of Titanium sheets. After nanotubes are removed by mechanical stress, residual structures or traces on the surface of titanium sheets can be observed. These traces show iridescent effects. In this paper we carry out both experimental and theoretical study of those interesting and novel optical properties. For the experimental analysis we use angle resolved UV-vis spectroscopy while in the theoretical study is evaluated the photonic spectra using numerical simulations into the frequency-domain and the framework of the wave plane approximation. The iridescent effect is a strong property and independent of the sample. This behavior can be important to design new materials or compounds for several applications such as, cosmetic industry, optoelectronic devices, photocatalysis, sensors, among others.
Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis
NASA Astrophysics Data System (ADS)
Schäfer, Tobias; Ramberger, Benjamin; Kresse, Georg
2017-03-01
We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O ( N 4 ) , with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.
Plane-wave pseudopotential study of point defects in uranium dioxide
NASA Astrophysics Data System (ADS)
Crocombette, J. P.; Jollet, F.; Nga, L. Thien; Petit, T.
2001-09-01
A study on uranium and oxygen point defects in uranium dioxide using the ab initio plane-wave pseudopotential method in the local density approximation of the density functional theoretical framework is presented. Norm conserving pseudopotentials are used to describe oxygen and uranium atoms. The uranium pseudopotential is specifically described. Its validity is ascertained thanks to a detailed structural study of uranium dioxide and of three phases of metallic uranium (fcc, bcc, and α phase). The free energies of formation of both intrinsic (Frenkel pairs and Schottky defect) and extrinsic (single vacancies or interstitials) defects are calculated. The obtained values form a reliable set of numerical data that are analyzed in the framework of the point defect model which is commonly used to assess defect concentrations in uranium dioxide and their variation with stoichiometry. From the obtained results, the ability of the point defect model to accurately reproduce defect concentrations in uranium dioxide is discussed.
NASA Technical Reports Server (NTRS)
Yarrow, Maurice; Vastano, John A.; Lomax, Harvard
1992-01-01
Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.
Fully converged plane-wave-based self-consistent G W calculations of periodic solids
NASA Astrophysics Data System (ADS)
Cao, Huawei; Yu, Zhongyuan; Lu, Pengfei; Wang, Lin-Wang
2017-01-01
The G W approximation is a well-known method to obtain the quasiparticle and spectral properties of systems ranging from molecules to solids. In practice, G W calculations are often employed with many different approximations and truncations. In this work, we describe the implementation of a fully self-consistent G W approach based on the solution of the Dyson equation using a plane wave basis set. Algorithmic, numerical, and technical details of the self-consistent G W approach are presented. The fully self-consistent G W calculations are performed for GaAs, ZnO, and CdS including semicores in the pseudopotentials. No further approximations and truncations apart from the truncation on the plane wave basis set are made in our implementation of the G W calculation. After adopting a special potential technique, a ˜100 Ry energy cutoff can be used without the loss of accuracy. We found that the self-consistent G W (sc-G W ) significantly overestimates the bulk band gaps, and this overestimation is likely due to the underestimation of the macroscopic dielectric constants. On the other hand, the sc-G W accurately predicts the d -state positions, most likely because the d -state screening does not sensitively depend on the macroscopic dielectric constant. Our work indicates the need to include the high-order vertex term in order for the many-body perturbation theory to accurately predict the semiconductor band gaps. It also sheds some light on why, in some cases, the G0W0 bulk calculation is more accurate than the fully self-consistent G W calculation, because the initial density-functional theory has a better dielectric constant compared to experiments.
Radiation of de-excited electrons at large times in a strong electromagnetic plane wave
Kazinski, P.O.
2013-12-15
The late time asymptotics of the physical solutions to the Lorentz–Dirac equation in the electromagnetic external fields of simple configurations–the constant homogeneous field, the linearly polarized plane wave (in particular, the constant uniform crossed field), and the circularly polarized plane wave–are found. The solutions to the Landau–Lifshitz equation for the external electromagnetic fields admitting a two-parametric symmetry group, which include as a particular case the above mentioned field configurations, are obtained. Some general properties of the total radiation power of a charged particle are established. In particular, for a circularly polarized wave and constant uniform crossed fields, the total radiation power in the asymptotic regime is independent of the charge and the external field strength, when expressed in terms of the proper-time, and equals a half the rest energy of a charged particle divided by its proper-time. The spectral densities of the radiation power formed on the late time asymptotics are derived for a charged particle moving in the external electromagnetic fields of the simple configurations pointed above. This provides a simple method to verify experimentally that the charged particle has reached the asymptotic regime. -- Highlights: •Late time asymptotics of the solutions to the Lorentz–Dirac equation are studied. •General properties of the total radiation power of electrons are established. •The total radiation power equals a half the rest energy divided by the proper-time. •Spectral densities of radiation formed on the late time asymptotics are derived. •Possible experimental verification of the results is proposed.
Axisymmetric diffraction of a cylindrical transverse wave by a viscoelastic spherical inclusion
NASA Astrophysics Data System (ADS)
Schwartz, Benjamin L.; Liu, Yifei; Royston, Thomas J.; Magin, Richard L.
2016-03-01
In this paper, the scattering and diffraction of a cylindrical transverse shear wave in a viscoelastic isotropic medium by a spherical heterogeneity is analytically solved. The waves are generated by the harmonic longitudinal oscillations of the cylinder walls. The spherical inclusion is located at the radial center of the cylinder and differs from the cylindrical material only in its complex shear modulus. Small amplitude motion is assumed, such that linear system theory is valid. By employing multi-pole expansions, the incident and scattered wave fields are each defined in both cylindrical and spherical coordinates allowing for the satisfaction of the boundary conditions at the surfaces of these multiply connected bodies. The solution involves an infinite sum of improper integrals, which are evaluated numerically. The wave field is determined for a hydrogel (alginate) bead suspended in a different hydrogel (agarose) that fills a glass test tube. Numerical examples showing the effect on displacement fields of varying the stiffness of the inclusion are presented. This solution is further validated with a finite element simulation showing excellent agreement with the analytic results.
Dispersion of circumferential waves in cylindrically anisotropic layered pipes in plane strain.
Vasudeva, R Y; Sudheer, G; Vema, Anu Radha
2008-06-01
Dispersion spectra of circumferential waves along the periphery of circular pipes made of layered anisotropic materials do not seem to be available in literature. This note attempts to partially fill this gap by providing the dispersion spectra in two and three layered cylindrically anisotropic pipes in plane strain motion. The spectra for pipes executing time harmonic vibrations in plane strain condition are obtained as roots of a numerical characteristic equation derived extending a weighted residual method of solution of the governing equations for a single layer pipe [Towfighi et al., J. Appl. Mech. 69, 283-291 (2002)] to a general N layered pipe. The anisotropic elastic coefficients are considered to be independent of position coordinates and the bond condition at interfaces of the layers is assumed to be perfect. Numerical illustrations are presented for two and three layered pipes with anisotropy directions differing in adjacent layers. Increase in curvature of the pipe and inclination of the fiber orientation in the outermost layers to propagation direction are factors that seem to influence the mode number and pattern within the limited examples worked out.
NASA Astrophysics Data System (ADS)
Seo, Yong Gon; Kim, Jihoon; Hwang, Sung-Min; Kim, Jihyun; Jang, Soohwan; Kim, Heesan; Baik, Kwang Hyeon
2015-02-01
This work examines the anisotropic microstructure and the lattice distortions of nonpolar a-plane GaN ( a-GaN) films by using the grazing-incidence X-ray diffraction technique. Faulted a-GaN films typically exhibit an in-plane anisotropy of the structural properties along the X-ray in-beam directions. For this reason, the anisotropic peak broadenings of the X-ray rocking curves (XRCs) were observed for various angle (phi) rotations for a-GaN films with and without SiN x interlayers. Analysis revealed the peak widths of the XRCs displayed an isotropic behavior for a nonpolar a-GaN bulk crystal. Thus, the in-plane anisotropy of the XRC peak widths for nonpolar a-GaN films apparently originates from the heteroepitaxial growth of the a-GaN layer on a foreign substrate. The lattice distortion analysis identified the presence of compressive strains in both the two in-plane directions (the c- and the m-axis), as well as a tensile strain along the normal growth direction. In addition, the observed frequency shifts in the Raman E2 (high) mode for the a-GaN films showed the existence of considerable in-plane compressive strain on both a-GaN films, as confirmed by the lattice distortion analysis performed using the grazing-incidence XRD method.
NASA Technical Reports Server (NTRS)
Reddy, C. J.; Deshpande, M. D.; Cockrell, C. R.; Beck, F. B.
1996-01-01
A technique using hybrid Finite Element Method (FEM)/Method of Moments (MoM), and Geometrical Theory of Diffraction (GTD) is presented to analyze the radiation characteristics of cavity fed aperture antennas in a finite ground plane. The cavity which excites the aperture is assumed to be fed by a cylindrical transmission line. The electromagnetic (EM) fields inside the cavity are obtained using FEM. The EM fields and their normal derivatives required for FEM solution are obtained using (1) the modal expansion in the feed region and (2) the MoM for the radiating aperture region(assuming an infinite ground plane). The finiteness of the ground plane is taken into account using GTD. The input admittance of open ended circular, rectangular, and coaxial line radiating into free space through an infinite ground plane are computed and compared with earlier published results. Radiation characteristics of a coaxial cavity fed circular aperture in a finite rectangular ground plane are verified with experimental results.
The impedance problem of wave diffraction by a strip with higher order boundary conditions
Castro, L. P.; Simões, A. M.
2013-10-17
This work is devoted to analyse an impedance boundary-transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. A constructive approach of operator relations is built, which allows a transparent interpretation of the problem in an operator theory framework. In particular, different types of operator relations are exhibited for different types of operators acting between Lebesgue and Sobolev spaces on a finite interval and the positive half-line. All this has consequences in the understanding of the structure of this type of problems. In particular, a Fredholm characterization of the problem is obtained in terms of the initial space order parameters. At the request of the author and the Proceedings Editor the above article has been replaced with a corrected version. The original PDF file supplied to AIP Publishing contained an error in the title of the article. The original title appeared as: 'The Impedance Problem of Wave Diffraction by a trip with Higher Order Boundary Conditions.' This article has been replaced and the title now appears correctly online. The corrected article was published on 8 November 2013.
Exact scattering and diffraction of antiplane shear waves by a vertical edge crack
NASA Astrophysics Data System (ADS)
Tsaur, Deng-How
2010-06-01
Scattering and diffraction problems of a vertical edge crack connected to the surface of a half space are considered for antiplane shear wave incidence. The method of separation of variables is adopted to derive an exact series solution. The total displacement field is expressed as infinite series containing products of radial and angular Mathieu functions with unknown coefficients. An exact analytical determination of unknown coefficients is carried out by insuring the vanishing of normal stresses on crack faces. Frequency-domain results are given for extremely near, near, and far fields, whereas time-domain ones are for horizontal surface and subsurface motions. Comparisons with published data for the dynamic stress intensity factor show good agreement. The exact analytical nature of proposed solutions can be applied very conveniently and rapidly to high-frequency steady-state cases, enhancing the computation efficiency in transient cases when performing the fast Fourier transform. A sampled set of time slices for underground wave propagation benefits the interpretation of scattering and diffraction phenomena induced by a vertical edge crack.
The impedance problem of wave diffraction by a strip with higher order boundary conditions
NASA Astrophysics Data System (ADS)
Castro, L. P.; Simões, A. M.
2013-10-01
This work is devoted to analyse an impedance boundary-transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. A constructive approach of operator relations is built, which allows a transparent interpretation of the problem in an operator theory framework. In particular, different types of operator relations are exhibited for different types of operators acting between Lebesgue and Sobolev spaces on a finite interval and the positive half-line. All this has consequences in the understanding of the structure of this type of problems. In particular, a Fredholm characterization of the problem is obtained in terms of the initial space order parameters. At the request of the author and the Proceedings Editor the above article has been replaced with a corrected version. The original PDF file supplied to AIP Publishing contained an error in the title of the article. The original title appeared as: "The Impedance Problem of Wave Diffraction by a trip with Higher Order Boundary Conditions." This article has been replaced and the title now appears correctly online. The corrected article was published on 8 November 2013.
Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan
2013-09-01
Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.
NASA Astrophysics Data System (ADS)
Zhou, Changguo; Haber, Fred; Jaggard, Dwight L.
1991-02-01
The authors present a deterministic approach to the resolution analysis of the MUSIC algorithm for resolving plane waves contaminated by coherent interference when ensemble average covariance matrices are used. In the analysis, a resolution measure to describe the resolution potential of MUSIC in resolving two plane waves in noise is introduced. A closed-form solution for the resolution measure is given, and the result is compared to the resolution threshold derived by Kaveh and Barabell (1986) when the covariance matrices are estimated from a finite number of snapshots. In the presence of coherent interference, the resolution potential of MUSIC is severely limited, determined mainly by the signal-to-interference ratio (SIR). An approximate expression for the threshold SIR is derived for the cases when SIRs are large and the coherent interference and direct arrivals are well separated in spatial frequency. In these cases, it is shown that the threshold SIR is inversely proportional to the resolution measure, and the spectral estimates at the spatial frequencies of plane wave arrivals are approximately equal to the SIR when the arrivals are resolved. Illustrations are given, using an 11-element uniform array, for the cases of plane wave reflection from an infinite plane and scattering from an infinite conducting circular cylinder.
A plane wave source with minimal harmonic distortion for investigating nonlinear acoustic properties
Lloyd, Christopher W.; Wallace, Kirk D.; Holland, Mark R.; Miller, James G.
2008-01-01
The objective of this investigation is to introduce and validate a practical ultrasound source to be used in the investigation of the nonlinear material properties of liquids and soft tissues studied in vitro. Methods based on the progressive distortion of finite amplitude ultrasonic waves in the low megahertz frequency-range are most easily implemented under the assumption of plane wave propagation. However, achieving an approximately planar ultrasonic field over substantial propagation distances can be challenging. Furthermore, undesired harmonic distortion of the ultrasonic field prior to insonification of the specified region of interest represents another serious limitation. This paper introduces an approach based on the use of the ultrasonic field emanating from a stainless-steel delay line. Both simulation and direct experimental measurement demonstrate that such a field exhibits relatively planar wavefronts to a good approximation (such that a 3 mm diameter receiver would be exposed to no more than 3 dB of loss across its face) and is free from the significant harmonic distortion that would occur in a conventional water path. PMID:17614467
NASA Astrophysics Data System (ADS)
Rahman, Arifur; Duerr, Erik K.; de Lange, Gert; Hu, Qing
1997-06-01
We have combined silicon micromachining technology with planar circuits to fabricated room-temperature niobium microbolometers for millimeter-wave detection. In this type of detector, a thin niobium film, with a dimension much smaller than the wavelength, is fabricated on a 1-micrometers thick Si3N4 membrane of square and cross geometries. The Nb film acts both as a radiation absorber and temperature sensor. Incident radiation is coupled into the microbolometer by a 0.37 (lambda) dipole antenna with a center frequency of 95 GHz and a 3-db bandwidth of 15%, which is impedance matched with the Nb film. The dipole antennas is placed inside a micromachined pyramidal cavity formed by anisotropically etched Si wafers. To increase the Gaussian beam coupling efficiency, a machined square or circular horn is placed in front of the micromachined section. Circular horns interface more easily with die-based manufacturing processes; therefore, we have developed simulation tools that allow us to model circular machined horns. We have fabricated both single element receivers and 3 X 3 focal-plane arrays using uncooled Nb microbolometers. An electrical NEP level of 8.3 X 10-11 W/(root)Hz has been achieved for a single- element receiver. This NEP level is better than that of the commercial room-temperature pyroelectric millimeter-wave detectors. The frequency response of the microbolometer has a ln(1/f) dependence with frequency, and the roll-off frequency is approximately 35 kHz.
Effects of Non-Elevation-Focalized Linear Array Transducer on Ultrasound Plane-Wave Imaging
Wang, Congzhi; Xiao, Yang; Xia, Jingjing; Qiu, Weibao; Zheng, Hairong
2016-01-01
Plane-wave ultrasound imaging (PWUS) has become an important method of ultrasound imaging in recent years as its frame rate has exceeded 10,000 frames per second, allowing ultrasound to be used for two-dimensional shear wave detection and functional brain imaging. However, compared to the traditional focusing and scanning method, PWUS images always suffer from a degradation of lateral resolution and contrast. To improve the image quality of PWUS, many different beamforming algorithms have been proposed and verified. Yet the influence of transducer structure is rarely studied. For this paper, the influence of using an acoustic lens for PWUS was evaluated. Two linear array transducers were fabricated. One was not self-focalized in the elevation direction (non-elevation-focalized transducer, NEFT); the other one was a traditional elevation-focalized transducer (EFT). An initial simulation was conducted to show the influence of elevation focusing. Then the images obtained with NEFT on a standard ultrasound imaging phantom were compared with those obtained with EFT. It was demonstrated that, in a relatively deep region, the contrast of an NEFT image is better than that of an EFT image. These results indicate that a more sophisticated design of ultrasound transducer would further improve the image quality of PWUS. PMID:27845751
Formulation of the Augmented Plane-Wave and Muffin-Tin Orbital Method
NASA Astrophysics Data System (ADS)
Kotani, Takao; Kino, Hiori; Akai, Hisazumu
2015-03-01
The augmented plane waves and the muffin-tin orbitals method (the PMT method) was proposed by Kotani and van Schilfgaarde in http://dx.doi.org/10.1103/PhysRevB.81.125117, Phys. Rev. B 81, 125117 (2010). It is a mixed basis all-electron full-potential method, which uses two types of augmented waves simultaneously, in addition to the local orbitals. In this paper, this mixed basis method is reformulated on the basis of a new formalism named as the 3-component formalism, which is a mathematically transparent version of the additive augmentation originally proposed by Soler and Williams in http://dx.doi.org/10.1103/PhysRevB.47.6784, Phys. Rev. B 47, 6784 (1993). Atomic forces are easily derived systematically. We discuss some problems in the mixed basis method and ways to manage them. In addition, we compare the method with the PAW method on the same footing. This PMT method is the basis for our new development of the quasiparticle self-consistent GW method in http://dx.doi.org/10.7566/JPSJ.83.094711, J. Phys. Soc. Jpn. 83, 094711 (2014), available as the ecalj package at github.
NASA Astrophysics Data System (ADS)
Zheng, Chang-Jun; Chen, Hai-Bo; Chen, Lei-Lei
2013-04-01
This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/plane-symmetric acoustic wave problems. The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only. Moreover, a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived, and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating, translating and saving the multipole/local expansion coefficients of the image domain. The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems. As for exterior acoustic problems, the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method. Details on the implementation of the present method are described, and numerical examples are given to demonstrate its accuracy and efficiency.
Microscopic theory of spin-wave instabilities in parallel-pumped easy-plane ferromagnets
NASA Astrophysics Data System (ADS)
Lim, S. P.; Huber, D. L.
1988-04-01
Spin-wave instabilities in parallel-pumped easy-plane ferromagnets are investigated using the S-theory formalism of Zakharov et al. The parameters in the theory are related to the interaction constants in a microscopic Hamiltonian with exchange anisotropy. A numerical study of two- and five-mode systems shows that the nonequilibrium stationary states are ones where all of the spin-wave pair correlation functions have the same phase. It is also found that the phases lock to a common value before the stationary state is reached. From the form of the equations it is argued that a similar result holds for a macroscopic number of modes. Results are presented for the stationary magnon population. The approach to a stationary state in the phase-locked regime is governed by two coupled first-order differential equations. When the equations are linearized about the fixed points, it is found that the approach to the stationary state involves purely exponential decay just above threshold and damped oscillatory decay at higher power levels. Possible experimental tests of the theory are discussed.
Baroclinic waves on the β plane using low-order Discontinuous Galerkin discretisation
NASA Astrophysics Data System (ADS)
Orgis, Thomas; Läuter, Matthias; Handorf, Dörthe; Dethloff, Klaus
2017-06-01
A classic Discontinuous Galerkin Method with low-order polynomials and explicit as well as semi-implicit time-stepping is applied to an atmospheric model employing the Euler equations on the β plane. The method, which was initially proposed without regard for the source terms and their balance with the pressure gradient that dominates atmospheric dynamics, needs to be adapted to be able to keep the combined geostrophic and hydrostatic balance in three spatial dimensions. This is achieved inside the discretisation through a polynomial mapping of both source and flux terms without imposing filters between time steps. After introduction and verification of this balancing, the realistic development of barotropic and baroclinic waves in the model is demonstrated, including the formation of a retrograde Rossby wave pattern. A prerequesite is the numerical solution of the thermal wind equation to construct geostrophically balanced initial states in z coordinates with arbitrary prescribed zonal wind profile, offering a new set of test cases for atmospheric models employing z coordinates. The resulting simulations demonstrate that the balanced low-order Discontinuous Galerkin discretisation with polynomial degrees down to k = 1 can be a viable option for atmospheric modelling.
Large-scale W-band focal plane array developments for passive millimeter-wave imaging
NASA Astrophysics Data System (ADS)
Kuroda, Roger T.; Dow, G. Samuel; Moriarty, Dan T.; Johnson, Ronald L.; Quil, Avery Y.; Tran, Steve D.; Pajo, Voltaire; Fornaca, Steven W.; Yujiri, Larry
1998-08-01
A state-of-the-art W-Band passive millimeter wave focal plane array (FPA) consisting of 1040 highly integrated direct detection pixel has been designed, developed, assembled and tested. The FPA has been integrated into a passive millimeter wave video camera and has generated real time images. Each pixel is a highly integrated MMIC chip receiver. The MMIC chip is a wide band, high gain, low noise, 0.1 micrometer InGaAs HEMT amplifier with an integrated switch and Schottky barrier diode detector. The FPA uses a brick architecture. Each brick or module consists of 4 MMIC chips or pixels and lay side-by- side on the card. Many cards are stacked to create the array of pixels. In the next generation FPA, the 1 X 4 modules and cards have been dramatically simplified with 50% less assembly time. In addition, the module and card still require no tuning and minimal test time. Thus a significant cost reduction in the FPA is expected over the first generation FPA without sacrificing performance. To further reduce cost and improve performance, new MMIC chips are being designed.
Wang, Yu; Jiang, Jingfeng
2017-07-01
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.
ABINIT: Plane-Wave-Based Density-Functional Theory on High Performance Computers
NASA Astrophysics Data System (ADS)
Torrent, Marc
2014-03-01
For several years, a continuous effort has been produced to adapt electronic structure codes based on Density-Functional Theory to the future computing architectures. Among these codes, ABINIT is based on a plane-wave description of the wave functions which allows to treat systems of any kind. Porting such a code on petascale architectures pose difficulties related to the many-body nature of the DFT equations. To improve the performances of ABINIT - especially for what concerns standard LDA/GGA ground-state and response-function calculations - several strategies have been followed: A full multi-level parallelisation MPI scheme has been implemented, exploiting all possible levels and distributing both computation and memory. It allows to increase the number of distributed processes and could not be achieved without a strong restructuring of the code. The core algorithm used to solve the eigen problem (``Locally Optimal Blocked Congugate Gradient''), a Blocked-Davidson-like algorithm, is based on a distribution of processes combining plane-waves and bands. In addition to the distributed memory parallelization, a full hybrid scheme has been implemented, using standard shared-memory directives (openMP/openACC) or porting some comsuming code sections to Graphics Processing Units (GPU). As no simple performance model exists, the complexity of use has been increased; the code efficiency strongly depends on the distribution of processes among the numerous levels. ABINIT is able to predict the performances of several process distributions and automatically choose the most favourable one. On the other hand, a big effort has been carried out to analyse the performances of the code on petascale architectures, showing which sections of codes have to be improved; they all are related to Matrix Algebra (diagonalisation, orthogonalisation). The different strategies employed to improve the code scalability will be described. They are based on an exploration of new diagonalization
Structure and magnetism of bulk Fe and Cr: from plane waves to LCAO methods.
Soulairol, R; Fu, Chu-Chun; Barreteau, C
2010-07-28
Magnetic, structural and energetic properties of bulk Fe and Cr were studied using first-principles calculations within density functional theory (DFT). We aimed to identify the dependence of these properties on key approximations of DFT, namely the exchange-correlation functional, the pseudopotential and the basis set. We found a smaller effect of pseudopotentials (PPs) on Fe than on Cr. For instance, the local magnetism of Cr was shown to be particularly sensitive to the potentials representing the core electrons, i.e. projector augmented wave and Vanderbilt ultrasoft PPs predict similar results, whereas standard norm-conserving PPs tend to overestimate the local magnetic moments of Cr in bcc Cr and in dilute bcc FeCr alloys. This drawback is suggested to be closely correlated to the overestimation of Cr solution energy in the latter system. On the other hand, we point out that DFT methods with very reduced localized basis sets (LCAO: linear combination of atomic orbitals) give satisfactory results compared with more robust plane-wave approaches. A minimal-basis representation of '3d' electrons comes to be sufficient to describe non-trivial magnetic phases including spin spirals in both fcc Fe and bcc Cr, as well as the experimental magnetic ground state of bcc Cr showing a spin density wave (SDW) state. In addition, a magnetic 'spd' tight binding model within the Stoner formalism was proposed and validated for Fe and Cr. The respective Stoner parameters were obtained by fitting to DFT data. This efficient semiempirical approach was shown to be accurate enough for studying various collinear and non-collinear phases of bulk Fe and Cr. It also enabled a detailed investigation of different polarization states of SDW in bcc Cr, where the longitudinal state was suggested to be the ground state, consistent with existing experimental data.
NASA Astrophysics Data System (ADS)
Trappe, N.; Bucher, M.; De Bernardis, P.; Delabrouille, J.; Deo, P.; DePetris, M.; Doherty, S.; Ghribi, A.; Gradziel, M.; Kuzmin, L.; Maffei, B.; Mahashabde, S.; Masi, S.; Murphy, J. A.; Noviello, F.; O'Sullivan, C.; Pagano, L.; Piacentini, F.; Piat, M.; Pisano, G.; Robinson, M.; Stompor, R.; Tartari, A.; van der Vorst, M.; Verhoeve, P.
2016-07-01
The main objective of this activity is to develop new focal plane coupling array concepts and technologies that optimise the coupling from reflector optics to the large number of detectors for next generation sub millimetre wave telescopes particularly targeting measurement of the polarization of the cosmic microwave background (CMB). In this 18 month TRP programme the consortium are tasked with developing, manufacturing and experimentally verifying a prototype multichroic pixel which would be suitable for the large focal plane arrays which will be demanded to reach the required sensitivity of future CMB polarization missions. One major development was to have multichroic operation to potentially reduce the required focal plane size of a CMB mission. After research in the optimum telescope design and definition of requirements based on a stringent science case review, a number of compact focal plane architecture concepts were investigated before a pixel demonstrator consisting of a planar mesh lens feeding a backend Resonant Cold Electron Bolometer RCEB for filtering and detection of the dual frequency signal was planned for manufacture and test. In this demonstrator the frequencies of the channels was chosen to be 75 and 105 GHz in the w band close to the peak CMB signal. In the next year the prototype breadboards will be developed to test the beams produced by the manufactured flat lenses fed by a variety of antenna configurations and the spectral response of the RCEBs will also be verified.
Prego-Borges, José L; Zamboni-Rached, Michel; Recami, Erasmo; Costa, Eduardo Tavares
2014-08-01
The so-called Localized Waves (LW), and the "Frozen Waves" (FW), have raised significant attention in the areas of Optics and Ultrasound, because of their surprising energy localization properties. The LWs resist the effects of diffraction for large distances, and possess an interesting self-reconstruction -self-healing- property (after obstacles with size smaller than the antenna's); while the FWs, a sub-class of LWs, offer the possibility of arbitrarily modeling the longitudinal field intensity pattern inside a prefixed interval, for instance 0⩽z⩽L, of the wave propagation axis. More specifically, the FWs are localized fields "at rest", that is, with a static envelope (within which only the carrier wave propagates), and can be endowed moreover with a high transverse localization. In this paper we investigate, by simulated experiments, various cases of generation of ultrasonic FW fields, with the frequency of f0=1 MHz in a water-like medium, taking account of the effects of attenuation. We present results of FWs for distances up to L=80 mm, in attenuating media with absorption coefficient α in the range 70⩽α⩽170 dB/m. Such simulated FW fields are constructed by using a procedure developed by us, via appropriate finite superpositions of monochromatic ultrasonic Bessel beams. We pay due attention to the selection of the FW parameters, constrained by the rather tight restrictions imposed by experimental Acoustics, as well as to some practical implications of the transducer design. The energy localization properties of the Frozen Waves can find application even in many medical apparatus, such as bistouries or acoustic tweezers, as well as for treatment of diseased tissues (in particular, for the destruction of tumor cells, without affecting the surrounding tissues; also for kidney stone shuttering, etc.).
Diffraction of electromagnetic waves in the gravitational field of the Sun
NASA Astrophysics Data System (ADS)
Turyshev, Slava G.; Toth, Viktor T.
2017-07-01
We consider the propagation of electromagnetic (EM) waves in the gravitational field of the Sun within the first post-Newtonian approximation of the general theory of relativity. We solve Maxwell's equations for the EM field propagating on the background of a static mass monopole and find an exact closed form solution for the Debye potentials, which, in turn, yield a solution to the problem of diffraction of EM waves in the gravitational field of the Sun. The solution is given in terms of the confluent hypergeometric function and, as such, it is valid for all distances and angles. Using this solution, we develop a wave-theoretical description of the solar gravitational lens (SGL) and derive expressions for the EM field and energy flux in the immediate vicinity of the focal line of the SGL. Aiming at the potential practical applications of the SGL, we study its optical properties and discuss its suitability for direct high-resolution imaging of a distant exoplanet.
NASA Astrophysics Data System (ADS)
Filippov, A. I.; Akhmetova, O. V.; Koval‧skii, A. A.
2016-11-01
The filtration-wave process in the central layer of a three-layer anisotropic medium is described as an equivalent plane wave with a modified asymptotic method accurate in the mean. The initial problem is parametrized and broken down into simpler problems for the coefficients of expansion in an asymptotic parameter. The zero expansion coefficient describes the sought plane wave, whereas the first coefficient ensures refinement of the wave-front geometry. The exact solution of the parametrized problem is obtained on the basis of the Fourier sine transformation. The correctness of the developed method is confirmed by comparing the obtained asymptotic solutions and the coefficients of Maclaurin-series expansion of the exact solution of the parametrized problem in a formal parameter.
Guzatov, D V; Gaida, L S; Afanas'ev, Anatolii A
2008-12-31
The light pressure force acting on a spherical dielectric particle in the interference field of two plane monochromatic electromagnetic waves is studied in detail for different particle radii and angles of incidence of waves. (light pressure)
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.
A projection-free method for representing plane-wave DFT results in an atom-centered basis
Dunnington, Benjamin D.; Schmidt, J. R.
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 strict 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.
Catastrophe optics of sharp-edge diffraction.
Borghi, Riccardo
2016-07-01
A classical problem of diffraction theory, namely plane wave diffraction by sharp-edge apertures, is here reformulated from the viewpoint of the fairly new subject of catastrophe optics. On using purely geometrical arguments, properly embedded into a wave optics context, uniform analytical estimates of the diffracted wavefield at points close to fold caustics are obtained, within paraxial approximation, in terms of the Airy function and its first derivative. Diffraction from parabolic apertures is proposed to test reliability and accuracy of our theoretical predictions.
Kawashima, Yukio; Hirao, Kimihiko
2017-03-09
We introduced two methods to correct the singularity in the calculation of long-range Hartree-Fock (HF) exchange for long-range-corrected density functional theory (LC-DFT) calculations in plane-wave basis sets. The first method introduces an auxiliary function to cancel out the singularity. The second method introduces a truncated long-range Coulomb potential, which has no singularity. We assessed the introduced methods using the LC-BLYP functional by applying it to isolated systems of naphthalene and pyridine. We first compared the total energies and the HOMO energies of the singularity-corrected and uncorrected calculations and confirmed that singularity correction is essential for LC-DFT calculations using plane-wave basis sets. The LC-DFT calculation results converged rapidly with respect to the cell size as the other functionals, and their results were in good agreement with the calculated results obtained using Gaussian basis sets. LC-DFT succeeded in obtaining accurate orbital energies and excitation energies. We next applied LC-DFT with singularity correction methods to the electronic structure calculations of the extended systems, Si and SiC. We confirmed that singularity correction is important for calculations of extended systems as well. The calculation results of the valence and conduction bands by LC-BLYP showed good convergence with respect to the number of k points sampled. The introduced methods succeeded in overcoming the singularity problem in HF exchange calculation. We investigated the effect of the singularity correction on the excitation state calculation and found that careful treatment of the singularities is required compared to ground-state calculations. We finally examined the excitonic effect on the band gap of the extended systems. We calculated the excitation energies to the first excited state of the extended systems using a supercell model at the Γ point and found that the excitonic binding energy, supposed to be small for
G W with linearized augmented plane waves extended by high-energy local orbitals
NASA Astrophysics Data System (ADS)
Jiang, Hong; Blaha, Peter
2016-03-01
Many-body perturbation theory in the G W approximation is currently the most accurate and robust first-principles approach to determine the electronic band structure of weakly correlated insulating materials without any empirical input. Recent G W results for ZnO with more careful investigation of the convergence with respect to the number of unoccupied states have led to heated debates regarding the numerical accuracy of previously reported G W results using either pseudopotential plane waves or all-electron linearized augmented plane waves (LAPWs). The latter has been arguably regarded as the most accurate scheme for electronic-structure theory for solids. This work aims to solve the ZnO puzzle via a systematic investigation of the effects of including high-energy local orbitals (HLOs) in the LAPW-based G W calculations of semiconductors. Using ZnO as the prototypical example, it is shown that the inclusion of HLOs has two main effects: it improves the description of high-lying unoccupied states by reducing the linearization errors of the standard LAPW basis, and in addition it provides an efficient way to achieve the completeness in the summation of states in G W calculations. By investigating the convergence of G W band gaps with respect to the number of HLOs for several other typical examples, it was found that the effects of HLOs are highly system-dependent, and in most cases the inclusion of HLOs changes the band gap by less than 0.2 eV. Compared to its effects on the band gap, the consideration of HLOs has even stronger effects on the G W correction to the valence-band maximum, which is of great significance for the G W prediction of the ionization potentials of semiconductors. By considering an extended set of semiconductors with relatively well-established experimental band gaps, it was found that in general using a HLO-enhanced LAPW basis significantly improves the agreement with experiment for both the band gap and the ionization potential, and overall
Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics
NASA Technical Reports Server (NTRS)
Hahne, G. E.
1993-01-01
The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.
NASA Astrophysics Data System (ADS)
Shepherd, James J.; Grüneis, Andreas; Booth, George H.; Kresse, Georg; Alavi, Ali
2012-07-01
Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete-basis-set (CBS) limit in methods utilizing plane-wave wave-function expansions. Simple analytic and numerical results from second-order Møller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis-set truncation when constructing many-electron wave functions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wave-function methods, from MP2 to coupled-cluster doubles theory and the random-phase approximation plus second-order screened exchange. Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane-wave basis and thereby allow application of these methods to more realistic physical problems. We demonstrate this explicitly for solid and molecular lithium hydride.
Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space
NASA Astrophysics Data System (ADS)
Ba, Zhenning; Liang, Jianwen; Zhang, Yanju
2017-01-01
The scattering of plane SH-waves by topographic features in a layered transversely isotropic (TI) half-space is investigated by using an indirect boundary element method (IBEM). Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green's functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green's functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.
Influence of orbital symmetry on diffraction imaging with rescattering electron wave packets
Pullen, M. G.; Wolter, B.; Le, A. -T.; Baudisch, M.; Sclafani, M.; Pires, H.; Schroter, C. D.; Ullrich, J.; Moshammer, R.; Pfeifer, T.; Lin, C. D.; Biegert, J.
2016-06-22
The ability to directly follow and time-resolve the rearrangement of the nuclei within molecules is a frontier of science that requires atomic spatial and few-femtosecond temporal resolutions. While laser-induced electron diffraction can meet these requirements, it was recently concluded that molecules with particular orbital symmetries (such as pg) cannot be imaged using purely backscattering electron wave packets without molecular alignment. Here, we demonstrate, in direct contradiction to these findings, that the orientation and shape of molecular orbitals presents no impediment for retrieving molecular structure with adequate sampling of the momentum transfer space. We overcome previous issues by showcasing retrieval of the structure of randomly oriented O_{2} and C_{2}H_{2} molecules, with π_{g} and π_{u} symmetries, respectively, and where their ionization probabilities do not maximize along their molecular axes. As a result, while this removes a serious bottleneck for laser-induced diffraction imaging, we find unexpectedly strong backscattering contributions from low-Z atoms.
Influence of orbital symmetry on diffraction imaging with rescattering electron wave packets
Pullen, M. G.; Wolter, B.; Le, A. -T.; ...
2016-06-22
The ability to directly follow and time-resolve the rearrangement of the nuclei within molecules is a frontier of science that requires atomic spatial and few-femtosecond temporal resolutions. While laser-induced electron diffraction can meet these requirements, it was recently concluded that molecules with particular orbital symmetries (such as pg) cannot be imaged using purely backscattering electron wave packets without molecular alignment. Here, we demonstrate, in direct contradiction to these findings, that the orientation and shape of molecular orbitals presents no impediment for retrieving molecular structure with adequate sampling of the momentum transfer space. We overcome previous issues by showcasing retrieval ofmore » the structure of randomly oriented O2 and C2H2 molecules, with πg and πu symmetries, respectively, and where their ionization probabilities do not maximize along their molecular axes. As a result, while this removes a serious bottleneck for laser-induced diffraction imaging, we find unexpectedly strong backscattering contributions from low-Z atoms.« less
Influence of orbital symmetry on diffraction imaging with rescattering electron wave packets
Pullen, M. G.; Wolter, B.; Le, A. -T.; Baudisch, M.; Sclafani, M.; Pires, H.; Schröter, C. D.; Ullrich, J.; Moshammer, R.; Pfeifer, T.; Lin, C. D.; Biegert, J.
2016-01-01
The ability to directly follow and time-resolve the rearrangement of the nuclei within molecules is a frontier of science that requires atomic spatial and few-femtosecond temporal resolutions. While laser-induced electron diffraction can meet these requirements, it was recently concluded that molecules with particular orbital symmetries (such as πg) cannot be imaged using purely backscattering electron wave packets without molecular alignment. Here, we demonstrate, in direct contradiction to these findings, that the orientation and shape of molecular orbitals presents no impediment for retrieving molecular structure with adequate sampling of the momentum transfer space. We overcome previous issues by showcasing retrieval of the structure of randomly oriented O2 and C2H2 molecules, with πg and πu symmetries, respectively, and where their ionization probabilities do not maximize along their molecular axes. While this removes a serious bottleneck for laser-induced diffraction imaging, we find unexpectedly strong backscattering contributions from low-Z atoms. PMID:27329236
NASA Astrophysics Data System (ADS)
Lee, Young Ok; Chen, Fu; Lee, Kee Keun
2016-06-01
We have developed acoustic-optic (AO) based display units for implementing a handheld hologram display by modulating light deflection through wide bandwidth surface acoustic wave (SAW). The developed AO device consists of a metal layer, a ZnS waveguide layer, SAW inter digital transducers (IDTs), and a screen for display. When RF power with a particular resonant frequency was applied to IDTs, SAW was radiated and interfered with confined beam propagating along ZnS waveguide layer. The AO interacted beam was deflected laterally toward a certain direction depending on Bragg diffraction condition, exited out of the waveguide layer and then directed to the viewing screen placed at a certain distance from the device to form a single pixel. The deflected angles was adjusted by modulating the center frequency of the SAW IDT (SAW grating), the RF power of SAW, and the angles between propagating light beam path along waveguide and radiating SAW. The diffraction efficiency was also characterized in terms of waveguide thickness, SAW RF input power, and aperture length. Coupling of mode (COM) modeling was fulfilled to find optimal device parameters prior to fabrication. All the parameters affecting the deflection angle and efficiency to form a pixel for a three-dimensional (3D) hologram image were characterized and then discussed.
NASA Astrophysics Data System (ADS)
King, B.; Hu, H.
2016-12-01
We consider a scalar particle in a background formed by two counterpropagating plane waves. Two cases are studied: (i) dynamics at a magnetic node and (ii) zero initial transverse canonical momentum. The Lorentz and Klein-Gordon equations are solved for these cases and approximations analyzed. For the magnetic-node solution (homogeneous, time-dependent electric field), the modified Volkov wave function which arises from a high-energy approximation is found to be inaccurate for all energies and the solution itself unstable when the photon emission (nonlinear Compton scattering) is included. For the zero initial transverse canonical momentum case, in both quantum and classical cases, forbidden parameter regimes, absent in the plane-wave model, are identified.
Mkrtichyan, G. S.
2015-07-15
The trajectories of electrons with large longitudinal momenta in the phase plane in the course of their surfatron acceleration by an electromagnetic wave propagating in space plasma across the external magnetic field are analyzed. Electrons with large longitudinal momenta are trapped immediately if the initial wave phase Ψ(0) on the particle trajectory is positive. For negative values of Ψ(0), no electrons trapping by the wave is observed over the available computational times. According to numerical calculations, the trajectories of trapped particles in the phase plane have a singular point of the stable focus type and the behavior of the trajectory corresponds to the motion in a complex nonstationary effective potential well. For some initial phases, electrons are confined in the region of the accelerating electric field for relatively short time, the energy gain being about 50–130% and more.
NASA Astrophysics Data System (ADS)
Maity, Narottam; Barik, S. P.; Chaudhuri, P. K.
2016-09-01
In this paper, plane wave propagation in a rotating anisotropic material of general nature under the action of a magnetic field of constant magnitude has been investigated. The material is supposed to be porous in nature and contains voids. Following the concept of [Cowin S. C. and Nunziato, J. W. [1983] “Linear elastic materials with voids,” J. Elasticity 13, 125-147.] the governing equations of motion have been written in tensor notation taking account of rotation, magnetic field effect and presence of voids in the medium and the possibility of plane wave propagation has been examined. A number of particular cases have been derived from our general results to match with previously obtained results in this area. Effects of various parameters on the velocity of wave propagation have been presented graphically.
Spin-wave spectra and stability of the in-plane vortex state in two-dimensional magnetic nanorings
Mamica, S.
2013-12-21
We study theoretically two-dimensional nanorings assumed to have the in-plane vortex magnetic configuration. Using a discrete dipole model we examine the spectrum of normal spin-wave modes vs. the dipolar-to-exchange interaction ratio. We systematize the spin-wave excitations by their azimuthal and radial wave numbers. The lowest-frequency mode, the fundamental (quasiuniform) mode, and the mode hybridization are analyzed; the discussion of the influence of effective pinning at the ring boundaries is provided as well. We study the stability of the in-plane vortex state and discuss the role of the size of the ring and the type of lattice arrangement of the magnetic moments within it. To facilitate comparison with our results we provide the relationships between microscopic parameters, used in our model, and those used in the case of continuous medium.
Mitri, F G; Fellah, Z E A
2008-08-01
Acoustic plane progressive waves incident on a sphere immersed in a nonviscous fluid exert a steady force acting along the direction of wave motion. It is shown here that when an elastic gold sphere is coated with a polymer-type (polyethylene) viscoelastic layer, this force becomes a force of attraction in the long wavelength limit. Kinetic, potential and Reynolds stress energy densities are defined and evaluated with and in the absence of absorption in the layer. Without absorption, the mechanical energy density counteracts the Reynolds stress energy density, which causes a repulsive force. However, in the case of absorption, the attractive force is predicted to be a physical consequence of a mutual contribution of both the mechanical and the Reynolds stress energy densities. This condition provides an impetus for further designing acoustic tweezers operating with plane progressive waves as well as fabricating polymer-coated gold particles for specific biophysical and biomedical applications.
Performance bounds for passive sensor arrays operating in a turbulent medium: Plane-wave analysis
NASA Astrophysics Data System (ADS)
Collier, S. L.; Wilson, D. K.
2003-05-01
The performance bounds of a passive acoustic array operating in a turbulent medium with fluctuations described by a von Kármán spectrum are investigated. This treatment considers a single, monochromatic, plane-wave source at near-normal incidence. A line-of-sight propagation path is assumed. The primary interests are in calculating the Cramer-Rao lower bounds of the azimuthal and elevational angles of arrival and in observing how these bounds change with the introduction of additional unknowns, such as the propagation distance, turbulence parameters, and signal-to-noise ratio. In both two and three dimensions, it is found that for large values of the index-of-refraction variance, the Cramer-Rao lower bounds of the angles of arrival increase significantly at large values of the normalized propagation distance. For small values of the index-of-refraction variance and normalized propagation distance, the signal-to-noise ratio is found to be the limiting factor. In the two-dimensional treatment, it is found that the estimate of the angle of arrival will decouple from the estimates of the other parameters with the appropriate choice of array geometry. In three dimensions, again with an appropriate choice of array geometry, the estimates of the azimuth and elevation will decouple from the estimates of the other parameters, but due to the constraints of the model, will remain coupled to one another.
Ab initio Sternheimer-GW method for quasiparticle calculations using plane waves
NASA Astrophysics Data System (ADS)
Lambert, Henry; Giustino, Feliciano
2013-08-01
We report on the extension and implementation of the Sternheimer-GW method introduced by Giustino [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.81.115105 81, 115105 (2010)] to the case of first-principles pseudopotential calculations based on a plane-waves basis. The Sternheimer-GW method consists of calculating the GW self-energy operator without resorting to the standard expansion over unoccupied Kohn-Sham electronic states. The Green's function is calculated by solving linear systems for frequencies along the real axis. The screened Coulomb interaction is calculated for frequencies along the imaginary axis by using the Sternheimer equation. Analytic continuation to the real axis is performed using Padé approximants. The generalized plasmon-pole approximation is avoided by performing explicit calculations at multiple frequencies using Frommer's multishift solver. We demonstrate our methodology by reporting tests on common insulators and semiconductors, including Si, diamond, LiCl, and SiC. Our calculated quasiparticle energies are in agreement with the results of fully converged calculations based on the sum-over-states approach. As the Sternheimer-GW method yields the complete self-energy Σ(r,r',ω) and not only its expectation values on Kohn-Sham states, this work opens the way to nonperturbative GW calculations and to direct calculations of spectral functions for angle-resolved photoemission spectroscopy. As an example of the capabilities of the method we calculate the G0W0 spectral functions of silicon and diamond.
Three-dimensional plane-wave full-band quantum transport using empirical pseudopotentials
NASA Astrophysics Data System (ADS)
Fang, Jingtian; Vandenberghe, William; Fischetti, Massimo
2015-03-01
We study theoretically the ballistic performance of future sub-5 nm Field-Effect Transistors (FETs) using an atomistic quantum transport formalism based on empirical pseudopotentials, with armchair Graphene NanoRibbons (aGNRs), Silicon NanoWires (SiNWs) and zigzag Carbon NanoTubes (zCNTs) as channel structures. Due to the heavy computational burden from the plane-wave basis set, we restrict our study to ultrasmall devices, characterized by 5 nm channel lengths and 0.7 nm × 0.7 nm cross-sectional areas. Band structure calculations show that aGNRs have an oscillating chirality-dependent band gap. AGNRs with dimer lines N=3p+1 have large band gaps and aGNRFETs show promising device performance in terms of high Ion/Ioff, small drain-induced barrier lowering and limited short channel effects due to their very thin body and associated excellent electrostatics control. N=3p+2 aGNRs have small band gaps and band-to-band tunneling generates a large current at high bias. We also discuss spurious solutions introduced by the envelope function approximation. Device characteristics of SiNWFETs and zCNTFETs are compared to aGNRFETs as well. We acknowledge the support of Nanoelectronics Research Initiatives's (NRI's) Southwest Academy of Nanoelectronics (SWAN).
Discontinuous Galerkin methods with plane waves for time-harmonic problems
Gabard, Gwenael . E-mail: gabard@soton.ac.uk
2007-08-10
A general framework for discontinuous Galerkin methods in the frequency domain with numerical flux is presented. The main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element. The method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two-dimensional linearized Euler equations. It is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high-order DRP schemes. In addition, the conditioning of the method is found to be high but not critical in practice. It is shown that the Ultra-Weak Variational Formulation is in fact a subset of the present discontinuous Galerkin method. A special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles. Aeroacoustic problems with non-uniform flows are also considered and results are presented for the sound radiated from a two-dimensional jet.