Spherical Harmonic Decomposition of Gravitational Waves Across Mesh Refinement Boundaries

NASA Technical Reports Server (NTRS)

Fiske, David R.; Baker, John; vanMeter, James R.; Centrella, Joan M.

2005-01-01

We evolve a linearized (Teukolsky) solution of the Einstein equations with a non-linear Einstein solver. Using this testbed, we are able to show that such gravitational waves, defined by the Weyl scalars in the Newman-Penrose formalism, propagate faithfully across mesh refinement boundaries, and use, for the first time to our knowledge, a novel algorithm due to Misner to compute spherical harmonic components of our waveforms. We show that the algorithm performs extremely well, even when the extraction sphere intersects refinement boundaries.

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

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Hennig, Jörg

2018-03-01

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

Random Choice Solutions for Weak Spherical Shock-Wave Transitions of N-Waves in Air with Vibrational Excitation.

DTIC Science & Technology

1983-07-01

ionalI relaxat in dii icons whe-re kricrw-i aitMSo~lli-l-ic cirrd it ions could efc-tes for spherical I\\ -svrmetric wave s . bc obitani rd - It will lit...of cibirat jona 1 nonequ iiib rium cont rihuteCs to tr univ for weak waves. The rise times for the ieI ciCUlatijun for cases A5 , 81l, Cl and DI real...I ibrium thle c;iI itid ma iuum oci-rpressiire t I pIm1 atid in) :ompairisoni with c-ase A5 . hi ile almxost the same the half diii t iou tdI

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Simulation and scaling analysis of a spherical particle-laden blast wave

NASA Astrophysics Data System (ADS)

Ling, Y.; Balachandar, S.

2018-02-01

A spherical particle-laden blast wave, generated by a sudden release of a sphere of compressed gas-particle mixture, is investigated by numerical simulation. The present problem is a multiphase extension of the classic finite-source spherical blast-wave problem. The gas-particle flow can be fully determined by the initial radius of the spherical mixture and the properties of gas and particles. In many applications, the key dimensionless parameters, such as the initial pressure and density ratios between the compressed gas and the ambient air, can vary over a wide range. Parametric studies are thus performed to investigate the effects of these parameters on the characteristic time and spatial scales of the particle-laden blast wave, such as the maximum radius the contact discontinuity can reach and the time when the particle front crosses the contact discontinuity. A scaling analysis is conducted to establish a scaling relation between the characteristic scales and the controlling parameters. A length scale that incorporates the initial pressure ratio is proposed, which is able to approximately collapse the simulation results for the gas flow for a wide range of initial pressure ratios. This indicates that an approximate similarity solution for a spherical blast wave exists, which is independent of the initial pressure ratio. The approximate scaling is also valid for the particle front if the particles are small and closely follow the surrounding gas.

Simulation and scaling analysis of a spherical particle-laden blast wave

NASA Astrophysics Data System (ADS)

Ling, Y.; Balachandar, S.

2018-05-01

A spherical particle-laden blast wave, generated by a sudden release of a sphere of compressed gas-particle mixture, is investigated by numerical simulation. The present problem is a multiphase extension of the classic finite-source spherical blast-wave problem. The gas-particle flow can be fully determined by the initial radius of the spherical mixture and the properties of gas and particles. In many applications, the key dimensionless parameters, such as the initial pressure and density ratios between the compressed gas and the ambient air, can vary over a wide range. Parametric studies are thus performed to investigate the effects of these parameters on the characteristic time and spatial scales of the particle-laden blast wave, such as the maximum radius the contact discontinuity can reach and the time when the particle front crosses the contact discontinuity. A scaling analysis is conducted to establish a scaling relation between the characteristic scales and the controlling parameters. A length scale that incorporates the initial pressure ratio is proposed, which is able to approximately collapse the simulation results for the gas flow for a wide range of initial pressure ratios. This indicates that an approximate similarity solution for a spherical blast wave exists, which is independent of the initial pressure ratio. The approximate scaling is also valid for the particle front if the particles are small and closely follow the surrounding gas.

Massive graviton geons

NASA Astrophysics Data System (ADS)

Aoki, Katsuki; Maeda, Kei-ichi; Misonoh, Yosuke; Okawa, Hirotada

2018-02-01

We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects massive graviton geons. The basic equations can be reduced to the Schrödinger-Poisson equations with the tensor "wave function" in the Newtonian limit. We obtain a nonspherically symmetric solution with j =2 , ℓ=0 as well as a spherically symmetric solution with j =0 , ℓ=2 in this system where j is the total angular momentum quantum number and ℓ is the orbital angular momentum quantum number, respectively. The energy eigenvalue of the Schrödinger equation in the nonspherical solution is smaller than that in the spherical solution. We then study the perturbative stability of the spherical solution and find that there is an unstable mode in the quadrupole mode perturbations which may be interpreted as the transition mode to the nonspherical solution. The results suggest that the nonspherically symmetric solution is the ground state of the massive graviton geon. The massive graviton geons may decay in time due to emissions of gravitational waves but this timescale can be quite long when the massive gravitons are nonrelativistic and then the geons can be long-lived. We also argue possible prospects of the massive graviton geons: applications to the ultralight dark matter scenario, nonlinear (in)stability of the Minkowski spacetime, and a quantum transition of the spacetime.

Vector matter waves in two-component Bose-Einstein condensates with spatially modulated nonlinearities

NASA Astrophysics Data System (ADS)

Xu, Si-Liu; He, Jun-Rong; Xue, Li; Belić, Milivoj R.

2018-02-01

We demonstrate three-dimensional (3D) vector solitary waves in the coupled (3 + 1)-D nonlinear Gross-Pitaevskii equations with variable nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing novel localized solutions that depend on three modal numbers, l, m, and n. Using the similarity transformation (ST) method in 3D, vector solitary waves are built with the help of a combination of harmonic and trapping potentials, including multipole solutions and necklace rings. In general, the solutions found are stable for low values of the modal numbers; for values larger than 2, the solutions are found to be unstable. Variable nonlinearity allows the utilization of soliton management methods.

The structure of shock wave in a gas consisting of ideally elastic, rigid spherical molecules

NASA Technical Reports Server (NTRS)

Cheremisin, F. G.

1972-01-01

Principal approaches are examined to the theoretical study of the shock layer structure. The choice of a molecular model is discussed and three procedures are formulated. These include a numerical calculation method, solution of the kinetic relaxation equation, and solution of the Boltzmann equation.

On computing special functions in marine engineering

NASA Astrophysics Data System (ADS)

Constantinescu, E.; Bogdan, M.

2015-11-01

Important modeling applications in marine engineering conduct us to a special class of solutions for difficult differential equations with variable coefficients. In order to be able to solve and implement such models (in wave theory, in acoustics, in hydrodynamics, in electromagnetic waves, but also in many other engineering fields), it is necessary to compute so called special functions: Bessel functions, modified Bessel functions, spherical Bessel functions, Hankel functions. The aim of this paper is to develop numerical solutions in Matlab for the above mentioned special functions. Taking into account the main properties for Bessel and modified Bessel functions, we shortly present analytically solutions (where possible) in the form of series. Especially it is studied the behavior of these special functions using Matlab facilities: numerical solutions and plotting. Finally, it will be compared the behavior of the special functions and point out other directions for investigating properties of Bessel and spherical Bessel functions. The asymptotic forms of Bessel functions and modified Bessel functions allow determination of important properties of these functions. The modified Bessel functions tend to look more like decaying and growing exponentials.

Effects of Earth's curvature in full-wave modeling of VLF propagation

NASA Astrophysics Data System (ADS)

Qiu, L.; Lehtinen, N. G.; Inan, U. S.; Stanford VLF Group

2011-12-01

We show how to include curvature in the full-wave finite element approach to calculate ELF/VLF wave propagation in horizontally stratified earth-ionosphere waveguide. A general curvilinear stratified system is considered, and the numerical solutions of full-wave method in curvilinear system are compared with the analytic solutions in the cylindrical and spherical waveguides filled with an isotropic medium. We calculate the attenuation and height gain for modes in the Earth-ionosphere waveguide, taking into account the anisotropicity of ionospheric plasma, for different assumptions about the Earth's curvature, and quantify the corrections due to the curvature. The results are compared with the results of previous models, such as LWPC, as well as with ground and satellite observations, and show improved accuracy compared with full-wave method without including the curvature effect.

The numerical design of a spherical baroclinic experiment for Spacelab flights

NASA Technical Reports Server (NTRS)

Fowlis, W. W.; Roberts, G. O.

1982-01-01

The near-zero G environment of Spacelab is the basis of a true spherical experimental model of synoptic scale baroclinic atmospheric processes, using a radial dielectric body force analogous to gravity over a volume of liquid within two concentric spheres. The baroclinic motions are generated by corotating the spheres and imposing thermal boundary conditions, such that the liquid is subjected to a stable radial gradient and a latitudinal gradient. Owing to mathematical difficulties associated with the spherical geometry, quantitative design criteria can be acquired only by means of numerical models. The procedure adopted required the development of two computer codes based on the Navier-Stokes equations. The codes, of which the first calculates axisymmetric steady flow solutions and the second determines the growth or decay rates of linear wave perturbations with different wave numbers, are combined to generate marginal stability curves.

Initial decay of flow properties of planar, cylindrical and spherical blast waves

NASA Astrophysics Data System (ADS)

Sadek, H. S. I.; Gottlieb, J. J.

1983-10-01

Analytical expressions are presented for the initial decay of all major flow properties just behind planar, cylindrical, and spherical shock wave fronts whose trajectories are known as a function of either distance versus time or shock overpressure versus distance. These expressions give the time and/or distance derivatives of the flow properties not only along constant time and distance lines but also along positive and negative characteristic lines and a fluid-particle path. Conventional continuity, momentum and energy equations for the nonstationary motion of an inviscid, non-heat conducting, compressible gas are used in their derivation, along with the equation of state of a perfect gas. All analytical expressions are validated by comparing the results to those obtained indirectly from known self-similar solutions for planar, cylindrical and spherical shock-wave flows generated both by a sudden energy release and by a moving piston. Futhermore, time derivatives of pressure and flow velocity are compared to experimental data from trinitrotoluene (TNT), pentolite, ammonium nitrate-fuel oil (ANFO) and propane-oxygen explosions, and good agreement is obtained.

Scattering of elastic waves by a spheroidal inclusion

NASA Astrophysics Data System (ADS)

Johnson, Lane R.

2018-03-01

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

Coherent backscattering of light by complex random media of spherical scatterers: numerical solution

NASA Astrophysics Data System (ADS)

Muinonen, Karri

2004-07-01

Novel Monte Carlo techniques are described for the computation of reflection coefficient matrices for multiple scattering of light in plane-parallel random media of spherical scatterers. The present multiple scattering theory is composed of coherent backscattering and radiative transfer. In the radiative transfer part, the Stokes parameters of light escaping from the medium are updated at each scattering process in predefined angles of emergence. The scattering directions at each process are randomized using probability densities for the polar and azimuthal scattering angles: the former angle is generated using the single-scattering phase function, whereafter the latter follows from Kepler's equation. For spherical scatterers in the Rayleigh regime, randomization proceeds semi-analytically whereas, beyond that regime, cubic spline presentation of the scattering matrix is used for numerical computations. In the coherent backscattering part, the reciprocity of electromagnetic waves in the backscattering direction allows the renormalization of the reversely propagating waves, whereafter the scattering characteristics are computed in other directions. High orders of scattering (~10 000) can be treated because of the peculiar polarization characteristics of the reverse wave: after a number of scatterings, the polarization state of the reverse wave becomes independent of that of the incident wave, that is, it becomes fully dictated by the scatterings at the end of the reverse path. The coherent backscattering part depends on the single-scattering albedo in a non-monotonous way, the most pronounced signatures showing up for absorbing scatterers. The numerical results compare favourably to the literature results for nonabsorbing spherical scatterers both in and beyond the Rayleigh regime.

Instantaneous axial force of a high-order Bessel vortex beam of acoustic waves incident upon a rigid movable sphere.

PubMed

Mitri, F G; Fellah, Z E A

2011-08-01

The present investigation examines the instantaneous force resulting from the interaction of an acoustical high-order Bessel vortex beam (HOBVB) with a rigid sphere. The rigid sphere case is important in fluid dynamics applications because it perfectly simulates the interaction of instantaneous sound waves in a reduced gravity environment with a levitated spherical liquid soft drop in air. Here, a closed-form solution for the instantaneous force involving the total pressure field as well as the Bessel beam parameters is obtained for the case of progressive, stationary and quasi-stationary waves. Instantaneous force examples for progressive waves are computed for both a fixed and a movable rigid sphere. The results show how the instantaneous force per unit cross-sectional surface and unit pressure varies versus the dimensionless frequency ka (k is the wave number in the fluid medium and a is the sphere's radius), the half-cone angle β and the order m of the HOBVB. It is demonstrated here that the instantaneous force is determined only for (m,n) = (0,1) (where n is the partial-wave number), and vanishes for m>0 because of symmetry. In addition, the instantaneous force and normalized amplitude velocity results are computed and compared with those of a rigid immovable (fixed) sphere. It is shown that they differ significantly for ka values below 5. The proposed analysis may be of interest in the analysis of instantaneous forces on spherical particles for particle manipulation, filtering, trapping and drug delivery. The presented solutions may also serve as a method for comparison to other solutions obtained by strictly numerical or asymptotic approaches. Copyright © 2011 Elsevier B.V. All rights reserved.

Relativistic self-similar dynamic gravitational collapses of a quasi-spherical general polytropic magnetofluid

NASA Astrophysics Data System (ADS)

Lou, Yu-Qing; Xia, Yu-Kai

2017-05-01

We study magnetohydrodynamic (MHD) self-similar collapses and void evolution, with or without shocks, of a general polytropic quasi-spherical magnetofluid permeated by random transverse magnetic fields under the Paczynski-Wiita gravity that captures essential general relativistic effects of a Schwarzschild black hole (BH) with a growing mass. Based on the derived set of non-linear MHD ordinary differential equations, we obtain various asymptotic MHD solutions, the geometric and analytical properties of the magnetosonic critical curve (MSCC) and MHD shock jump conditions. Novel asymptotic MHD solution behaviours near the rim of central expanding voids are derived analytically. By exploring numerical global MHD solutions, we identify allowable boundary conditions at large radii that accommodate a smooth solution and show that a reasonable amount of magnetization significantly increases the mass accretion rate in the expansion-wave-collapse solution scenario. We also construct the counterparts of envelope-expansion-core-collapse solutions that cross the MSCC twice, which are found to be closely paired with a sequence of global smooth solutions satisfying a novel type of central MHD behaviours. MHD shocks with static outer and various inner flow profiles are also examined. Astrophysical applications include dynamic core collapses of magnetized massive stars and compact objects as well as formation of supermassive, hypermassive, dark matter and mixed matter BHs in the Universe, including the early Universe. Such gigantic BHs can be detected in X-ray/gamma-ray sources, quasars, ultraluminous infrared galaxies or extremely luminous infrared galaxies and dark matter overwhelmingly dominated elliptical galaxies as well as massive dark matter halos, etc. Gravitational waves and electromagnetic wave emissions in broad band (including e.g., gamma-ray bursts and fast radio bursts) can result from this type of dynamic collapses of forming BHs involving magnetized media.

Dispersion of gravitational waves in cold spherical interstellar medium

NASA Astrophysics Data System (ADS)

Barta, Dániel; Vasúth, Mátyás

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

YASEIS: Yet Another computer program to calculate synthetic SEISmograms for a spherically multi-layered Earth model

NASA Astrophysics Data System (ADS)

Ma, Yanlu

2013-04-01

Although most researches focus on the lateral heterogeneity of 3D Earth nowadays, a spherically multi-layered model where the parameters depend only on depth still represents a good first order approximation of real Earth. Such 1D models could be used as starting models for seismic tomographic inversion or as background model where the source mechanisms are inverted. The problem of wave propagation in a spherically layered model had been solved theoretically long time ago (Takeuchi and Saito, 1972). The existing computer programs such as Mineos (developed by G. Master, J. Woodhouse and F. Gilbert), Gemini (Friederich and Dalkolmo 1995), DSM (Kawai et. al. 2006) and QSSP (Wang 1999) tackled the computational aspects of the problem. A new simple and fast program for computing the Green's function of a stack of spherical dissipative layers is presented here. The analytical solutions within each homogeneous spherical layer are joined through the continuous boundary conditions and propagated from the center of model up to the level of source depth. Another solution is built by propagating downwardly from the free surface of model to the source level. The final solution is then constructed in frequency domain from the previous two solutions to satisfy the discontinuities of displacements and stresses at the source level which are required by the focal mechanism. The numerical instability in the propagator approach is solved by complementing the matrix propagating with an orthonormalization procedure (Wang 1999). Another unstable difficulty due to the high attenuation in the upper mantle low velocity zone is overcome by switching the bases of solutions from the spherical Bessel functions to the spherical Hankel functions when necessary. We compared the synthetic seismograms obtained from the new program YASEIS with those computed by Gemini and QSSP. In the range of near distances, the synthetics by a reflectivity code for the horizontally layers are also compared with those from YASEIS. Finally the static displacements in the source region are computed by choosing a very small frequency value in YASEIS which is designed for computing the dynamic response, and compared with the results in a homogeneous half-space model (Okada 1992). [1] Friederich, W. and J. Dalkolmo (1995). Complete synthetic seismograms for a spherically symmetric Earth a numerical computation of the Green's function in the frequency domain, Geophys. J. Int., vol. 122, 537-550. [2] Kawai, K., N. Takeuchi, and R.J. Geller (2006). Complete synthetic seismograms up to 2Hz for transversely isotropic spherically symmetric media, Geophys. J. Int., vol. 164, 411-424. [3] Okada, Y. (1992). Internal deformation due to shear and tensile faults in a half space, Bull. Seismol. Soc. Am., vol. 82, no. 2, 1018-1040. [4] Takeuchi, H. and M. Saito (1972). Seismic surface waves, Methods in computational physics, vol. II, 217-295. [5] Wang, R. (1999). A simple orthonormalization method for stable and efficient computation of Green's functions, Bull. Seismol. Soc. Am., vol. 89, no. 3, 733-741.

The transmission or scattering of elastic waves by an inhomogeneity of simple geometry: A comparison of theories

NASA Technical Reports Server (NTRS)

Sheu, Y. C.; Fu, L. S.

1983-01-01

The extended method of equivalent inclusions is applied to study the specific wave problems: (1) the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and (2) the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. Eigenstrains are expanded as a geometric series and a method of integration based on the inhomogeneous Helmholtz operator is adopted. This study compares results, obtained by using limited number of terms in the eigenstrain expansion, with exact solutions for the layer problem and that for a perfect sphere.

Rapid calculation of acoustic fields from arbitrary continuous-wave sources.

PubMed

Treeby, Bradley E; Budisky, Jakub; Wise, Elliott S; Jaros, Jiri; Cox, B T

2018-01-01

A Green's function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions to be calculated in a single step using two fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically focused bowl transducers, and multi-element linear and hemispherical arrays.

On the completeness and the linear dependence of the Cartesian multipole series in representing the solution to the Helmholtz equation.

PubMed

Liu, Yangfan; Bolton, J Stuart

2016-08-01

The (Cartesian) multipole series, i.e., the series comprising monopole, dipoles, quadrupoles, etc., can be used, as an alternative to the spherical or cylindrical wave series, in representing sound fields in a wide range of problems, such as source radiation, sound scattering, etc. The proofs of the completeness of the spherical and cylindrical wave series in these problems are classical results, and it is also generally agreed that the Cartesian multipole series spans the same space as the spherical waves: a rigorous mathematical proof of that statement has, however, not been presented. In the present work, such a proof of the completeness of the Cartesian multipole series, both in two and three dimensions, is given, and the linear dependence relations among different orders of multipoles are discussed, which then allows one to easily extract a basis from the multipole series. In particular, it is concluded that the multipoles comprising the two highest orders in the series form a basis of the whole series, since the multipoles of all the lower source orders can be expressed as a linear combination of that basis.

Comparison of approximate solutions to the phonon Boltzmann transport equation with the relaxation time approximation: Spherical harmonics expansions and the discrete ordinates method

NASA Astrophysics Data System (ADS)

Christenson, J. G.; Austin, R. A.; Phillips, R. J.

2018-05-01

The phonon Boltzmann transport equation is used to analyze model problems in one and two spatial dimensions, under transient and steady-state conditions. New, explicit solutions are obtained by using the P1 and P3 approximations, based on expansions in spherical harmonics, and are compared with solutions from the discrete ordinates method. For steady-state energy transfer, it is shown that analytic expressions derived using the P1 and P3 approximations agree quantitatively with the discrete ordinates method, in some cases for large Knudsen numbers, and always for Knudsen numbers less than unity. However, for time-dependent energy transfer, the PN solutions differ qualitatively from converged solutions obtained by the discrete ordinates method. Although they correctly capture the wave-like behavior of energy transfer at short times, the P1 and P3 approximations rely on one or two wave velocities, respectively, yielding abrupt, step-changes in temperature profiles that are absent when the angular dependence of the phonon velocities is captured more completely. It is shown that, with the gray approximation, the P1 approximation is formally equivalent to the so-called "hyperbolic heat equation." Overall, these results support the use of the PN approximation to find solutions to the phonon Boltzmann transport equation for steady-state conditions. Such solutions can be useful in the design and analysis of devices that involve heat transfer at nanometer length scales, where continuum-scale approaches become inaccurate.

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

PubMed

Reintjes, Moritz; Temple, Blake

2015-05-08

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

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

PubMed Central

Reintjes, Moritz; Temple, Blake

2015-01-01

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

Magnetogasdynamic spherical shock wave in a non-ideal gas under gravitational field with conductive and radiative heat fluxes

NASA Astrophysics Data System (ADS)

Nath, G.; Vishwakarma, J. P.

2016-11-01

Similarity solutions are obtained for the flow behind a spherical shock wave in a non-ideal gas under gravitational field with conductive and radiative heat fluxes, in the presence of a spatially decreasing azimuthal magnetic field. The shock wave is driven by a piston moving with time according to power law. The radiation is considered to be of the diffusion type for an optically thick grey gas model and the heat conduction is expressed in terms of Fourier's law for heat conduction. Similarity solutions exist only when the surrounding medium is of constant density. The gas is assumed to have infinite electrical conductivity and to obey a simplified van der Waals equation of state. It is shown that an increase of the gravitational parameter or the Alfven-Mach number or the parameter of the non-idealness of the gas decreases the compressibility of the gas in the flow-field behind the shock, and hence there is a decrease in the shock strength. The pressure and density vanish at the inner surface (piston) and hence a vacuum is formed at the center of symmetry. The shock waves in conducting non-ideal gas under gravitational field with conductive and radiative heat fluxes can be important for description of shocks in supernova explosions, in the study of a flare produced shock in the solar wind, central part of star burst galaxies, nuclear explosion etc. The solutions obtained can be used to interpret measurements carried out by space craft in the solar wind and in neighborhood of the Earth's magnetosphere.

Propagation of mechanical waves through a stochastic medium with spherical symmetry

NASA Astrophysics Data System (ADS)

Avendaño, Carlos G.; Reyes, J. Adrián

2018-01-01

We theoretically analyze the propagation of outgoing mechanical waves through an infinite isotropic elastic medium possessing spherical symmetry whose Lamé coefficients and density are spatial random functions characterized by well-defined statistical parameters. We derive the differential equation that governs the average displacement for a system whose properties depend on the radial coordinate. We show that such an equation is an extended version of the well-known Bessel differential equation whose perturbative additional terms contain coefficients that depend directly on the squared noise intensities and the autocorrelation lengths in an exponential decay fashion. We numerically solve the second order differential equation for several values of noise intensities and autocorrelation lengths and compare the corresponding displacement profiles with that of the exact analytic solution for the case of absent inhomogeneities.

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

NASA Astrophysics Data System (ADS)

Khusainov, T. A.; Shalashov, A. G.; Gospodchikov, E. D.

2018-05-01

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.

Fully vectorial accelerating diffraction-free Helmholtz beams.

PubMed

Aleahmad, Parinaz; Miri, Mohammad-Ali; Mills, Matthew S; Kaminer, Ido; Segev, Mordechai; Christodoulides, Demetrios N

2012-11-16

We show that new families of diffraction-free nonparaxial accelerating optical beams can be generated by considering the symmetries of the underlying vectorial Helmholtz equation. Both two-dimensional transverse electric and magnetic accelerating wave fronts are possible, capable of moving along elliptic trajectories. Experimental results corroborate these predictions when these waves are launched from either the major or minor axis of the ellipse. In addition, three-dimensional spherical nondiffracting field configurations are presented along with their evolution dynamics. Finally, fully vectorial self-similar accelerating optical wave solutions are obtained via oblate-prolate spheroidal wave functions. In all occasions, these effects are illustrated via pertinent examples.

On hydromagnetic oscillations in a rotating cavity.

NASA Technical Reports Server (NTRS)

Gans, R. F.

1971-01-01

Time-dependent hydromagnetic phenomena in a rotating spherical cavity are investigated in the framework of an interior boundary-layer expansion. The first type of wave is a modification of the hydrodynamic inertial wave, the second is a pseudo-geostrophic wave and is involved in spinup, and the third is related to the MAC waves of Braginskii (1967). It is shown that the MAC waves must satisfy more than the usual normal boundary conditions, and that reference must be made to the boundary-layer solution to resolve the ambiguity regarding which conditions are to be taken. The boundary-layer structure is investigated in detail to display the interactions between applied field, viscosity, electrical conductivity, frequency and latitu de.

Nearly spherical constant power detonation waves driven by focused radiation

NASA Technical Reports Server (NTRS)

George, Y. H.

1973-01-01

Shape and inner flow of a tridimensional spark are studied. The spark is created by focusing a laser beam in a gas. A second order fully non-linear equation is derived for the radial velocity on the axis of symmetry in the neighborhood of the origin. Solutions to that equation display the existence of a forbidden region near the focus, thus indicating the limits of applicability of a small perturbation solution.

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

NASA Astrophysics Data System (ADS)

Joshi, Narahari V.

2012-03-01

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

Natural oscillations of a gas bubble in a liquid-filled cavity located in a viscoelastic medium

NASA Astrophysics Data System (ADS)

Doinikov, Alexander A.; Marmottant, Philippe

2018-04-01

The present study is motivated by cavitation phenomena that occur in the stems of trees. The internal pressure in tree conduits can drop down to significant negative values. This drop gives rise to cavitation bubbles, which undergo high-frequency eigenmodes. The aim of the present study is to determine the parameters of the bubble natural oscillations. To this end, a theory is developed that describes the pulsation of a spherical bubble located at the center of a spherical cavity surrounded by an infinite solid medium. It is assumed that the medium inside the bubble is a gas-vapor mixture, the cavity is filled with a compressible viscous liquid, and the medium surrounding the cavity behaves as a viscoelastic solid. The theoretical solution takes into account the outgoing acoustic wave produced by the bubble pulsation, the incoming wave caused by reflection from the liquid-solid boundary, and the outgoing wave propagating in the solid. A dispersion equation for the calculation of complex wavenumbers of the bubble eigenmodes is derived. Approximate analytical solutions to the dispersion equation are found. Numerical simulations are performed to reveal the effect of different physical parameters on the resonance frequency and the attenuation coefficient of the bubble oscillations.

A theoretical study of hot plasma spheroids in the presence of low-frequency electromagnetic waves

NASA Astrophysics Data System (ADS)

Ahmadizadeh, Y.; Jazi, B.; Barjesteh, S.

2016-07-01

While taking into account thermal motion of electrons, scattering of electromagnetic waves with low frequency from hot plasma spheroids is investigated. In this theoretical research, ions are heavy to respond to electromagnetic fluctuations. The solution of scalar wave equation in spheroidal coordinates for electric potential inside the plasma spheroids are obtained. The variations of resonance frequencies vs. Debye length are studied and consistency between the obtained results in this paper and the results for the well-known plasma objects such as plasma column and spherical plasma have been proved.

Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating.

PubMed

George, Jineesh; Ebenezer, D D; Bhattacharyya, S K

2010-10-01

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.

Study on Pressure Wave Propagation in a Liquid Containing Spherical Bubbles in a Rectangular Duct

NASA Astrophysics Data System (ADS)

Kawahara, Junya; Watanabe, Masao; Kobayashi, Kazumichi

2015-12-01

Pressure wave propagation in a liquid containing several bubbles is numerically investigated. We simulate liner plane wave propagation in a liquid containing 10 spherical bubbles in a rectangular duct with the equation of motion for N spherical bubbles. The sound pressures of the reflected waves from the rigid walls are calculated by using the method of images. The result shows that the phase velocity of the pressure wave propagating in the liquid containing 10 spherical bubbles in the duct agrees well with the low-frequency speed of sound in a homogeneous bubbly liquid.

Exact solution of equations for proton localization in neutron star matter

NASA Astrophysics Data System (ADS)

Kubis, Sebastian; Wójcik, Włodzimierz

2015-11-01

The rigorous treatment of proton localization phenomenon in asymmetric nuclear matter is presented. The solution of proton wave function and neutron background distribution is found by the use of the extended Thomas-Fermi approach. The minimum of energy is obtained in the Wigner-Seitz approximation of a spherically symmetric cell. The analysis of four different nuclear models suggests that the proton localization is likely to take place in the interior of a neutron star.

Spherical solitons in Earth'S mesosphere plasma

NASA Astrophysics Data System (ADS)

Annou, K.; Annou, R.

2016-01-01

Soliton formation in Earth's mesosphere plasma is described. Nonlinear acoustic waves in plasmas with two-temperature ions and a variable dust charge where transverse perturbation is dealt with are studied in bounded spherical geometry. Using the perturbation method, a spherical Kadomtsev-Petviashvili equation that describes dust acoustic waves is derived. It is found that the parameters taken into account have significant effects on the properties of nonlinear waves in spherical geometry.

Spherical solitons in Earth’S mesosphere plasma

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

Annou, K., E-mail: kannou@cdta.dz; Annou, R.

2016-01-15

Soliton formation in Earth’s mesosphere plasma is described. Nonlinear acoustic waves in plasmas with two-temperature ions and a variable dust charge where transverse perturbation is dealt with are studied in bounded spherical geometry. Using the perturbation method, a spherical Kadomtsev–Petviashvili equation that describes dust acoustic waves is derived. It is found that the parameters taken into account have significant effects on the properties of nonlinear waves in spherical geometry.

Energy, momentum and propagation of non-paraxial high-order Gaussian beams in the presence of an aperture

NASA Astrophysics Data System (ADS)

Stilgoe, Alexander B.; Nieminen, Timo A.; Rubinsztein-Dunlop, Halina

2015-12-01

Non-paraxial theories of wave propagation are essential to model the interaction of highly focused light with matter. Here we investigate the energy, momentum and propagation of the Laguerre-, Hermite- and Ince-Gaussian solutions (LG, HG, and IG) of the paraxial wave equation in an apertured non-paraxial regime. We investigate the far-field relationships between the LG, HG, and IG solutions and the vector spherical wave function (VSWF) solutions of the vector Helmholtz wave equation. We investigate the convergence of the VSWF and the various Gaussian solutions in the presence of an aperture. Finally, we investigate the differences in linear and angular momentum evaluated in the paraxial and non-paraxial regimes. The non-paraxial model we develop can be applied to calculations of the focusing of high-order Gaussian modes in high-resolution microscopes. We find that the addition of an aperture in high numerical aperture optical systems does not greatly affect far-field properties except when the beam is significantly clipped by an aperture. Diffraction from apertures causes large distortions in the near-field and will influence light-matter interactions. The method is not limited to a particular solution of the paraxial wave equation. Our model is constructed in a formalism that is commonly used in scattering calculations. It is thus applicable to optical trapping and other optical investigations of matter.

Do cyanobacteria swim using traveling surface waves?

PubMed Central

Ehlers, K M; Samuel, A D; Berg, H C; Montgomery, R

1996-01-01

Bacteria that swim without the benefit of flagella might do so by generating longitudinal or transverse surface waves. For example, swimming speeds of order 25 microns/s are expected for a spherical cell propagating longitudinal waves of 0.2 micron length, 0.02 micron amplitude, and 160 microns/s speed. This problem was solved earlier by mathematicians who were interested in the locomotion of ciliates and who considered the undulations of the envelope swept out by ciliary tips. A new solution is given for spheres propagating sinusoidal waveforms rather than Legendre polynomials. The earlier work is reviewed and possible experimental tests are suggested. Images Fig. 1 PMID:8710872

Gravitational waves from rotating and precessing rigid bodies. 2: General solutions and computationally useful formulae

NASA Technical Reports Server (NTRS)

Zimmerman, M.

1979-01-01

The classical mechanics results for free precession which are needed in order to calculate the weak field, slow-motion, quadrupole-moment gravitational waves are reviewed. Within that formalism, algorithms are given for computing the exact gravitational power radiated and waveforms produced by arbitrary rigid-body freely-precessing sources. The dominant terms are presented in series expansions of the waveforms for the case of an almost spherical object precessing with a small wobble angle. These series expansions, which retain the precise frequency dependence of the waves, may be useful for gravitational astronomers when freely-precessing sources begin to be observed.

Fusion yield: Guderley model and Tsallis statistics

NASA Astrophysics Data System (ADS)

Haubold, H. J.; Kumar, D.

2011-02-01

The reaction rate probability integral is extended from Maxwell-Boltzmann approach to a more general approach by using the pathway model introduced by Mathai in 2005 (A pathway to matrix-variate gamma and normal densities. Linear Algebr. Appl. 396, 317-328). The extended thermonuclear reaction rate is obtained in the closed form via a Meijer's G-function and the so-obtained G-function is represented as a solution of a homogeneous linear differential equation. A physical model for the hydrodynamical process in a fusion plasma-compressed and laser-driven spherical shock wave is used for evaluating the fusion energy integral by integrating the extended thermonuclear reaction rate integral over the temperature. The result obtained is compared with the standard fusion yield obtained by Haubold and John in 1981 (Analytical representation of the thermonuclear reaction rate and fusion energy production in a spherical plasma shock wave. Plasma Phys. 23, 399-411). An interpretation for the pathway parameter is also given.

Acoustic propagation operators for pressure waves on an arbitrarily curved surface in a homogeneous medium

NASA Astrophysics Data System (ADS)

Sun, Yimin; Verschuur, Eric; van Borselen, Roald

2018-03-01

The Rayleigh integral solution of the acoustic Helmholtz equation in a homogeneous medium can only be applied when the integral surface is a planar surface, while in reality almost all surfaces where pressure waves are measured exhibit some curvature. In this paper we derive a theoretically rigorous way of building propagation operators for pressure waves on an arbitrarily curved surface. Our theory is still based upon the Rayleigh integral, but it resorts to matrix inversion to overcome the limitations faced by the Rayleigh integral. Three examples are used to demonstrate the correctness of our theory - propagation of pressure waves acquired on an arbitrarily curved surface to a planar surface, on an arbitrarily curved surface to another arbitrarily curved surface, and on a spherical cap to a planar surface, and results agree well with the analytical solutions. The generalization of our method for particle velocities and the calculation cost of our method are also discussed.

Spherical ion acoustic waves in pair ion plasmas with nonthermal electrons

NASA Astrophysics Data System (ADS)

Selim, M. M.

2016-04-01

Propagation of nonplanar ion acoustic waves in a plasma composed of negative and positive ions and nonthermally distributed electrons is investigated using reductive perturbation theory. The spherical Kadomtsev-Petviashvili (SKP) equation which describes the dynamics of the nonlinear spherical ion acoustic waves is derived. It is found that compressive and rarefactive ion-acoustic solitary wave characteristics significantly depend on the density and mass ratios of the positive to negative ions, the nonthermal electron parameter, and the geometry factor. The possible regions for the existence of spherical ion acoustic waves are defined precisely for typical parameters of (H+, O2 -) and (H+, H-) plasmas in the D and F-regions of the Earth's ionosphere, as well as for laboratory plasma (Ar+, F-).

Variational treatment of electron-polyatomic-molecule scattering calculations using adaptive overset grids

NASA Astrophysics Data System (ADS)

Greenman, Loren; Lucchese, Robert R.; McCurdy, C. William

2017-11-01

The complex Kohn variational method for electron-polyatomic-molecule scattering is formulated using an overset-grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free-particle Green's function and potential Ĝ0+V ̂ on the overset grid in a Born-Arnoldi solution of the working equations. The theory is shown to be equivalent to a specific Padé approximant to the T matrix and has rapid convergence properties, in both the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF4 in the static-exchange approximation and compared in detail with calculations performed with the numerical Schwinger variational approach based on single-center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.

Collapsing shells and black holes: a quantum analysis

NASA Astrophysics Data System (ADS)

Leal, P.; Bernardini, A. E.; Bertolami, O.

2018-06-01

The quantization of a spherically symmetric null shells is performed and extended to the framework of phase-space noncommutative (NC) quantum mechanics. This shell is considered to be inside a black hole event horizon. The encountered properties are investigated making use of the Israel junction conditions on the shell, considering that it is the boundary between two spherically symmetric spacetimes. Using this method, and considering two different Kantowski–Sachs spacetimes as a representation for the Schwarzschild spacetime, the relevant quantities on the shell are computed, such as its stress-energy tensor and the action for the whole spacetime. From the obtained action, the Wheeler–deWitt equation is deduced in order to provide the quantum framework for the system. Solutions for the wave function of the system are found on both the commutative and NC scenarios. It is shown that, on the commutative version, the wave function has a purely oscillatory behavior in the interior of the shell. In the NC setting, it is shown that the wave function vanishes at the singularity, as well as, at the event horizon of the black hole.

Spherical nonlinear ion-acoustic solitary waves in Titan's atmosphere

NASA Astrophysics Data System (ADS)

Selim, M. M.

2016-03-01

Propagation of spherical nonlinear ion-acoustic solitary waves in positive and negative ion plasmas with superthermal electrons is investigated. The effects of perturbations of the azimuthal and zenith-angle as well as the radial coordinate on the solitary wave profile are reported. The existence domains and the characteristics of the spherical solitary pulses are examined. The solitary excitations are found to be strongly dependent on the plasma parameters; the mass ratio of the positive-to-negative ions, electrons superthermality, and the spherical geometry. The role of superthermal electrons in formation of the spherical nonlinear ion-acoustic solitary excitations for two ion mass groups in Titan's upper atmosphere is investigated.

Sound wave generation by a spherically symmetric outburst and AGN feedback in galaxy clusters

NASA Astrophysics Data System (ADS)

Tang, Xiaping; Churazov, Eugene

2017-07-01

We consider the evolution of an outburst in a uniform medium under spherical symmetry, having in mind active galactic nucleus feedback in the intracluster medium. For a given density and pressure of the medium, the spatial structure and energy partition at a given time tage (since the onset of the outburst) are fully determined by the total injected energy Einj and the duration tb of the outburst. We are particularly interested in the late phase evolution when the strong shock transforms into a sound wave. We studied the energy partition during such transition with different combinations of Einj and tb. For an instantaneous outburst with tb → 0, which corresponds to the extension of classic Sedov-Taylor solution with counter-pressure, the fraction of energy that can be carried away by sound waves is ≲12 per cent of Einj. As tb increases, the solution approaches the 'slow piston' limit, with the fraction of energy in sound waves approaching zero. We then repeat the simulations using radial density and temperature profiles measured in Perseus and M87/Virgo clusters. We find that the results with a uniform medium broadly reproduce an outburst in more realistic conditions once proper scaling is applied. We also develop techniques to map intrinsic properties of an outburst (Einj, tb and tage) to the observables like the Mach number of the shock and radii of the shock and ejecta. For the Perseus cluster and M87, the estimated (Einj, tb and tage) agree with numerical simulations tailored for these objects with 20-30 per cent accuracy.

Propagation of a shock wave in a radiating spherically symmetric distribution of matter

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

Herrera, L.; Nunez, L.

1987-08-01

A method used to study the evolution of radiating spheres reported by Herrera et al. (1980) is extended to the case in which the sphere is divided in two regions by a shock wave front. The equations of state at both sides of the shock are different, and the solutions are matched on it via the Rankine-Hugoniot conditions. The outer-region metric is matched with a Vaidya solution on the boundary surface of the sphere. As an example of the procedure, two known solutions for radiating systems are considered. The matter distribution is free of singularities everywhere within the sphere andmore » a Gaussian-like pulse is assumed to carry out a fraction of the total mass. Exploding models are then obtained. Finally, the results are discussed in the light of recent work on gravitational collapse and supernovae. 29 references.« less

Scattering of plane transverse waves by spherical inclusions in a poroelastic medium

NASA Astrophysics Data System (ADS)

Liu, Xu; Greenhalgh, Stewart; Zhou, Bing

2009-03-01

The scattering of plane transverse waves by a spherical inclusion embedded in an infinite poroelastic medium is treated for the first time in this paper. The vector displacement wave equations of Biot's theory are solved as an infinite series of vector spherical harmonics for the case of a plane S-wave impinging from a porous medium onto a spherical inclusion which itself is assumed to be another porous medium. Based on the single spherical scattering theory and dynamic composite elastic medium theory, the non-self-consistent shear wavenumber is derived for a porous rock having numerous spherical inclusions of another medium. The frequency dependences of the shear wave velocity and the shear wave attenuation have been calculated for both the patchy saturation model (inclusions having the same solid frame as the host but with a different pore fluid from the host medium) and the double porosity model (inclusions having a different solid frame than the host but the same pore fluid as the host medium) with dilute concentrations of identical inclusions. Unlike the case of incident P-wave scattering, we show that although the fluid and the heterogeneity of the rock determine the shear wave velocity of the composite, the attenuation of the shear wave caused by scattering is actually contributed by the heterogeneity of the rock for spherical inclusions. The scattering of incident shear waves in the patchy saturation model is quite different from that of the double porosity model. For the patchy saturation model, the gas inclusions do not significantly affect the shear wave dispersion characteristic of the water-filled host medium. However, the softer inclusion with higher porosity in the double porosity model can cause significant shear wave scattering attenuation which occurs at a frequency at which the wavelength of the shear wave is approximately equal to the characteristic size of the inclusion and depends on the volume fraction. Compared with analytic formulae for the low frequency limit of the shear velocity, our scattering model yields discrepancies within 4.0 per cent. All calculated shear velocities of the composite medium with dilute inclusion concentrations approach the high frequency limit of the host material.

Finite element solution of transient fluid-structure interaction problems

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Cheng, Raymond S.; Hambric, Stephen A.

1991-01-01

A finite element approach using NASTRAN is developed for solving time-dependent fluid-structure interaction problems, with emphasis on the transient scattering of acoustic waves from submerged elastic structures. Finite elements are used for modeling both structure and fluid domains to facilitate the graphical display of the wave motion through both media. For the liquid, the use of velocity potential as the fundamental unknown results in a symmetric matrix equation. The approach is illustrated for the problem of transient scattering from a submerged elastic spherical shell subjected to an incident tone burst. The use of an analogy between the equations of elasticity and the wave equation of acoustics, a necessary ingredient to the procedure, is summarized.

The classical D-type expansion of spherical H II regions

NASA Astrophysics Data System (ADS)

Williams, Robin J. R.; Bibas, Thomas G.; Haworth, Thomas J.; Mackey, Jonathan

2018-06-01

Recent numerical and analytic work has highlighted some shortcomings in our understanding of the dynamics of H II region expansion, especially at late times, when the H II region approaches pressure equilibrium with the ambient medium. Here we reconsider the idealized case of a constant radiation source in a uniform and spherically symmetric ambient medium, with an isothermal equation of state. A thick-shell solution is developed which captures the stalling of the ionization front and the decay of the leading shock to a weak compression wave as it escapes to large radii. An acoustic approximation is introduced to capture the late-time damped oscillations of the H II region about the stagnation radius. Putting these together, a matched asymptotic equation is derived for the radius of the ionization front which accounts for both the inertia of the expanding shell and the finite temperature of the ambient medium. The solution to this equation is shown to agree very well with the numerical solution at all times, and is superior to all previously published solutions. The matched asymptotic solution can also accurately model the variation of H II region radius for a time-varying radiation source.

Explosive plane-wave lens

DOEpatents

Marsh, Stanley P.

1988-01-01

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

Explosive plane-wave lens

DOEpatents

Marsh, S.P.

1988-03-08

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

Analytical solution of the problem of a shock wave in the collapsing gas in Lagrangian coordinates

NASA Astrophysics Data System (ADS)

Kuropatenko, V. F.; Shestakovskaya, E. S.

2016-10-01

It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in Lagrangian coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t0 the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and Lagrangian coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For Lagrangian coordinates the problem is first solved. It is fundamentally different from previously known formulations of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.

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

El-Labany, S. K., E-mail: skellabany@hotmail.com; Zedan, N. A., E-mail: nesreenplasma@yahoo.com; El-Taibany, W. F., E-mail: eltaibany@hotmail.com, E-mail: eltaibany@du.edu.eg

The nonplanar amplitude modulation of dust acoustic (DA) envelope solitary waves in a strongly coupled dusty plasma (SCDP) has been investigated. By using a reductive perturbation technique, a modified nonlinear Schrödinger equation (NLSE) including the effects of geometry, polarization, and ion superthermality is derived. The modulational instability (MI) of the nonlinear DA wave envelopes is investigated in both planar and nonplanar geometries. There are two stable regions for the DA wave propagation strongly affected by polarization and ion superthermality. Moreover, it is found that the nonlinear DA waves in spherical geometry are the more structurally stable. The larger growth ratemore » of the nonlinear DA MI is observed in the cylindrical geometry. The salient characteristics of the MI in the nonplanar geometries cannot be found in the planar one. The DA wave propagation and the NLSE solutions are investigated both analytically and numerically.« less

Momentum and energy transport by waves in the solar atmosphere and solar wind

NASA Technical Reports Server (NTRS)

Jacques, S. A.

1977-01-01

The fluid equations for the solar wind are presented in a form which includes the momentum and energy flux of waves in a general and consistent way. The concept of conservation of wave action is introduced and is used to derive expressions for the wave energy density as a function of heliocentric distance. The explicit form of the terms due to waves in both the momentum and energy equations are given for radially propagating acoustic, Alfven, and fast mode waves. The effect of waves as a source of momentum is explored by examining the critical points of the momentum equation for isothermal spherically symmetric flow. We find that the principal effect of waves on the solutions is to bring the critical point closer to the sun's surface and to increase the Mach number at the critical point. When a simple model of dissipation is included for acoustic waves, in some cases there are multiple critical points.

Strong shock implosion, approximate solution

NASA Astrophysics Data System (ADS)

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

1983-01-01

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

Numerical and theoretical analyses of underground explosion cavity decoupling

NASA Astrophysics Data System (ADS)

Jensen, R.; Aldridge, D. F.; Chael, E. P.

2013-12-01

It has long been established that the amplitudes of seismic waves radiated from an underground explosion can be reduced by detonating the explosive within a fluid-filled cavity of adequate size. Significant amplitude reduction occurs because the reflection coefficient at the fluid/rock interface (i.e., the cavity wall) is large. In fact, the DC frequency limit of the reflection coefficient for a spherically-diverging seismic wave incident upon a concentric spherical interface is -1.0, independent of radius of curvature and all material properties. In order to quantify to the degree of amplitude reduction expected in various realistic scenarios, we are conducting mathematical and numerical investigations into the so-called 'cavity decoupling problem' for a buried explosion. Our working tool is a numerical algorithm for simulating fully-coupled seismic and acoustic wave propagation in mixed solid/fluid media. Solution methodology involves explicit, time-domain, finite differencing of the elastodynamic velocity-stress partial differential system on a three-dimensional staggered spatial grid. Conditional logic is used to avoid shear stress updating within fluid zones; this approach leads to computational efficiency gains for models containing a significant proportion of ideal fluid. Numerical stability and accuracy are maintained at air/rock interfaces (where the contrast in mass density is on the order of 1 to 2000) via an FD operator 'order switching' formalism. The fourth-order spatial FD operator used throughout the bulk of the earth model is reduced to second-order in the immediate vicinity of a high-contrast interface. Point explosions detonated at the center of an air-filled or water-filled spherical cavity lead to strong resonant oscillations in radiated seismic energy, with period controlled by cavity radius and sound speed of the fill fluid. If the explosion is off-center, or the cavity is non-spherical, shear waves are generated in the surrounding elastic wholespace. Equilibrating the moment magnitudes of explosions for differing fill materials leads to misleading results in the amplitudes of the radiated elastic waves. The proper procedure entails equalizing the intrinsic energies of the explosions. Numerically-calculated results are in reasonable agreement with a theoretical model based on acoustic and elastic spherical wave propagation from a point center of symmetry. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Explosive plane-wave lens

DOEpatents

Marsh, S.P.

1987-03-12

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

Scattering theory derivation of a 3D acoustic cloaking shell.

PubMed

Cummer, Steven A; Popa, Bogdan-Ioan; Schurig, David; Smith, David R; Pendry, John; Rahm, Marco; Starr, Anthony

2008-01-18

Through acoustic scattering theory we derive the mass density and bulk modulus of a spherical shell that can eliminate scattering from an arbitrary object in the interior of the shell--in other words, a 3D acoustic cloaking shell. Calculations confirm that the pressure and velocity fields are smoothly bent and excluded from the central region as for previously reported electromagnetic cloaking shells. The shell requires an anisotropic mass density with principal axes in the spherical coordinate directions and a radially dependent bulk modulus. The existence of this 3D cloaking shell indicates that such reflectionless solutions may also exist for other wave systems that are not isomorphic with electromagnetics.

Analytical study of the effects of clouds on the light produced by lightning

NASA Technical Reports Server (NTRS)

Phanord, Dieudonne D.

1990-01-01

Researchers consider the scattering of visible and infrared light due to lightning by cubic, cylindrical and spherical clouds. The researchers extend to cloud physics the work by Twersky for single and multiple scattering of electromagnetic waves. They solve the interior problem separately to obtain the bulk parameters for the scatterer equivalent to the ensemble of spherical droplets. With the interior solution or the equivalent medium approach, the multiple scattering problem is reduced to that of a single scatterer in isolation. Hence, the computing methods of Wiscombe or Bohren specialized to Mie scattering with the possibility for absorption were used to generate numerical results in short computer time.

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

PubMed

Wang, Yan; Chen, Kean

2017-10-01

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

Efficient Terahertz Wide-Angle NUFFT-Based Inverse Synthetic Aperture Imaging Considering Spherical Wavefront.

PubMed

Gao, Jingkun; Deng, Bin; Qin, Yuliang; Wang, Hongqiang; Li, Xiang

2016-12-14

An efficient wide-angle inverse synthetic aperture imaging method considering the spherical wavefront effects and suitable for the terahertz band is presented. Firstly, the echo signal model under spherical wave assumption is established, and the detailed wavefront curvature compensation method accelerated by 1D fast Fourier transform (FFT) is discussed. Then, to speed up the reconstruction procedure, the fast Gaussian gridding (FGG)-based nonuniform FFT (NUFFT) is employed to focus the image. Finally, proof-of-principle experiments are carried out and the results are compared with the ones obtained by the convolution back-projection (CBP) algorithm. The results demonstrate the effectiveness and the efficiency of the presented method. This imaging method can be directly used in the field of nondestructive detection and can also be used to provide a solution for the calculation of the far-field RCSs (Radar Cross Section) of targets in the terahertz regime.

Ion-acoustic solitons do not exist in cylindrical and spherical geometries

NASA Astrophysics Data System (ADS)

Sheridan, T. E.

2017-09-01

We investigate the time evolution of one-dimensional, compressive, ion acoustic solitary waves for planar, cylindrical, and spherical geometries in a plasma of cold fluid ions and Boltzmann electrons. For cylindrical and spherical geometries, we show that inward (outward) going solitary waves cannot be localized (i.e., always have a tail) since the effect of a unipolar velocity perturbation is to shift ions inward (outward) to smaller (larger) radii, thereby increasing (decreasing) the local ion density. That is, there are no quasi-particle soliton states in the cylindrical and spherical cases. These results are confirmed and expanded using a plasma simulation for the cylindrical case. We initialize the system with an inward propagating planar soliton. We find supersonic solitary waves which increase in speed as they near the origin, while the wave amplitude increases as r-1/2. All solitary waves develop the predicted tail, but for larger amplitudes, the tail is unstable and evolves into an acoustic wave train.

Dirac-Kähler particle in Riemann spherical space: boson interpretation

NASA Astrophysics Data System (ADS)

Ishkhanyan, A. M.; Florea, O.; Ovsiyuk, E. M.; Red'kov, V. M.

2015-11-01

In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself one may expect to have a discrete energy spectrum. In the case of the minimal value of the total angular momentum, $j=0$, the radial equations are reduced to second-order ordinary differential equations, which are straightforwardly solved in terms of the hypergeometric functions. For non-zero values of the total angular momentum, however, the radial equations are reduced to a pair of complicated fourth-order differential equations. Employing the factorization approach, we derive the general solution of these equations involving four independent fundamental solutions written in terms of combinations of the hypergeometric functions. The corresponding discrete energy spectrum is then determined via termination of the involved hypergeometric series, resulting in quasi-polynomial wave-functions. The constructed solutions lead to notable observations when compared with those for the ordinary Dirac particle. The energy spectrum for the Dirac-K\\"ahler particle in spherical space is much more complicated. Its structure substantially differs from that for the Dirac particle since it consists of two paralleled energy level series each of which is twofold degenerate. Besides, none of the two separate series coincides with the series for the Dirac particle. Thus, the Dirac--K\\"ahler field cannot be interpreted as a system of four Dirac fermions. Additional arguments supporting this conclusion are discussed.

Astrophysical fluid dynamics

NASA Astrophysics Data System (ADS)

Ogilvie, Gordon I.

2016-06-01

> These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation and internal dynamics of stars and giant planets, the workings of jets and accretion discs around stars and black holes and the dynamics of the expanding Universe. Effects that can be important in astrophysical fluids include compressibility, self-gravitation and the dynamical influence of the magnetic field that is `frozen in' to a highly conducting plasma. The basic models introduced and applied in this course are Newtonian gas dynamics and magnetohydrodynamics (MHD) for an ideal compressible fluid. The mathematical structure of the governing equations and the associated conservation laws are explored in some detail because of their importance for both analytical and numerical methods of solution, as well as for physical interpretation. Linear and nonlinear waves, including shocks and other discontinuities, are discussed. The spherical blast wave resulting from a supernova, and involving a strong shock, is a classic problem that can be solved analytically. Steady solutions with spherical or axial symmetry reveal the physics of winds and jets from stars and discs. The linearized equations determine the oscillation modes of astrophysical bodies, as well as their stability and their response to tidal forcing.

An instability of the standard model of cosmology creates the anomalous acceleration without dark energy

NASA Astrophysics Data System (ADS)

Smoller, Joel; Temple, Blake; Vogler, Zeke

2017-11-01

We identify the condition for smoothness at the centre of spherically symmetric solutions of Einstein's original equations without the cosmological constant or dark energy. We use this to derive a universal phase portrait which describes general, smooth, spherically symmetric solutions near the centre of symmetry when the pressure p=0. In this phase portrait, the critical k=0 Friedmann space-time appears as a saddle rest point which is unstable to spherical perturbations. This raises the question as to whether the Friedmann space-time is observable by redshift versus luminosity measurements looking outwards from any point. The unstable manifold of the saddle rest point corresponding to Friedmann describes the evolution of local uniformly expanding space-times whose accelerations closely mimic the effects of dark energy. A unique simple wave perturbation from the radiation epoch is shown to trigger the instability, match the accelerations of dark energy up to second order and distinguish the theory from dark energy at third order. In this sense, anomalous accelerations are not only consistent with Einstein's original theory of general relativity, but are a prediction of it without the cosmological constant or dark energy.

An instability of the standard model of cosmology creates the anomalous acceleration without dark energy.

PubMed

Smoller, Joel; Temple, Blake; Vogler, Zeke

2017-11-01

We identify the condition for smoothness at the centre of spherically symmetric solutions of Einstein's original equations without the cosmological constant or dark energy. We use this to derive a universal phase portrait which describes general, smooth, spherically symmetric solutions near the centre of symmetry when the pressure p =0. In this phase portrait, the critical k =0 Friedmann space-time appears as a saddle rest point which is unstable to spherical perturbations. This raises the question as to whether the Friedmann space-time is observable by redshift versus luminosity measurements looking outwards from any point. The unstable manifold of the saddle rest point corresponding to Friedmann describes the evolution of local uniformly expanding space-times whose accelerations closely mimic the effects of dark energy. A unique simple wave perturbation from the radiation epoch is shown to trigger the instability, match the accelerations of dark energy up to second order and distinguish the theory from dark energy at third order. In this sense, anomalous accelerations are not only consistent with Einstein's original theory of general relativity, but are a prediction of it without the cosmological constant or dark energy.

Simulation and Analysis of Converging Shock Wave Test Problems

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

Ramsey, Scott D.; Shashkov, Mikhail J.

2012-06-21

Results and analysis pertaining to the simulation of the Guderley converging shock wave test problem (and associated code verification hydrodynamics test problems involving converging shock waves) in the LANL ASC radiation-hydrodynamics code xRAGE are presented. One-dimensional (1D) spherical and two-dimensional (2D) axi-symmetric geometric setups are utilized and evaluated in this study, as is an instantiation of the xRAGE adaptive mesh refinement capability. For the 2D simulations, a 'Surrogate Guderley' test problem is developed and used to obviate subtleties inherent to the true Guderley solution's initialization on a square grid, while still maintaining a high degree of fidelity to the originalmore » problem, and minimally straining the general credibility of associated analysis and conclusions.« less

Surface motion of a fluid planet induced by impacts

NASA Astrophysics Data System (ADS)

Ni, Sidao; Ahrens, Thomas J.

2006-10-01

In order to approximate the free-surface motion of an Earth-sized planet subjected to a giant impact, we have described the excitation of body and surface waves in a spherical compressible fluid planet without gravity or intrinsic material attenuation for a buried explosion source. Using the mode summation method, we obtained an analytical solution for the surface motion of the fluid planet in terms of an infinite series involving the products of spherical Bessel functions and Legendre polynomials. We established a closed form expression for the mode summation excitation coefficient for a spherical buried explosion source, and then calculated the surface motion for different spherical explosion source radii a (for cases of a/R = 0.001 to 0.035, R is the radius of the Earth) We also studied the effect of placing the explosion source at different radii r0 (for cases of r0/R = 0.90 to 0.96) from the centre of the planet. The amplitude of the quasi-surface waves depends substantially on a/R, and slightly on r0/R. For example, in our base-line case, a/R = 0.03, r0/R = 0.96, the free-surface velocity above the source is 0.26c, whereas antipodal to the source, the peak free surface velocity is 0.19c. Here c is the acoustic velocity of the fluid planet. These results can then be applied to studies of atmosphere erosion via blow-off caused by asteroid impacts.

Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts

NASA Astrophysics Data System (ADS)

Rossikhin, Yury A.; Shitikova, Marina V.

2013-06-01

The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong

2014-02-01

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects. Copyright © 2013 Elsevier B.V. All rights reserved.

Accurate boundary conditions for exterior problems in gas dynamics

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.

1988-01-01

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Accurate boundary conditions for exterior problems in gas dynamics

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.

1988-01-01

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far-field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far-field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

The transmission or scattering of elastic waves by an inhomogeneity of simple geometry: A comparison of theories

NASA Technical Reports Server (NTRS)

Sheu, Y. C.; Fu, L. S.

1982-01-01

The extended method of equivalent inclusion developed is applied to study the specific wave problems of the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and of the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. The eigenstrains are expanded as a geometric series and the method of integration for the inhomogeneous Helmholtz operator given by Fu and Mura is adopted. The results obtained by using a limited number of terms in the eigenstrain expansion are compared with exact solutions for the layer problem and for a perfect sphere. Two parameters are singled out for this comparison: the ratio of elastic moduli, and the ratio of the mass densities. General trends for three different situations are shown.

Photographic laboratory studies of explosions.

NASA Technical Reports Server (NTRS)

Kamel, M. M.; Oppenheim, A. K.

1973-01-01

Description of a series of cinematographic studies of explosions made with a high-speed rotating-mirror streak camera which uses a high-frequency stroboscopic ruby laser as the light source. The results obtained mainly concern explosions initiated by focused laser irradiation from a pulsed neodymium laser in a detonating gas consisting essentially of an equimolar mixture of acetylene and oxygen at an initial pressure of 100 torr at room temperature. Among the most significant observations were observations of a spherical blast wave preceded by a Chapman-Jouguet detonation which is stabilized immediately after initiation, the merging of a spherical flame with a shock front of the blast wave in which the flame is propagating, the division of a spherical detonation front into a shock wave and flame, and the generation of shock waves by a network of spherical flames.

Bohr Hamiltonian for γ = 30° with Davidson potential

NASA Astrophysics Data System (ADS)

Yigitoglu, Ibrahim; Gokbulut, Melek

2018-03-01

A γ-rigid solution of the Bohr Hamiltonian for γ = 30° is constructed with the Davidson potential in the β part. This solution is going to be called Z(4)-D. The energy eigenvalues and wave functions are obtained by using the analytic method developed by Nikiforov and Uvarov. The calculated intraband and interband B(E2) transitions rates are presented and compared with the Z(4) model predictions. The staggering behavior in γ-bands is considered to search Z(4) -D candidate nuclei. A variational procedure is applied to demonstrate that the Z(4) model is a solution of the critical point at the shape phase transition from spherical to rigid triaxial rotor.

Spherical-wave expansions of piston-radiator fields.

PubMed

Wittmann, R C; Yaghjian, A D

1991-09-01

Simple spherical-wave expansions of the continuous-wave fields of a circular piston radiator in a rigid baffle are derived. These expansions are valid throughout the illuminated half-space and are useful for efficient numerical computation in the near-field region. Multipole coefficients are given by closed-form expressions which can be evaluated recursively.

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

PubMed

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

2010-11-01

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

Eshelby's problem of a spherical inclusion eccentrically embedded in a finite spherical body

PubMed Central

He, Q.-C.

2017-01-01

Resorting to the superposition principle, the solution of Eshelby's problem of a spherical inclusion located eccentrically inside a finite spherical domain is obtained in two steps: (i) the solution to the problem of a spherical inclusion in an infinite space; (ii) the solution to the auxiliary problem of the corresponding finite spherical domain subjected to appropriate boundary conditions. Moreover, a set of functions called the sectional and harmonic deviators are proposed and developed to work out the auxiliary solution in a series form, including the displacement and Eshelby tensor fields. The analytical solutions are explicitly obtained and illustrated when the geometric and physical parameters and the boundary condition are specified. PMID:28293141

Vector spherical quasi-Gaussian vortex beams

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2014-02-01

Model equations for describing and efficiently computing the radiation profiles of tightly spherically focused higher-order electromagnetic beams of vortex nature are derived stemming from a vectorial analysis with the complex-source-point method. This solution, termed as a high-order quasi-Gaussian (qG) vortex beam, exactly satisfies the vector Helmholtz and Maxwell's equations. It is characterized by a nonzero integer degree and order (n,m), respectively, an arbitrary waist w0, a diffraction convergence length known as the Rayleigh range zR, and an azimuthal phase dependency in the form of a complex exponential corresponding to a vortex beam. An attractive feature of the high-order solution is the rigorous description of strongly focused (or strongly divergent) vortex wave fields without the need of either the higher-order corrections or the numerically intensive methods. Closed-form expressions and computational results illustrate the analysis and some properties of the high-order qG vortex beams based on the axial and transverse polarization schemes of the vector potentials with emphasis on the beam waist.

Investigation of the Wave Propagation of Vector Modes of Light in a Spherically Symmetric Refractive Index Profile

NASA Astrophysics Data System (ADS)

Pozderac, Preston; Leary, Cody

We investigated the solutions to the Helmholtz equation in the case of a spherically symmetric refractive index using three different methods. The first method involves solving the Helmholtz equation for a step index profile and applying further constraints contained in Maxwell's equations. Utilizing these equations, we can simultaneously solve for the electric and magnetic fields as well as the allowed energies of photons propagating in this system. The second method applies a perturbative correction to these energies, which surfaces when deriving a Helmholtz type equation in a medium with an inhomogeneous refractive index. Applying first order perturbation theory, we examine how the correction term affects the energy of the photon. In the third method, we investigate the effects of the above perturbation upon solutions to the scalar Helmholtz equation, which are separable with respect to its polarization and spatial degrees of freedom. This work provides insights into the vector field structure of a photon guided by a glass microsphere.

Stability of stagnation via an expanding accretion shock wave

NASA Astrophysics Data System (ADS)

Velikovich, A. L.; Murakami, M.; Taylor, B. D.; Giuliani, J. L.; Zalesak, S. T.; Iwamoto, Y.

2016-05-01

Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy-density plasma physics, the examples ranging from plasma flows in x-ray-generating Z pinches [Maron et al., Phys. Rev. Lett. 111, 035001 (2013)] to the experiments in support of the recently suggested concept of impact ignition in ICF [Azechi et al., Phys. Rev. Lett. 102, 235002 (2009); Murakami et al., Nucl. Fusion 54, 054007 (2014)]. Some experimental evidence indicates that stagnation via an expanding shock wave is stable, but its stability has never been studied theoretically. We present such analysis for the stagnation that does not involve a rarefaction wave behind the expanding shock front and is described by the classic ideal-gas Noh solution in spherical and cylindrical geometry. In either case, the stagnated flow has been demonstrated to be stable, initial perturbations exhibiting a power-law, oscillatory or monotonic, decay with time for all the eigenmodes. This conclusion has been supported by our simulations done both on a Cartesian grid and on a curvilinear grid in spherical coordinates. Dispersion equation determining the eigenvalues of the problem and explicit formulas for the eigenfunction profiles corresponding to these eigenvalues are presented, making it possible to use the theory for hydrocode verification in two and three dimensions.

Stability of stagnation via an expanding accretion shock wave

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

Velikovich, A. L.; Giuliani, J. L.; Murakami, M.

Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy-density plasma physics, the examples ranging from plasma flows in x-ray-generating Z pinches [Maron et al., Phys. Rev. Lett. 111, 035001 (2013)] to the experiments in support of the recently suggested concept of impact ignition in ICF [Azechi et al., Phys. Rev. Lett. 102, 235002 (2009); Murakami et al., Nucl. Fusion 54, 054007 (2014)]. Some experimental evidence indicates that stagnation via an expanding shock wave is stable, but its stability has never beenmore » studied theoretically. We present such analysis for the stagnation that does not involve a rarefaction wave behind the expanding shock front and is described by the classic ideal-gas Noh solution in spherical and cylindrical geometry. In either case, the stagnated flow has been demonstrated to be stable, initial perturbations exhibiting a power-law, oscillatory or monotonic, decay with time for all the eigenmodes. This conclusion has been supported by our simulations done both on a Cartesian grid and on a curvilinear grid in spherical coordinates. Dispersion equation determining the eigenvalues of the problem and explicit formulas for the eigenfunction profiles corresponding to these eigenvalues are presented, making it possible to use the theory for hydrocode verification in two and three dimensions.« less

Surface wave scattering from sharp lateral discontinuities

NASA Astrophysics Data System (ADS)

Pollitz, Fred F.

1994-11-01

The problem of surface wave scattering is re-explored, with quasi-degenerate normal mode coupling as the starting point. For coupling among specified spheroidal and toroidal mode dispersion branches, a set of coupled wave equations is derived in the frequency domain for first-arriving Rayleigh and Love waves. The solutions to these coupled wave equations using linear perturbation theory are surface integrals over the unit sphere covering the lateral distribution of perturbations in Earth structure. For isotropic structural perturbations and surface topographic perturbations, these solutions agree with the Born scattering theory previously obtained by Snieder and Romanowicz. By transforming these surface integrals into line integrals along the boundaries of the heterogeneous regions in the case of sharp discontinuities, and by using uniformly valid Green's functions, it is possible to extend the solution to the case of multiple scattering interactions. The proposed method allows the relatively rapid calculation of exact second order scattered wavefield potentials for scattering by sharp discontinuities, and it has many advantages not realized in earlier treatments. It employs a spherical Earth geometry, uses no far field approximation, and implicitly contains backward as well as forward scattering. Comparisons of asymptotic scattering and an exact solution with single scattering and multiple scattering integral formulations show that the phase perturbation predicted by geometrical optics breaks down for scatterers less than about six wavelengths in diameter, and second-order scattering predicts well both the amplitude and phase pattern of the exact wavefield for sufficiently small scatterers, less than about three wavelengths in diameter for anomalies of a few percent.

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

NASA Astrophysics Data System (ADS)

Paldor, N.

2017-12-01

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

Nonlinear Interaction of Waves in Rotating Spherical Layers

NASA Astrophysics Data System (ADS)

Zhilenko, D.; Krivonosova, O.; Gritsevich, M.

2018-01-01

Flows of a viscous incompressible fluid in a spherical layer that are due to rotational oscillations of its inner boundary at two frequencies with respect to the state of rest are numerically studied. It is found that an increase in the amplitude of oscillations of the boundary at the higher frequency can result in a significant enhancement of the low-frequency mode in a flow near the outer boundary. The direction of propagation of the low-frequency wave changes from radial to meridional, whereas the high-frequency wave propagates in the radial direction in a limited inner region of the spherical layer. The role of the meridional circulation in the energy exchange between spaced waves is demonstrated.

Expressions for the spherical-wave-structure function based on a bump spectrum model for the index of refraction

NASA Astrophysics Data System (ADS)

Richardson, Christina E.; Andrews, Larry C.

1991-07-01

New spectra models have recently been developed for the spatial power spectra of temperature and refractive index fluctuations in the atmospheric boundary layer showing the characteristic 'bump' just prior to the dissipation ranges. Theoretical work involving these new models has led to new expressions for the phase structure function associated with a plane optical wave, although most experimental work has involved spherical waves. Following techniques similar to those used for the plane wave analysis, new expressions valid in geometrical and diffraction regimes are developed here for the phase structure function of a spherical optical wave propagating through clear-air atmospheric turbulence. Useful asymptotic formulas for small separation distances and the inertial subrange are derived from these general expressions.

Eulerian Simulation of Acoustic Waves Over Long Range in Realistic Environments

NASA Astrophysics Data System (ADS)

Chitta, Subhashini; Steinhoff, John

2015-11-01

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

Development of indirect EFBEM for radiating noise analysis including underwater problems

NASA Astrophysics Data System (ADS)

Kwon, Hyun-Wung; Hong, Suk-Yoon; Song, Jee-Hun

2013-09-01

For the analysis of radiating noise problems in medium-to-high frequency ranges, the Energy Flow Boundary Element Method (EFBEM) was developed. EFBEM is the analysis technique that applies the Boundary Element Method (BEM) to Energy Flow Analysis (EFA). The fundamental solutions representing spherical wave property for radiating noise problems in open field and considering the free surface effect in underwater are developed. Also the directivity factor is developed to express wave's directivity patterns in medium-to-high frequency ranges. Indirect EFBEM by using fundamental solutions and fictitious source was applied to open field and underwater noise problems successfully. Through numerical applications, the acoustic energy density distributions due to vibration of a simple plate model and a sphere model were compared with those of commercial code, and the comparison showed good agreement in the level and pattern of the energy density distributions.

On the Interaction and Coalescence if Spherical Blast Waves

NASA Technical Reports Server (NTRS)

Kandula, Max; Freeman, Robert J.

2005-01-01

The scaling and similarity laws concerning the propagation of isolated spherical blast waves are briefly reviewed. Both point source explosions and high pressure gas explosions are considered. Test data on blast overpressure from the interaction and coalescence of spherical blast waves emanating from explosives in the form of shaped charges of different strength placed in the vicinity of a solid propellant stack are presented. These data are discussed with regard to the scaling laws concerning the decay of blast overpressure. The results point out the possibility of detecting source explosions from far-field pressure measurements.

Quantum dot properties in the multiband envelope-function approximation using boundary conditions based upon first-principles quantum calculations

NASA Astrophysics Data System (ADS)

Flory, Curt A.; Musgrave, Charles B.; Zhang, Zhiyong

2008-05-01

A number of physical processes involving quantum dots depend critically upon the “evanescent” electron eigenstate wave function that extends outside of the material surface into the surrounding region. These processes include electron tunneling through quantum dots, as well as interactions between multiple quantum dot structures. In order to unambiguously determine these evanescent fields, appropriate boundary conditions have been developed to connect the electronic solutions interior to the semiconductor quantum dot to exterior vacuum solutions. In standard envelope function theory, the interior wave function consists of products of band edge and envelope functions, and both must be considered when matching to the external solution. While the envelope functions satisfy tractable equations, the band edge functions are generally not known. In this work, symmetry arguments in the spherically symmetric approximation are used in conjunction with the known qualitative behavior of bonding and antibonding orbitals to catalog the behavior of the band edge functions at the unit cell boundary. This physical approximation allows consolidation of the influence of the band edge functions to two simple surface parameters that are incorporated into the boundary conditions and are straightforwardly computed by using numerical first-principles quantum techniques. These new boundary conditions are employed to analyze an isolated spherically symmetric semiconductor quantum dot in vacuum within the analytical model of Sercel and Vahala [Phys. Rev. Lett. 65, 239 (1990); Phys. Rev. B 42, 3690 (1990)]. Results are obtained for quantum dots made of GaAs and InP, which are compared with ab initio calculations that have appeared in the literature.

Second-harmonic generation from a thin spherical layer and No-generation conditions

NASA Astrophysics Data System (ADS)

Kapshai, V. N.; Shamyna, A. A.

2017-09-01

In the Rayleigh-Gans-Debye approximation, we solve the problem of second-harmonic generation by an elliptically polarized electromagnetic wave incident on the surface of a spherical particle that is coated by an optically nonlinear layer and is placed in a dielectric. The formulas obtained characterize the spatial distribution of the electric field of the second harmonic in the far-field zone. The most general form of the second-order dielectric susceptibility tensor is considered, which contains four independent components, with three of them being nonchiral and one, chiral. Consistency and inconsistencies between the obtained solution and formulas from works of other authors are found. We analyze the directivity patterns that characterize the spatial distribution of the generated radiation for the nonchiral layer and their dependences on the anisotropy and ellipticity coefficients of the incident wave. It is found that, with increasing radius of the nonlinear layer, the generated radiation becomes more directional. Combinations of parameters for which no radiation is generated are revealed. Based on this, we propose methods for experimental determination of the anisotropy coefficients.

Invariant and partially-invariant solutions of the equations describing a non-stationary and isentropic flow for an ideal and compressible fluid in (3 + 1) dimensions

NASA Astrophysics Data System (ADS)

Grundland, A. M.; Lalague, L.

1996-04-01

This paper presents a new method of constructing, certain classes of solutions of a system of partial differential equations (PDEs) describing the non-stationary and isentropic flow for an ideal compressible fluid. A generalization of the symmetry reduction method to the case of partially-invariant solutions (PISs) has been formulated. We present a new algorithm for constructing PISs and discuss in detail the necessary conditions for the existence of non-reducible PISs. All these solutions have the defect structure 0305-4470/29/8/019/img1 and are computed from four-dimensional symmetric subalgebras. These theoretical considerations are illustrated by several examples. Finally, some new classes of invariant solutions obtained by the symmetry reduction method are included. These solutions represent central, conical, rational, spherical, cylindrical and non-scattering double waves.

Numerical solutions of the macroscopic Maxwell equations for scattering by non-spherical particles: A tutorial review

NASA Astrophysics Data System (ADS)

Kahnert, Michael

2016-07-01

Numerical solution methods for electromagnetic scattering by non-spherical particles comprise a variety of different techniques, which can be traced back to different assumptions and solution strategies applied to the macroscopic Maxwell equations. One can distinguish between time- and frequency-domain methods; further, one can divide numerical techniques into finite-difference methods (which are based on approximating the differential operators), separation-of-variables methods (which are based on expanding the solution in a complete set of functions, thus approximating the fields), and volume integral-equation methods (which are usually solved by discretisation of the target volume and invoking the long-wave approximation in each volume cell). While existing reviews of the topic often tend to have a target audience of program developers and expert users, this tutorial review is intended to accommodate the needs of practitioners as well as novices to the field. The required conciseness is achieved by limiting the presentation to a selection of illustrative methods, and by omitting many technical details that are not essential at a first exposure to the subject. On the other hand, the theoretical basis of numerical methods is explained with little compromises in mathematical rigour; the rationale is that a good grasp of numerical light scattering methods is best achieved by understanding their foundation in Maxwell's theory.

Towards anti-causal Green's function for three-dimensional sub-diffraction focusing

NASA Astrophysics Data System (ADS)

Ma, Guancong; Fan, Xiying; Ma, Fuyin; de Rosny, Julien; Sheng, Ping; Fink, Mathias

2018-06-01

In causal physics, the causal Green's function describes the radiation of a point source. Its counterpart, the anti-causal Green's function, depicts a spherically converging wave. However, in free space, any converging wave must be followed by a diverging one. Their interference gives rise to the diffraction limit that constrains the smallest possible dimension of a wave's focal spot in free space, which is half the wavelength. Here, we show with three-dimensional acoustic experiments that we can realize a stand-alone anti-causal Green's function in a large portion of space up to a subwavelength distance from the focus point by introducing a near-perfect absorber for spherical waves at the focus. We build this subwavelength absorber based on membrane-type acoustic metamaterial, and experimentally demonstrate focusing of spherical waves beyond the diffraction limit.

Method for making fine and ultrafine spherical particles of zirconium titanate and other mixed metal oxide systems

DOEpatents

Hu, Michael Z.

2006-05-23

Disclosed is a method for making amorphous spherical particles of zirconium titanate and crystalline spherical particles of zirconium titanate comprising the steps of mixing an aqueous solution of zirconium salt and an aqueous solution of titanium salt into a mixed solution having equal moles of zirconium and titanium and having a total salt concentration in the range from 0.01 M to about 0.5 M. A stearic dispersant and an organic solvent is added to the mixed salt solution, subjecting the zirconium salt and the titanium salt in the mixed solution to a coprecipitation reaction forming a solution containing amorphous spherical particles of zirconium titanate wherein the volume ratio of the organic solvent to aqueous part is in the range from 1 to 5. The solution of amorphous spherical particles is incubated in an oven at a temperature .ltoreq.100.degree. C. for a period of time .ltoreq.24 hours converting the amorphous particles to fine or ultrafine crystalline spherical particles of zirconium titanate.

Removal of pinned scroll waves in cardiac tissues by electric fields in a generic model of three-dimensional excitable media.

PubMed

Pan, De-Bei; Gao, Xiang; Feng, Xia; Pan, Jun-Ting; Zhang, Hong

2016-02-24

Spirals or scroll waves pinned to heterogeneities in cardiac tissues may cause lethal arrhythmias. To unpin these life-threatening spiral waves, methods of wave emission from heterogeneities (WEH) induced by low-voltage pulsed DC electric fields (PDCEFs) and circularly polarized electric fields (CPEFs) have been used in two-dimensional (2D) cardiac tissues. Nevertheless, the unpinning of scroll waves in three-dimensional (3D) cardiac systems is much more difficult than that of spiral waves in 2D cardiac systems, and there are few reports on the removal of pinned scroll waves in 3D cardiac tissues by electric fields. In this article, we investigate in detail the removal of pinned scroll waves in a generic model of 3D excitable media using PDCEF, AC electric field (ACEF) and CPEF, respectively. We find that spherical waves can be induced from the heterogeneities by these electric fields in initially quiescent excitable media. However, only CPEF can induce spherical waves with frequencies higher than that of the pinned scroll wave. Such higher-frequency spherical waves induced by CPEF can be used to drive the pinned scroll wave out of the cardiac systems. We hope this remarkable ability of CPEF can provide a better alternative to terminate arrhythmias caused by pinned scroll waves.

Waveform inversion for 3-D earth structure using the Direct Solution Method implemented on vector-parallel supercomputer

NASA Astrophysics Data System (ADS)

Hara, Tatsuhiko

2004-08-01

We implement the Direct Solution Method (DSM) on a vector-parallel supercomputer and show that it is possible to significantly improve its computational efficiency through parallel computing. We apply the parallel DSM calculation to waveform inversion of long period (250-500 s) surface wave data for three-dimensional (3-D) S-wave velocity structure in the upper and uppermost lower mantle. We use a spherical harmonic expansion to represent lateral variation with the maximum angular degree 16. We find significant low velocities under south Pacific hot spots in the transition zone. This is consistent with other seismological studies conducted in the Superplume project, which suggests deep roots of these hot spots. We also perform simultaneous waveform inversion for 3-D S-wave velocity and Q structure. Since resolution for Q is not good, we develop a new technique in which power spectra are used as data for inversion. We find good correlation between long wavelength patterns of Vs and Q in the transition zone such as high Vs and high Q under the western Pacific.

Remote listening and passive acoustic detection in a 3-D environment

NASA Astrophysics Data System (ADS)

Barnhill, Colin

Teleconferencing environments are a necessity in business, education and personal communication. They allow for the communication of information to remote locations without the need for travel and the necessary time and expense required for that travel. Visual information can be communicated using cameras and monitors. The advantage of visual communication is that an image can capture multiple objects and convey them, using a monitor, to a large group of people regardless of the receiver's location. This is not the case for audio. Currently, most experimental teleconferencing systems' audio is based on stereo recording and reproduction techniques. The problem with this solution is that it is only effective for one or two receivers. To accurately capture a sound environment consisting of multiple sources and to recreate that for a group of people is an unsolved problem. This work will focus on new methods of multiple source 3-D environment sound capture and applications using these captured environments. Using spherical microphone arrays, it is now possible to capture a true 3-D environment A spherical harmonic transform on the array's surface allows us to determine the basis functions (spherical harmonics) for all spherical wave solutions (up to a fixed order). This spherical harmonic decomposition (SHD) allows us to not only look at the time and frequency characteristics of an audio signal but also the spatial characteristics of an audio signal. In this way, a spherical harmonic transform is analogous to a Fourier transform in that a Fourier transform transforms a signal into the frequency domain and a spherical harmonic transform transforms a signal into the spatial domain. The SHD also decouples the input signals from the microphone locations. Using the SHD of a soundfield, new algorithms are available for remote listening, acoustic detection, and signal enhancement The new algorithms presented in this paper show distinct advantages over previous detection and listening algorithms especially for multiple speech sources and room environments. The algorithms use high order (spherical harmonic) beamforming and power signal characteristics for source localization and signal enhancement These methods are applied to remote listening, surveillance, and teleconferencing.

Numerical Study of Wave Propagation in a Non-Uniform Flow

NASA Technical Reports Server (NTRS)

Povitsky, Alex; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

The propagation of acoustic waves originating from cylindrical and spherical pulses, in a non-uniform mean flow, and in the presence of a reflecting wall is investigated by Hardin and Pope approach using compact approximation of spatial derivatives. The 2-D and 3-D stagnation flows and a flow around a cylinder are taken as prototypes of real world flows with strong gradients of mean pressure and velocity. The intensity and directivity of acoustic wave patterns appear to be quite different from the benchmark solutions obtained in a static environment for the same geometry. The physical reasons for amplification and weakening of sound are discussed in terms of dynamics of wave profile and redistribution of acoustic energy and its potential and kinetic components. For an acoustic wave in the flow around a cylinder, the observed mean acoustic pressure is approximately doubled (upstream pulse position) and halved (downstream pulse position) in comparison with the sound propagation in static ambient conditions.

Numerical Simulation of Focused Shock Shear Waves in Soft Solids and a Two-Dimensional Nonlinear Homogeneous Model of the Brain

PubMed Central

Giammarinaro, B.; Coulouvrat, F.; Pinton, G.

2016-01-01

Shear waves that propagate in soft solids, such as the brain, are strongly nonlinear and can develop into shock waves in less than one wavelength. We hypothesize that these shear shock waves could be responsible for certain types of traumatic brain injuries (TBI) and that the spherical geometry of the skull bone could focus shear waves deep in the brain, generating diffuse axonal injuries. Theoretical models and numerical methods that describe nonlinear polarized shear waves in soft solids such as the brain are presented. They include the cubic nonlinearities that are characteristic of soft solids and the specific types of nonclassical attenuation and dispersion observed in soft tissues and the brain. The numerical methods are validated with analytical solutions, where possible, and with self-similar scaling laws where no known solutions exist. Initial conditions based on a human head X-ray microtomography (CT) were used to simulate focused shear shock waves in the brain. Three regimes are investigated with shock wave formation distances of 2.54 m, 0.018 m, and 0.0064 m. We demonstrate that under realistic loading scenarios, with nonlinear properties consistent with measurements in the brain, and when the shock wave propagation distance and focal distance coincide, nonlinear propagation can easily overcome attenuation to generate shear shocks deep inside the brain. Due to these effects, the accelerations in the focal are larger by a factor of 15 compared to acceleration at the skull surface. These results suggest that shock wave focusing could be responsible for diffuse axonal injuries. PMID:26833489

An Electron is the God Particle

NASA Astrophysics Data System (ADS)

Wolff, Milo

2001-04-01

Philosophers, Clifford, Mach, Einstein, Wyle, Dirac & Schroedinger, believed that only a wave structure of particles could satisfy experiment and fulfill reality. A quantum Wave Structure of Matter is described here. It predicts the natural laws more accurately and completely than classic laws. Einstein reasoned that the universe depends on particles which are "spherically, spatially extended in space." and "Hence a discrete material particle has no place as a fundamental concept in a field theory." Thus the discrete point particle was wrong. He deduced the true electron is primal because its force range is infinite. Now, it is found the electron's wave structure contains the laws of Nature that rule the universe. The electron plays the role of creator - the God particle. Electron structure is a pair of spherical outward/inward quantum waves, convergent to a center in 3D space. This wave pair creates a h/4pi quantum spin when the in-wave spherically rotates to become the out-wave. Both waves form a spinor satisfying the Dirac Equation. Thus, the universe is binary like a computer. Reference: http://members.tripod.com/mwolff

Gasdynamics of explosions today.

NASA Technical Reports Server (NTRS)

Brode, H. L.; Glass, I. I.; Oppenheim, A. K.

1971-01-01

A brief review is given of blast and detonation wave phenomena and some of their uses in war and peace. It is concluded that great strides have been made over the last three decades toward the physical understanding, the analytical-numerical solution, and the measurement of dynamic and thermodynamic quantities, also taking into consideration severe environments and extremely short durations. Questions of internal ballistics are discussed together with hypervelocity launchers and shock tubes, collapsing cylindrical drivers, spherical implosions, explosive weapons, dynamic response, and equation of state data.

Huygens-Fresnel picture for electron-molecule elastic scattering★

NASA Astrophysics Data System (ADS)

Baltenkov, Arkadiy S.; Msezane, Alfred Z.

2017-11-01

The elastic scattering cross sections for a slow electron by C2 and H2 molecules have been calculated within the framework of the non-overlapping atomic potential model. For the amplitudes of the multiple electron scattering by a target the wave function of the molecular continuum is represented as a combination of a plane wave and two spherical waves generated by the centers of atomic spheres. This wave function obeys the Huygens-Fresnel principle according to which the electron wave scattering by a system of two centers is accompanied by generation of two spherical waves; their interaction creates a diffraction pattern far from the target. Each of the Huygens waves, in turn, is a superposition of the partial spherical waves with different orbital angular momenta l and their projections m. The amplitudes of these partial waves are defined by the corresponding phases of electron elastic scattering by an isolated atomic potential. In numerical calculations the s- and p-phase shifts are taken into account. So the number of interfering electron waves is equal to eight: two of which are the s-type waves and the remaining six waves are of the p-type with different m values. The calculation of the scattering amplitudes in closed form (rather than in the form of S-matrix expansion) is reduced to solving a system of eight inhomogeneous algebraic equations. The differential and total cross sections of electron scattering by fixed-in-space molecules and randomly oriented ones have been calculated as well. We conclude by discussing the special features of the S-matrix method for the case of arbitrary non-spherical potentials. Contribution to the Topical Issue "Low energy positron and electron interactions", edited by James Sullivan, Ron White, Michael Bromley, Ilya Fabrikant, and David Cassidy.

New generalized Noh solutions for HEDP hydrocode verification

NASA Astrophysics Data System (ADS)

Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.; Tangri, V.

2017-10-01

The classic Noh solution describing stagnation of a cold ideal gas in a strong accretion shock wave has been the workhorse of compressible hydrocode verification for over three decades. We describe a number of its generalizations available for HEDP code verification. First, for an ideal gas, we have obtained self-similar solutions that describe adiabatic convergence either of a finite-pressure gas into an empty cavity or of a finite-amplitude sound wave into a uniform resting gas surrounding the center or axis of symmetry. At the moment of collapse such a flow produces a uniform gas whose velocity at each point is constant and directed towards the axis or the center, i. e. the initial condition similar to the classic solution but with a finite pressure of the converging gas. After that, a constant-velocity accretion shock propagates into the incident gas whose pressure and velocity profiles are not flat, in contrast with the classic solution. Second, for an arbitrary equation of state, we demonstrate the existence of self-similar solutions of the Noh problem in cylindrical and spherical geometry. Examples of such solutions with a three-term equation of state that includes cold, thermal ion/lattice, and thermal electron contributions are presented for aluminum and copper. These analytic solutions are compared to our numerical simulation results as an example of their use for code verification. Work supported by the US DOE/NNSA.

Formation and propagation of Love waves in a surface layer with a P-wave source. Technical report

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

Florence, A.L.; Miller, S.A.

The objective of this research is to investigate experimentally, and support with theoretical calculations, the formation and propagation of Love waves from a P-wave source due to scattering at material heterogeneities. The P-wave source is a spherical piezoelectric crystal cast in a surface layer of rock simulant overlaying a higher impedance granite substrate. Excitation of the piezoelectric crystal with a known voltage applies a spherical compressional pulse of known amplitude to the surrounding medium. Lateral heterogeneities cast in the surface layer convert incident P-wave energy into shear waves. The horizontally polarized shear waves (SH waves) trapped in the surface layermore » wave guide are the Love waves we will measure at the surface.« less

Ultrasonic power transfer from a spherical acoustic wave source to a free-free piezoelectric receiver: Modeling and experiment

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

Shahab, S.; Gray, M.; Erturk, A., E-mail: alper.erturk@me.gatech.edu

2015-03-14

Contactless powering of small electronic components has lately received growing attention for wireless applications in which battery replacement or tethered charging is undesired or simply impossible, and ambient energy harvesting is not a viable solution. As an alternative to well-studied methods of contactless energy transfer, such as the inductive coupling method, the use of ultrasonic waves transmitted and received by piezoelectric devices enables larger power transmission distances, which is critical especially for deep-implanted electronic devices. Moreover, energy transfer by means of acoustic waves is well suited in situations where no electromagnetic fields are allowed. The limited literature of ultrasonic acousticmore » energy transfer is mainly centered on proof-of-concept experiments demonstrating the feasibility of this method, lacking experimentally validated modeling efforts for the resulting multiphysics problem that couples the source and receiver dynamics with domain acoustics. In this work, we present fully coupled analytical, numerical, and experimental multiphysics investigations for ultrasonic acoustic energy transfer from a spherical wave source to a piezoelectric receiver bar that operates in the 33-mode of piezoelectricity. The fluid-loaded piezoelectric receiver under free-free mechanical boundary conditions is shunted to an electrical load for quantifying the electrical power output for a given acoustic source strength of the transmitter. The analytical acoustic-piezoelectric structure interaction modeling framework is validated experimentally, and the effects of system parameters are reported along with optimal electrical loading and frequency conditions of the receiver.« less

Analysis of scattering by a linear chain of spherical inclusions in an optical fiber

NASA Astrophysics Data System (ADS)

Chremmos, Ioannis D.; Uzunoglu, Nikolaos K.

2006-12-01

The scattering by a linear chain of spherical dielectric inclusions, embedded along the axis of an optical fiber, is analyzed using a rigorous integral equation formulation, based on the dyadic Green's function theory. The coupled electric field integral equations are solved by applying the Galerkin technique with Mie-type expansion of the field inside the spheres in terms of spherical waves. The analysis extends the previously studied case of a single spherical inhomogeneity inside a fiber to the multisphere-scattering case, by utilizing the classic translational addition theorems for spherical waves in order to analytically extract the direct-intersphere-coupling coefficients. Results for the transmitted and reflected power, on incidence of the fundamental HE11 mode, are presented for several cases.

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

PubMed

Abbasi, Bilal; Craig, Walter

2014-09-08

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

Removal of pinned scroll waves in cardiac tissues by electric fields in a generic model of three-dimensional excitable media

PubMed Central

Pan, De-Bei; Gao, Xiang; Feng, Xia; Pan, Jun-Ting; Zhang, Hong

2016-01-01

Spirals or scroll waves pinned to heterogeneities in cardiac tissues may cause lethal arrhythmias. To unpin these life-threatening spiral waves, methods of wave emission from heterogeneities (WEH) induced by low-voltage pulsed DC electric fields (PDCEFs) and circularly polarized electric fields (CPEFs) have been used in two-dimensional (2D) cardiac tissues. Nevertheless, the unpinning of scroll waves in three-dimensional (3D) cardiac systems is much more difficult than that of spiral waves in 2D cardiac systems, and there are few reports on the removal of pinned scroll waves in 3D cardiac tissues by electric fields. In this article, we investigate in detail the removal of pinned scroll waves in a generic model of 3D excitable media using PDCEF, AC electric field (ACEF) and CPEF, respectively. We find that spherical waves can be induced from the heterogeneities by these electric fields in initially quiescent excitable media. However, only CPEF can induce spherical waves with frequencies higher than that of the pinned scroll wave. Such higher-frequency spherical waves induced by CPEF can be used to drive the pinned scroll wave out of the cardiac systems. We hope this remarkable ability of CPEF can provide a better alternative to terminate arrhythmias caused by pinned scroll waves. PMID:26905367

Wave-driven winds from cool stars. I - Some effects of magnetic field geometry

NASA Technical Reports Server (NTRS)

Hartmann, L.; Macgregor, K. B.

1982-01-01

The wave-driven wind theory of Hartmann and MacGregor (1980) is extended to include effects due to non-radial divergence of the flow. Specifically, isothermal expansion within a flow tube whose cross-sectional area increases outward faster than the square of the radius near the stellar surface is considered. It is found that the qualitative conclusions of Hartmann and MacGregor concerning the physical properties of Alfven wave-driven winds are largely unaffected. In particular, mass fluxes of similar magnitude are obtained, and wave dissipation is still necessary to produce acceptably small terminal velocities. Increasingly divergent flow geometries generally lead to higher initial wind speeds and slightly lower terminal velocities. For some cases of extremely rapid flow tube divergence, steady supersonic wind solutions which extend to infinity with vanishing gas pressure cannot be obtained. In addition, departures from spherical symmetry can cause the relative Alfven wave amplitude delta-B/B to become approximately greater than 1 within several stellar radii of the base of the wind, suggesting that nonlinear processes may contribute to the wave dissipation required by the theory.

Orbiting naked singularities in large-ω Brans-Dicke gravity

NASA Astrophysics Data System (ADS)

Chauvineau, Bertrand

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

Duan, Xueyang

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

A Generalization of the Einstein-Maxwell Equations

NASA Astrophysics Data System (ADS)

Cotton, Fredrick

2016-03-01

The proposed modifications of the Einstein-Maxwell equations include: (1) the addition of a scalar term to the electromagnetic side of the equation rather than to the gravitational side, (2) the introduction of a 4-dimensional, nonlinear electromagnetic constitutive tensor and (3) the addition of curvature terms arising from the non-metric components of a general symmetric connection. The scalar term is defined by the condition that a spherically symmetric particle be force-free and mathematically well-behaved everywhere. The constitutive tensor introduces two auxiliary fields which describe the particle structure. The additional curvature terms couple both to particle solutions and to electromagnetic and gravitational wave solutions. http://sites.google.com/site/fwcotton/em-30.pdf

LETTER TO THE EDITOR: A disintegrating cosmic string

NASA Astrophysics Data System (ADS)

Griffiths, J. B.; Docherty, P.

2002-06-01

We present a simple sandwich gravitational wave of the Robinson-Trautman family. This is interpreted as representing a shock wave with a spherical wavefront which propagates into a Minkowski background minus a wedge (i.e. the background contains a cosmic string). The deficit angle (the tension) of the string decreases through the gravitational wave, which then ceases. This leaves an expanding spherical region of Minkowski space behind it. The decay of the cosmic string over a finite interval of retarded time may be considered to generate the gravitational wave.

Mathematical Development and Computational Analysis of Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) Based on Bloch Nuclear Magnetic Resonance (NMR) Diffusion Model for Myocardial Motion.

PubMed

Dada, Michael O; Jayeoba, Babatunde; Awojoyogbe, Bamidele O; Uno, Uno E; Awe, Oluseyi E

2017-09-13

Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) is a tagged image analysis method that can measure myocardial motion and strain in near real-time and is considered a potential candidate to make magnetic resonance tagging clinically viable. However, analytical expressions of radially tagged transverse magnetization in polar coordinates (which is required to appropriately describe the shape of the heart) have not been explored because the physics required to directly connect myocardial deformation of tagged Nuclear Magnetic Resonance (NMR) transverse magnetization in polar geometry and the appropriate harmonic phase parameters are not yet available. The analytical solution of Bloch NMR diffusion equation in spherical geometry with appropriate spherical wave tagging function is important for proper analysis and monitoring of heart systolic and diastolic deformation with relevant boundary conditions. In this study, we applied Harmonic Phase MRI method to compute the difference between tagged and untagged NMR transverse magnetization based on the Bloch NMR diffusion equation and obtained radial wave tagging function for analysis of myocardial motion. The analytical solution of the Bloch NMR equations and the computational simulation of myocardial motion as developed in this study are intended to significantly improve healthcare for accurate diagnosis, prognosis and treatment of cardiovascular related deceases at the lowest cost because MRI scan is still one of the most expensive anywhere. The analysis is fundamental and significant because all Magnetic Resonance Imaging techniques are based on the Bloch NMR flow equations.

New two-metric theory of gravity with prior geometry

NASA Technical Reports Server (NTRS)

Lightman, A. P.; Lee, D. L.

1973-01-01

A Lagrangian-based metric theory of gravity is developed with three adjustable constants and two tensor fields, one of which is a nondynamic 'flat space metric' eta. With a suitable cosmological model and a particular choice of the constants, the 'post-Newtonian limit' of the theory agrees, in the current epoch, with that of general relativity theory (GRT); consequently the theory is consistent with current gravitation experiments. Because of the role of eta, the gravitational 'constant' G is time-dependent and gravitational waves travel null geodesics of eta rather than the physical metric g. Gravitational waves possess six degrees of freedom. The general exact static spherically-symmetric solution is a four-parameter family. Future experimental tests of the theory are discussed.

Optimal secondary source position in exterior spherical acoustical holophony

NASA Astrophysics Data System (ADS)

Pasqual, A. M.; Martin, V.

2012-02-01

Exterior spherical acoustical holophony is a branch of spatial audio reproduction that deals with the rendering of a given free-field radiation pattern (the primary field) by using a compact spherical loudspeaker array (the secondary source). More precisely, the primary field is known on a spherical surface surrounding the primary and secondary sources and, since the acoustic fields are described in spherical coordinates, they are naturally subjected to spherical harmonic analysis. Besides, the inverse problem of deriving optimal driving signals from a known primary field is ill-posed because the secondary source cannot radiate high-order spherical harmonics efficiently, especially in the low-frequency range. As a consequence, a standard least-squares solution will overload the transducers if the primary field contains such harmonics. Here, this is avoided by discarding the strongly decaying spherical waves, which are identified through inspection of the radiation efficiency curves of the secondary source. However, such an unavoidable regularization procedure increases the least-squares error, which also depends on the position of the secondary source. This paper deals with the above-mentioned questions in the context of far-field directivity reproduction at low and medium frequencies. In particular, an optimal secondary source position is sought, which leads to the lowest reproduction error in the least-squares sense without overloading the transducers. In order to address this issue, a regularization quality factor is introduced to evaluate the amount of regularization required. It is shown that the optimal position improves significantly the holophonic reconstruction and maximizes the regularization quality factor (minimizes the amount of regularization), which is the main general contribution of this paper. Therefore, this factor can also be used as a cost function to obtain the optimal secondary source position.

Mean-square angle-of-arrival difference between two counter-propagating spherical waves in the presence of atmospheric turbulence.

PubMed

Chen, Chunyi; Yang, Huamin; Tong, Shoufeng; Lou, Yan

2015-09-21

The mean-square angle-of-arrival (AOA) difference between two counter-propagating spherical waves in atmospheric turbulence is theoretically formulated. Closed-form expressions for the path weighting functions are obtained. It is found that the diffraction and refraction effects of turbulent cells make negative and positive contributions to the mean-square AOA difference, respectively, and the turbulent cells located at the midpoint of the propagation path have no contributions to the mean-square AOA difference. If the mean-square AOA difference is separated into the refraction and diffraction parts, the refraction part always dominates the diffraction one, and the ratio of the diffraction part to the refraction one is never larger than 0.5 for any turbulence spectrum. Based on the expressions for the mean-square AOA difference, formulae for the correlation coefficient between the angles of arrival of two counter-propagating spherical waves in atmospheric turbulence are derived. Numerical calculations are carried out by considering that the turbulence spectrum has no path dependence. It is shown that the mean-square AOA difference always approximates to the variance of AOA fluctuations. It is found that the correlation coefficient between the angles of arrival in the x or y direction of two counter-propagating spherical waves ranges from 0.46 to 0.5, implying that the instantaneous angles of arrival of two counter-propagating spherical waves in atmospheric turbulence are far from being perfectly correlated even when the turbulence spectrum does not vary along the path.

An analytically solvable three-body break-up model problem in hyperspherical coordinates

NASA Astrophysics Data System (ADS)

Ancarani, L. U.; Gasaneo, G.; Mitnik, D. M.

2012-10-01

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behavior. Since the coordinates' coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude.

Boundary causality versus hyperbolicity for spherical black holes in Gauss-Bonnet gravity

NASA Astrophysics Data System (ADS)

Andrade, Tomás; Cáceres, Elena; Keeler, Cynthia

2017-07-01

We explore the constraints boundary causality places on the allowable Gauss-Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss-Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss-Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss-Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes.

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1974-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear ti surfaces. The spherical mean is the average of u over a constant ti surface. The conditions on the linear differential operator, L, and on the orthogonal coordinates (ti, eta, zeta) are established so that the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be determined directly as a problem with only space variable. Conditions are then established so that the spherical mean of the solution in one concial region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Bumps of the wave structure function in non-Kolmogorov turbulence

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

The analytical solution of the problem of a shock focusing in a gas for one-dimensional case

NASA Astrophysics Data System (ADS)

Shestakovskaya, E. S.; Magazov, F. G.

2018-03-01

The analytical solution of the problem of an imploding shock wave in the vessel with an impermeable wall is constructed for the cases of planar, cylindrical and spherical symmetry. The negative velocity is set at the vessel boundary. The velocity of cold ideal gas is zero. At the initial time the shock spreads from this point into the center of symmetry. The boundary moves under the particular law which conforms to the movement of the shock. In Euler variables it moves but in Lagrangian variables its trajectory is a vertical line. Equations that determine the structure of the gas flow between the shock front and the boundary as a function of time and the Lagrangian coordinate as well as the dependence of the entropy on the shock wave velocity are obtained. Self-similar coefficients and corresponding critical values of self-similar coordinates were found for a wide range of adiabatic index. The problem is solved for Lagrangian coordinates.

Extended fusion yield integral using pathway idea in case of Shock-compressed heated plasma

NASA Astrophysics Data System (ADS)

Kumar, Dilip; Haubold, Hans

The extended non-resonant thermonuclear reaction rate probability integral obtained in Haubold and Kumar [Haubold, H.J. and Kumar, D.: 2008, Extension of thermonuclear functions through the pathway model including Maxwell-Boltzmann and Tsallis distributions, Astroparticle Physics, 29, 70-76] is used to evaluate the fusion energy by itegrating it over temperature. The closed form representation of the extended reaction rate integral via Meijer's G-function is expressed as a solution of a homogeneous differential equation. A physical model of Guderley[Guderley G. :1942, Starke kugelige und zylindrische Verdichtungsstsse in der Nhe des Kugelmittelpunktes bzw. der Zylinderachse, Luftfahrtforschung, 19, 302] has been considered for the laser driven hydrodynamical process in a compressed fusion plasma and heated strong spherical shock wave. The fusion yield integral obtained in the paper is compared with the standard fusion yield ob-tained by Haubold and John [Haubold, H.J. and John, R.W.:1981, Analytical representation of the thermonuclear reaction rate and fusion energy production in a spherical plasma shock wave, Plasma Physics, 5, 399-411]. The pathway parameter used in this paper is given an interpretation in terms of moments.

Two-component dark-bright solitons in three-dimensional atomic Bose-Einstein condensates.

PubMed

Wang, Wenlong; Kevrekidis, P G

2017-03-01

In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3D) form. Motivated by earlier studies of dark-bright solitons in the 1D case, we explore the stability of these structures in their fully 3D form in two variants. In one the dark soliton is planar and trapping a planar bright (disk) soliton. In the other case, a dark spherical shell soliton creates an effective potential in which a bright spherical shell of atoms is trapped in the second component. We identify these solutions as numerically exact states (up to a prescribed accuracy) and perform a Bogolyubov-de Gennes linearization analysis that illustrates that both structures can be dynamically stable in suitable intervals of sufficiently low chemical potentials. We corroborate this finding theoretically by analyzing the stability via degenerate perturbation theory near the linear limit of the system. When the solitary waves are found to be unstable, we explore their dynamical evolution via direct numerical simulations which, in turn, reveal wave forms that are more robust. Finally, using the SO(2) symmetry of the model, we produce multi-dark-bright planar or shell solitons involved in pairwise oscillatory motion.

A Spherical to Plane Wave Transformation Using a Reflectarray

NASA Technical Reports Server (NTRS)

Zaman, Afroz J.; Lee, Richard Q.

1997-01-01

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

Grating tuned unstable resonator laser cavity

DOEpatents

Johnson, Larry C.

1982-01-01

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

Spherical combustion clouds in explosions

NASA Astrophysics Data System (ADS)

Kuhl, A. L.; Bell, J. B.; Beckner, V. E.; Balakrishnan, K.; Aspden, A. J.

2013-05-01

This study explores the properties of spherical combustion clouds in explosions. Two cases are investigated: (1) detonation of a TNT charge and combustion of its detonation products with air, and (2) shock dispersion of aluminum powder and its combustion with air. The evolution of the blast wave and ensuing combustion cloud dynamics are studied via numerical simulations with our adaptive mesh refinement combustion code. The code solves the multi-phase conservation laws for a dilute heterogeneous continuum as formulated by Nigmatulin. Single-phase combustion (e.g., TNT with air) is modeled in the fast-chemistry limit. Two-phase combustion (e.g., Al powder with air) uses an induction time model based on Arrhenius fits to Boiko's shock tube data, along with an ignition temperature criterion based on fits to Gurevich's data, and an ignition probability model that accounts for multi-particle effects on cloud ignition. Equations of state are based on polynomial fits to thermodynamic calculations with the Cheetah code, assuming frozen reactants and equilibrium products. Adaptive mesh refinement is used to resolve thin reaction zones and capture the energy-bearing scales of turbulence on the computational mesh (ILES approach). Taking advantage of the symmetry of the problem, azimuthal averaging was used to extract the mean and rms fluctuations from the numerical solution, including: thermodynamic profiles, kinematic profiles, and reaction-zone profiles across the combustion cloud. Fuel consumption was limited to ˜ 60-70 %, due to the limited amount of air a spherical combustion cloud can entrain before the turbulent velocity field decays away. Turbulent kinetic energy spectra of the solution were found to have both rotational and dilatational components, due to compressibility effects. The dilatational component was typically about 1 % of the rotational component; both seemed to preserve their spectra as they decayed. Kinetic energy of the blast wave decayed due to the pressure field. Turbulent kinetic energy of the combustion cloud decayed due to enstrophy overline{ω 2} and dilatation overline{Δ 2}.

Acoustic manipulation of oscillating spherical bodies: Emergence of axial negative acoustic radiation force

NASA Astrophysics Data System (ADS)

Rajabi, Majid; Mojahed, Alireza

2016-11-01

In this paper, emergence of negative axial acoustic radiation force on a rigid oscillating spherical body is investigated for acoustic manipulation purposes. The problem of plane acoustic wave scattering from an oscillating spherical body submerged in an ideal acoustic fluid medium is solved. For the case of oscillating direction collinear with the wave propagation wave number vector (desired path), it has been shown that the acoustic radiation force, as a result of nonlinear acoustic wave interaction with bodies can be expressed as a linear function of incident wave field and the oscillation properties of the oscillator (i.e., amplitude and phase of oscillation). The negative (i.e., pulling effects) and positive (i.e., pushing effects) radiation force situations are divided in oscillation complex plane with a specific frequency-dependant straight line. This characteristic line defines the radiation force cancellation state. In order to investigate the stability of the mentioned manipulation strategy, the case of misaligned oscillation of sphere with the wave propagation direction is studied. The proposed methodology may suggest a novel concept of single-beam acoustic handling techniques based on smart carriers.

A novel approach to gravitation from fluid theory: Titius-Bode structures, flat rotation rate of galaxies, and other predictions

NASA Astrophysics Data System (ADS)

Munera, Hector A.

Following the discovery of quantum phenomena at laboratory scale (Couder & Fort 2006), de Broglie pilot wave theory (De Broglie 1962) has been revived under a hydrodynamic guise (Bush 2015). Theoretically, it boils down to solving the transport equations for the energy and linear momentum densities of a postulated fundamental fluid in terms of classical wave equations, which inherently are Lorentz-invariant and scale-invariant. Instead of the conventional harmonic solutions, for astronomical and gravitational problems the novel solutions for the homogeneous wave equation in spherical coordinates are more suitable (Munera et al. 1995, Munera & Guzman 1997, and Munera 2000). Two groups of solutions are particularly relevant: (a) The inherently-quantized helicoidal solutions that may be applicable to describe spiral galaxies, and (b) The non-harmonic solutions with time (t) and distance (r) entangled in the single variable q = Ct/r (C is the two-way local electromagnetic speed). When these functions are plotted against 1/q they manifestly depict quantum effects in the near field, and Newtonian-like gravity in the far-field. The near-field predicts quantized effects similar to ring structures and to Titius-Bode structures, both in our own solar system and in exoplanets, the correlation between predicted and observed structures being typically larger than 99 per cent. In the far-field, some non-harmonic functions have a rate of decrement with distance slower than inverse-square thus explaining the flat rotation rate of galaxies. Additional implications for Trojan orbits, and quantized effects in photon deflection were also noted.

Rotation of a metal gear disk in an ultrasonic levitator

NASA Astrophysics Data System (ADS)

Rendon, Pablo L.; Boullosa, Ricardo R.; Salazar, Laura

2016-11-01

The phenomenon known as acoustic radiation pressure is well-known to be associated with the time-averaged momentum flux of an acoustic wave, and precisely because it is a time-averaged effect, it is relatively easy to observe experimentally. An ultrasonic levitator makes use of this effect to levitate small particles. Although it is a less-well studied effect, the transfer of angular momentum using acoustic waves in air or liquids has nonetheless been the subject of some recent studies. This transfer depends on the scattering and absorbing properties of the object and is achieved, typically, through the generation of acoustic vortex beams. In the present study, we examine the manner in which the acoustic standing wave located between two disks of an ultrasonic levitator in air may transfer angular momentum to objects with different shapes. In this case, a non-spherical object is subjected to, in addition to the radiation force, a torque which induces rotation. Analytical solutions for the acoustic force and torque are available, but limited to a few simple cases. In general, a finite element model must be used to obtain solutions. Thus, we develop and validate a finite element simulation in order to calculate directly the torque and radiation force.

Exploration of high harmonic fast wave heating on the National Spherical Torus Experiment

NASA Astrophysics Data System (ADS)

Wilson, J. R.; Bell, R. E.; Bernabei, S.; Bitter, M.; Bonoli, P.; Gates, D.; Hosea, J.; LeBlanc, B.; Mau, T. K.; Medley, S.; Menard, J.; Mueller, D.; Ono, M.; Phillips, C. K.; Pinsker, R. I.; Raman, R.; Rosenberg, A.; Ryan, P.; Sabbagh, S.; Stutman, D.; Swain, D.; Takase, Y.; Wilgen, J.

2003-05-01

High harmonic fast wave (HHFW) heating has been proposed as a particularly attractive means for plasma heating and current drive in the high beta plasmas that are achievable in spherical torus (ST) devices. The National Spherical Torus Experiment (NSTX) [M. Ono, S. M. Kaye, S. Neumeyer et al., in Proceedings of the 18th IEEE/NPSS Symposium on Fusion Engineering, Albuquerque, 1999 (IEEE, Piscataway, NJ, 1999), p. 53] is such a device. An rf heating system has been installed on the NSTX to explore the physics of HHFW heating, current drive via rf waves and for use as a tool to demonstrate the attractiveness of the ST concept as a fusion device. To date, experiments have demonstrated many of the theoretical predictions for HHFW. In particular, strong wave absorption on electrons over a wide range of plasma parameters and wave parallel phase velocities, wave acceleration of energetic ions, and indications of current drive for directed wave spectra have been observed. In addition HHFW heating has been used to explore the energy transport properties of NSTX plasmas, to create H-mode discharges with a large fraction of bootstrap current and to control the plasma current profile during the early stages of the discharge.

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1975-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear xi lines and by two truncating xi surfaces. The spherical mean is the average of u over a constant xi surface. Conditions on the linear differential operator, L, and on the orthogonal coordinates xi, eta, and zeta are established so that the problem for the determination of the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be reduced to a problem with only one space variable. Conditions are then established so that the spherical mean of the solution in one conical region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

A fixed energy fixed angle inverse scattering in interior transmission problem

NASA Astrophysics Data System (ADS)

Chen, Lung-Hui

2017-06-01

We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

Shear wave induced resonance elastography of spherical masses with polarized torsional waves

NASA Astrophysics Data System (ADS)

Hadj Henni, Anis; Schmitt, Cédric; Trop, Isabelle; Cloutier, Guy

2012-03-01

Shear wave induced resonance (SWIR) is a technique for dynamic ultrasound elastography of confined mechanical inclusions. It was developed for breast tumor imaging and tissue characterization. This method relies on the polarization of torsional shear waves modeled with the Helmholtz equation in spherical coordinates. To validate modeling, an invitro set-up was used to measure and image the first three eigenfrequencies and eigenmodes of a soft sphere. A preliminary invivo SWIR measurement on a breast fibroadenoma is also reported. Results revealed the potential of SWIR elastography to detect and mechanically characterize breast lesions for early cancer detection.

Shear wave induced resonance elastography of spherical masses with polarized torsional waves.

PubMed

Henni, Anis Hadj; Schmitt, Cédric; Trop, Isabelle; Cloutier, Guy

2012-03-26

Shear Wave Induced Resonance (SWIR) is a technique for dynamic ultrasound elastography of confined mechanical inclusions. It was developed for breast tumor imaging and tissue characterization. This method relies on the polarization of torsional shear waves modeled with the Helmholtz equation in spherical coordinates. To validate modeling, an in vitro set-up was used to measure and image the first three eigenfrequencies and eigenmodes of a soft sphere. A preliminary in vivo SWIR measurement on a breast fibroadenoma is also reported. Results revealed the potential of SWIR elastography to detect and mechanically characterize breast lesions for early cancer detection.

Symmetry of spherically converging shock waves through reflection, relating to the shock ignition fusion energy scheme.

PubMed

Davie, C J; Evans, R G

2013-05-03

We examine the properties of perturbed spherically imploding shock waves in an ideal fluid through the collapse, bounce, and development into an outgoing shock wave. We find broad conservation of the size and shape of ingoing and outgoing perturbations when viewed at the same radius. The outgoing shock recovers the velocity of the unperturbed shock outside the strongly distorted core. The results are presented in the context of the robustness of the shock ignition approach to inertial fusion energy.

Sound Source Localization Using Non-Conformal Surface Sound Field Transformation Based on Spherical Harmonic Wave Decomposition

PubMed Central

Zhang, Lanyue; Ding, Dandan; Yang, Desen; Wang, Jia; Shi, Jie

2017-01-01

Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acoustic holography. The reconstruction surface and holography surface are conformal surfaces in the conventional sound field transformation based on generalized Fourier transform. When the sound source is on the cylindrical surface, it is difficult to locate by using spherical surface conformal transform. The non-conformal sound field transformation by making a transfer matrix based on spherical harmonic wave decomposition is proposed in this paper, which can achieve the transformation of a spherical surface into a cylindrical surface by using spherical array data. The theoretical expressions of the proposed method are deduced, and the performance of the method is simulated. Moreover, the experiment of sound source localization by using a spherical array with randomly and uniformly distributed elements is carried out. Results show that the non-conformal surface sound field transformation from a spherical surface to a cylindrical surface is realized by using the proposed method. The localization deviation is around 0.01 m, and the resolution is around 0.3 m. The application of the spherical array is extended, and the localization ability of the spherical array is improved. PMID:28489065

Similarity solutions for unsteady flow behind an exponential shock in a self-gravitating non-ideal gas with azimuthal magnetic field

NASA Astrophysics Data System (ADS)

Nath, G.; Pathak, R. P.; Dutta, Mrityunjoy

2018-01-01

Similarity solutions for the flow of a non-ideal gas behind a strong exponential shock driven out by a piston (cylindrical or spherical) moving with time according to an exponential law is obtained. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The effects of variation of ambient magnetic field, non-idealness of the gas, adiabatic exponent and gravitational parameter are worked out in detail. It is shown that the increase in the non-idealness of the gas or the adiabatic exponent of the gas or presence of magnetic field have decaying effect on the shock wave. Consideration of the isothermal flow and the self-gravitational field increase the shock strength. Also, the consideration of isothermal flow or the presence of magnetic field removes the singularity in the density distribution, which arises in the case of adiabatic flow. The result of our study may be used to interpret measurements carried out by space craft in the solar wind and in neighborhood of the Earth's magnetosphere.

Wave propagation in media having negative permittivity and permeability.

PubMed

Ziolkowski, R W; Heyman, E

2001-11-01

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

Acoustic manipulation of active spherical carriers: Generation of negative radiation force

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

Rajabi, Majid, E-mail: majid_rajabi@iust.ac.ir; Mojahed, Alireza

2016-09-15

This paper examines theoretically a novel mechanism of generating negative (pulling) radiation force for acoustic manipulation of spherical carriers equipped with piezoelectric actuators in its inner surface. In this mechanism, the spherical particle is handled by common plane progressive monochromatic acoustic waves instead of zero-/higher- order Bessel beams or standing waves field. The handling strategy is based on applying a spatially uniform harmonic electrical voltage at the piezoelectric actuator with the same frequency of handling acoustic waves, in order to change the radiation force effect from repulsive (away from source) to attractive (toward source). This study may be considered asmore » a start point for development of contact-free precise handling and entrapment technology of active carriers which are essential in many engineering and medicine applications.« less

Electron Bernstein waves in spherical torus plasmas

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

Saveliev, A. N.

2006-11-30

Propagation and absorption of the electron Bernstein waves (EBWs) in spherical tokamaks (STs) have been intensively discussed in recent years because the EBWs coupled with an externally launched electromagnetic beam seem to be the only opportunity for microwave plasma heating and current drive in the electron cyclotron (EC) frequency range in the STs. The whole problem of the electron Bernstein heating and current drive (EBWHCD) in spherical plasmas is naturally divided into three major parts: coupling of incident electromagnetic waves (EMWs) to the EBWs near the upper hybrid resonance (UHR) surface, propagation and absorption of the EBWs in the plasmamore » interior and generation of noninductive current driven by the EBWs. The present paper is a brief survey of the most important theoretical and numerical results on the issue of EBWs.« less

Approximation method for a spherical bound system in the quantum plasma

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

Mehramiz, A.; Sobhanian, S.; Mahmoodi, J.

2010-08-15

A system of quantum hydrodynamic equations has been used for investigating the dielectric tensor and dispersion equation of a semiconductor as a quantum magnetized plasma. Dispersion relations and their modifications due to quantum effects are derived for both longitudinal and transverse waves. The number of states and energy levels are analytically estimated for a spherical bound system embedded in a semiconductor quantum plasma. The results show that longitudinal waves decay rapidly and do not interact with the spherical bound system. The energy shifts caused by the spin-orbit interaction and the Zeeman effect are calculated.

Anomalous optical scattering from intersecting fine particles

NASA Astrophysics Data System (ADS)

Paley, Alina V.; Radchik, Alex V.; Smith, Geoffrey B.

1995-09-01

There are many areas of science and technology where the scattering of electromagnetic waves by clusters or merging particles are of interest. The merging particles under study might be inclusions in high-density composites, liquid drops, biological cells, macroscopic ceramic particles, etc. As intersecting particles are bounded by a complex physical surface, the problem of scattering from these particles valid for any degree of merging, including touching, and for arbitrary materials of the constituents, has received limited attention. Here we present solutions which are valid and exact in the long wavelength limit compared with the size of intersecting spherical particles and cardioidal particles of similar dimensions. Both shapes are almost coincident everywhere except in the region of intersection. We treat the case when the waves are polarized along the common axis (longitudinal field). The solutions of Laplace's equation are integrals (spheres) or sums (cardioids) over continuous or discrete eigenvalue spectra respectively. The spectral dependencies of the resulting extinction coefficients and the scattering for the spherical and cardioidal particles are quite distinct. There is an enormous difference in the magnitude of absorption responses. Overall the cardioidal particle behaves as if it is almost invisible in terms of effects on the external field for a very broad band of optical frequencies. THe latter result was checked for a number of dielectric permittivities and seems to be universal. It scatters far more weakly than the isolated sphere. In constrast the intersecting sphere has an extinction band which is broad and is much enhanced at longer wavelegnths relative to the simple sphere. This result has significant implications for the design of surfaces with minimum scattering.

Spherical shock-wave propagation in three-dimensional granular packings.

PubMed

Xue, Kun; Bai, Chun-Hua

2011-02-01

We investigate numerically the spherical shock-wave propagation in an open dense granular packing perturbed by the sudden expansion of a spherical intruder in the interior of the pack, focusing on the correlation between geometrical fabrics and propagating properties. The measurements of the temporal and spatial variations in a variety of propagating properties define a consistent serrated wave substructure with characteristic length on the orders of particle diameters. Further inspection of particle packing reveals a well-defined particle layering that persists several particle diameters away from the intruder, although its dominant effects are only within one to two diameters. This interface-induced layering not only exactly coincides with the serrated wave profile, but also highlights the competition between two energy transmission mechanisms involving distinct transport speeds. The alternating dominances between these two mechanisms contribute to the nonlinear wave propagation on the particle scale. Moreover, the proliferation of intricate three-dimensional contact force networks suggests the anisotropic stress transmission, which is found to also arise from the localized packing structure in the vicinity of the intruder.

Shock waves raised by explosions in space as sources of ultra-high-energy cosmic rays

NASA Astrophysics Data System (ADS)

Kichigin, Gennadiy

2015-03-01

The paper discusses the possibility of particle acceleration up to ultrahigh energies in the relativistic waves generated by various explosive processes in the interstellar medium. We propose to use the surfatron mechanism of acceleration (surfing) of charged particles trapped in the front of relativistic waves as a generator of high-energy cosmic rays (CRs). Conditions under which surfing in these waves can be made are studied thoroughly. Ultra-high-energy CRs (up to 10^20 eV) are shown to be obtained due to the surfing in the relativistic plane and spherical waves. Surfing is supposed to take place in nonlinear Langmuir waves excited by powerful electromagnetic radiation or relativistic beams of charged particles, as well as in strong shock waves generated by relativistic jets or spherical formations that expand fast (fireballs).

An analytical model for the evolution of the coldest component of the Boomerang Nebula

NASA Astrophysics Data System (ADS)

Bohigas, J.

2017-04-01

The most striking feature of the Boomerang Nebula is a large nearly spherical cloud where the temperature is close to 2 K. At its inner and outer boundaries, this cloud is expanding at velocities close to 35 and 180 km s-1. The cloud surrounds an asymptotic giant branch (AGB) star and a smaller bipolar molecular cloud, expanding much more slowly. The ultracold spherical cloud has been and still is expanding into a rarefied medium, since there is no trace of a shock wave. This ultracold cloud is modelled using the analytical solution for a power-driven expansion of a spherically symmetric cloud, followed by an adiabatic expansion phase, both into a vacuum. Assuming that the cloud is at a distance of 1500 pc, the present temperature and velocity profile are reproduced with a model where the cloud has an energy close to 8.5 × 1046 erg per solar mass and was ejected 1000 yr ago. In this model, the power-driven phase lasts for ˜10 yr and half of the energy is injected in less than a year. The general features of this model, are amenable with what is found in other spherical shells surrounding AGB stars, the small amount of mass lost by massive OH/IR stars and evolutionary models indicating that there may be extremely high and abrupt mass-loss phases in AGB stars. The energy and time-scale suggest that the ejection of the cold spherical cloud was an intermediate luminosity transient.

Quintic quasi-topological gravity

NASA Astrophysics Data System (ADS)

Cisterna, Adolfo; Guajardo, Luis; Hassaïne, Mokhtar; Oliva, Julio

2017-04-01

We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing {\\mathcal{R}}^5 terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff's Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler's polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in arXiv:1003.4773, the general geometric structure of these Lagrangians remains an open problem.

Exploration of High Harmonic Fast Wave Heating on the National Spherical Torus Experiment

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

J.R. Wilson; R.E. Bell; S. Bernabei

2003-02-11

High Harmonic Fast Wave (HHFW) heating has been proposed as a particularly attractive means for plasma heating and current drive in the high-beta plasmas that are achievable in spherical torus (ST) devices. The National Spherical Torus Experiment (NSTX) [Ono, M., Kaye, S.M., Neumeyer, S., et al., Proceedings, 18th IEEE/NPSS Symposium on Fusion Engineering, Albuquerque, 1999, (IEEE, Piscataway, NJ (1999), p. 53.)] is such a device. An radio-frequency (rf) heating system has been installed on NSTX to explore the physics of HHFW heating, current drive via rf waves and for use as a tool to demonstrate the attractiveness of the STmore » concept as a fusion device. To date, experiments have demonstrated many of the theoretical predictions for HHFW. In particular, strong wave absorption on electrons over a wide range of plasma parameters and wave parallel phase velocities, wave acceleration of energetic ions, and indications of current drive for directed wave spectra have been observed. In addition HHFW heating has been used to explore the energy transport properties of NSTX plasmas, to create H-mode (high-confinement mode) discharges with a large fraction of bootstrap current and to control the plasma current profile during the early stages of the discharge.« less

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

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

Mass change from GRACE: a simulated comparison of Level-1B analysis techniques

NASA Astrophysics Data System (ADS)

Andrews, Stuart B.; Moore, Philip; King, Matt. A.

2015-01-01

Spherical harmonic and mascon parameters have both been successfully applied in the recovery of time-varying gravity fields from Gravity Recovery and Climate Experiment (GRACE). However, direct comparison of any mass flux is difficult with solutions generated by different groups using different codes and algorithms. It is therefore opportune to compare these methodologies, within a common software base, to understand potential limitations associated with each technique. Here we use simulations to recover a known monthly surface mass distribution from GRACE KBRR data. The ability of spherical harmonic and mascon parameters to resolve basin-level mass change is quantified with an assessment of how the noise and errors, inherent in GRACE solutions, are handled. Recovery of a noise and error free GLDAS anomaly revealed no quantifiable difference between spherical harmonic and mascon parameters. Expansion of the GLDAS anomaly to degree and order 120 shows that both spherical harmonic and mascon parameters are affected by comparable omission errors. However, the inclusion of realistic KBRR noise and errors in the simulations reveals the advantage of the mascon parameters over spherical harmonics at reducing noise and errors in the higher degree and order harmonics with an rms (cm of EWH) to the GLDAS anomaly of 10.0 for the spherical harmonic solution and 8.8 (8.6) for the 4°(2°) mascon solutions. The introduction of a constraint matrix in the mascon solution based on parameters that share geophysical similarities is shown to further reduce the signal lost at all degrees. The recovery of a simulated Antarctic mass loss signal shows that the mascon methodology is superior to spherical harmonics for this region with an rms (cm of EWH) of 8.7 for the 2° mascon solution compared to 10.0 for the spherical harmonic solution. Investigating the noise and errors for a month when the satellites were in resonance revealed both the spherical harmonic and mascon methodologies are able to recover the GLDAS and Antarctic mass loss signal with either a comparable (spherical harmonic) or improved (mascon) rms compared to non-resonance periods.

Discontinuity-free edge-diffraction model for characterization of focused wave fields.

PubMed

Sedukhin, Andrey G

2010-03-01

A model of discontinuity-free edge diffraction is proposed that is valid in the framework of the scalar Debye approximation and describes the formation process and approximate structure of the stationary diffracted field of a monochromatic converging spherical wave of limited angular opening throughout the whole space about the focus. The field is represented semianalytically in terms of the sum of a direct quasi-spherical wave and two edge quasi-conical waves of the zeroth and first order. The angular spectrum amplitudes of all these waves have smooth continuous variations of the real and imaginary parts in polar angle and radius, the separable nonanalytic functions defining the polar-angle variations of the amplitudes being found by optimization techniques.

Analysis of Multi-Layered Materials Under High Velocity Impact Using CTH

DTIC Science & Technology

2008-03-01

of state . The other relationship deals with the deviatoric stress and is taken care of by the constitutive equations which are discussed in the next...models in CTH decompose the total stress tensor into the spherical and deviatoric parts. The spherical part of the stress tensor is the equation of state ...investigate the effects of wave propagation. Waves in rods are considered to create a state of

Measuring the radiation force of megahertz ultrasound acting on a solid spherical scatterer

NASA Astrophysics Data System (ADS)

Nikolaeva, A. V.; Tsysar, S. A.; Sapozhnikov, O. A.

2016-01-01

The paper considers the problem of precise measurement of the acoustic radiation force of an ultrasonic beam on targets in the form of solid spherical scatterers. Using known analytic relations, a numerical model is developed to perform calculations for different sizes of spherical scatterers and arbitrary frequencies of the incident acoustic wave. A novel method is proposed for measuring the radiation force, which is based on the principle of acoustic echolocation. The radiation force is measured experimentally in a wide range of incident wave intensities using two chosen methods differing in the way the location of the target is controlled.

Observation of beat oscillation generation by coupled waves associated with parametric decay during radio frequency wave heating of a spherical tokamak plasma.

PubMed

Nagashima, Yoshihiko; Oosako, Takuya; Takase, Yuichi; Ejiri, Akira; Watanabe, Osamu; Kobayashi, Hiroaki; Adachi, Yuuki; Tojo, Hiroshi; Yamaguchi, Takashi; Kurashina, Hiroki; Yamada, Kotaro; An, Byung Il; Kasahara, Hiroshi; Shimpo, Fujio; Kumazawa, Ryuhei; Hayashi, Hiroyuki; Matsuzawa, Haduki; Hiratsuka, Junichi; Hanashima, Kentaro; Kakuda, Hidetoshi; Sakamoto, Takuya; Wakatsuki, Takuma

2010-06-18

We present an observation of beat oscillation generation by coupled modes associated with parametric decay instability (PDI) during radio frequency (rf) wave heating experiments on the Tokyo Spherical Tokamak-2. Nearly identical PDI spectra, which are characterized by the coexistence of the rf pump wave, the lower-sideband wave, and the low-frequency oscillation in the ion-cyclotron range of frequency, are observed at various locations in the edge plasma. A bispectral power analysis was used to experimentally discriminate beat oscillation from the resonant mode for the first time. The pump and lower-sideband waves have resonant mode components, while the low-frequency oscillation is exclusively excited by nonlinear coupling of the pump and lower-sideband waves. Newly discovered nonlocal transport channels in spectral space and in real space via PDI are described.

Acoustically excited surface waves on empty or fluid-filled cylindrical and spherical shells

NASA Astrophysics Data System (ADS)

Ahyi, A. Claude; Cao, H.; Raju, P. K.; Werby, M. F.; Bao, X. L.; Überall, H.

2002-05-01

A comparative study is presented of the acoustical excitation of circumferential (surface) waves on fluid-immersed cylindrical or spherical metal shells, which may be either evacuated, or filled with the same or a different fluid. The excited surface waves can manifest themselves by the resonances apparent in the sound scattering amplitude, which they cause upon phase matching following repeated circumnavigations of the target object, or by their re-radiation into the external fluid in the manner of head waves. We plot dispersion curves versus frequency of the surface waves, which for evacuated shells have a generally rising character, while the fluid filling adds an additional set of circumferential waves that descend with frequency. The resonances of these latter waves may also be interpreted as being due to phase matching, but they may alternately be interpreted as constituting the eigenfrequencies of the internal fluid contained in an elastic enclosure.

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

PubMed Central

Sapozhnikov, Oleg A.; Bailey, Michael R.

2013-01-01

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

Refraction at a curved dielectric interface - Geometrical optics solution

NASA Technical Reports Server (NTRS)

Lee, S.-W.; Sheshadri, M. S.; Mittra, R.; Jamnejad, V.

1982-01-01

The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. Explicit matrix formulas for calculating DF are given, and its physical significance is illustrated via examples.

Photoacoustic Effect Generated from an Expanding Spherical Source

NASA Astrophysics Data System (ADS)

Bai, Wenyu; Diebold, Gerald J.

2018-02-01

Although the photoacoustic effect is typically generated by amplitude-modulated continuous or pulsed radiation, the form of the wave equation for pressure that governs the generation of sound indicates that optical sources moving in an absorbing fluid can produce sound as well. Here, the characteristics of the acoustic wave produced by a radially symmetric Gaussian source expanding outwardly from the origin are found. The unique feature of the photoacoustic effect from the spherical source is a trailing compressive wave that arises from reflection of an inwardly propagating component of the wave. Similar to the one-dimensional geometry, an unbounded amplification effect is found for the Gaussian source expanding at the sound speed.

Sonar Imaging of Elastic Fluid-Filled Cylindrical Shells.

NASA Astrophysics Data System (ADS)

Dodd, Stirling Scott

1995-01-01

Previously a method of describing spherical acoustic waves in cylindrical coordinates was applied to the problem of point source scattering by an elastic infinite fluid -filled cylindrical shell (S. Dodd and C. Loeffler, J. Acoust. Soc. Am. 97, 3284(A) (1995)). This method is applied to numerically model monostatic oblique incidence scattering from a truncated cylinder by a narrow-beam high-frequency imaging sonar. The narrow beam solution results from integrating the point source solution over the spatial extent of a line source and line receiver. The cylinder truncation is treated by the method of images, and assumes that the reflection coefficient at the truncation is unity. The scattering form functions, calculated using this method, are applied as filters to a narrow bandwidth, high ka pulse to find the time domain scattering response. The time domain pulses are further processed and displayed in the form of a sonar image. These images compare favorably to experimentally obtained images (G. Kaduchak and C. Loeffler, J. Acoust. Soc. Am. 97, 3289(A) (1995)). The impact of the s_{ rm o} and a_{rm o} Lamb waves is vividly apparent in the images.

Air-ground interface: Surface waves, surface impedance and acoustic-to-seismic coupling coefficient

NASA Technical Reports Server (NTRS)

Daigle, Gilles; Embleton, Tony

1990-01-01

In atmospheric acoustics, the subject of surface waves has been an area of discussion for many years. The existence of an acoustic surface wave is now well established theoretically. The mathematical solution for spherical wave propagation above an impedance boundary includes the possibility of a contribution that possesses all the standard properties for a surface wave. Surface waves exist when the surface is sufficiently porous, relative to its acoustical resistance, that it can influence the airborne particle velocity near the surface and reduce the phase velocity of sound waves in air at the surface. This traps some of the sound energy in the air to remain near the surface as it propagates. Above porous grounds, the existence of surface waves has eluded direct experimental confirmation (pulse experiments have failed to show a separate arrival expected from the reduced phase speed) and indirect evidence for its existence has appeared contradictory. The experimental evidence for the existence of an acoustical surface wave above porous boundaries is reviewed. Recent measurements including pulse experiments are also described. A few years ago the acoustic impedance of a grass-covered surface was measured in the frequency range 30 to 300 Hz. Here, further measurements on the same site are discussed. These measurements include core samples, a shallow refractive survey to determine the seismic velocities, and measurements of the acoustic-to-seismic coupling coefficient.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Greengard, Leslie F; Waag, Robert C

2010-02-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators

PubMed Central

Hesford, Andrew J.; Astheimer, Jeffrey P.; Greengard, Leslie F.; Waag, Robert C.

2010-01-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method. PMID:20136208

Klein–Gordon equation in curved space-time

NASA Astrophysics Data System (ADS)

Lehn, R. D.; Chabysheva, S. S.; Hiller, J. R.

2018-07-01

We report the methods and results of a computational physics project on the solution of the relativistic Klein–Gordon equation for a light particle gravitationally bound to a heavy central mass. The gravitational interaction is prescribed by the metric of a spherically symmetric space-time. Metrics are considered for an impenetrable sphere, a soft sphere of uniform density, and a soft sphere with a linear transition from constant to zero density; in each case the radius of the central mass is chosen to be sufficient to avoid any event horizon. The solutions are obtained numerically and compared with nonrelativistic Coulomb-type solutions, both directly and in perturbation theory, to study the general-relativistic corrections to the quantum solutions for a 1/r potential. The density profile with a linear transition is chosen to avoid singularities in the wave equation that can be caused by a discontinuous derivative of the density. This project should be of interest to instructors and students of computational physics at the graduate and advanced undergraduate levels.

Higher-order jump conditions for conservation laws

NASA Astrophysics Data System (ADS)

Oksuzoglu, Hakan

2018-04-01

The hyperbolic conservation laws admit discontinuous solutions where the solution variables can have finite jumps in space and time. The jump conditions for conservation laws are expressed in terms of the speed of the discontinuity and the state variables on both sides. An example from the Gas Dynamics is the Rankine-Hugoniot conditions for the shock speed. Here, we provide an expression for the acceleration of the discontinuity in terms of the state variables and their spatial derivatives on both sides. We derive a jump condition for the shock acceleration. Using this general expression, we show how to obtain explicit shock acceleration formulas for nonlinear hyperbolic conservation laws. We start with the Burgers' equation and check the derived formula with an analytical solution. We next derive formulas for the Shallow Water Equations and the Euler Equations of Gas Dynamics. We will verify our formulas for the Euler Equations using an exact solution for the spherically symmetric blast wave problem. In addition, we discuss the potential use of these formulas for the implementation of shock fitting methods.

Droplet characteristic measurement in Fourier interferometry imaging and behavior at the rainbow angle.

PubMed

Briard, Paul; Saengkaew, Sawitree; Wu, Xuecheng; Meunier-Guttin-Cluzel, Siegfried; Chen, Linghong; Cen, Kefa; Gréhan, Gérard

2013-01-01

This paper presents the possibility of measuring the three-dimensional (3D) relative locations and diameters of a set of spherical particles and discusses the behavior of the light recorded around the rainbow angle, an essential step toward refractive index measurements. When a set of particles is illuminated by a pulsed incident wave, the particles act as spherical light wave sources. When the pulse duration is short enough to fix the particle location (typically about 10 ns), interference fringes between these different spherical waves can be recorded. The Fourier transform of the fringes divides the complex fringe systems into a series of spots, with each spot characterizing the interference between a pair of particles. The analyses of these spots (in position and shape) potentially allow the measurement of particle characteristics (3D relative position, particle diameter, and particle refractive index value).

Solitary waves in shallow water hydrodynamics and magnetohydrodynamics in rotating spherical coordinates

NASA Astrophysics Data System (ADS)

London, Steven D.

2018-01-01

In a recent paper (London, Geophys. Astrophys. Fluid Dyn. 2017, vol. 111, pp. 115-130, referred to as L1), we considered a perfect electrically conducting rotating fluid in the presence of an ambient toroidal magnetic field, governed by the shallow water magnetohydrodynamic (MHD) equations in a modified equatorial ?-plane approximation. In conjunction with a WKB type approximation, we used a multiple scale asymptotic scheme, previously developed by Boyd (J. Phys. Oceanogr. 1980, vol. 10, pp. 1699-1717) for equatorial solitary hydrodynamic waves, and found solitary MHD waves. In this paper, as in L1, we apply a WKB type approximation in order to extend the results of L1 from the modified ?-plane to the full spherical geometry. We have included differential rotation in the analysis in order to make the results more relevant to the solar case. In addition, we consider the case of hydrodynamic waves on the rotating sphere in the presence of a differential rotation intended to roughly model the varying large scale currents in the oceans and atmosphere. In the hydrodynamic case, we find the usual equatorial solitary waves as found by Boyd, as well as waves in bands away from the equator for sufficiently strong currents. In the MHD case, we find basically the same equatorial waves found in L1. L1 also found non-equatorial modes; no such modes are found in the full spherical geometry.

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

NASA Technical Reports Server (NTRS)

Podhorodeski, R. P.; Fenton, R. G.; Goldenberg, A. A.

1989-01-01

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Investigation on plasmonic responses in multilayered nanospheres including asymmetry and spatial nonlocal effects

NASA Astrophysics Data System (ADS)

Dong, Tianyu; Shi, Yi; Liu, Hui; Chen, Feng; Ma, Xikui; Mittra, Raj

2017-12-01

In this work, we present a rigorous approach for analyzing the optical response of multilayered spherical nano-particles comprised of either plasmonic metal or dielectric, when there is no longer radial symmetry and when nonlocality is included. The Lorenz-Mie theory is applied, and a linearized hydrodynamic Drude model as well as the general nonlocal optical response model for the metals are employed. Additional boundary conditions, viz., the continuity of normal components of polarization current density and the continuity of first-order pressure of free electron density, respectively, are incorporated when handling interfaces involving metals. The application of spherical addition theorems, enables us to express a spherical harmonic about one origin to spherical harmonics about a different origin, and leads to a linear system of equations for the inward- and outward-field modal coefficients for all the layers in the nanoparticle. Scattering matrices at interfaces are obtained and cascaded to obtain the expansion coefficients, to yield the final solution. Through extensive modelling of stratified concentric and eccentric metal-involved spherical nanoshells illuminating by a plane wave, we show that, within a nonlocal description, significant modifications of plasmonic response appear, e.g. a blue-shift in the extinction / scattering spectrum and a broadening spectrum of the resonance. In addition, it has been demonstrated that core-shell nanostructures provide an option for tunable Fano-resonance generators. The proposed method shows its capability and flexibility to analyze the nonlocal response of eccentric hybrid metal-dielectric multilayer structures as well as adjoined metal-involved nanoparticles, even when the number of layers is large.

Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles.

PubMed

Weinberg, Kerstin; Ortiz, Michael

2009-08-01

In shock-wave lithotripsy--a medical procedure to fragment kidney stones--the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries to the surrounding kidney tissue arise, is still under investigation. To contribute to the solution of this problem, two- and three-dimensional numerical simulations of a human kidney under shock-wave loading are presented. For this purpose a constitutive model of the bio-mechanical system kidney is introduced, which is able to map large visco-elastic deformations and, in particular, material damage. The specific phenomena of cavitation induced oscillating bubbles is modeled here as an evolution of spherical pores within the soft kidney tissue. By means of large scale finite element simulations, we study the shock-wave propagation into the kidney tissue, adapt unknown material parameters and analyze the resulting stress states. The simulations predict localized damage in the human kidney in the same regions as observed in animal experiments. Furthermore, the numerical results suggest that in first instance the pressure amplitude of the shock wave impulse (and not so much its exact time-pressure profile) is responsible for damaging the kidney tissue.

Observation of interaction of shock wave with gas bubble by image converter camera

NASA Astrophysics Data System (ADS)

Yoshii, M.; Tada, M.; Tsuji, T.; Isuzugawa, Kohji

1995-05-01

When a spark discharge occurs at the first focal point of a semiellipsoid or a reflector located in water, a spherical shock wave is produced. A part of the wave spreads without reflecting on the reflector and is called direct wave in this paper. Another part reflects on the semiellipsoid and converges near the second focal point, that is named the focusing wave, and locally produces a high pressure. This phenomenon is applied to disintegrators of kidney stone. But it is concerned that cavitation bubbles induced in the body by the expansion wave following the focusing wave will injure human tissue around kidney stone. In this paper, in order to examine what happens when shock waves strike bubbles on human tissue, the aspect that an air bubble is truck by the spherical shock wave or its behavior is visualized by the schlieren system and its photographs are taken using an image converter camera. Besides,the variation of the pressure amplitude caused by the shock wave and the flow of water around the bubble is measured with a pressure probe.

Nonplanar ion acoustic waves with kappa-distributed electrons

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

Sahu, Biswajit

2011-06-15

Using the standard reductive perturbation technique, nonlinear cylindrical and spherical Kadomtsev-Petviashvili equations are derived for the propagation of ion acoustic solitary waves in an unmagnetized collisionless plasma with kappa distributed electrons and warm ions. The influence of kappa-distributed electrons and the effects caused by the transverse perturbation on cylindrical and spherical ion acoustic waves (IAWs) are investigated. It is observed that increase in the kappa distributed electrons (i.e., decreasing {kappa}) decreases the amplitude of the solitary electrostatic potential structures. The numerical results are presented to understand the formation of ion acoustic solitary waves with kappa-distributed electrons in nonplanar geometry. Themore » present investigation may have relevance in the study of propagation of IAWs in space and laboratory plasmas.« less

Hydrodynamic interactions of cilia on a spherical body

NASA Astrophysics Data System (ADS)

Nasouri, Babak; Elfring, Gwynn J.

2015-11-01

The emergence of metachronal waves in ciliated microorganisms can arise solely from the hydrodynamic interactions between the cilia. For a chain of cilia attached to a flat ciliate, it was observed that fluid forces can lead the system to form a metachronal wave. However, several microorganisms such as paramecium and volvox possess a curved shaped ciliate body. To understand the effect of this geometry on the formation of metachronal waves, we evaluate the hydrodynamic interactions of cilia near a large spherical body. Using a minimal model, we show that for a chain of cilia around the sphere, the embedded periodicity in the geometry leads the system to synchronize. We also report an emergent wave-like behavior when an asymmetry is introduced to the system.

Sound field reproduction as an equivalent acoustical scattering problem.

PubMed

Fazi, Filippo Maria; Nelson, Philip A

2013-11-01

Given a continuous distribution of acoustic sources, the determination of the source strength that ensures the synthesis of a desired sound field is shown to be identical to the solution of an equivalent acoustic scattering problem. The paper begins with the presentation of the general theory that underpins sound field reproduction with secondary sources continuously arranged on the boundary of the reproduction region. The process of reproduction by a continuous source distribution is modeled by means of an integral operator (the single layer potential). It is then shown how the solution of the sound reproduction problem corresponds to that of an equivalent scattering problem. Analytical solutions are computed for two specific instances of this problem, involving, respectively, the use of a secondary source distribution in spherical and planar geometries. The results are shown to be the same as those obtained with analyses based on High Order Ambisonics and Wave Field Synthesis, respectively, thus bringing to light a fundamental analogy between these two methods of sound reproduction. Finally, it is shown how the physical optics (Kirchhoff) approximation enables the derivation of a high-frequency simplification for the problem under consideration, this in turn being related to the secondary source selection criterion reported in the literature on Wave Field Synthesis.

Acoustical tweezers using single spherically focused piston, X-cut, and Gaussian beams.

PubMed

Mitri, Farid G

2015-10-01

Partial-wave series expansions (PWSEs) satisfying the Helmholtz equation in spherical coordinates are derived for circular spherically focused piston (i.e., apodized by a uniform velocity amplitude normal to its surface), X-cut (i.e., apodized by a velocity amplitude parallel to the axis of wave propagation), and Gaussian (i.e., apodized by a Gaussian distribution of the velocity amplitude) beams. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSEs assuming weakly focused beams (with focusing angle α ⩽ 20°) in the Fresnel-Kirchhoff (parabolic) approximation. In contrast with previous analytical models, the derived expressions allow computing the scattering and acoustic radiation force from a sphere of radius a without restriction to either the Rayleigh (a ≪ λ, where λ is the wavelength of the incident radiation) or the ray acoustics (a ≫λ) regimes. The analytical formulations are valid for wavelengths largely exceeding the radius of the focused acoustic radiator, when the viscosity of the surrounding fluid can be neglected, and when the sphere is translated along the axis of wave propagation. Computational results illustrate the analysis with particular emphasis on the sphere's elastic properties and the axial distance to the center of the concave surface, with close connection of the emergence of negative trapping forces. Potential applications are in single-beam acoustical tweezers, acoustic levitation, and particle manipulation.

Design and analysis of aspherical multilayer imaging X-ray microscope

NASA Technical Reports Server (NTRS)

Shealy, David L.; Jiang, WU; Hoover, Richard B.

1991-01-01

Spherical Schwarzschild microscopes for soft X-ray applications in microscopy and projection lithography employ two concentric spherical mirrors that are configured such that the third-order spherical aberration and coma are zero. Based on incoherent, sine-wave MTF calculations, the object-plane resolution of a magnification-factor-20 microscope is presently analyzed as a function of object height and numerical aperture of the primary for several spherical Schwarzschild, conic, and aspherical two-mirror microscope configurations.

Spherical indentation of a freestanding circular membrane revisited: Analytical solutions and experiments

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

Jin, Congrui; Davoodabadi, Ali; Li, Jianlin

Because of the development of novel micro-fabrication techniques to produce ultra-thin materials and increasing interest in thin biological membranes, in recent years, the mechanical characterization of thin films has received a significant amount of attention. To provide a more accurate solution for the relationship among contact radius, load and deflection, the fundamental and widely applicable problem of spherical indentation of a freestanding circular membrane have been revisited. The work presented here significantly extends the previous contributions by providing an exact analytical solution to the governing equations of Föppl–Hecky membrane indented by a frictionless spherical indenter. In this study, experiments ofmore » spherical indentation has been performed, and the exact analytical solution presented in this article is compared against experimental data from existing literature as well as our own experimental results.« less

Spherical indentation of a freestanding circular membrane revisited: Analytical solutions and experiments

DOE PAGES

Jin, Congrui; Davoodabadi, Ali; Li, Jianlin; ...

2017-01-11

Because of the development of novel micro-fabrication techniques to produce ultra-thin materials and increasing interest in thin biological membranes, in recent years, the mechanical characterization of thin films has received a significant amount of attention. To provide a more accurate solution for the relationship among contact radius, load and deflection, the fundamental and widely applicable problem of spherical indentation of a freestanding circular membrane have been revisited. The work presented here significantly extends the previous contributions by providing an exact analytical solution to the governing equations of Föppl–Hecky membrane indented by a frictionless spherical indenter. In this study, experiments ofmore » spherical indentation has been performed, and the exact analytical solution presented in this article is compared against experimental data from existing literature as well as our own experimental results.« less

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.

Vaporization of irradiated droplets

NASA Astrophysics Data System (ADS)

Armstrong, R. L.; O'Rourke, P. J.; Zardecki, A.

1986-11-01

The vaporization of a spherically symmetric liquid droplet subject to a high-intensity laser flux is investigated on the basis of a hydrodynamic description of the system composed of the vapor and ambient gas. In the limit of the convective vaporization, the boundary conditions at the fluid-gas interface are formulated by using the notion of a Knudsen layer in which translational equilibrium is established. This leads to approximate jump conditions at the interface. For homogeneous energy deposition, the hydrodynamic equations are solved numerically with the aid of the CON1D computer code (``CON1D: A computer program for calculating spherically symmetric droplet combustion,'' Los Alamos National Laboratory Report No. LA-10269-MS, December, 1984), based on the implict continuous-fluid Eulerian (ICE) [J. Comput. Phys. 8, 197 (1971)] and arbitrary Lagrangian-Eulerian (ALE) [J. Comput. Phys. 14, 1227 (1974)] numerical mehtods. The solutions exhibit the existence of two shock waves propagating in opposite directions with respect to the contact discontinuity surface that separates the ambient gas and vapor.

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

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

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

2015-11-14

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

Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas

NASA Technical Reports Server (NTRS)

Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.

1997-01-01

We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.

Spherical Harmonics Reveal Standing EEG Waves and Long-Range Neural Synchronization during Non-REM Sleep.

PubMed

Sivakumar, Siddharth S; Namath, Amalia G; Galán, Roberto F

2016-01-01

Previous work from our lab has demonstrated how the connectivity of brain circuits constrains the repertoire of activity patterns that those circuits can display. Specifically, we have shown that the principal components of spontaneous neural activity are uniquely determined by the underlying circuit connections, and that although the principal components do not uniquely resolve the circuit structure, they do reveal important features about it. Expanding upon this framework on a larger scale of neural dynamics, we have analyzed EEG data recorded with the standard 10-20 electrode system from 41 neurologically normal children and adolescents during stage 2, non-REM sleep. We show that the principal components of EEG spindles, or sigma waves (10-16 Hz), reveal non-propagating, standing waves in the form of spherical harmonics. We mathematically demonstrate that standing EEG waves exist when the spatial covariance and the Laplacian operator on the head's surface commute. This in turn implies that the covariance between two EEG channels decreases as the inverse of their relative distance; a relationship that we corroborate with empirical data. Using volume conduction theory, we then demonstrate that superficial current sources are more synchronized at larger distances, and determine the characteristic length of large-scale neural synchronization as 1.31 times the head radius, on average. Moreover, consistent with the hypothesis that EEG spindles are driven by thalamo-cortical rather than cortico-cortical loops, we also show that 8 additional patients with hypoplasia or complete agenesis of the corpus callosum, i.e., with deficient or no connectivity between cortical hemispheres, similarly exhibit standing EEG waves in the form of spherical harmonics. We conclude that spherical harmonics are a hallmark of spontaneous, large-scale synchronization of neural activity in the brain, which are associated with unconscious, light sleep. The analogy with spherical harmonics in quantum mechanics suggests that the variances (eigenvalues) of the principal components follow a Boltzmann distribution, or equivalently, that standing waves are in a sort of "thermodynamic" equilibrium during non-REM sleep. By extension, we speculate that consciousness emerges as the brain dynamics deviate from such equilibrium.

Spherical Harmonics Reveal Standing EEG Waves and Long-Range Neural Synchronization during Non-REM Sleep

PubMed Central

Sivakumar, Siddharth S.; Namath, Amalia G.; Galán, Roberto F.

2016-01-01

Previous work from our lab has demonstrated how the connectivity of brain circuits constrains the repertoire of activity patterns that those circuits can display. Specifically, we have shown that the principal components of spontaneous neural activity are uniquely determined by the underlying circuit connections, and that although the principal components do not uniquely resolve the circuit structure, they do reveal important features about it. Expanding upon this framework on a larger scale of neural dynamics, we have analyzed EEG data recorded with the standard 10–20 electrode system from 41 neurologically normal children and adolescents during stage 2, non-REM sleep. We show that the principal components of EEG spindles, or sigma waves (10–16 Hz), reveal non-propagating, standing waves in the form of spherical harmonics. We mathematically demonstrate that standing EEG waves exist when the spatial covariance and the Laplacian operator on the head's surface commute. This in turn implies that the covariance between two EEG channels decreases as the inverse of their relative distance; a relationship that we corroborate with empirical data. Using volume conduction theory, we then demonstrate that superficial current sources are more synchronized at larger distances, and determine the characteristic length of large-scale neural synchronization as 1.31 times the head radius, on average. Moreover, consistent with the hypothesis that EEG spindles are driven by thalamo-cortical rather than cortico-cortical loops, we also show that 8 additional patients with hypoplasia or complete agenesis of the corpus callosum, i.e., with deficient or no connectivity between cortical hemispheres, similarly exhibit standing EEG waves in the form of spherical harmonics. We conclude that spherical harmonics are a hallmark of spontaneous, large-scale synchronization of neural activity in the brain, which are associated with unconscious, light sleep. The analogy with spherical harmonics in quantum mechanics suggests that the variances (eigenvalues) of the principal components follow a Boltzmann distribution, or equivalently, that standing waves are in a sort of “thermodynamic” equilibrium during non-REM sleep. By extension, we speculate that consciousness emerges as the brain dynamics deviate from such equilibrium. PMID:27445777

Wave Amplitude Dependent Engineering Model of Propellant Slosh in Spherical Tanks

NASA Technical Reports Server (NTRS)

Brodnick, Jacob; Westra, Douglas G.; Eberhart, Chad J.; Yang, Hong Q.; West, Jeffrey S.

2016-01-01

Liquid propellant slosh is often a concern for the controllability of flight vehicles. Anti-slosh devices are traditionally included in propellant tank designs to limit the amount of sloshing allowed during flight. These devices and any necessary supports can be quite heavy to meet various structural requirements. Some of the burden on anti-slosh devices can be relieved by exploiting the nonlinear behavior of slosh waves in bare smooth wall tanks. A nonlinear regime slosh model for bare spherical tanks was developed through a joint analytical and experimental effort by NASA/MSFC. The developed slosh model accounts for the large damping inherent in nonlinear slosh waves which is more accurate and drives conservatism from vehicle stability analyses that use traditional bare tank slosh models. A more accurate slosh model will result in more realistic predicted slosh forces during flight reducing or removing the need for active controls during a maneuver or baffles in the tank design. Lower control gains and smaller or fewer tank baffles can reduce cost and system complexity while increasing vehicle performance. Both Computational Fluid Dynamics (CFD) simulation and slosh testing of three different spherical tank geometries were performed to develop the proposed slosh model. Several important findings were made during this effort in addition to determining the parameters to the nonlinear regime slosh model. The linear regime slosh damping trend for spherical tanks reported in NASA SP-106 was shown to be inaccurate for certain regions of a tank. Additionally, transition to the nonlinear regime for spherical tanks was only found to occur at very large wave amplitudes in the lower hemisphere and was a strong function of the propellant fill level in the upper hemisphere. The nonlinear regime damping trend was also found to be a function of the propellant fill level.

Analysis of Ultrasonic Wave Scattering for Characterization of Defects in Solids

DTIC Science & Technology

1976-05-01

embedded in a solid matrix.’ The results of this work have been partially reported in a paper sub- mitted to the "Journal of the Acoustical Society of...America." The abstract of this paper is presented here: a. "Scattering of Longitudinal Waves Incident on a Spherical Cavity in a Solid," B. R. Tittmann...F I 7 ... .OCT..9 UM... ... .. . ... U SCS7g. 31R 2. Scattering by a Spherical Inclusion During this past year the experimental portion of the

Short-scale turbulent fluctuations driven by the electron-temperature gradient in the national spherical torus experiment.

PubMed

Mazzucato, E; Smith, D R; Bell, R E; Kaye, S M; Hosea, J C; LeBlanc, B P; Wilson, J R; Ryan, P M; Domier, C W; Luhmann, N C; Yuh, H; Lee, W; Park, H

2008-08-15

Measurements with coherent scattering of electromagnetic waves in plasmas of the National Spherical Torus Experiment indicate the existence of turbulent fluctuations in the range of wave numbers k perpendicular rho(e)=0.1-0.4, corresponding to a turbulence scale length nearly equal to the collisionless skin depth. Experimental observations and agreement with numerical results from a linear gyrokinetic stability code support the conjecture that the observed turbulence is driven by the electron-temperature gradient.

Full wave simulations of fast wave efficiency and power losses in the scrape-off layer of tokamak plasmas in mid/high harmonic and minority heating regimes

DOE PAGES

Bertelli, N.; Jaeger, E. F.; Hosea, J. C.; ...

2015-12-17

Here, several experiments on different machines and in different fast wave (FW) heating regimes, such as hydrogen minority heating and high harmonic fast waves (HHFW), have found strong interaction between radio-frequency (RF) waves and the scrape-off layer (SOL) region. This paper examines the propagation and the power loss in the SOL by using the full wave code AORSA, in which the edge plasma beyond the last closed flux surface (LCFS) is included in the solution domain and a collisional damping parameter is used as a proxy to represent the real, and most likely nonlinear, damping processes. 2D and 3D AORSAmore » results for the National Spherical Torus eXperiment (NSTX) have shown a strong transition to higher SOL power losses (driven by the RF field) when the FW cut-off is removed from in front of the antenna by increasing the edge density. Here, full wave simulations have been extended for 'conventional' tokamaks with higher aspect ratios, such as the DIII-D, Alcator C-Mod, and EAST devices. DIII-D results in HHFW regime show similar behavior found in NSTX and NSTX-U, consistent with previous DIII-D experimental observations. In contrast, a different behavior has been found for C-Mod and EAST, which operate in the minority heating regime.« less

Treatment of late time instabilities in finite-difference EMP scattering codes

NASA Astrophysics Data System (ADS)

Simpson, L. T.; Holland, R.; Arman, S.

1982-12-01

Constraints applicable to a finite difference mesh for solution of Maxwell's equations are defined. The equations are applied in the time domain for computing electromagnetic coupling to complex structures, e.g., rectangular, cylindrical, or spherical. In a spatially varying grid, the amplitude growth of high frequency waves becomes exponential through multiple reflections from the outer boundary in cases of late-time solution. The exponential growth of the numerical noise exceeds the value of the real signal. The correction technique employs an absorbing surface and a radiating boundary, along with tailored selection of the grid mesh size. High frequency noise is removed through use of a low-pass digital filter, a linear least squares fit is made to thy low frequency filtered response, and the original, filtered, and fitted data are merged to preserve the high frequency early-time response.

Forced sound transmission through a finite-sized single leaf panel subject to a point source excitation.

PubMed

Wang, Chong

2018-03-01

In the case of a point source in front of a panel, the wavefront of the incident wave is spherical. This paper discusses spherical sound waves transmitting through a finite sized panel. The forced sound transmission performance that predominates in the frequency range below the coincidence frequency is the focus. Given the point source located along the centerline of the panel, forced sound transmission coefficient is derived through introducing the sound radiation impedance for spherical incident waves. It is found that in addition to the panel mass, forced sound transmission loss also depends on the distance from the source to the panel as determined by the radiation impedance. Unlike the case of plane incident waves, sound transmission performance of a finite sized panel does not necessarily converge to that of an infinite panel, especially when the source is away from the panel. For practical applications, the normal incidence sound transmission loss expression of plane incident waves can be used if the distance between the source and panel d and the panel surface area S satisfy d/S>0.5. When d/S ≈0.1, the diffuse field sound transmission loss expression may be a good approximation. An empirical expression for d/S=0  is also given.

Dielectric Covered Planar Antennas

NASA Technical Reports Server (NTRS)

Llombart Juan, Nuria (Inventor); Lee, Choonsup (Inventor); Chattopadhyay, Goutam (Inventor); Gill, John J. (Inventor); Skalare, Anders J. (Inventor); Siegel, Peter H. (Inventor)

2014-01-01

An antenna element suitable for integrated arrays at terahertz frequencies is disclosed. The antenna element comprises an extended spherical (e.g. hemispherical) semiconductor lens, e.g. silicon, antenna fed by a leaky wave waveguide feed. The extended spherical lens comprises a substantially spherical lens adjacent a substantially planar lens extension. A couple of TE/TM leaky wave modes are excited in a resonant cavity formed between a ground plane and the substantially planar lens extension by a waveguide block coupled to the ground plane. Due to these modes, the primary feed radiates inside the lens with a directive pattern that illuminates a small sector of the lens. The antenna structure is compatible with known semiconductor fabrication technology and enables production of large format imaging arrays.

Wave field synthesis of moving virtual sound sources with complex radiation properties.

PubMed

Ahrens, Jens; Spors, Sascha

2011-11-01

An approach to the synthesis of moving virtual sound sources with complex radiation properties in wave field synthesis is presented. The approach exploits the fact that any stationary sound source of finite spatial extent radiates spherical waves at sufficient distance. The angular dependency of the radiation properties of the source under consideration is reflected by the amplitude and phase distribution on the spherical wave fronts. The sound field emitted by a uniformly moving monopole source is derived and the far-field radiation properties of the complex virtual source under consideration are incorporated in order to derive a closed-form expression for the loudspeaker driving signal. The results are illustrated via numerical simulations of the synthesis of the sound field of a sample moving complex virtual source.

Acoustic and elastic multiple scattering and radiation from cylindrical structures

NASA Astrophysics Data System (ADS)

Amirkulova, Feruza Abdukadirovna

Multiple scattering (MS) and radiation of waves by a system of scatterers is of great theoretical and practical importance and is required in a wide variety of physical contexts such as the implementation of "invisibility" cloaks, the effective parameter characterization, and the fabrication of dynamically tunable structures, etc. The dissertation develops fast, rapidly convergent iterative techniques to expedite the solution of MS problems. The formulation of MS problems reduces to a system of linear algebraic equations using Graf's theorem and separation of variables. The iterative techniques are developed using Neumann expansion and Block Toeplitz structure of the linear system; they are very general, and suitable for parallel computations and a large number of MS problems, i.e. acoustic, elastic, electromagnetic, etc., and used for the first time to solve MS problems. The theory is implemented in Matlab and FORTRAN, and the theoretical predictions are compared to computations obtained by COMSOL. To formulate the MS problem, the transition matrix is obtained by analyzing an acoustic and an elastic single scattering of incident waves by elastic isotropic and anisotropic solids. The mathematical model of wave scattering from multilayered cylindrical and spherical structures is developed by means of an exact solution of dynamic 3D elasticity theory. The recursive impedance matrix algorithm is derived for radially heterogeneous anisotropic solids. An explicit method for finding the impedance in piecewise uniform, transverse-isotropic material is proposed; the solution is compared to elasticity theory solutions involving Buchwald potentials. Furthermore, active exterior cloaking devices are modeled for acoustic and elastic media using multipole sources. A cloaking device can render an object invisible to some incident waves as seen by some external observer. The active cloak is generated by a discrete set of multipole sources that destructively interfere with an incident wave to produce zero total field over a finite spatial region. The approach precisely determines the necessary source amplitudes and enables a cloaked region to be determined using Graf's theorem. To apply the approach, the infinite series of multipole expansions are truncated, and the accuracy of cloaking is studied by modifying the truncation parameter.

Preparation and Optical Properties of Spherical Inverse Opals by Liquid Phase Deposition Using Spherical Colloidal Crystals

NASA Astrophysics Data System (ADS)

Aoi, Y.; Tominaga, T.

2013-03-01

Titanium dioxide (TiO2) inverse opals in spherical shape were prepared by liquid phase deposition (LPD) using spherical colloidal crystals as templates. Spherical colloidal crystals were produced by ink-jet drying technique. Aqueous emulsion droplets that contain polystyrene latex particles were ejected into air and dried. Closely packed colloidal crystals with spherical shape were obtained. The obtained spherical colloidal crystals were used as templates for the LPD. The templates were dispersed in the deposition solution of the LPD, i.e. a mixed solution of ammonium hexafluorotitanate and boric acid and reacted for 4 h at 30 °C. After the LPD process, the interstitial spaces of the spherical colloidal crystals were completely filled with titanium oxide. Subsequent heat treatment resulted in removal of templates and spherical titanium dioxide inverse opals. The spherical shape of the template was retained. SEM observations indicated that the periodic ordered voids were surrounded by titanium dioxide. The optical reflectance spectra indicated that the optical properties of the spherical titanium dioxide inverse opals were due to Bragg diffractions from the ordered structure. Filling in the voids of the inverse opals with different solvents caused remarkable changes in the reflectance peak.

Schroedinger's Wave Structure of Matter (WSM)

NASA Astrophysics Data System (ADS)

Wolff, Milo; Haselhurst, Geoff

2009-10-01

The puzzling electron is due to the belief that it is a discrete particle. Einstein deduced this structure was impossible since Nature does not allow the discrete particle. Clifford (1876) rejected discrete matter and suggested structures in `space'. Schroedinger, (1937) also eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). He rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff and Geoff Haselhurst (SpaceAndMotion.com) using the Scalar Wave Equation to find spherical wave solutions in a 3D quantum space. This WSM, the origin of all the Natural Laws, contains all the electron's properties including the Schroedinger Equation. The origin of Newton's Law F=ma is no longer a puzzle; It originates from Mach's principle of inertia (1883) that depends on the space medium and the WSM. Carver Mead (1999) at CalTech used the WSM to design Intel micro-chips correcting errors of Maxwell's magnetic Equations. Applications of the WSM also describe matter at molecular dimensions: alloys, catalysts, biology and medicine, molecular computers and memories. See ``Schroedinger's Universe'' - at Amazon.com

Schroedinger's Wave Structure of Matter (WSM)

NASA Astrophysics Data System (ADS)

Wolff, Milo

2009-05-01

The puzzling electron is due to the belief that it is a discrete particle. Einstein deduced this structure impossible since Nature does not match the discrete particle. Clifford (1876) rejected discrete matter and suggested structures in `space'. Schroedinger, (1937) also eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). He rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff and Geoff Haselhurst (http://www.SpaceAndMotion.com) using the Scalar Wave Equation to find spherical wave solutions in a 3D quantum space. This WSM is the origin of all the Natural Laws; thus it contains all the electron's properties including the Schroedinger Equation. The origin of Newton's Law F=ma is no longer a puzzle; it is shown to originate from Mach's principle of inertia (1883) that depends on the space medium. Carver Mead (1999) applied the WSM to design Intel micro-chips correcting errors of Maxwell's magnetic Equations. Applications of the WSM describe matter at molecular dimensions: alloys, catalysts, the mechanisms of biology and medicine, molecular computers and memories. See http://www.amazon.com/Schro at Amazon.com.

Seismic wave interaction with underground cavities

NASA Astrophysics Data System (ADS)

Schneider, Felix M.; Esterhazy, Sofi; Perugia, Ilaria; Bokelmann, Götz

2016-04-01

Realization of the future Comprehensive Nuclear Test Ban Treaty (CTBT) will require ensuring its compliance, making the CTBT a prime example of forensic seismology. Following indications of a nuclear explosion obtained on the basis of the (IMS) monitoring network further evidence needs to be sought at the location of the suspicious event. For such an On-Site Inspection (OSI) at a possible nuclear test site the treaty lists several techniques that can be carried out by the inspection team, including aftershock monitoring and the conduction of active seismic surveys. While those techniques are already well established, a third group of methods labeled as "resonance seismometry" is less well defined and needs further elaboration. A prime structural target that is expected to be present as a remnant of an underground nuclear explosion is a cavity at the location and depth the bomb was fired. Originally "resonance seismometry" referred to resonant seismic emission of the cavity within the medium that could be stimulated by an incident seismic wave of the right frequency and observed as peaks in the spectrum of seismic stations in the vicinity of the cavity. However, it is not yet clear which are the conditions for which resonant emissions of the cavity could be observed. In order to define distance-, frequency- and amplitude ranges at which resonant emissions could be observed we study the interaction of seismic waves with underground cavities. As a generic model for possible resonances we use a spherical acoustic cavity in an elastic full-space. To solve the forward problem for the full elastic wave field around acoustic spherical inclusions, we implemented an analytical solution (Korneev, 1993). This yields the possibility of generating scattering cross-sections, amplitude spectrums and synthetic seismograms for plane incident waves. Here, we focus on the questions whether or not we can expect resonant responses in the wave field scattered from the cavity. We show results for varying input parameters such as dimensions, densities, and seismic velocities in and around the cavity, in order to discuss the applicability of such observations during an OSI.

Atmospheric-radiation boundary conditions for high-frequency waves in time-distance helioseismology

NASA Astrophysics Data System (ADS)

Fournier, D.; Leguèbe, M.; Hanson, C. S.; Gizon, L.; Barucq, H.; Chabassier, J.; Duruflé, M.

2017-12-01

The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency ( 5.3 mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computing the propagation of high-frequency waves in the solar atmosphere. We consider recently developed and published radiative boundary conditions for atmospheres in which sound-speed is constant and density decreases exponentially with radius. We compute the cross-covariance function using a finite element method in spherical geometry and in the frequency domain. The ratio between first- and second-skip amplitudes in the time-distance diagram is used as a diagnostic to compare boundary conditions and to compare with observations. We find that a boundary condition applied 500 km above the photosphere and derived under the approximation of small angles of incidence accurately reproduces the "infinite atmosphere" solution for high-frequency waves. When the radiative boundary condition is applied 2 Mm above the photosphere, we find that the choice of atmospheric model affects the time-distance diagram. In particular, the time-distance diagram exhibits double-ridge structure when using a Vernazza Avrett Loeser atmospheric model.

Analytical expression for a class of spherically symmetric solutions in Lorentz-breaking massive gravity

NASA Astrophysics Data System (ADS)

Li, Ping; Li, Xin-zhou; Xi, Ping

2016-06-01

We present a detailed study of the spherically symmetric solutions in Lorentz-breaking massive gravity. There is an undetermined function { F }(X,{w}1,{w}2,{w}3) in the action of Stückelberg fields {S}φ ={{{Λ }}}4\\int {{{d}}}4x\\sqrt{-g}{ F }, which should be resolved through physical means. In general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also plays a crucial role in Lorentz-breaking massive gravity. { F } will satisfy the constraint equation {T}01=0 from the spherically symmetric Einstein tensor {G}01=0, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The Stückelberg field {φ }i is taken as a ‘hedgehog’ configuration {φ }i=φ (r){x}i/r, whose stability is guaranteed by the topological one. Under this ansätz, {T}01=0 is reduced to d{ F }=0. The functions { F } for d{ F }=0 form a commutative ring {R}{ F }. We obtain an expression of the solution to the functional differential equation with spherical symmetry if { F }\\in {R}{ F }. If { F }\\in {R}{ F } and \\partial { F }/\\partial X=0, the functions { F } form a subring {S}{ F }\\subset {R}{ F }. We show that the metric is Schwarzschild, Schwarzschild-AdS or Schwarzschild-dS if { F }\\in {S}{ F }. When { F }\\in {R}{ F } but { F }\

Black holes in vector-tensor theories

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

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic andmore » quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.« less

Tunable dielectric properties of mesoporous carbon hollow microspheres via textural properties.

PubMed

Xu, Hailong; Yin, Xiaowei; Li, Zhaochen; Liu, Chenglong; Wang, Zeyu; Li, Minghang; Zhang, Litong; Cheng, Laifei

2018-05-04

In this study, mesoporous carbon hollow microspheres (PCHMs) with tunable textural properties have been prepared through a facile hard template etching method. The PCHMs were characterized by scanning electron microscopy, transmission electron microscopy, x-ray diffraction, Raman spectra, and nitrogen adsorption and desorption systems. Uniform PCHMs with shell thickness ranging from 23 nm to 55 nm are realized. PCHMs with different textural properties can regulate dielectric and electromagnetic (EM) wave absorption effectively. The composite of paraffin wax mixed with 10 wt% PCHMs (the shell thickness of PCHMs is 35 nm) exhibits a minimum coefficient value of -53.8 dB at 8.8 GHz, with a thickness of 3.4 mm. Besides, it is remarkable that the effective absorption bandwidth covers all the X band with as low as a 10 wt% filler ratio, compared with other spherical EM wave absorbers. The excellent EM wave absorption capability of PCHMs can be ascribed to the better impendence matching and strong EM wave attenuation constant based on tunable textural properties. Our results provide a facile strategy to tune dielectric properties of spherical carbon absorbers based on textural properties, and can be extended to other spherical absorbers.

Tunable dielectric properties of mesoporous carbon hollow microspheres via textural properties

NASA Astrophysics Data System (ADS)

Xu, Hailong; Yin, Xiaowei; Li, Zhaochen; Liu, Chenglong; Wang, Zeyu; Li, Minghang; Zhang, Litong; Cheng, Laifei

2018-05-01

In this study, mesoporous carbon hollow microspheres (PCHMs) with tunable textural properties have been prepared through a facile hard template etching method. The PCHMs were characterized by scanning electron microscopy, transmission electron microscopy, x-ray diffraction, Raman spectra, and nitrogen adsorption and desorption systems. Uniform PCHMs with shell thickness ranging from 23 nm to 55 nm are realized. PCHMs with different textural properties can regulate dielectric and electromagnetic (EM) wave absorption effectively. The composite of paraffin wax mixed with 10 wt% PCHMs (the shell thickness of PCHMs is 35 nm) exhibits a minimum coefficient value of -53.8 dB at 8.8 GHz, with a thickness of 3.4 mm. Besides, it is remarkable that the effective absorption bandwidth covers all the X band with as low as a 10 wt% filler ratio, compared with other spherical EM wave absorbers. The excellent EM wave absorption capability of PCHMs can be ascribed to the better impendence matching and strong EM wave attenuation constant based on tunable textural properties. Our results provide a facile strategy to tune dielectric properties of spherical carbon absorbers based on textural properties, and can be extended to other spherical absorbers.

Waves in Radial Gravity Using Magnetic Fluid

NASA Technical Reports Server (NTRS)

Ohlsen, D. R.; Hart, J. E.; Weidman, P. D.

1999-01-01

Terrestrial laboratory experiments studying various fluid dynamical processes are constrained, by being in an Earth laboratory, to have a gravitational body force which is uniform and unidirectional. Therefore fluid free-surfaces are horizontal and flat. Such free surfaces must have a vertical solid boundary to keep the fluid from spreading horizontally along a gravitational potential surface. In atmospheric, oceanic, or stellar fluid flows that have a horizontal scale of about one-tenth the body radius or larger, sphericity is important in the dynamics. Further, fluids in spherical geometry can cover an entire domain without any sidewall effects, i.e. have truly periodic boundary conditions. We describe spherical body-force laboratory experiments using ferrofluid. Ferrofluids are dilute suspensions of magnetic dipoles, for example magnetite particles of order 10 nm diameter, suspended in a carrier fluid. Ferrofluids are subject to an additional body force in the presence of an applied magnetic field gradient. We use this body force to conduct laboratory experiments in spherical geometry. The present study is a laboratory technique improvement. The apparatus is cylindrically axisymmetric. A cylindrical ceramic magnet is embedded in a smooth, solid, spherical PVC ball. The geopotential field and its gradient, the body force, were made nearly spherical by careful choice of magnet height-to-diameter ratio and magnet size relative to the PVC ball size. Terrestrial gravity is eliminated from the dynamics by immersing the "planet" and its ferrofluid "ocean" in an immiscible silicone oil/freon mixture of the same density. Thus the earth gravity is removed from the dynamics of the ferrofluid/oil interface and the only dynamically active force there is the radial magnetic gravity. The entire apparatus can rotate, and waves are forced on the ferrofluid surface by exterior magnets. The biggest improvement in technique is in the wave visualization. Fluorescing dye is added to the oil/freon mixture and an argon ion laser generates a horizontal light that can be scanned vertically. Viewed from above, the experiment is a black circle with wave deformations surrounded by a light background. A contour of the image intensity at any light sheet position gives the surface of the ferrofluid "ocean" at that "latitude". Radial displacements of the waves as a function of longitude are obtained by subtracting the contour line positions from a no-motion contour at that laser sheet latitude. The experiments are run by traversing the forcing magnet with the laser sheet height fixed and images are frame grabbed to obtain a time-series at one latitude. The experiment is then re-run with another laser-sheet height to generate a full picture of the three-dimensional wave structure in the upper hemisphere of the ball as a function of time. We concentrate here on results of laboratory studies of waves that are important in Earth's atmosphere and especially the ocean. To get oceanic scaling in the laboratory, the experiment must rotate rapidly (4-second rotation period) so that the wave speed is slow compared to the planetary rotation speed as in the ocean. In the Pacific Ocean, eastward propagating Kelvin waves eventually run into the South American coast. Theory predicts that some of the wave energy should scatter into coastal-trapped Kelvin waves that propagate north and south along the coast. Some of this coastal wave energy might then scatter into mid-latitude Rossby waves that propagate back westward. Satellite observations of the Pacific Ocean sea-surface temperature and height seem to show signatures of westward propagating mid-latitude Rossby waves, 5 to 10 years after the 1982-83 El Nino. The observational data is difficult to interpret unambiguously owing to the large range of motions that fill the ocean at shorter timescales. This series of reflections giving eastward, north- ward, and then westward traveling waves is observed cleanly in the laboratory experiments, confirming the theoretical expectations.

First Octahedral Spherical Hohlraum Energetics Experiment at the SGIII Laser Facility

NASA Astrophysics Data System (ADS)

Huo, Wen Yi; Li, Zhichao; Chen, Yao-Hua; Xie, Xufei; Ren, Guoli; Cao, Hui; Li, Shu; Lan, Ke; Liu, Jie; Li, Yongsheng; Li, Sanwei; Guo, Liang; Liu, Yonggang; Yang, Dong; Jiang, Xiaohua; Hou, Lifei; Du, Huabing; Peng, Xiaoshi; Xu, Tao; Li, Chaoguang; Zhan, Xiayu; Wang, Zhebin; Deng, Keli; Wang, Qiangqiang; Deng, Bo; Wang, Feng; Yang, Jiamin; Liu, Shenye; Jiang, Shaoen; Yuan, Guanghui; Zhang, Haijun; Jiang, Baibin; Zhang, Wei; Gu, Qianqian; He, Zhibing; Du, Kai; Deng, Xuewei; Zhou, Wei; Wang, Liquan; Huang, Xiaoxia; Wang, Yuancheng; Hu, Dongxia; Zheng, Kuixing; Zhu, Qihua; Ding, Yongkun

2018-04-01

The first octahedral spherical hohlraum energetics experiment is accomplished at the SGIII laser facility. For the first time, the 32 laser beams are injected into the octahedral spherical hohlraum through six laser entrance holes. Two techniques are used to diagnose the radiation field of the octahedral spherical hohlraum in order to obtain comprehensive experimental data. The radiation flux streaming out of laser entrance holes is measured by six flat-response x-ray detectors (FXRDs) and four M -band x-ray detectors, which are placed at different locations of the SGIII target chamber. The radiation temperature is derived from the measured flux of FXRD by using the blackbody assumption. The peak radiation temperature inside hohlraum is determined by the shock wave technique. The experimental results show that the octahedral spherical hohlraum radiation temperature is in the range of 170-182 eV with drive laser energies of 71 kJ to 84 kJ. The radiation temperature inside the hohlraum determined by the shock wave technique is about 175 eV at 71 kJ. For the flat-top laser pulse of 3 ns, the conversion efficiency of gas-filled octahedral spherical hohlraum from laser into soft x rays is about 80% according to the two-dimensional numerical simulation.

Convoluted Quasi Sturmian basis for the two-electron continuum

NASA Astrophysics Data System (ADS)

Ancarani, Lorenzo Ugo; Zaytsev, A. S.; Zaytsev, S. A.

2016-09-01

In the construction of solutions for the Coulomb three-body scattering problem one encounters a series of mathematical and numerical difficulties, one of which are the cumbersome boundary conditions the wave function should obey. We propose to describe a Coulomb three-body system continuum with a set of two-particle functions, named Convoluted Quasi Sturmian (CQS) in. They are built using recently introduced Quasi Sturmian (QS) functions which have the merit of possessing a closed form. Unlike a simple product of two one-particle functions, by construction, the CQS functions look asymptotically like a six-dimensional outgoing spherical wave. The proposed CQS basis is tested through the study of the double ionization of helium by high-energy electron impact in the framework of the Temkin-Poet model. An adequate logarithmic-like phase factor is further included in order to take into account the Coulomb interelectronic interaction and formally build the correct asymptotic behavior when all interparticle distances are large. With such a phase-factor (that can be easily extended to take into account higher partial waves) rapid convergence of the expansion can be obtained.

AR Scorpii and possible gravitational wave radiation from pulsar white dwarfs

NASA Astrophysics Data System (ADS)

Franzon, B.; Schramm, S.

2017-06-01

In view of the new recent observation and measurement of the rotating and highly magnetized white dwarf AR Scorpii, we determine bounds of its moment of inertia, magnetic fields and radius. Moreover, we investigate the possibility of fast rotating and/or magnetized white dwarfs to be sources of detectable gravitational wave (GW) emission. Numerical stellar models at different baryon masses are constructed. For each star configuration, we compute self-consistent relativistic solutions for white dwarfs endowed with poloidal magnetic fields by solving the Einstein-Maxwell field equations in a self-consistent way. The magnetic field supplies an anisotropic pressure, leading to the braking of the spherical symmetry of the star. In this case, we compute the quadrupole moment of the mass distribution. Next, we perform an estimate of the GW of such objects. Finally, we show that the new recent observation and measurement pulsar white dwarf AR Scorpii, as well as other stellar models, might generate GW radiation that lies in the bandwidth of the discussed next generation of space-based GW detectors DECI-hertz Interferometer Gravitational wave Observatory (DECIGO) and Big Bang Observer (BBO).

Characterisation of columnar inertial modes in rapidly rotating spheres and spheroids

NASA Astrophysics Data System (ADS)

Maffei, S.; Jackson, A.; Livermore, P. W.

2017-12-01

We consider fluid-filled spheres and spheroidal containers of eccentricity ɛ in rapid rotation, as a proxy for the interior dynamics of stars and planets. The fluid motion is assumed to be quasi-geostrophic (QG): horizontal motions are invariant parallel to the rotation axis z, a characteristic which is handled by use of a stream function formulation which additionally enforces mass conservation and non-penetration at the boundary. By linearising about a quiescent background state, we investigate a variety of methods to study the QG inviscid inertial wave modes which are compared with fully 3-D calculations. We consider the recently-proposed weak formulation of the inviscid system valid in spheroids of arbitrary eccentricity, to which we present novel closed-form polynomial solutions. Our modal solutions accurately represent, in both spatial structure and frequency, the most z-invariant of the inertial wave modes in a spheroid, and constitute a simple basis set for the analysis of rotationally- dominated fluids. We further show that these new solutions are more accurate than those of the classical axial-vorticity equation, which is independent of ɛ and thus fails to properly encode the container geometry. We also consider the effects of viscosity for the cases of both no-slip and stress-free boundary conditions for a spherical container. Calculations performed under the columnar approximation are compared with 3-D solutions and excellent agreement has been found despite fundamental differences in the two formulations.

Distortion of ultrashort pulses caused by aberrations

NASA Astrophysics Data System (ADS)

Horváth, Z. L.; Kovács, A. P.; Bor, Zs.

The effect of the primary wave aberrations (spherical aberration, astigmatism and coma) on ultrashort pulses is studied by the Nijboer-Zernike theory. The results of the geometrical and the wave optical treatments are compared.

Cosmic dust-ion-acoustic waves, spherical modified Kadomtsev-Petviashvili model, and symbolic computation

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

Gao Yitian; Tian Bo; State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100083

2006-11-15

The spherical modified Kadomtsev-Petviashvili (smKP) model is hereby derived with symbolic computation for the dust-ion-acoustic waves with zenith-angle perturbation in a cosmic dusty plasma. Formation and properties of both dark and bright smKP nebulons are obtained and discussed. The relevance of those smKP nebulons to the supernova shells and Saturn's F-ring is pointed out, and possibly observable nebulonic effects for the future cosmic plasma experiments are proposed. The difference of the smKP nebulons from other types of nebulons is also analyzed.

Wollaston prism phase-stepping point diffraction interferometer and method

DOEpatents

Rushford, Michael C.

2004-10-12

A Wollaston prism phase-stepping point diffraction interferometer for testing a test optic. The Wollaston prism shears light into reference and signal beams, and provides phase stepping at increased accuracy by translating the Wollaston prism in a lateral direction with respect to the optical path. The reference beam produced by the Wollaston prism is directed through a pinhole of a diaphragm to produce a perfect spherical reference wave. The spherical reference wave is recombined with the signal beam to produce an interference fringe pattern of greater accuracy.

Focusing of Finite-Amplitude Cylindrical and Spherical Sound Waves in a Viscous and Heat-Conducting Medium. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chu, T.

1971-01-01

The focusing of acoustic pulses is studied analytically by considering the region of study in three parts: the converging, interaction and diverging regions. First, the linear problem of a pulse of infinitesimal amplitude is studied. For the spherical case, the expected phase change as a result of focusing is verified. The nonlinear case of finite-amplitude pulses leads to the development of M-waves, as determined by applying the method of matched-asymptotic expansions to Burges equation.

Surface tension and negative pressure interior of a non-singular ‘black hole’

NASA Astrophysics Data System (ADS)

Mazur, Pawel O.; Mottola, Emil

2015-11-01

The constant density interior Schwarzschild solution for a static, spherically symmetric collapsed star has a divergent pressure when its radius R≤slant \\frac{9}{8}{R}s=\\frac{9}{4}{GM}. We show that this divergence is integrable, and induces a non-isotropic transverse stress with a finite redshifted surface tension on a spherical surface of radius {R}0=3R\\sqrt{1-\\frac{8}{9}\\frac{R }{{R}s}}. For r\\lt {R}0 the interior Schwarzschild solution exhibits negative pressure. When R={R}s, the surface is localized at the Schwarzschild radius itself, {R}0={R}s, and the solution has constant negative pressure p=-\\bar{ρ } everywhere in the interior r\\lt {R}s, thereby describing a gravitational condensate star, a fully collapsed non-singular state already inherent in and predicted by classical general relativity. The redshifted surface tension of the condensate star surface is given by {τ }s={{Δ }}κ /8π G, where {{Δ }}κ ={κ }+-{κ }-=2{κ }+=1/{R}s is the difference of equal and opposite surface gravities between the exterior and interior Schwarzschild solutions. The First Law, {{d}}M={{d}}{E}V+{τ }s {{d}}A is recognized as a purely mechanical classical relation at zero temperature and zero entropy, describing the volume energy and surface energy change respectively. The Schwarzschild time t of such a non-singular gravitational condensate star is a global time, fully consistent with unitary time evolution in quantum theory. A clear observational test of gravitational condensate stars with a physical surface versus black holes is the discrete surface modes of oscillation which should be detectable by their gravitational wave signatures.

Development of an ejecta particle size measurement diagnostic based on Mie scattering

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

Schauer, Martin Michael; Buttler, William Tillman; Frayer, Daniel K.

The goal of this work is to determine the feasibility of extracting the size of particles ejected from shocked metal surfaces (ejecta) from the angular distribution of light scattered by a cloud of such particles. The basis of the technique is the Mie theory of scattering, and implicit in this approach are the assumptions that the scattering particles are spherical and that single scattering conditions prevail. The meaning of this latter assumption, as far as experimental conditions are concerned, will become clear later. The solution to Maxwell’s equations for spherical particles illuminated by a plane electromagnetic wave was derived bymore » Gustav Mie more than 100 years ago, but several modern treatises discuss this solution in great detail. The solution is a complicated series expansion of the scattered electric field, as well as the field within the particle, from which the total scattering and absorption cross sections as well as the angular distribution of scattered intensity can be calculated numerically. The detailed nature of the scattering is determined by the complex index of refraction of the particle material as well as the particle size parameter, x, which is the product of the wavenumber of the incident light and the particle radius, i.e. x = 2rπ= λ. Figure 1 shows the angular distribution of scattered light for different particle size parameters and two orthogonal incident light polarizations as calculated using the Mie solution. It is obvious that the scattering pattern is strongly dependent on the particle size parameter, becoming more forward-directed and less polarizationdependent as the particle size parameter increases. This trend forms the basis for the diagnostic design.« less

Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability

NASA Astrophysics Data System (ADS)

Nearing, G. S.; Halem, M.; Chapman, D. R.; Pelissier, C. S.

2014-12-01

Data assimilation is one of the ubiquitous and computationally hard problems in the Earth Sciences. In particular, ensemble-based methods require a large number of model evaluations to estimate the prior probability density over system states, and variational methods require adjoint calculations and iteration to locate the maximum a posteriori solution in the presence of nonlinear models and observation operators. Quantum annealing computers (QAC) like the new D-Wave housed at the NASA Ames Research Center can be used for optimization and sampling, and therefore offers a new possibility for efficiently solving hard data assimilation problems. Coding on the QAC is not straightforward: a problem must be posed as a Quadratic Unconstrained Binary Optimization (QUBO) and mapped to a spherical Chimera graph. We have developed a method for compiling nonlinear 4D-Var problems on the D-Wave that consists of five steps: Emulating the nonlinear model and/or observation function using radial basis functions (RBF) or Chebyshev polynomials. Truncating a Taylor series around each RBF kernel. Reducing the Taylor polynomial to a quadratic using ancilla gadgets. Mapping the real-valued quadratic to a fixed-precision binary quadratic. Mapping the fully coupled binary quadratic to a partially coupled spherical Chimera graph using ancilla gadgets. At present the D-Wave contains 512 qbits (with 1024 and 2048 qbit machines due in the next two years); this machine size allows us to estimate only 3 state variables at each satellite overpass. However, QAC's solve optimization problems using a physical (quantum) system, and therefore do not require iterations or calculation of model adjoints. This has the potential to revolutionize our ability to efficiently perform variational data assimilation, as the size of these computers grows in the coming years.

Spherical harmonic expansion of the Levitus Sea surface topography

NASA Technical Reports Server (NTRS)

Engelis, Theodossios

1987-01-01

Prior information for the stationary sea surface topography (SST) may be needed in altimetric solutions that intend to simultaneously improve the gravity field and determine the SST. For this purpose the oceanographically derived SST estimates are represented by a spherical harmonic expansion. The spherical harmonic coefficients are computed from a least squares adjustment of the data covering the majority of the oceanic regions of the world. Several tests are made to determine the optimum maximum degree of solution and the best configuration of the geometry of the data in order to obtain a solution that fits the data and also provides a good spectral representation of the SST.

Bulk Viscosity of Bubbly Magmas and the Amplification of Pressure Waves

NASA Astrophysics Data System (ADS)

Navon, O.; Lensky, N. G.; Neuberg, J. W.; Lyakhovsky, V.

2001-12-01

The bulk viscosity of magma is needed in order to describe the dynamics of a compressible bubbly magma flowing in conduits and to follow the attenuation of pressure waves travelling through a compressible magma. We developed a model for the bulk viscosity of a suspension of gas bubbles in an incompressible Newtonian liquid that exsolves volatiles (e.g. magma). The suspension is modeled as a close pack of spherical cells, consisting of gas bubbles centered in spherical shells of a volatile-bearing liquid. Following a drop in the ambient pressure the resulting dilatational motion and driving pressure are obtained in terms of the two-phase cell parameters, i.e. bubble radius and gas pressure. By definition, the bulk viscosity of a fluid is the relation between changes of the driving pressure with respect to changes in the resulted expansion strain-rate. Thus, we can use the two-phase solution to define the bulk viscosity of a hypothetical cell, composed of a homogeneously compressible, one-phase, continuous fluid. The resulted bulk viscosity is highly non-linear. At the beginning of the expansion process, when gas exsolution is efficient, the expansion rate grows exponentially while the driving pressure decreases slightly. That means that bulk viscosity is formally negative. The negative value reflects the release of the energy stored in the supersaturated liquid (melt) and its conversion to mechanical work during exsolution. Later, when bubbles are large enough and the gas influx decreases significantly, the strain rate decelerates and the bulk viscosity becomes positive as expected in a dissipative system. We demonstrate that amplification of seismic wave travelling through a volcanic conduit filled with a volatile saturated magma may be attributed to the negative bulk viscosity of the compressible magma. Amplification of an expansion wave may, at some level in the conduit, damage the conduit walls and initiate opening of new pathways for magma to erupt.

Connection between black-hole quasinormal modes and lensing in the strong deflection limit.

PubMed

Stefanov, Ivan Zh; Yazadjiev, Stoytcho S; Gyulchev, Galin G

2010-06-25

The purpose of the current Letter is to give some relations between gravitational lensing in the strong-deflection limit and the frequencies of the quasinormal modes of spherically symmetric, asymptotically flat black holes. On the one side, the relations obtained can give a physical interpretation of the strong-deflection limit parameters. On the other side, they also give an alternative method for the measurement of the frequencies of the quasinormal modes of spherically symmetric, asymptotically flat black holes. They could be applied to the localization of the sources of gravitational waves and could tell us what frequencies of the gravitational waves we could expect from a black hole acting simultaneously as a gravitational lens and a source of gravitational waves.

Calculation of the acoustic radiation force on coated spherical shells in progressive and standing plane waves.

PubMed

Mitri, F G

2006-07-01

In this paper, analytical equations are derived for the time-averaged radiation force induced by progressive and standing acoustic waves incident on elastic spherical shells covered with a layer of viscoelastic and sound-absorbing material. The fluid surrounding the shells is considered compressible and nonviscous. The incident field is assumed to be moderate so that the scattered field from the shells is taken to linear approximation. The analytical results are illustrated by means of a numerical example in which the radiation force function curves are displayed, with particular emphasis on the coating thickness and the content of the hollow region of the shells. The fluid-loading on the radiation force function curves is analysed as well. This study attempts to generalize the various treatments of radiation force due to both progressive and standing waves on spherically-shaped structures immersed in ideal fluids. The results show that various ways can be effectively used for damping resonance peaks, such as by changing the fluid in the interior hollow region of the shells or by changing the coating thickness.

Spectroscopy of a plasma formed in the vicinity of implosion of the shock wave generated by underwater electrical explosion of spherical wire array

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

Antonov, O.; Efimov, S.; Gurovich, V. Tz.

The results of visible spectroscopy of the plasma formed inside a copper capillary placed at the equatorial plane of an underwater electrically exploded spherical wire array (30 mm in diameter; 40 wires, each of 100 μm in diameter) are reported. In the experiments, a pulsed power generator with current amplitude of ∼300 kA and rise time of ∼1.1 μs was used to produce wire array explosion accompanied by the formation of a converging strong shock wave. The data obtained support the assumption of uniformity of the shock wave along the main path of its convergence. The spectroscopic measurements show that this rather simple methodmore » of formation of a converging strong shock wave can be used successfully for studying the shock wave's interaction with matter and the evaporation processes of atoms from a target.« less

Underwater optical communication performance for laser beam propagation through weak oceanic turbulence.

PubMed

Yi, Xiang; Li, Zan; Liu, Zengji

2015-02-20

In clean ocean water, the performance of a underwater optical communication system is limited mainly by oceanic turbulence, which is defined as the fluctuations in the index of refraction resulting from temperature and salinity fluctuations. In this paper, using the refractive index spectrum of oceanic turbulence under weak turbulence conditions, we carry out, for a horizontally propagating plane wave and spherical wave, analysis of the aperture-averaged scintillation index, the associated probability of fade, mean signal-to-noise ratio, and mean bit error rate. Our theoretical results show that for various values of the rate of dissipation of mean squared temperature and the temperature-salinity balance parameter, the large-aperture receiver leads to a remarkable decrease of scintillation and consequently a significant improvement on the system performance. Such an effect is more noticeable in the plane wave case than in the spherical wave case.

Spherical space Bessel-Legendre-Fourier localized modes solver for electromagnetic waves.

PubMed

Alzahrani, Mohammed A; Gauthier, Robert C

2015-10-05

Maxwell's vector wave equations are solved for dielectric configurations that match the symmetry of a spherical computational domain. The electric or magnetic field components and the inverse of the dielectric profile are series expansion defined using basis functions composed of the lowest order spherical Bessel function, polar angle single index dependant Legendre polynomials and azimuthal complex exponential (BLF). The series expressions and non-traditional form of the basis functions result in an eigenvalue matrix formulation of Maxwell's equations that are relatively compact and accurately solvable on a desktop PC. The BLF matrix returns the frequencies and field profiles for steady states modes. The key steps leading to the matrix populating expressions are provided. The validity of the numerical technique is confirmed by comparing the results of computations to those published using complementary techniques.

Aberration corrected STEM by means of diffraction gratings

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

Linck, Martin; Ercius, Peter A.; Pierce, Jordan S.

In the past 15 years, the advent of aberration correction technology in electron microscopy has enabled materials analysis on the atomic scale. This is made possible by precise arrangements of multipole electrodes and magnetic solenoids to compensate the aberrations inherent to any focusing element of an electron microscope. In this paper, we describe an alternative method to correct for the spherical aberration of the objective lens in scanning transmission electron microscopy (STEM) using a passive, nanofabricated diffractive optical element. This holographic device is installed in the probe forming aperture of a conventional electron microscope and can be designed to removemore » arbitrarily complex aberrations from the electron's wave front. In this work, we show a proof-of-principle experiment that demonstrates successful correction of the spherical aberration in STEM by means of such a grating corrector (GCOR). Our GCOR enables us to record aberration-corrected high-resolution high-angle annular dark field (HAADF-) STEM images, although yet without advancement in probe current and resolution. Finally, improvements in this technology could provide an economical solution for aberration-corrected high-resolution STEM in certain use scenarios.« less

Aberration corrected STEM by means of diffraction gratings

DOE PAGES

Linck, Martin; Ercius, Peter A.; Pierce, Jordan S.; ...

2017-06-12

In the past 15 years, the advent of aberration correction technology in electron microscopy has enabled materials analysis on the atomic scale. This is made possible by precise arrangements of multipole electrodes and magnetic solenoids to compensate the aberrations inherent to any focusing element of an electron microscope. In this paper, we describe an alternative method to correct for the spherical aberration of the objective lens in scanning transmission electron microscopy (STEM) using a passive, nanofabricated diffractive optical element. This holographic device is installed in the probe forming aperture of a conventional electron microscope and can be designed to removemore » arbitrarily complex aberrations from the electron's wave front. In this work, we show a proof-of-principle experiment that demonstrates successful correction of the spherical aberration in STEM by means of such a grating corrector (GCOR). Our GCOR enables us to record aberration-corrected high-resolution high-angle annular dark field (HAADF-) STEM images, although yet without advancement in probe current and resolution. Finally, improvements in this technology could provide an economical solution for aberration-corrected high-resolution STEM in certain use scenarios.« less

Numerical modeling of a spherical buoy moored by a cable in three dimensions

NASA Astrophysics Data System (ADS)

Zhu, Xiangqian; Yoo, Wan-Suk

2016-05-01

Floating facilities have been studied based on the static analysis of mooring cables over the past decades. To analyze the floating system of a spherical buoy moored by a cable with a higher accuracy than before, the dynamics of the cables are considered in the construction of the numerical modeling. The cable modeling is established based on a new element frame through which the hydrodynamic loads are expressed efficiently. The accuracy of the cable modeling is verified with an experiment that is conducted by a catenary chain moving in a water tank. In addition, the modeling of a spherical buoy is established with respect to a spherical coordinate in three dimensions, which can suffers the gravity, the variable buoyancy and Froude-Krylov loads. Finally, the numerical modeling for the system of a spherical buoy moored by a cable is established, and a virtual simulation is proceeded with the X- and Y-directional linear waves and the X-directional current. The comparison with the commercial simulation code ProteusDS indicates that the system is accurately analyzed by the numerical modeling. The tensions within the cable, the motions of the system, and the relationship between the motions and waves are illustrated according to the defined sea state. The dynamics of the cables should be considered in analyzing the floating system of a spherical buoy moored by a cable.

A Wave-Optics Approach to Paraxial Geometrical Laws Based on Continuity at Boundaries

ERIC Educational Resources Information Center

Linares, J.; Nistal, M. C.

2011-01-01

We present a derivation of the paraxial geometrical laws starting from a wave-optics approach, in particular by using simple continuity conditions of paraxial spherical waves at boundaries (discontinuities) between optical media. Paraxial geometrical imaging and magnification laws, under refraction and reflection at boundaries, are derived for…

Spherical thin-shell wormholes and modified Chaplygin gas

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

Sharif, M.; Azam, M., E-mail: msharif.math@pu.edu.pk, E-mail: azammath@gmail.com

2013-05-01

The purpose of this paper is to construct spherical thin-shell wormhole solutions through cut and paste technique and investigate the stability of these solutions in the vicinity of modified Chaplygin gas. The Darmois-Israel formalism is used to formulate the stresses of the surface concentrating the exotic matter. We explore the stability of the wormhole solutions by using the standard potential method. We conclude that there exist more stable as well as unstable solutions than the previous study with generalized Chaplygin gas [19].

Enhanced kidney stone fragmentation by short delay tandem conventional and modified lithotriptor shock waves: a numerical analysis.

PubMed

Tham, Leung-Mun; Lee, Heow Pueh; Lu, Chun

2007-07-01

We evaluated the effectiveness of modified lithotriptor shock waves using computer models. Finite element models were used to simulate the propagation of lithotriptor shock waves in human renal calculi in vivo. Kidney stones were assumed to be spherical, homogeneous, isotropic and linearly elastic, and immersed in a continuum fluid. Single and tandem shock wave pulses modified to intensify the collapse of cavitation bubbles near the stone surface to increase fragmentation efficiency and suppress the expansion of intraluminal bubbles for decreased vascular injury were analyzed. The effectiveness of the modified shock waves was assessed by comparing the states of loading in the renal calculi induced by these shock waves to those produced by conventional shock waves. Our numerical simulations revealed that modified shock waves produced marginally lower stresses in spherical renal calculi than those produced by conventional shock waves. Tandem pulses of conventional or modified shock waves produced peak stresses in the front and back halves of the renal calculi. However, the single shock wave pulses generated significant peak stresses in only the back halves of the renal calculi. Our numerical simulations suggest that for direct stress wave induced fragmentation modified shock waves should be as effective as conventional shock waves for fragmenting kidney stones. Also, with a small interval of 20 microseconds between the pulses tandem pulse lithotripsy using modified or conventional shock waves could be considerably more effective than single pulse lithotripsy for fragmenting kidney stones.

Amplitude-phase characteristics of electromagnetic fields diffracted by a hole in a thin film with realistic optical properties

NASA Astrophysics Data System (ADS)

Dorofeyev, Illarion

2009-03-01

Characteristics of a quasi-spherical wave front of an electromagnetic field diffracted by a subwavelength hole in a thin film with real optical properties are studied. Related diffraction problem is solved in general by use of the scalar and vector Green's theorems and related Green's function of a boundary-value problem. Local phase deviations of a diffracted wave front from an ideal spherical front are calculated. Diffracted patterns are calculated for the coherent incident fields in case of holes array in a screen of perfect conductivity.

Combined approach to the Hubble Space Telescope wave-front distortion analysis

NASA Astrophysics Data System (ADS)

Roddier, Claude; Roddier, Francois

1993-06-01

Stellar images taken by the HST at various focus positions have been analyzed to estimate wave-front distortion. Rather than using a single algorithm, we found that better results were obtained by combining the advantages of various algorithms. For the planetary camera, the most accurate algorithms consistently gave a spherical aberration of -0.290-micron rms with a maximum deviation of 0.005 micron. Evidence was found that the spherical aberration is essentially produced by the primary mirror. The illumination in the telescope pupil plane was reconstructed and evidence was found for a slight camera misalignment.

A Variational Formulation for the Finite Element Analysis of Sound Wave Propagation in a Spherical Shell

NASA Technical Reports Server (NTRS)

Lebiedzik, Catherine

1995-01-01

Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.

Characterization of photoacoustic sources in tissue using time domain measurements

NASA Astrophysics Data System (ADS)

Viator, John Andrew

Photoacoustic phenomenon in tissue and tissue phantoms is investigated with the particular goal of discrimination of diseased and healthy tissue. Propagation of broadband photoacoustic sources in tissue phantoms is studied with emphasis on attenuation, dispersion, and diffraction. Attenuation of photoacoustic waves induced by a circular laser spot on an absorber/air interface is modeled by the on-axis approximation of the acoustic field of a baffled piston source. Dispersion is studied in a diffraction free situation, where the disk of irradiation was created by a 5 mm laser spot on a 200 cm -1 solution. The genesis of diffraction in an absorbing solution was displayed by showing the merging of a boundary wave with a plane wave from a circular laser spot on an absorbing solution. Depth profiling of absorbing tissue phantoms and stained tissue was shown using a photoacoustic method. Acrylamide gels with layers of different optical absorption and stained elastin biomaterials were irradiated with stress confined laser pulses. The resulting acoustic waves were detected with a lithium niobate wideband acoustic transducer and processed in an algorithm to determine absorption coefficient as a function of depth. Spherical photoacoustic sources were generated in optically clear and turbid tissue phantoms. Propagation time and acoustic pulse duration were used to determine location and size, respectively. The photoacoustic sources were imaged using a multiplicative backprojection scheme. Image sources from acoustic boundaries were detected and dipole sources were detected and imaged. Finally an endoscopic photoacoustic probe was designed, built, and tested for use in determining treatment depth after palliative photodynamic therapy of esophageal cancer. The probe was less than 2.5 mm in diameter and consisted of a side firing 600 mum optical fiber to deliver laser energy and a 890 mum diameter, side viewing piezoelectric detector. The sensitivity of the probe was determined. The probe was also tested on coagulated and non-coagulated liver, ex vivo and on normally perfused and underperfused human skin, in vivo.

Partial Wave Analysis of Coupled Photonic Structures

NASA Technical Reports Server (NTRS)

Fuller, Kirk A.; Smith, David D.; Curreri, Peter A. (Technical Monitor)

2002-01-01

The very high quality factors sustained by microcavity optical resonators are relevant to applications in wavelength filtering, routing, switching, modulation, and multiplexing/demultiplexing. Increases in the density of photonic elements require that attention be paid to how electromagnetic (EM) coupling modifies their optical properties. This is especially true when cavity resonances are involved, in which case, their characteristics may be fundamentally altered. Understanding the optical properties of microcavities that are near or in contact with photonic elements---such as other microcavities, nanostructures, couplers, and substrates---can be expected to advance our understanding of the roles that these structures may play in VLSI photonics, biosensors and similar device technologies. Wc present results from recent theoretical studies of the effects of inter- and intracavity coupling on optical resonances in compound spherical particles. Concentrically stratified spheres and bispheres constituted from homogeneous and stratified spheres are subjects of this investigation. A new formulation is introduced for the absorption of light in an arbitrary layer of a multilayered sphere, which is based on multiple reflections of the spherical partial waves of the Lorenz-Mie solution for scattering by a sphere. Absorption efficiencies, which can be used to profile cavity resonances and to infer fluorescence yields or the onset of nonlinear optical processes in the microcavities, are presented. Splitting of resonances in these multisphere systems is paid particular attention, and consequences for photonic device development and possible performance enhancements through carefully designed architectures that exploit EM coupling are considered.

Weakly nonlinear incompressible Rayleigh-Taylor instability in spherical and planar geometries

NASA Astrophysics Data System (ADS)

Zhang, J.; Wang, L. F.; Ye, W. H.; Guo, H. Y.; Wu, J. F.; Ding, Y. K.; Zhang, W. Y.; He, X. T.

2018-02-01

The relationship between the weakly nonlinear (WN) solutions of the Rayleigh-Taylor instability in spherical geometry [Zhang et al., Phys. Plasmas 24, 062703 (2017)] and those in planar geometry [Wang et al., Phys. Plasmas 19, 112706 (2012)] is analyzed. In the high-mode perturbation limit ( Pn(cos θ), n ≫1 ), it is found that at the equator, the contributions of mode P2 n along with its neighboring modes, mode P3 n along with its neighboring modes, and mode Pn at the third order along with its neighboring modes are equal to those of the second harmonic, the third harmonic, and the third-order feedback to the fundamental mode, respectively, in the planar case with a perturbation of the same wave vector and amplitude as those at the equator. The trends of WN results in spherical geometry towards the corresponding planar counterparts are found, and the convergence behaviors of the neighboring modes of Pn, P2 n , and P3 n are analyzed. Moreover, the spectra generated from the high-mode perturbations in the WN regime are provided. For low-mode perturbations, it is found that the fundamental modes saturate at larger amplitudes than the planar result. The geometry effect makes the bubbles at or near the equator grow faster than the bubbles in planar geometry in the WN regime.

Wavespace-Based Coherent Deconvolution

NASA Technical Reports Server (NTRS)

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

2012-01-01

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

Dynamic behaviour of a two-microbubble system under ultrasonic wave excitation.

PubMed

Huang, Xiao; Wang, Qian-Xi; Zhang, A-Man; Su, Jian

2018-05-01

Acoustic bubbles have wide and important applications in ultrasonic cleaning, sonochemistry and medical ultrasonics. A two-microbubble system (TMS) under ultrasonic wave excitation is explored in the present study, by using the boundary element method (BEM) based on the potential flow theory. A parametric study of the behaviour of a TMS has been carried out in terms of the amplitude and direction of ultrasound as well as the sizes and separation distance of the two bubbles. Three regimes of the dynamic behaviour of the TMS have been identified in terms of the pressure amplitude of the ultrasonic wave. When subject to a strong wave with the pressure amplitude of 1 atm or larger, the two microbubbles become non-spherical during the first cycle of oscillation, with two counter liquid jets formed. When subject to a weak wave with the pressure amplitude of less than 0.5 atm, two microbubbles may be attracted, repelled, or translate along the wave direction with periodic stable separation distance, depending on their size ratio. However, for the TMS under moderate waves, bubbles undergo both non-spherical oscillation and translation as well as liquid jet rebounding. Copyright © 2018 Elsevier B.V. All rights reserved.

Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid.

PubMed

Mitri, Farid G

2015-10-01

Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (θ = π) in the near field and the backscattering form function in the far field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) because of the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3-D directivity patterns illustrate the near- and far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.

II. Comment on “Critique and correction of the currently accepted solution of the infinite spherical well in quantum mechanics” by Huang Young-Sea and Thomann Hans-Rudolph

NASA Astrophysics Data System (ADS)

Prados, Antonio; Plata, Carlos A.

2016-12-01

We comment on the paper "Critique and correction of the currently accepted solution of the infinite spherical well in quantum mechanics" by Huang Young-Sea and Thomann Hans-Rudolph, EPL 115, 60001 (2016) .

Acoustic radiation force acting on elastic and viscoelastic spherical shells placed in a plane standing wave field.

PubMed

Mitri, F G

2005-08-01

The theory of the acoustic radiation force acting on elastic spherical shells suspended in a plane standing wave field is developed in relation to their thickness and the content of their hollow regions. The theory is modified to include the effect of a hysteresis type of absorption of compressional and shear waves in the material. The fluid-loading effect on the acoustic radiation force function Y(st) is analyzed as well. Results of numerical calculations are presented for a number of elastic and viscoelastic materials, with the hollow region filled with water or air. These results show how the damping due to absorption, the change of the interior fluid inside the shells' hollow regions, and the exterior fluid surrounding their structures, affect the acoustic radiation force.

Using Tikhonov Regularization for Spatial Projections from CSR Regularized Spherical Harmonic GRACE Solutions

NASA Astrophysics Data System (ADS)

Save, H.; Bettadpur, S. V.

2013-12-01

It has been demonstrated before that using Tikhonov regularization produces spherical harmonic solutions from GRACE that have very little residual stripes while capturing all the signal observed by GRACE within the noise level. This paper demonstrates a two-step process and uses Tikhonov regularization to remove the residual stripes in the CSR regularized spherical harmonic coefficients when computing the spatial projections. We discuss methods to produce mass anomaly grids that have no stripe features while satisfying the necessary condition of capturing all observed signal within the GRACE noise level.

A novel embeddable spherical smart aggregate for structural health monitoring: part I. Fabrication and electrical characterization

NASA Astrophysics Data System (ADS)

Kong, Qingzhao; Fan, Shuli; Bai, Xiaolong; Mo, Y. L.; Song, Gangbing

2017-09-01

Recently developed piezoceramic-based transducers, known as smart aggregates (SAs), have shown their applicability and versatility in various applications of structural health monitoring (SHM). The lead zirconate titanate (PZT) patches embedded inside SAs have different modes that are more suitable for generating or receiving different types of stress waves (e.g. P and S waves, each of which has a unique role in SHM). However, due to the geometry of the 2D PZT patch, the embedded SA can only generate or receive the stress wave in a single direction and thus greatly limits its applications. This paper is the first of a series of two companion papers that introduces the authors’ latest work in developing a novel, embeddable spherical smart aggregate (SSA) for the health monitoring of concrete structures. In addition to the 1D guided wave produced by SA, the SSA embedded in concrete structures can generate or receive omni-directional stress waves that can significantly improve the detection aperture and provide additional functionalities in SHM. In the first paper (Part I), the detailed fabrication procedures with the help of 3D printing technology and electrical characterization of the proposed SSA is presented. The natural frequencies of the SSA were experimentally obtained and further compared with the numerical results. In addition, the influence of the components’ thickness (spherical piezoceramic shell and epoxy) and outer radius (spherical piezoceramic shell and protection concrete) on the natural frequencies of the SSA were analytically studied. The results will help elucidate the key parameters that determine the natural frequencies of the SSA. The natural frequencies of the SSA can thus be designed for suitability in the damage detection of concrete structures. In the second paper (Part II), further numerical and experimental verifications on the performance of the proposed SSA in concrete structures will be discussed.

Electromagnetic retroreflection augmented by spherical and conical metasurfaces

NASA Astrophysics Data System (ADS)

Shang, Yuping; Shen, Zhongxiang

2017-11-01

The focus of this paper is on phase gradient metasurfaces conformal to spherical and conical bodies of revolution, with an aim of engineering retroreflections and therefore augmenting backscattering cross-sections of those three-dimensional geometries under the illumination of a plane electromagnetic wave. Based on the conducting sphere and cone, the effect of the geometric revolution property on the selection of the unit inclusion of metasurfaces is considered. The procedure for using the selected unit inclusion to implement the proper reflection phase gradient onto the illuminated surfaces of those objects is formulated in detail. Retroreflections resembling conducting plates under normal incidence are observed for both the conducting sphere and cone coated with conformal metasurfaces. As a result, the redirection-induced retroreflection effectively contributes to the backscattering cross-section enhancement. A good agreement between full-wave simulations and measurements demonstrates the validity and effectiveness of backscattering cross-section enhancement using spherical and conical metasurfaces.

On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening

NASA Astrophysics Data System (ADS)

Leigh, N. W. C.; Geller, A. M.; McKernan, B.; Ford, K. E. S.; Mac Low, M.-M.; Bellovary, J.; Haiman, Z.; Lyra, W.; Samsing, J.; O'Dowd, M.; Kocsis, B.; Endlich, S.

2018-03-01

We assess the contribution of dynamical hardening by direct three-body scattering interactions to the rate of stellar-mass black hole binary (BHB) mergers in galactic nuclei. We derive an analytic model for the single-binary encounter rate in a nucleus with spherical and disc components hosting a super-massive black hole (SMBH). We determine the total number of encounters NGW needed to harden a BHB to the point that inspiral due to gravitational wave emission occurs before the next three-body scattering event. This is done independently for both the spherical and disc components. Using a Monte Carlo approach, we refine our calculations for NGW to include gravitational wave emission between scattering events. For astrophysically plausible models, we find that typically NGW ≲ 10. We find two separate regimes for the efficient dynamical hardening of BHBs: (1) spherical star clusters with high central densities, low-velocity dispersions, and no significant Keplerian component and (2) migration traps in discs around SMBHs lacking any significant spherical stellar component in the vicinity of the migration trap, which is expected due to effective orbital inclination reduction of any spherical population by the disc. We also find a weak correlation between the ratio of the second-order velocity moment to velocity dispersion in galactic nuclei and the rate of BHB mergers, where this ratio is a proxy for the ratio between the rotation- and dispersion-supported components. Because discs enforce planar interactions that are efficient in hardening BHBs, particularly in migration traps, they have high merger rates that can contribute significantly to the rate of BHB mergers detected by the advanced Laser Interferometer Gravitational-Wave Observatory.

Topics in electromagnetic, acoustic, and potential scattering theory

NASA Astrophysics Data System (ADS)

Nuntaplook, Umaporn

With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves --- is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering in radially symmetric media is sufficient to gain insight into scattering in more complex media. Meeting the challenge of variable refractive indices and possibly complicated boundary conditions therefore requires accurate and efficient numerical methods, and where possible, analytic solutions to the radial equations from the governing scalar and vector wave equations (in acoustics and electromagnetic theory, respectively). Until relatively recently, researchers assumed a constant refractive index throughout the medium of interest. However, the most interesting and increasingly useful cases are those with non-constant refractive index profiles. In the majority of this dissertation the focus is on media with piecewise constant refractive indices in radially symmetric media. The method discussed is based on the solution of Maxwell's equations for scattering of plane electromagnetic waves from a dielectric (or "transparent") sphere in terms of the related Helmholtz equation. The main body of the dissertation (Chapters 2 and 3) is concerned with scattering from (i) a uniform spherical inhomogeneity embedded in an external medium with different properties, and (ii) a piecewise-uniform central inhomogeneity in the external medium. The latter results contain a natural generalization of the former (previously known) results. The link with time-independent quantum mechanical scattering, via morphology-dependent resonances (MDRs), is discussed in Chapter 2. This requires a generalization of the classical problem for scattering of a plane wave from a uniform spherically-symmetric inhomogeneity (in which the velocity of propagation is a function only of the radial coordinate r. i.e.. c = c(r)) to a piecewise-uniform inhomogeneity. In Chapter 3 the Jost-function formulation of potential scattering theory is used to solve the radial differential equation for scattering which can be converted into an integral equation corresponding via the Jost boundary conditions. The first two iterations for the zero angular momentum case l = 0 are provided for both two-layer and three-layer models. It is found that the iterative technique is most useful for long wavelengths and sufficiently small ratios of interior and exterior wavenumbers. Exact solutions are also provided for these cases. In Chapter 4 the time-independent quantum mechanical 'connection' is exploited further by generalizing previous work on a spherical well potential to the case where a delta 'function' potential is appended to the exterior of the well (for l ≠ 0). This corresponds to an idealization of the former approach to the case of a 'coated sphere'. The poles of the associated 'S-matrix' are important in this regard, since they correspond directly with the morphology-dependent resonances discussed in Chapter 2. These poles (for the l = 0 case, to compare with Nussenzveig's analysis) are tracked in the complex wavenumber plane as the strength of the delta function potential changes. Finally, a set of 4 Appendices is provided to clarify some of the connections between (i) the scattering of acoustic/electromagnetic waves from a penetrable/dielectric sphere and (ii) time-independent potential scattering theory in quantum mechanics. This, it is hoped, will be the subject of future work.

The frequency-difference and frequency-sum acoustic-field autoproducts.

PubMed

Worthmann, Brian M; Dowling, David R

2017-06-01

The frequency-difference and frequency-sum autoproducts are quadratic products of solutions of the Helmholtz equation at two different frequencies (ω + and ω - ), and may be constructed from the Fourier transform of any time-domain acoustic field. Interestingly, the autoproducts may carry wave-field information at the difference (ω + - ω - ) and sum (ω + + ω - ) frequencies even though these frequencies may not be present in the original acoustic field. This paper provides analytical and simulation results that justify and illustrate this possibility, and indicate its limitations. The analysis is based on the inhomogeneous Helmholtz equation and its solutions while the simulations are for a point source in a homogeneous half-space bounded by a perfectly reflecting surface. The analysis suggests that the autoproducts have a spatial phase structure similar to that of a true acoustic field at the difference and sum frequencies if the in-band acoustic field is a plane or spherical wave. For multi-ray-path environments, this phase structure similarity persists in portions of the autoproduct fields that are not suppressed by bandwidth averaging. Discrepancies between the bandwidth-averaged autoproducts and true out-of-band acoustic fields (with potentially modified boundary conditions) scale inversely with the product of the bandwidth and ray-path arrival time differences.

Pressure Distribution in a Squeeze Film Spherical Bearing with Rough Surfaces Lubricated by an Ellis Fluid

NASA Astrophysics Data System (ADS)

Jurczak, P.; Falicki, J.

2016-08-01

In this paper, the solution to a problem of pressure distribution in a curvilinear squeeze film spherical bearing is considered. The equations of motion of an Ellis pseudo-plastic fluid are presented. Using Christensen's stochastic model of rough surfaces, different forms of Reynolds equation for various types of surface roughness pattern are obtained. The analytical solutions of these equations for the cases of externally pressurized bearing and squeeze film bearing are presented. Analytical solutions for the film pressure are found for the longitudinal and circumferential roughness patterns. As a result the formulae expressing pressure distribution in the clearance of bearing lubricated by an Ellis fluid was obtained. The numerical considerations for a spherical bearing are given in detail.

The effect of reflector geometry on the acoustic field and bubble dynamics produced by an electrohydraulic shock wave lithotripter.

PubMed

Zhou, Yufeng; Zhong, Pei

2006-06-01

A theoretical model for the propagation of shock wave from an axisymmetric reflector was developed by modifying the initial conditions for the conventional solution of a nonlinear parabolic wave equation (i.e., the Khokhlov-Zabolotskaya-Kuznestsov equation). The ellipsoidal reflector of an HM-3 lithotripter is modeled equivalently as a self-focusing spherically distributed pressure source. The pressure wave form generated by the spark discharge of the HM-3 electrode was measured by a fiber optic probe hydrophone and used as source conditions in the numerical calculation. The simulated pressure wave forms, accounting for the effects of diffraction, nonlinearity, and thermoviscous absorption in wave propagation and focusing, were compared with the measured results and a reasonably good agreement was found. Furthermore, the primary characteristics in the pressure wave forms produced by different reflector geometries, such as that produced by a reflector insert, can also be predicted by this model. It is interesting to note that when the interpulse delay time calculated by linear geometric model is less than about 1.5 micros, two pulses from the reflector insert and the uncovered bottom of the original HM-3 reflector will merge together. Coupling the simulated pressure wave form with the Gilmore model was carried out to evaluate the effect of reflector geometry on resultant bubble dynamics in a lithotripter field. Altogether, the equivalent reflector model was found to provide a useful tool for the prediction of pressure wave form generated in a lithotripter field. This model may be used to guide the design optimization of reflector geometries for improving the performance and safety of clinical lithotripters.

The effect of reflector geometry on the acoustic field and bubble dynamics produced by an electrohydraulic shock wave lithotripter

PubMed Central

Zhou, Yufeng; Zhong, Pei

2007-01-01

A theoretical model for the propagation of shock wave from an axisymmetric reflector was developed by modifying the initial conditions for the conventional solution of a nonlinear parabolic wave equation (i.e., the Khokhlov–Zabolotskaya–Kuznestsov equation). The ellipsoidal reflector of an HM-3 lithotripter is modeled equivalently as a self-focusing spherically distributed pressure source. The pressure wave form generated by the spark discharge of the HM-3 electrode was measured by a fiber optic probe hydrophone and used as source conditions in the numerical calculation. The simulated pressure wave forms, accounting for the effects of diffraction, nonlinearity, and thermoviscous absorption in wave propagation and focusing, were compared with the measured results and a reasonably good agreement was found. Furthermore, the primary characteristics in the pressure wave forms produced by different reflector geometries, such as that produced by a reflector insert, can also be predicted by this model. It is interesting to note that when the interpulse delay time calculated by linear geometric model is less than about 1.5 μs, two pulses from the reflector insert and the uncovered bottom of the original HM-3 reflector will merge together. Coupling the simulated pressure wave form with the Gilmore model was carried out to evaluate the effect of reflector geometry on resultant bubble dynamics in a lithotripter field. Altogether, the equivalent reflector model was found to provide a useful tool for the prediction of pressure wave form generated in a lithotripter field. This model may be used to guide the design optimization of reflector geometries for improving the performance and safety of clinical lithotripters. PMID:16838506

Development of fully non-inductive plasmas heated by medium and high-harmonic fast waves in the national spherical torus experiment upgrade

NASA Astrophysics Data System (ADS)

Taylor, G.; Poli, F.; Bertelli, N.; Harvey, R. W.; Hosea, J. C.; Mueller, D.; Perkins, R. J.; Phillips, C. K.; Raman, R.

2015-12-01

A major challenge for spherical tokamak development is to start-up and ramp-up the plasma current (Ip) without using a central solenoid. Experiments in the National Spherical Torus eXperiment (NSTX) demonstrated that 1.4 MW of 30 MHz high-harmonic fast wave (HHFW) power could generate an Ip = 300 kA H-mode discharge with a non-inductive Ip fraction, fNI ˜ 0.7. The discharge had an axial toroidal magnetic field (BT(0)) of 0.55 T, the maximum BT(0) available on NSTX. NSTX has undergone a major upgrade (NSTX-U), that will eventually allow the generation of BT(0) ≤ 1 T and Ip ≤ 2 MA plasmas. Full wave simulations of 30 MHz HHFW and medium harmonic fast wave (MHFW) heating in NSTX-U predict significantly reduced FW power loss in the plasma edge at the higher BT(0) achievable in NSTX-U. HHFW experiments will aim to generate stable, fNI ˜ 1, Ip = 300 kA H-mode plasmas and to ramp Ip from 250 to 400 kA with FW power. Time-dependent TRANSP simulations are used to develop non-inductive Ip ramp-up and sustainment using 30 MHz FW power. This paper presents results from these RF simulations and plans for developing non-inductive plasmas heated by FW power.

Exact simulation of polarized light reflectance by particle deposits

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

On the Exit Boundary Condition for One-Dimensional Calculations of Pulsed Detonation Engine Performance

NASA Technical Reports Server (NTRS)

Wilson, Jack; Paxson, Daniel E.

2002-01-01

In one-dimensional calculations of pulsed detonation engine (PDE) performance, the exit boundary condition is frequently taken to be a constant static pressure. In reality, for an isolated detonation tube, after the detonation wave arrives at the exit plane, there will be a region of high pressure, which will gradually return to ambient pressure as an almost spherical shock wave expands away from the exit, and weakens. Initially, the flow is supersonic, unaffected by external pressure, but later becomes subsonic. Previous authors have accounted for this situation either by assuming the subsonic pressure decay to be a relaxation phenomenon, or by running a two-dimensional calculation first, including a domain external to the detonation tube, and using the resulting exit pressure temporal distribution as the boundary condition for one-dimensional calculations. These calculations show that the increased pressure does affect the PDE performance. In the present work, a simple model of the exit process is used to estimate the pressure decay time. The planar shock wave emerging from the tube is assumed to transform into a spherical shock wave. The initial strength of the spherical shock wave is determined from comparison with experimental results. Its subsequent propagation, and resulting pressure at the tube exit, is given by a numerical blast wave calculation. The model agrees reasonably well with other, limited, results. Finally, the model was used as the exit boundary condition for a one-dimensional calculation of PDE performance to obtain the thrust wall pressure for a hydrogen-air detonation in tubes of length to diameter ratio (L/D) of 4, and 10, as well as for the original, constant pressure boundary condition. The modified boundary condition had no performance impact for values of L/D > 10, and moderate impact for L/D = 4.

The Numerical Studies Program for the Atmospheric General Circulation Experiment (AGCE) for Spacelab Flights

NASA Technical Reports Server (NTRS)

Fowlis, W. W. (Editor); Davis, M. H. (Editor)

1981-01-01

The atmospheric general circulation experiment (AGCE) numerical design for Spacelab flights was studied. A spherical baroclinic flow experiment which models the large scale circulations of the Earth's atmosphere was proposed. Gravity is simulated by a radial dielectric body force. The major objective of the AGCE is to study nonlinear baroclinic wave flows in spherical geometry. Numerical models must be developed which accurately predict the basic axisymmetric states and the stability of nonlinear baroclinic wave flows. A three dimensional, fully nonlinear, numerical model and the AGCE based on the complete set of equations is required. Progress in the AGCE numerical design studies program is reported.

Absolute Equation-of-State Measurement for Polystyrene from 25 - 60 Mbar Using a Spherically Converging Shock Wave

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

Glenzer, Siegfried

We have developed an experimental platform for the National Ignition Facility (NIF) that uses spherically converging shock waves for absolute equation of state (EOS) measurements along the principal Hugoniot. In this Letter we present radiographic compression measurements for polystyrene that were taken at shock pressures reaching 60 Mbar (6 TPa). This significantly exceeds previously published results obtained on the Nova laser [Cauble et al., Phys. Rev. Lett. 80, 1248 (1998)] at strongly improved precision, allowing to discriminate between different EOS models. We find excellent agreement with Kohn-Sham Density Functional Theory based molecular dynamics simulations.

Practical algorithms for simulation and reconstruction of digital in-line holograms.

PubMed

Latychevskaia, Tatiana; Fink, Hans-Werner

2015-03-20

Here we present practical methods for simulation and reconstruction of in-line digital holograms recorded with plane and spherical waves. The algorithms described here are applicable to holographic imaging of an object exhibiting absorption as well as phase-shifting properties. Optimal parameters, related to distances, sampling rate, and other factors for successful simulation and reconstruction of holograms are evaluated and criteria for the achievable resolution are worked out. Moreover, we show that the numerical procedures for the reconstruction of holograms recorded with plane and spherical waves are identical under certain conditions. Experimental examples of holograms and their reconstructions are also discussed.

On the generation of horizontal shear waves by underground explosions in jointed rocks

DOE PAGES

Vorobiev, Oleg; Ezzedine, Souheil; Antoun, Tarabay; ...

2015-02-04

This paper describes computational studies of non-spherical ground motions generated by spherical explosions in a heavily jointed granite formation. Various factors affecting the shear wave generation are considered, including joint spacing, orientation, persistence and properties. Simulations are performed both in 2D for a single joint set to elucidate the basic response mechanisms, and in 3D for multiple joint sets to realistically represent in situ conditions in a realistic geologic setting. The joints are modeled explicitly using both contact elements and weakness planes in the material. Simulations are performed both deterministically and stochastically to quantify the effects of geologic uncertainties onmore » near field ground motions. The mechanical properties of the rock and the joints as well as the joint spacing and orientation are taken from experimental test data and geophysical logs corresponding to the Climax Stock granitic outcrop, which is the geologic setting of the Source Physics Experiment (SPE). Agreement between simulation results and near field wave motion data from SPE enables newfound understanding of the origin and extent of non-spherical motions associated with underground explosions in fractured geologic media.« less

Transient Flows in a Pipe System with Pump Shut-Down and the Simultaneous Closing of a Spherical Valve

NASA Astrophysics Data System (ADS)

Zhang, Zh.

2016-11-01

Because of the limited value of the wave propagation speed in water the propagation of a pressure surge in transient flows can be tracked in the time series. This enables both the pressure head and the flow velocity in pipe flows to be determined as a function of both the coordinate along the pipe and the time. The propagation of the pressure surge includes both wave transmission and reflection. The latter occurs where the flow section is changed. The wave tracking method has been demonstrated as highly accurate and subsequently was applied to much more complex hydraulic systems, in which the pump is shut off and the spherical valve is simultaneously progressively closed. A combined four-quadrant characteristic of the pump and a spherical valve has been worked out, with which the computational procedure for the transient flow in the complex system could be significantly simplified. It has been demonstrated that not only the pressure surge in the hydraulic system but also the rotational speed of the pump could be satisfactorily computed. The computational algorithm has been demonstrated as quite simple, so that all calculations could be performed simply by means of the Microsoft Excel module.

Laboratory Experiments to Study Spherical, Iron Oxide Concretion Growth Without Solid Nuclei: Implications for Understanding Meridiani "Blueberries"

NASA Astrophysics Data System (ADS)

Ormö, J.; Souza-Egipsy, V.; Chan, M. A.; Park, A. J.; Stich, M.; Komatsu, G.

2006-03-01

Spherical hematite concretions can form without a nucleus. Self-organized zones of super-saturated solution cause spherical precipitates of amorphous iron-hydroxide. Diffusion of Fe ions towards the outer perimeter of the amorphous sphere forms a rind, which then grows inwards.

A complete set of two-dimensional harmonic vortices on a spherical surface

NASA Astrophysics Data System (ADS)

Esparza, Christian; Rendón, Pablo Luis; Ley Koo, Eugenio

2018-03-01

The solutions of the Euler equations on a spherical surface are constructed, starting from a vector velocity potential A in the radial direction and with a two-dimensional spherical harmonic variation of order m and well-defined parity under \\varphi \\mapsto -\\varphi . The solutions are well-behaved on the entire surface and continuous at the position of a parallel circle θ ={θ }0, where the vorticity is shown to be harmonically distributed. The velocity field is evaluated as the curl of the vector potential: it is shown that the velocity is divergenceless and distributed on the spherical surface. Its polar components at the parallel circle are shown to be continuous, confirming its divergenceless nature, while its azimuthal components are discontinuous at the circle, and their discontinuity is a measure of the vorticity in the radial direction. A closed form for the velocity field lines is also obtained in terms of fixed values of the scalar harmonic function associated with the vector potential. Additionally, the connections of the solutions on a spherical surface with their circular, elliptic and bipolar counterparts on the equatorial plane are implemented via stereographic projections.

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

NASA Astrophysics Data System (ADS)

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

2004-12-01

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

Inertial modes and their transition to turbulence in a differentially rotating spherical gap flow

NASA Astrophysics Data System (ADS)

Hoff, Michael; Harlander, Uwe; Andrés Triana, Santiago; Egbers, Christoph

2016-04-01

We present a study of inertial modes in a spherical shell experiment. Inertial modes are Coriolis-restored linear wave modes, often arise in rapidly-rotating fluids (e.g. in the Earth's liquid outer core [1]). Recent experimental works showed that inertial modes exist in differentially rotating spherical shells. A set of particular inertial modes, characterized by (l,m,ˆω), where l, m is the polar and azimuthal wavenumber and ˆω = ω/Ωout the dimensionless frequency [2], has been found. It is known that they arise due to eruptions in the Ekman boundary layer of the outer shell. But it is an open issue why only a few modes develop and how they get enhanced. Kelley et al. 2010 [3] showed that some modes draw their energy from detached shear layers (e.g. Stewartson layers) via over-reflection. Additionally, Rieutord et al. (2012) [4] found critical layers within the shear layers below which most of the modes cannot exist. In contrast to other spherical shell experiments, we have a full optical access to the flow. Therefore, we present an experimental study of inertial modes, based on Particle-Image-Velocimetry (PIV) data, in a differentially rotating spherical gap flow where the inner sphere is subrotating or counter-rotating at Ωin with respect to the outer spherical shell at Ωout, characterized by the Rossby number Ro = (Ωin - Ωout)/Ωout. The radius ratio of η = 1/3, with rin = 40mm and rout = 120mm, is close to that of the Earth's core. Our apparatus is running at Ekman numbers (E ≈ 10-5, with E = ν/(Ωoutrout2), two orders of magnitude higher than most of the other experiments. Based on a frequency-Rossby number spectrogram, we can partly confirm previous considerations with respect to the onset of inertial modes. In contrast, the behavior of the modes in the counter-rotation regime is different. We found a triad interaction between three dominant inertial modes, where one is a slow axisymmetric Rossby mode [5]. We show that the amplitude of the most dominant mode (l,m,ˆω) = (3,2,˜ 0.71) is increasing with increasing |Ro| until a critical Rossby number Rocrit. Accompanying with this is an increase of the zonal mean flow outside the tangent cylinder, leading to enhanced angular momentum transport. At the particular Rocrit, the wave mode, and the entire flow, breaks up into smaller-scale turbulence [6], together with a strong increase of the zonal mean flow inside the tangent cylinder. We found that the critical Rossby number scales approximately with E1/5. References [1] Aldridge, K. D.; Lumb, L. I. (1987): Inertial waves identified in the Earth's fluid outer core. Nature 325 (6103), S. 421-423. DOI: 10.1038/325421a0. [2] Greenspan, H. P. (1968): The theory of rotating fluids. London: Cambridge U.P. (Cambridge monographs on mechanics and applied mathematics). [3] Kelley, D. H.; Triana, S. A.; Zimmerman, D. S.; Lathrop, D. P. (2010): Selection of inertial modes in spherical Couette flow. Phys. Rev. E 81 (2), 26311. DOI: 10.1103/PhysRevE.81.026311. [4] Rieutord, M.; Triana, S. A.; Zimmerman, D. S.; Lathrop, D. P. (2012): Excitation of inertial modes in an experimental spherical Couette flow. Phys. Rev. E 86 (2), 026304. DOI: 10.1103/PhysRevE.86.026304. [5] Hoff, M., Harlander, U., Egbers, C. (2016): Experimental survey of linear and nonlinear inertial waves and wave instabilities in a spherical shell. J. Fluid Mech., (in print) [6] Kerswell, R. R. (1999): Secondary instabilities in rapidly rotating fluids: inertial wave breakdown. Journal of Fluid Mechanics 382, S. 283-306. DOI: 10.1017/S0022112098003954.

Mapping the African thunderstorm center in absolute units using Schumann resonance spectral decomposition method

NASA Astrophysics Data System (ADS)

Dyrda, Michal; Kulak, Andrzej; Mlynarczyk, Janusz

2015-04-01

Monitoring of the global lightning activity provides a very useful tool to study the global warming phenomenon and the other longer-scale climate changes induced by humans. The lightning activity is measured using various observational methods form space (optical satellite observations) as well as from the ground mostly by VLF /LF lightning detection networks, i.e. World Wide Lightning Location Network (WWLLN) or lightning detection network (LINET) in Europe. However, the global lightning activity measurements are possible only in the ELF range. Here we examine the African thunderstorm activity center, which is the most violent and active one. In a spherical damped resonator, such as the Earth-ionosphere cavity, the electromagnetic field is described by the solution of an inhomogeneous wave equation. For such equation the general solution can be expressed by the superposition of the solutions of the homogeneous equation, describing the resonance field, and the component, which is quite strong close to the source and weakens with source-observer separation. Thus, the superposition of the standing wave field with the field of traveling waves, which supply the energy from the lighting discharges to the global resonator, is a main reason for an asymmetric shape of the observational Schumann resonance (SR) power spectra, which highly deviate from the Lorentz curves. It is possible to separate this component from the signal using the spectrum decomposition method proposed by Kułak et al. [2006]. In our approach, we apply the inverse problem solution for determining the distance of the dominant lightning source. The distances to the thunderstorm centers are calculated using the analytical models for the electromagnetic waves propagation in the Earth-ionosphere cavity. Such forms of analytic solutions of the resonant field in the spherical cavity is the zonal harmonic series representation, described by Mushtak and Williams [2002] and we calculated the sets of such curves for different source-observer separations, starting at 1 Mm up to 20 Mm with a step of 0.1 Mm. We selected two observational data sets, collected during different seasons of the year, from our Hylaty station, located in Poland. The data were binned in 10-minute files for which the SR power spectra were derived. In the next step a decomposition curve describing 7 asymmetric SR modes was fitted to the observational data. To compare the resulted decomposed power spectra with analytic model we use chi-squared test and hence we obtained the distances to the dominant thunderstorm center, located in Africa. We computed the monthly lighting activity maps and possible locations on the African continent with the spatial resolution of 1 degree and temporal resolution of 10 minute. Moreover we calculated the thunderstorm intensities in physical units, which are of the order of 2 × 1011 [C2 m2 s-1]. We also notice the seasonal variations of the African thunderstorm centers distributions and as well as intensities. Finally, we compared our results with satellite data recorded by the Lighting Imaging Sensor (LIS) and we obtained very high correlation. Acknowledgements. This work has been supported by the National Science Centre grant 2012/04/M/ST10/00565. The numerical computations were done using the PL-Grid infrastructure.

An exact solution to the Einstein-Maxwell equations representing a nonspherical, highly charged object

NASA Astrophysics Data System (ADS)

Menon, Govind K.

The Reissner-Nordstrom solution possesses a naked singularity when e2 > m2, where m is the mass and e is the net charge of the system. Also, the singularity at r = 0 is repulsive (i.e., no timelike geodesics (neutral particles) can reach the singularity). These unusual properties of the Reissner-Nordstrom geometry are considered as an accident resulting from the highly symmetric nature of the space-time. Here we wish to generalize the condition of spherical symmetry to axial symmetry and to probe into the issues of naked singularity and gravitational repulsion. To do this, we must construct a nonspherical solution to the Einstein-Maxwell set of equations in the event that e2 > m2. The Erez-Rosen extension of the vacuum Schwarzschild solution to the non-spherical case gave one of the first physically significant solutions of the Einstein field equations. Nonvacuum extensions of the Erez-Rosen solution representing a non-spherical mass containing a very high net charge (i.e., when e2 > m2) will be discussed. The special case of spherical symmetry, as would be expected, results in the Reissner-Nordstrom solution. The search for the physical singularities involves the calculation of a nontrivial scalar constructed from the Riemann curvature tensor. As it turns out, the resulting geometry does indeed possess a naked singularity. In addition, the space-time also entertains gravitational repulsion. However, unlike the Reissner-Nordstrom solution, it has been found that all timelike geodesics are not necessarily repelled from the origin.

Properties of the Average Distribution of Equatorial Kelvin Waves Investigated with the GROGRAT Ray Tracer

DTIC Science & Technology

2009-01-01

spheric quasi-biennial oscillation ( QBO ). In this paper we combine several measured data sets with the Gravity wave Regional Or Global RAy Tracer (GROGRAT...equatorial wave modes and a broad spectrum of gravity waves (GWs) Kelvin waves are one of the main drivers of the quasi-biennial oscil- lation ( QBO ) of the...and dy- namics in the stratosphere and mesosphere (even at high lati- tudes) are modulated or influenced by the QBO , showing the importance of the

Introduction to Radar Polarimetry

DTIC Science & Technology

1991-04-23

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

Compact range for variable-zone measurements

DOEpatents

Burnside, Walter D.; Rudduck, Roger C.; Yu, Jiunn S.

1988-08-02

A compact range for testing antennas or radar targets includes a source for directing energy along a feedline toward a parabolic reflector. The reflected wave is a spherical wave with a radius dependent on the distance of the source from the focal point of the reflector.

Compact range for variable-zone measurements

DOEpatents

Burnside, Walter D.; Rudduck, Roger C.; Yu, Jiunn S.

1988-01-01

A compact range for testing antennas or radar targets includes a source for directing energy along a feedline toward a parabolic reflector. The reflected wave is a spherical wave with a radius dependent on the distance of the source from the focal point of the reflector.

Precision flyer initiator

DOEpatents

Frank, A.M.; Lee, R.S.

1998-05-26

A precision flyer initiator forms a substantially spherical detonation wave in a high explosive (HE) pellet. An explosive driver, such as a detonating cord, a wire bridge circuit or a small explosive, is detonated. A flyer material is sandwiched between the explosive driver and an end of a barrel that contains an inner channel. A projectile or ``flyer`` is sheared from the flyer material by the force of the explosive driver and projected through the inner channel. The flyer than strikes the HE pellet, which is supported above a second end of the barrel by a spacer ring. A gap or shock decoupling material delays the shock wave in the barrel from predetonating the HE pellet before the flyer. A spherical detonation wave is formed in the HE pellet. Thus, a shock wave traveling through the barrel fails to reach the HE pellet before the flyer strikes the HE pellet. The precision flyer initiator can be used in mining devices, well-drilling devices and anti-tank devices. 10 figs.

Precision flyer initiator

DOEpatents

Frank, Alan M.; Lee, Ronald S.

1998-01-01

A precision flyer initiator forms a substantially spherical detonation wave in a high explosive (HE) pellet. An explosive driver, such as a detonating cord, a wire bridge circuit or a small explosive, is detonated. A flyer material is sandwiched between the explosive driver and an end of a barrel that contains an inner channel. A projectile or "flyer" is sheared from the flyer material by the force of the explosive driver and projected through the inner channel. The flyer than strikes the HE pellet, which is supported above a second end of the barrel by a spacer ring. A gap or shock decoupling material delays the shock wave in the barrel from predetonating the HE pellet before the flyer. A spherical detonation wave is formed in the HE pellet. Thus, a shock wave traveling through the barrel fails to reach the HE pellet before the flyer strikes the HE pellet. The precision flyer initiator can be used in mining devices, well-drilling devices and anti-tank devices.

A numerical and experimental study of three-dimensional liquid sloshing in a rotating spherical container

NASA Technical Reports Server (NTRS)

Chen, Kuo-Huey; Kelecy, Franklyn J.; Pletcher, Richard H.

1992-01-01

A numerical and experimental study of three dimensional liquid sloshing inside a partially-filled spherical container undergoing an orbital rotating motion is described. Solutions of the unsteady, three-dimensional Navier-Stokes equations for the case of a gradual spin-up from rest are compared with experimental data obtained using a rotating test rig fitted with two liquid-filled spherical tanks. Data gathered from several experiments are reduced in terms of a dimensionless free surface height for comparison with transient results from the numerical simulations. The numerical solutions are found to compare favorably with the experimental data.

Schwarzschild and Kerr solutions of Einstein's field equation: An Introduction

NASA Astrophysics Data System (ADS)

Heinicke, Christian; Hehl, Friedrich W.

2015-12-01

Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric solution, the Kerr solution. The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. The Kerr solution is only unique if the multipole moments of its mass and its angular momentum take on prescribed values. Its metric can be interpreted as the exterior gravitational field of a suitably rotating mass distribution. Both solutions describe objects exhibiting an event horizon, a frontier of no return. The corresponding notion of a black hole is explained to some extent. Eventually, we present some generalizations of the Kerr solution.

Effect of zone size on the convergence of exact solutions for diffusion in single phase systems with planar, cylindrical or spherical geometry

NASA Technical Reports Server (NTRS)

Unnam, J.; Tenney, D. R.

1981-01-01

Exact solutions for diffusion in single phase binary alloy systems with constant diffusion coefficient and zero-flux boundary condition have been evaluated to establish the optimum zone size of applicability. Planar, cylindrical and spherical interface geometry, and finite, singly infinite, and doubly infinite systems are treated. Two solutions are presented for each geometry, one well suited to short diffusion times, and one to long times. The effect of zone-size on the convergence of these solutions is discussed. A generalized form of the diffusion solution for doubly infinite systems is proposed.

Mean-force-field and mean-spherical approximations for the electric microfield distribution at a charged point in the charged-hard-particles fluid

NASA Astrophysics Data System (ADS)

Rosenfeld, Yaakov

1989-01-01

The linearized mean-force-field approximation, leading to a Gaussian distribution, provides an exact formal solution to the mean-spherical integral equation model for the electric microfield distribution at a charged point in the general charged-hard-particles fluid. Lado's explicit solution for plasmas immediately follows this general observation.

Construction of SO(5)⊃SO(3) spherical harmonics and Clebsch-Gordan coefficients

NASA Astrophysics Data System (ADS)

Caprio, M. A.; Rowe, D. J.; Welsh, T. A.

2009-07-01

The SO(5)⊃SO(3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU(1,1)×SO(5) basis. We present a computer code for explicit construction of the SO(5)⊃SO(3) spherical harmonics and use them to compute the Clebsch-Gordan coefficients needed for collective model calculations in an SO(3)-coupled basis. With these Clebsch-Gordan coefficients it becomes possible to compute the matrix elements of collective model observables by purely algebraic methods. Program summaryProgram title: GammaHarmonic Catalogue identifier: AECY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 346 421 No. of bytes in distributed program, including test data, etc.: 16 037 234 Distribution format: tar.gz Programming language: Mathematica 6 Computer: Any which supports Mathematica Operating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux Classification: 4.2 Nature of problem: Explicit construction of SO(5) ⊃ SO(3) spherical harmonics on S. Evaluation of SO(3)-reduced matrix elements and SO(5) ⊃ SO(3) Clebsch-Gordan coefficients (isoscalar factors). Solution method: Construction of SO(5) ⊃ SO(3) spherical harmonics by orthonormalization, obtained from a generating set of functions, according to the method of Rowe, Turner, and Repka [1]. Matrix elements and Clebsch-Gordan coefficients follow by construction and integration of SO(3) scalar products. Running time: Depends strongly on the maximum SO(5) and SO(3) representation labels involved. A few minutes for the calculation in the Mathematica notebook. References: [1] D.J. Rowe, P.S. Turner, J. Repka, J. Math. Phys. 45 (2004) 2761.

Direct solution for thermal stresses in a nose cap under an arbitrary axisymmetric temperature distribution

NASA Technical Reports Server (NTRS)

Davis, Randall C.

1988-01-01

The design of a nose cap for a hypersonic vehicle is an iterative process requiring a rapid, easy to use and accurate stress analysis. The objective of this paper is to develop such a stress analysis technique from a direct solution of the thermal stress equations for a spherical shell. The nose cap structure is treated as a thin spherical shell with an axisymmetric temperature distribution. The governing differential equations are solved by expressing the stress solution to the thermoelastic equations in terms of a series of derivatives of the Legendre polynomials. The process of finding the coefficients for the series solution in terms of the temperature distribution is generalized by expressing the temperature along the shell and through the thickness as a polynomial in the spherical angle coordinate. Under this generalization the orthogonality property of the Legendre polynomials leads to a sequence of integrals involving powers of the spherical shell coordinate times the derivative of the Legendre polynomials. The coefficients of the temperature polynomial appear outside of these integrals. Thus, the integrals are evaluated only once and their values tabulated for use with any arbitrary polynomial temperature distribution.

Numerical and experimental investigations of dependence of photoacoustic signals from gold nanoparticles on the optical properties

NASA Astrophysics Data System (ADS)

Okawa, Shinpei; Hirasawa, Takeshi; Sato, Ryota; Kushibiki, Toshihiro; Ishihara, Miya; Teranishi, Toshiharu

2018-06-01

Gold nanoparticles (AuNPs) are used as a contrast agent of the photoacoustic (PA) imaging. The efficiency of AuNPs has been discussed with the absorption cross section. However, the effects of the scattering of the light by AuNPs and surrounding medium on the PA signal from AuNPs have not been discussed. The PA signals from the aqueous solution of AuNPs were examined in the numerical simulation and the experiment. In the numerical simulation, the absorption and scattering cross sections of spherical and polyhedral AuNPs were calculated by Mie theory and discrete dipole approximation. Monte Carlo simulation calculated the absorbed light energy in the aqueous solution of AuNPs. Based on the PA wave equation, the PA signals were simulated. In the experiment, the PA signal from the aqueous solution of AuNP was measured by use of a piezoelectric film and a Q-switched Nd:YAG laser operated at 532 nm. The results of the numerical simulation and the experiment agreed well. In the numerical simulation and the experiment, a single Au nanocube with 50-nm edge generated the peak value of the PA signal significantly. It was approximately 350 times and twice as large as the peak values of the spherical AuNPs with 10- and 50-nm diameters, respectively. The peak value of the PA signal depended on both the absorption and scattering coefficients of the AuNPs and the surrounding medium. The peak value increased with the scattering coefficient in a quadratic manner. The character of the temporal profile of the PA signal such as full width at half maximum depended on the scattering coefficient of the AuNPs.

Numerical and experimental investigations of dependence of photoacoustic signals from gold nanoparticles on the optical properties

NASA Astrophysics Data System (ADS)

Okawa, Shinpei; Hirasawa, Takeshi; Sato, Ryota; Kushibiki, Toshihiro; Ishihara, Miya; Teranishi, Toshiharu

2018-04-01

Gold nanoparticles (AuNPs) are used as a contrast agent of the photoacoustic (PA) imaging. The efficiency of AuNPs has been discussed with the absorption cross section. However, the effects of the scattering of the light by AuNPs and surrounding medium on the PA signal from AuNPs have not been discussed. The PA signals from the aqueous solution of AuNPs were examined in the numerical simulation and the experiment. In the numerical simulation, the absorption and scattering cross sections of spherical and polyhedral AuNPs were calculated by Mie theory and discrete dipole approximation. Monte Carlo simulation calculated the absorbed light energy in the aqueous solution of AuNPs. Based on the PA wave equation, the PA signals were simulated. In the experiment, the PA signal from the aqueous solution of AuNP was measured by use of a piezoelectric film and a Q-switched Nd:YAG laser operated at 532 nm. The results of the numerical simulation and the experiment agreed well. In the numerical simulation and the experiment, a single Au nanocube with 50-nm edge generated the peak value of the PA signal significantly. It was approximately 350 times and twice as large as the peak values of the spherical AuNPs with 10- and 50-nm diameters, respectively. The peak value of the PA signal depended on both the absorption and scattering coefficients of the AuNPs and the surrounding medium. The peak value increased with the scattering coefficient in a quadratic manner. The character of the temporal profile of the PA signal such as full width at half maximum depended on the scattering coefficient of the AuNPs.

Calculation of the Transition Matrix for the Scattering of Acoustic Waves from a Thin Elastic Spherical Shell Using the ATILA Finite Element Code

DTIC Science & Technology

1994-03-01

products of radial Hankel functions and spherical harmonics. The chosen driving frequency was 474 Hz, corresponding to a value of ka 1, where k is the...spherical harmonics. The chosen driving frequency was 474 Hz, corresponding to a value of ka = 1, where k is the wavenumber of sound in water and a is...wife Adriana for her support, understanding, and for her help in typing this thesis. vi I. INTRODUCTION The utilization of sonar systems in

Modeling of oxidation of aluminum nanoparticles by using Cabrera Mott Model

NASA Astrophysics Data System (ADS)

Ramazanova, Zamart; Zyskin, Maxim; Martirosyan, Karen

2012-10-01

Our research focuses on modeling new Nanoenergetic Gas-Generator (NGG) formulations that rapidly release a large amount of gaseous products and generates shock and pressure waves. Nanoenergetic thermite reagents include mixtures of Al and metal oxides such as bismuth trioxide and iodine pentoxide. The research problem is considered a spherically symmetric case and used the Cabrera Mott oxidation model to describe the kinetics of oxide growth on spherical Al nanoparticles for evaluating reaction time which a process of the reaction with oxidizer happens on the outer part of oxide layer of aluminum ions are getting in contact with an oxidizing agent and react. We assumed that a ball of Al of radius 20 to 50 nm is covered by a thin oxide layer 2-4 nm and is surrounded by abundant amount of oxygen stored by oxidizers. The ball is rapidly heated up to ignition temperature to initiate self-sustaining oxidation reaction. As a result highly exothermic reaction is generated. In the oxide layer of excess concentrations of electrons and ions are dependent on the electric field potential with the corresponding of the Gibbs factors and that it conducts to the solution of a nonlinear Poisson equation for the electric field potential in a moving boundary domain. Motion of the boundary is determined by the gradient of a solution on the boundary. We investigated oxidation model numerically, using the COMSOL software utilizing finite element analysis. The computing results demonstrate that oxidation rate increases with the decreasing particle radius.

A black hole with torsion in 5D Lovelock gravity

NASA Astrophysics Data System (ADS)

Cvetković, B.; Simić, D.

2018-03-01

We analyze static spherically symmetric solutions of five dimensional (5D) Lovelock gravity in the first order formulation. In the Riemannian sector, when torsion vanishes, the Boulware–Deser black hole represents a unique static spherically symmetric black hole solution for the generic choice of the Lagrangian parameters. We show that a special choice of the Lagrangian parameters, different from the Lovelock Chern–Simons gravity, leads to the existence of a static black hole solution with torsion, the metric of which is asymptotically anti-de Sitter (AdS). We calculate the conserved charges and thermodynamical quantities of this black hole solution.

Geometric scalar theory of gravity beyond spherical symmetry

NASA Astrophysics Data System (ADS)

Moschella, U.; Novello, M.

2017-04-01

We construct several exact solutions for a recently proposed geometric scalar theory of gravity. We focus on a class of axisymmetric geometries and a big-bang-like geometry and discuss their Lorentzian character. The axisymmetric solutions are parametrized by an integer angular momentum l . The l =0 (spherical) case gives rise to the Schwarzschild geometry. The other solutions have naked singular surfaces. While not a priori obvious, all the solutions that we present here are globally Lorentzian. The Lorentzian signature appears to be a robust property of the disformal geometries solving the vacuum geometric scalar theory of gravity equations.

Compact range for variable-zone measurements

DOEpatents

Burnside, W.D.; Rudduck, R.C.; Yu, J.S.

1987-02-27

A compact range for testing antennas or radar targets includes a source for directing energy along a feedline toward a parabolic reflector. The reflected wave is a spherical wave with a radius dependent on the distance of the source from the focal point of the reflector. 2 figs.

Development of response models for the Earth Radiation Budget Experiment (ERBE) sensors. Part 2: Analysis of the ERBE integrating sphere ground calibration

NASA Technical Reports Server (NTRS)

Halyo, Nesim; Taylor, Deborah B.

1987-01-01

An explicit solution of the spectral radiance leaving an arbitrary point on the wall of a spherical cavity with diffuse reflectivity is obtained. The solution is applicable to spheres with an arbitrary number of openings of any size and shape, an arbitrary number of light sources with possible non-diffuse characteristics, a non-uniform sphere wall temperature distribution, non-uniform and non-diffuse sphere wall emissivity and non-uniform but diffuse sphere wall spectral reflectivity. A general measurement equation describing the output of a sensor with a given field of view, angular and spectral response measuring the sphere output is obtained. The results are applied to the Earth Radiation Budget Experiment (ERBE) integrating sphere. The sphere wall radiance uniformity, loading effects and non-uniform wall temperature effects are investigated. It is shown that using appropriate interpretation and processing, a high-accuracy short-wave calibration of the ERBE sensors can be achieved.

Prospects for gravitational wave astronomy with next generation large-scale pulsar timing arrays

NASA Astrophysics Data System (ADS)

Wang, Yan; Mohanty, Soumya D.

2018-02-01

Next generation radio telescopes, namely the Five-hundred-meter Aperture Spherical Telescope (FAST) and the Square Kilometer Array (SKA), will revolutionize the pulsar timing arrays (PTAs) based gravitational wave (GW) searches. We review some of the characteristics of FAST and SKA, and the resulting PTAs, that are pertinent to the detection of gravitational wave signals from individual supermassive black hole binaries.

Annual, Seasonal, and Secular Changes in Time-Variable Gravity from GRACE

NASA Astrophysics Data System (ADS)

Lemoine, F. G.; Luthcke, S. B.; Klosko, S. M.; Rowlands, D. D.; Chinn, D. S.; McCarthy, J. J.; Ray, R. D.; Boy, J.

2007-12-01

The NASA/DLR GRACE mission, launched in 2002, has now operated for more than five years, producing monthly and ten-day snapshots of the variations of the gravity field of the Earth. The available solutions, either from spherical harmonics or from mascons, allow us new insights into the variations of surface gravity on the Earth at annual, inter-annual, and secular time scales. Our baseline time series, based on GGM02C, NCEP Atmospheric Gravity with IB, and GOT00 tides now is extended to July 2007, spanning four+ years, and we analyze both mascon and spherical harmonic solutions from this time series with respect to global hydrology variations. Our 4degx4deg mascon solutions are extended to cover all continental regions of the globe. Comparisons with hydrology (land-surface) models can offer insights into how these models might be improved. We compare our baseline time series, with new time series that include an updated Goddard Ocean Tide (GOT) model, ECMWF- 3hr atmosphere de-aliasing data, and the MOG-2D ocean dealiasing product. Finally, we intercompare the spherical harmonic solutions at low degree from GRACE from the various product centers (e.g., GFZ, CSR, GRGS), and look for secular signals in both the GSFC mascon and spherical harmonic solutions, taking care to compare the results for secular gravity field change with independent solutions developed over 25 years of independent tracking to geodetic satellites by Satellite Laser Ranging (SLR) and DORIS.

Facile room-temperature solution-phase synthesis of a spherical covalent organic framework for high-resolution chromatographic separation.

PubMed

Yang, Cheng-Xiong; Liu, Chang; Cao, Yi-Meng; Yan, Xiu-Ping

2015-08-07

A simple and facile room-temperature solution-phase synthesis was developed to fabricate a spherical covalent organic framework with large surface area, good solvent stability and high thermostability for high-resolution chromatographic separation of diverse important industrial analytes including alkanes, cyclohexane and benzene, α-pinene and β-pinene, and alcohols with high column efficiency and good precision.

Properties of Longitudinal Electromagnetic Oscillations in Metals and Their Excitation at Planar and Spherical Surfaces.

PubMed

Datsyuk, Vitaly V; Pavlyniuk, Oleg R

2017-12-01

The common definition of the spatially dispersive permittivity is revised. The response of the degenerate electron gas on an electric field satisfying the vector Helmholtz equation is found with a solution to the Boltzmann equation. The calculated longitudinal dielectric function coincides with that obtained by Klimontovich and Silin in 1952 and Lindhard in 1954. However, it depends on the square of the wavenumber, a parameter of the vector Helmholtz equation, but not the wave vector of a plane electromagnetic wave. This new concept simplifies simulation of the nonlocal effects, for example, with a generalized Lorents-Mie theory, since no Fourier transforms should be made. The Fresnel coefficients are generalized allowing for excitation of the longitudinal electromagnetic waves. To verify the theory, the extinction spectra for silver and gold nanometer-sized spheres are calculated. For these particles, the generalized Lorents-Mie theory gives the blue shift and broadening of the plasmon resonance which are in excellent agreement with experimental data. In addition, the nonlocal theory explains vanishing of the plasmon resonance observed for gold spheres with diameters less than or equal to 2 nm. The calculations using the Klimontovich-Silin-Lindhard and hydrodynamic dielectric functions for silver are found to give close results at photon energies from 3 to 4 eV. We show that the absolute values of the wavenumbers of the longitudinal waves in solids are much higher than those of the transverse waves.

Properties of Longitudinal Electromagnetic Oscillations in Metals and Their Excitation at Planar and Spherical Surfaces

NASA Astrophysics Data System (ADS)

Datsyuk, Vitaly V.; Pavlyniuk, Oleg R.

2017-08-01

The common definition of the spatially dispersive permittivity is revised. The response of the degenerate electron gas on an electric field satisfying the vector Helmholtz equation is found with a solution to the Boltzmann equation. The calculated longitudinal dielectric function coincides with that obtained by Klimontovich and Silin in 1952 and Lindhard in 1954. However, it depends on the square of the wavenumber, a parameter of the vector Helmholtz equation, but not the wave vector of a plane electromagnetic wave. This new concept simplifies simulation of the nonlocal effects, for example, with a generalized Lorents-Mie theory, since no Fourier transforms should be made. The Fresnel coefficients are generalized allowing for excitation of the longitudinal electromagnetic waves. To verify the theory, the extinction spectra for silver and gold nanometer-sized spheres are calculated. For these particles, the generalized Lorents-Mie theory gives the blue shift and broadening of the plasmon resonance which are in excellent agreement with experimental data. In addition, the nonlocal theory explains vanishing of the plasmon resonance observed for gold spheres with diameters less than or equal to 2 nm. The calculations using the Klimontovich-Silin-Lindhard and hydrodynamic dielectric functions for silver are found to give close results at photon energies from 3 to 4 eV. We show that the absolute values of the wavenumbers of the longitudinal waves in solids are much higher than those of the transverse waves.

A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers

NASA Astrophysics Data System (ADS)

Belafhal, A.; Ez-zariy, L.; Hricha, Z.

2016-11-01

By means of the expansion of the nondiffracting beams on plane waves with help of the Whittaker integral, an exact analytical expression of the far-field form function of the scattering of the acoustic and optical nondiffracting Lommel beams propagating in a medium containing spherical particles, considered as rigid and single spheres, is investigated in this work. The form function of the scattering of the high order Bessel beam by a rigid and isolated sphere is deduced, from our finding, as a special case. The effects of the wave number-sphere radius product (ka) , the polar angle (φ) , the propagation half-cone angle (β) and the scattering angle (θ) on the far-field form function of the scattered wave have been analyzed and discussed numerically. The numerical results show that the illumination of a rigid sphere by Lommel beams produces asymmetrical scattering.

Contribution to study of interfaces instabilities in plane, cylindrical and spherical geometry

NASA Astrophysics Data System (ADS)

Toque, Nathalie

1996-12-01

This thesis proposes several experiments of hydrodynamical instabilities which are studied, numerically and theoretically. The experiments are in plane and cylindrical geometry. Their X-ray radiographies show the evolution of an interface between two solid media crossed by a detonation wave. These materials are initially solid. They become liquide under shock wave or stay between two phases, solid and liquid. The numerical study aims at simulating with the codes EAD and Ouranos, the interfaces instabilities which appear in the experiments. The experimental radiographies and the numerical pictures are in quite good agreement. The theoretical study suggests to modelise a spatio-temporal part of the experiments to obtain the quantitative development of perturbations at the interfaces and in the flows. The models are linear and in plane, cylindrical and spherical geometry. They preceed the inoming study of transition between linear and non linear development of instabilities in multifluids flows crossed by shock waves.

The correlation function for density perturbations in an expanding universe. I - Linear theory

NASA Technical Reports Server (NTRS)

Mcclelland, J.; Silk, J.

1977-01-01

The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.

Solution of an eigenvalue problem for the Laplace operator on a spherical surface. M.S. Thesis - Maryland Univ.

NASA Technical Reports Server (NTRS)

Walden, H.

1974-01-01

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

The effect of cosmic-ray acceleration on supernova blast wave dynamics

NASA Astrophysics Data System (ADS)

Pais, M.; Pfrommer, C.; Ehlert, K.; Pakmor, R.

2018-05-01

Non-relativistic shocks accelerate ions to highly relativistic energies provided that the orientation of the magnetic field is closely aligned with the shock normal (quasi-parallel shock configuration). In contrast, quasi-perpendicular shocks do not efficiently accelerate ions. We model this obliquity-dependent acceleration process in a spherically expanding blast wave setup with the moving-mesh code AREPO for different magnetic field morphologies, ranging from homogeneous to turbulent configurations. A Sedov-Taylor explosion in a homogeneous magnetic field generates an oblate ellipsoidal shock surface due to the slower propagating blast wave in the direction of the magnetic field. This is because of the efficient cosmic ray (CR) production in the quasi-parallel polar cap regions, which softens the equation of state and increases the compressibility of the post-shock gas. We find that the solution remains self-similar because the ellipticity of the propagating blast wave stays constant in time. This enables us to derive an effective ratio of specific heats for a composite of thermal gas and CRs as a function of the maximum acceleration efficiency. We finally discuss the behavior of supernova remnants expanding into a turbulent magnetic field with varying coherence lengths. For a maximum CR acceleration efficiency of about 15 per cent at quasi-parallel shocks (as suggested by kinetic plasma simulations), we find an average efficiency of about 5 per cent, independent of the assumed magnetic coherence length.

Particlelike solutions of the Einstein-Dirac equations

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

1999-05-01

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.

Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

NASA Astrophysics Data System (ADS)

Da Rocha, R.; Capelas Oliveira, E.

2009-01-01

The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.

Spherical silicon-shell photonic band gap structures fabricated by laser-assisted chemical vapor deposition

NASA Astrophysics Data System (ADS)

Wang, H.; Yang, Z. Y.; Lu, Y. F.

2007-02-01

Laser-assisted chemical vapor deposition was applied in fabricating three-dimensional (3D) spherical-shell photonic band gap (PBG) structures by depositing silicon shells covering silica particles, which had been self-assembled into 3D colloidal crystals. The colloidal crystals of self-assembled silica particles were formed on silicon substrates using the isothermal heating evaporation approach. A continuous wave Nd:YAG laser (1064nm wavelength) was used to deposit silicon shells by thermally decomposing disilane gas. Periodic silicon-shell/silica-particle PBG structures were obtained. By removing the silica particles enclosed in the silicon shells using hydrofluoric acid, hollow spherical silicon-shell arrays were produced. This technique is capable of fabricating structures with complete photonic band gaps, which is predicted by simulations with the plane wave method. The techniques developed in this study have the potential to flexibly engineer the positions of the PBGs by varying both the silica particle size and the silicon-shell thickness. Ellipsometry was used to investigate the specific photonic band gaps for both structures.

Inviscid dynamics of a wet foam drop with monodisperse bubble size distribution

NASA Astrophysics Data System (ADS)

McDaniel, J. Gregory; Akhatov, Iskander; Holt, R. Glynn

2002-06-01

Motivated by recent experiments involving the acoustic levitation of foam drops, we develop a model for nonlinear oscillations of a spherical drop composed of monodisperse aqueous foam with void fraction below 0.1. The model conceptually divides a foam drop into many cells, each cell consisting of a spherical volume of liquid with a bubble at its center. By treating the liquid as incompressible and inviscid, a nonlinear equation is obtained for bubble motion due to a pressure applied at the outer radius of the liquid sphere. Upon linearizing this equation and connecting the cells at their outer radii, a wave equation is obtained with a dispersion relation for the sound waves in a bubbly liquid. For the spherical drop, this equation is solved by a normal mode expansion that yields the natural frequencies as functions of standard foam parameters. Numerical examples illustrate how the analysis may be used to extract foam parameters, such as void fraction and bubble radius, from the experimentally measured natural frequencies of a foam drop.

Cavitation studies in microgravity

NASA Astrophysics Data System (ADS)

Kobel, Philippe; Obreschkow, Danail; Farhat, Mohamed; Dorsaz, Nicolas; de Bosset, Aurele

The hydrodynamic cavitation phenomenon is a major source of erosion for many industrial systems such as cryogenic pumps for rocket propulsion, fast ship propellers, hydraulic pipelines and turbines. Erosive processes are associated with liquid jets and shockwaves emission fol-lowing the cavity collapse. Yet, fundamental understanding of these processes requires further cavitation studies inside various geometries of liquid volumes, as the bubble dynamics strongly depends the surrounding pressure field. To this end, microgravity represents a unique platform to produce spherical fluid geometries and remove the hydrostatic pressure gradient induced by gravity. The goal of our first experiment (flown on ESA's parabolic flight campaigns 2005 and 2006) was to study single bubble dynamics inside large spherical water drops (having a radius between 8 and 13 mm) produced in microgravity. The water drops were created by a micro-pump that smoothly expelled the liquid through a custom-designed injector tube. Then, the cavitation bubble was generated through a fast electrical discharge between two electrodes immersed in the liquid from above. High-speed imaging allowed to analyze the implications of isolated finite volumes and spherical free surfaces on bubble evolution, liquid jets formation and shock wave dynamics. Of particular interest are the following results: (A) Bubble lifetimes are shorter than in extended liquid volumes, which could be explain by deriving novel corrective terms to the Rayleigh-Plesset equation. (B) Transient crowds of micro-bubbles (smaller than 1mm) appeared at the instants of shockwaves emission. A comparison between high-speed visualizations and 3D N-particle simulations of a shock front inside a liquid sphere reveals that focus zones within the drop lead to a significantly increased density of induced cavitation. Considering shock wave crossing and focusing may hence prove crucially useful to understand the important process of cavitation erosion. The aim of our future microgravity experiment is to assess the direct effects of gravity on cavitation bubble collapse through a comparison of single cavitation bubbles collapsing in mi-crogravity, normal gravity, and hypergravity. In particular, we shall investigate the shape of the bubble in its final collapse stage and the amount of energy dissipated in the dominant collapse channels, such as liquid jet, shock wave, and rebound bubble. The highly spherical bubbles will be produced via a point-like plasma generated by a high power laser beam. One major hypothesis that we will test is an increase in shock wave energy with decreasing gravity as a consequence of the higher final sphericity and suppression of liquid jets. To support this, we introduce an analytical model for the gravity-perturbed asymmetric collapse of spherical bubbles, and demonstrate that all initially spherical bubbles develop a gravity-related vertical jet along their collapse.

A survey of electron Bernstein wave heating and current drive potential for spherical tokamaks

NASA Astrophysics Data System (ADS)

Urban, Jakub; Decker, Joan; Peysson, Yves; Preinhaelter, Josef; Shevchenko, Vladimir; Taylor, Gary; Vahala, Linda; Vahala, George

2011-08-01

The electron Bernstein wave (EBW) is typically the only wave in the electron cyclotron (EC) range that can be applied in spherical tokamaks for heating and current drive (H&CD). Spherical tokamaks (STs) operate generally in high-β regimes, in which the usual EC O- and X-modes are cut off. In this case, EBWs seem to be the only option that can provide features similar to the EC waves—controllable localized H&CD that can be used for core plasma heating as well as for accurate plasma stabilization. The EBW is a quasi-electrostatic wave that can be excited by mode conversion from a suitably launched O- or X-mode; its propagation further inside the plasma is strongly influenced by the plasma parameters. These rather awkward properties make its application somewhat more difficult. In this paper we perform an extensive numerical study of EBW H&CD performance in four typical ST plasmas (NSTX L- and H-mode, MAST Upgrade, NHTX). Coupled ray-tracing (AMR) and Fokker-Planck (LUKE) codes are employed to simulate EBWs of varying frequencies and launch conditions, which are the fundamental EBW parameters that can be chosen and controlled. Our results indicate that an efficient and universal EBW H&CD system is indeed viable. In particular, power can be deposited and current reasonably efficiently driven across the whole plasma radius. Such a system could be controlled by a suitably chosen launching antenna vertical position and would also be sufficiently robust.

Coherent electromagnetic waves in the presence of a half space of randomly distributed scatterers

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.

1988-01-01

The present investigation of coherent field propagation notes, upon solving the Foldy-Twersky integral equation for a half-space of small spherical scatterers illuminated by a plane wave at oblique incidence, that the coherent field for a horizontally-polarized incident wave exhibits reflectivity and transmissivity consistent with the Fresnel formula for an equivalent continuous effective medium. In the case of a vertically polarized incident wave, both the vertical and longitudinal waves obtained for the coherent field have reflectivities and transmissivities that do not agree with the Fresnel formula.

Solutions for the conductivity of multi-coated spheres and spherically symmetric inclusion problems

NASA Astrophysics Data System (ADS)

Pham, Duc Chinh

2018-02-01

Variational results on the macroscopic conductivity (thermal, electrical, etc.) of the multi-coated sphere assemblage have been used to derive the explicit expression of the respective field (thermal, electrical, etc.) within the spheres in d dimensions (d=2,3). A differential substitution approach has been developed to construct various explicit expressions or determining equations for the effective spherically symmetric inclusion problems, which include those with radially variable conductivity, different radially variable transverse and normal conductivities, and those involving imperfect interfaces, in d dimensions. When the volume proportion of the outermost spherical shell increases toward 1, one obtains the respective exact results for the most important specific cases: the dilute solutions for the compound inhomogeneities suspended in a major matrix phase. Those dilute solution results are also needed for other effective medium approximation schemes.

Description of an α-cluster tail in 8Be and 20Ne: Delocalization of the α cluster by quantum penetration

NASA Astrophysics Data System (ADS)

Kanada-En'yo, Yoshiko

2014-10-01

We analyze the α-cluster wave functions in cluster states of ^8Be and ^{20}Ne by comparing the exact relative wave function obtained by the generator coordinate method (GCM) with various types of trial functions. For the trial functions, we adopt the fixed range shifted Gaussian of the Brink-Bloch (BB) wave function, the spherical Gaussian with the adjustable range parameter of the spherical Tohsaki-Horiuchi-Schuck-Röpke (sTHSR), the deformed Gaussian of the deformed THSR (dTHSR), and a function with the Yukawa tail (YT). The quality of the description of the exact wave function with a trial function is judged by the squared overlap between the trial function and the GCM wave function. A better result is obtained with the sTHSR wave function than the BB wave function, and further improvement can be made with the dTHSR wave function because these wave functions can describe the outer tail better. The YT wave function gives almost an equal quality to or even better quality than the dTHSR wave function, indicating that the outer tail of α-cluster states is characterized by the Yukawa-like tail rather than the Gaussian tail. In weakly bound α-cluster states with small α separation energy and the low centrifugal and Coulomb barriers, the outer tail part is the slowly damping function described well by the quantum penetration through the effective barrier. This outer tail characterizes the almost zero-energy free α gas behavior, i.e., the delocalization of the cluster.

Effects of zonal flows on correlation between energy balance and energy conservation associated with nonlinear nonviscous atmospheric dynamics in a thin rotating spherical shell

NASA Astrophysics Data System (ADS)

Ibragimov, Ranis N.

2018-03-01

The nonlinear Euler equations are used to model two-dimensional atmosphere dynamics in a thin rotating spherical shell. The energy balance is deduced on the basis of two classes of functorially independent invariant solutions associated with the model. It it shown that the energy balance is exactly the conservation law for one class of the solutions whereas the second class of invariant solutions provides and asymptotic convergence of the energy balance to the conservation law.

Study of non-spherical bubble oscillations near a surface in a weak acoustic standing wave field.

PubMed

Xi, Xiaoyu; Cegla, Frederic; Mettin, Robert; Holsteyns, Frank; Lippert, Alexander

2014-04-01

The interaction of acoustically driven bubbles with a wall is important in many applications of ultrasound and cavitation, as the close boundary can severely alter the bubble dynamics. In this paper, the non-spherical surface oscillations of bubbles near a surface in a weak acoustic standing wave field are investigated experimentally and numerically. The translation, the volume, and surface mode oscillations of bubbles near a flat glass surface were observed by a high speed camera in a standing wave cell at 46.8 kHz. The model approach is based on a modified Keller-Miksis equation coupled to surface mode amplitude equations in the first order, and to the translation equations. Modifications are introduced due to the adjacent wall. It was found that a bubble's oscillation mode can change in the presence of the wall, as compared to the bubble in the bulk liquid. In particular, the wall shifts the instability pressure thresholds to smaller driving frequencies for fixed bubble equilibrium radii, or to smaller equilibrium radii for fixed excitation frequency. This can destabilize otherwise spherical bubbles, or stabilize bubbles undergoing surface oscillations in the bulk. The bubble dynamics observed in experiment demonstrated the same trend as the theoretical results.

Light scattering by nonspherical particles: Remote sensing and climatic implications

NASA Astrophysics Data System (ADS)

Liou, K. N.; Takano, Y.

Calculations of the scattering and adsorption properties of ice crystals and aerosols, which are usually nonspherical, require specific methodologies. There is no unique theoretical solution for the scattering by nonspherical particles. Practically, all the numerical solutions for the scattering of nonspherical particles, including the exact wave equation approach, integral equation method, and discrete-dipole approximation, are applicable only to size parameters less than about 20. Thus, these methods are useful for the study of radiation problems involving nonspherical aerosols and small ice crystals in the thermal infrared wavelengths. The geometric optics approximation has been used to evaluate the scattering, absorption and polarization properties of hexagonal ice crystals whose sizes are much larger than the incident wavelength. This approximation is generally valid for hexagonal ice crystals with size parameters larger than about 30. From existing laboratory data and theoretical results, we illustrate that nonspherical particles absorb less and have a smaller asymmetry factor than the equal-projected area/volume spherical counterparts. In particular, we show that hexagonal ice crystals exhibit numerous halo and arc features that cannot be obtained from spherical particles; and that ice crystals scatter more light in the 60° to 140° scattering angle regions than the spherical counterparts. Satellite remote sensing of the optical depth and height of cirrus clouds using visible and IR channels must use appropriate phase functions for ice crystals. Use of an equivalent sphere model would lead to a significant overestimation and underestimation of the cirrus optical depth and height, respectively. Interpretation of the measurements for polarization reflected from sunlight involving cirrus clouds cannot be made without an appropriate ice crystal model. Large deviations exist for the polarization patterns between spheres and hexagonal ice crystals. Interpretation of lidar backscattering and depolarization signals must also utilize the scattering characteristics of hexagonal ice crystals. Equivalent spherical models substantially underestimate the broadband solar albedos of ice crystal clouds because of stronger forward scattering and larger absorption by spherical particles than hexagonal ice crystals. We illustrate that the net cloud radiative forcing at the top of the atmosphere involving most cirrus clouds is positive, implying that the IR greenhouse effect outweighs the solar albedo effect. If the radiative properties of equivalent spheres are used, a significant increase in cloud radiative forcing occurs. Using a one-dimensional cloud and climate model, we further demonstrate that there is sufficient model sensitivity, in terms of temperature increase, to the use of ice crystal models in radiation calculations.

Analysis of long wavelength electromagnetic scattering by a magnetized cold plasma prolate spheroid

NASA Astrophysics Data System (ADS)

Ahmadizadeh, Yadollah; Jazi, Bahram; Abdoli-Arani, Abbas

2013-08-01

Using dielectric permittivity tensor of the magnetized prolate plasma, the scattering of long wavelength electromagnetic waves from the mentioned object is studied. The resonance frequency and differential scattering cross section for the backward scattered waves are presented. Consistency between the resonance frequency in this configuration and results obtained for spherical plasma are investigated. Finally, the effective factors on obtained results such as incident wave polarization, the frequency of the incident wave, the plasma frequency and the cyclotron frequency are analyzed.

Harmony: EEG/MEG Linear Inverse Source Reconstruction in the Anatomical Basis of Spherical Harmonics

PubMed Central

Petrov, Yury

2012-01-01

EEG/MEG source localization based on a “distributed solution” is severely underdetermined, because the number of sources is much larger than the number of measurements. In particular, this makes the solution strongly affected by sensor noise. A new way to constrain the problem is presented. By using the anatomical basis of spherical harmonics (or spherical splines) instead of single dipoles the dimensionality of the inverse solution is greatly reduced without sacrificing the quality of the data fit. The smoothness of the resulting solution reduces the surface bias and scatter of the sources (incoherency) compared to the popular minimum-norm algorithms where single-dipole basis is used (MNE, depth-weighted MNE, dSPM, sLORETA, LORETA, IBF) and allows to efficiently reduce the effect of sensor noise. This approach, termed Harmony, performed well when applied to experimental data (two exemplars of early evoked potentials) and showed better localization precision and solution coherence than the other tested algorithms when applied to realistically simulated data. PMID:23071497

The jump-off velocity of an impulsively loaded spherical shell

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

Chabaud, Brandon M.; Brock, Jerry S.

2012-04-13

We consider a constant temperature spherical shell of isotropic, homogeneous, linearly elastic material with density {rho} and Lame coefficients {lambda} and {mu}. The inner and outer radii of the shell are r{sub i} and r{sub o}, respectively. We assume that the inside of the shell is a void. On the outside of the shell, we apply a uniform, time-varying pressure p(t). We also assume that the shell is initially at rest. We want to compute the jump-off time and velocity of the pressure wave, which are the first time after t = 0 at which the pressure wave from themore » outer surface reaches the inner surface. This analysis computes the jump-off velocity and time for both compressible and incompressible materials. This differs substantially from [3], where only incompressible materials are considered. We will consider the behavior of an impulsively loaded, exponentially decaying pressure wave p(t) = P{sub 0{sup e}}{sup -{alpha}t}, where {alpha} {ge} 0. We notice that a constant pressure wave P(t) = P{sub 0} is a special case ({alpha} = 0) of a decaying pressure wave. Both of these boundary conditions are considered in [3].« less

Simulations towards the achievement of non-inductive current ramp-up and sustainment in the National Spherical Torus Experiment Upgrade

DOE PAGES

Poli, F. M.; Andre, R. G.; Bertelli, N.; ...

2015-10-30

One of the goals of the National Spherical Torus Experiment Upgrade (NSTX-U) (Menard et al 2012 Nucl. Fusion 52 083015) is the demonstration of fully non-inductive start-up, current ramp-up and sustainment. This work discusses predictive simulations where the available heating and current drive systems are combined to maximize the non-inductive current and minimize the solenoidal contribution. Radio-frequency waves at harmonics higher than the ion cyclotron resonance (high-harmonic fast waves (HHFW)) and neutral beam injection are used to ramp the plasma current non-inductively starting from an initial Ohmic plasma. An interesting synergy is observed in the simulations between the HHFW andmore » electron cyclotron (EC) wave heating. Furthermore, time-dependent simulations indicate that, depending on the phasing of the HHFW antenna, EC wave heating can significantly increase the effectiveness of the radio-frequency power, by heating the electrons and increasing the current drive efficiency, thus relaxing the requirements on the level of HHFW power that needs to be absorbed in the core plasma to drive the same amount of fast-wave current.« less

High-harmonic fast magnetosonic wave coupling, propagation, and heating in a spherical torus plasma

NASA Astrophysics Data System (ADS)

Menard, J.; Majeski, R.; Kaita, R.; Ono, M.; Munsat, T.; Stutman, D.; Finkenthal, M.

1999-05-01

A novel rotatable two-strap antenna has been installed in the current drive experiment upgrade (CDX-U) [T. Jones, Ph.D. thesis, Princeton University (1995)] in order to investigate high-harmonic fast wave coupling, propagation, and electron heating as a function of strap angle and strap phasing in a spherical torus plasma. Radio-frequency-driven sheath effects are found to fit antenna loading trends at very low power and become negligible above a few kilowatts. At sufficiently high power, the measured coupling efficiency as a function of strap angle is found to agree favorably with cold plasma wave theory. Far-forward microwave scattering from wave-induced density fluctuations in the plasma core tracks the predicted fast wave loading as the antenna is rotated. Signs of electron heating during rf power injection have been observed in CDX-U with central Thomson scattering, impurity ion spectroscopy, and Langmuir probes. While these initial results appear promising, damping of the fast wave on thermal ions at high ion-cyclotron-harmonic number may compete with electron damping at sufficiently high ion β—possibly resulting in a significantly reduced current drive efficiency and production of a fast ion population. Preliminary results from ray-tracing calculations which include these ion damping effects are presented.

Propagation analysis of the helicity-drive Alfven wave in the HIST spherical torus plasmas

NASA Astrophysics Data System (ADS)

Hyobu, T.; Hanao, T.; Hirono, H.; Ito, K.; Matsumoto, K.; Nakayama, T.; Kikuchi, Y.; Fukumoto, N.; Nagata, M.

2012-10-01

Coaxial Helicity Injection is an efficient current-drive method used in spherical torus experiments. It is a key issue to investigate the dynamo mechanism required to maintain the plasmas. The behavior of a low frequency Alfven wave being possibly related to the dynamo current drive has been studied on HIST. The observed magnetic fluctuation with about 80 kHz propagates along the open flux column (OFC) region, spreading toward the core region. The parallel phase velocity is estimated at 321 km/s from the propagation velocity measured axially along the OFC. The parallel phase velocity agrees well to the Alfven velocity. The radial perpendicular propagation of the Alfven wave can be calculated by a theory based on cold or warm plasma approximation with the Hall term. The theoretical calculation indicates that there are two resonance points and is a cut-off point. These resonance and cut-off points agree well with the magnetic measurement. A part of fluctuation propagates slowly beyond the first resonance point. The wave polarization is left-handed near the resonance point and then converts to be nearly liner outside the resonance point. From these results, we speculate that the torsional Alfven wave evolves to the kinetic Alfven wave during the radial propagation.

Comment on the Exterior Solutions and Their Geometry in Scalar-Tensor Theories of Gravity

NASA Astrophysics Data System (ADS)

Tsuchida, T.; Watanabe, K.

1999-01-01

We study series of stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent to the exterior solutions in some class of scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then establish a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behavior of the null geodesics.

Second-order spherical optoelectronic detector for 3D multi-particles wave emission and propagation in space time domains

NASA Astrophysics Data System (ADS)

Romano, Francesco; Cimmino, Rosario F.

2017-09-01

This paper concerns a feasibility study on a 2nd order spherical, or three-dimensional, angular momentum and linear momentum detector for photonic radiation applications. It has been developed in order to obtain a paraxial approximation of physical events observed under Coulomb gauge condition, which is essential to compute both the longitudinal and transverse rotational components of the observed 3-D vortex field, generally neglected by conventional detection systems under current usage. Since light and laser beams are neither full transversal or rotational phenomena, to measure directly and in the same time both the energy, mainly not-rotational, related to the relevant part of the linear momentum and the potential solenoidal energy (vortex), related to the angular momentum, 2nd order spherical, or 3-D, detector techniques are required. In addition, direct 2nd order measure techniques enable development of TEM + DEM [17] studies, therefore allowing for monochromatic complex wave detection with a paraxial accuracy in the relativistic time-space domain. Light and optic or Electromagnetic 2nd order 3-D AnM energy may usefully be used in tre-dimensional optical TEM, noTEM, DEM vortex or laser communications The paper illustrates an innovative quadratic order 3-D spherical model detector applied to directly measure a light source power spectrum and compares the performances of this innovative technique with those obtained with a traditional 1st order system. Results from a number of test experiments conducted in cooperation with INAF Observatories of ArcetriFlorence and Medicina-Bologna (Italy), and focused on telescopic observations of the inter-stellar electromagnetic radiations, are also summarized. The innovative quadratic-order spherical detector turns out to be optimal for optical and/or radio telescopes application, optical and optoelectronic sensors development and gravitational wave 2nd order detectors implementation. Although the proposed method is very innovative, it shows a very good adherence with results obtained with the conventional techniques in current usage.

Discrete sudden perturbation theory for inelastic scattering. I. Quantum and semiclassical treatment

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

Cross, R.J.

1985-12-01

A double perturbation theory is constructed to treat rotationally and vibrationally inelastic scattering. It uses both the elastic scattering from the spherically averaged potential and the infinite-order sudden (IOS) approximation as the unperturbed solutions. First, a standard perturbation expansion is done to express the radial wave functions in terms of the elastic wave functions. The resulting coupled equations are transformed to the discrete-variable representation where the IOS equations are diagonal. Then, the IOS solutions are removed from the equations which are solved by an exponential perturbation approximation. The results for Ar+N/sub 2/ are very much more accurate than the IOSmore » and somewhat more accurate than a straight first-order exponential perturbation theory. The theory is then converted into a semiclassical, time-dependent form by using the WKB approximation. The result is an integral of the potential times a slowly oscillating factor over the classical trajectory. A method of interpolating the result is given so that the calculation is done at the average velocity for a given transition. With this procedure, the semiclassical version of the theory is more accurate than the quantum version and very much faster. Calculations on Ar+N/sub 2/ show the theory to be much more accurate than the infinite-order sudden (IOS) approximation and the exponential time-dependent perturbation theory.« less

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

PubMed

Johnson, R S

2018-01-28

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

Close-in Blast Waves from Spherical Charges*

NASA Astrophysics Data System (ADS)

Howard, William; Kuhl, Allen

2011-06-01

We study the close-in blast waves created by the detonation of spherical high explosives (HE) charges, via numerical simulations with our Arbitrary-Lagrange-Eulerian (ALE3D) code. We used a finely-resolved, fixed Eulerian 2-D mesh (200 μm per cell) to capture the detonation of the charge, the blast wave propagation in air, and the reflection of the blast wave from an ideal surface. The thermodynamic properties of the detonation products and air were specified by the Cheetah code. A programmed-burn model was used to detonate the charge at a rate based on measured detonation velocities. The results were analyzed to evaluate the: (i) free air pressure-range curves: Δps (R) , (ii) free air impulse curves, (iii) reflected pressure-range curves, and (iv) reflected impulse-range curves. A variety of explosives were studied. Conclusions are: (i) close-in (R < 10 cm /g 1 / 3) , each explosive had its own (unique) blast wave (e.g., Δps (R , HE) ~ a /Rn , where n is different for each explosive); (ii) these close-in blast waves do not scale with the ``Heat of Detonation'' of the explosive (because close-in, there is not enough time to fully couple the chemical energy to the air via piston work); (iii) instead they are related to the detonation conditions inside the charge. Scaling laws will be proposed for such close-in blast waves.

The dynamics of magnetic Rossby waves in spherical dynamo simulations: A signature of strong-field dynamos?

NASA Astrophysics Data System (ADS)

Hori, K.; Teed, R. J.; Jones, C. A.

2018-03-01

We investigate slow magnetic Rossby waves in convection-driven dynamos in rotating spherical shells. Quasi-geostrophic waves riding on a mean zonal flow may account for some of the geomagnetic westward drifts and have the potential to allow the toroidal field strength within the planetary fluid core to be estimated. We extend the work of Hori et al. (2015) to include a wider range of models, and perform a detailed analysis of the results. We find that a predicted dispersion relation matches well with the longitudinal drifts observed in our strong-field dynamos. We discuss the validity of our linear theory, since we also find that the nonlinear Lorentz terms influence the observed waveforms. These wave motions are excited by convective instability, which determines the preferred azimuthal wavenumbers. Studies of linear rotating magnetoconvection have suggested that slow magnetic Rossby modes emerge in the magnetostrophic regime, in which the Lorentz and Coriolis forces are in balance in the vorticity equation. We confirm this to be predominant balance for the slow waves we have detected in nonlinear dynamo systems. We also show that a completely different wave regime emerges if the magnetic field is not present. Finally we report the corresponding radial magnetic field variations observed at the surface of the shell in our simulations and discuss the detectability of these waves in the geomagnetic secular variation.

Quasi Sturmian basis for the two-electon continuum

NASA Astrophysics Data System (ADS)

Zaytsev, A. S.; Ancarani, L. U.; Zaytsev, S. A.

2016-02-01

A new type of basis functions is proposed to describe a two-electron continuum which arises as a final state in electron-impact ionization and double photoionization of atomic systems. We name these functions, which are calculated in terms of the recently introduced quasi Sturmian functions, Convoluted Quasi Sturmian functions (CQS); by construction, they look asymptotically like a six-dimensional spherical wave. The driven equation describing an ( e, 3 e) process on helium in the framework of the Temkin-Poet model is solved numerically in the entire space (rather than in a finite region of space) using expansions on CQS basis functions. We show that quite rapid convergence of the solution expansion can be achieved by multiplying the basis functions by the logarithmic phase factor corresponding to the Coulomb electron-electron interaction.

An exact solution of the van der Waals interaction between two ground-state hydrogen atoms

NASA Astrophysics Data System (ADS)

Koga, Toshikatsu; Matsumoto, Shinya

1985-06-01

A momentum space treatment shows that perturbation equations for the H(1s)-H(1s) van der Waals interaction can be exactly solved in their Schrödinger forms without invoking any variational methods. Using the Fock transformation, which projects the momentum vector of an electron from the three-dimensional hyperplane onto the four-dimensional hypersphere, we solve the third order integral-type perturbation equation with respect to the reciprocal of the internuclear distance R. An exact third order wave function is found as a linear combination of infinite number of four-dimensional spherical harmonics. The result allows us to evaluate the exact dispersion energy E6R-6, which is completely determined by the first three coefficients of the above linear combination.

Modeling of the 2011 Tohoku-oki Tsunami and its Impacts on Hawaii

NASA Astrophysics Data System (ADS)

Cheung, K.; Yamazaki, Y.; Roeber, V.; Lay, T.

2011-12-01

The 2011 Tohoku-oki great earthquake (Mw 9.0) generated a destructive tsunami along the entire Pacific coast of northeastern Japan. The tsunami, which registered 6.7 m amplitude at a coastal GPS gauge and 1.75 m at an open-ocean DART buoy, triggered warnings across the Pacific. The waves reached Hawaii 7 hours after the earthquake and caused localized damage and persistent coastal oscillations along the island chain. Several tide gauges and a DART buoy west of Hawaii Island recorded clear signals of the tsunami. The Tsunami Observer Program of Hawaii State Civil Defense immediately conducted field surveys to gather runup and inundation data on Kauai, Oahu, Maui, and Hawaii Island. The extensive global seismic networks and geodetic instruments allows evaluation and validation of finite fault solutions for the tsunami modeling. We reconstruct the 2011 Tohoku-oki tsunami using the long-wave model NEOWAVE (Non-hydrostatic Evolution of Ocean WAVEs) and a finite fault solution based on inversion of teleseismic P waves. The depth-integrated model describes dispersive waves through the non-hydrostatic pressure and vertical velocity, which also account for tsunami generation from time histories of seafloor deformation. The semi-implicit, staggered finite difference model captures flow discontinuities associated with bores or hydraulic jumps through the momentum-conserved advection scheme. Four levels of two-way nested grids in spherical coordinates allow description of tsunami evolution processes of different time and spatial scales for investigation of the impacts around the Hawaiian Islands. The model results are validated with DART data across the Pacific as well as tide gauge and runup measurements in Hawaii. Spectral analysis of the computed surface elevation reveals a series of resonance modes over the insular shelf and slope complex along the archipelago. Resonance oscillations provide an explanation for the localized impacts and the persistent wave activities in the aftermath. The model results provide insights into effects of fringing reefs, which are present along 70% of Hawaii's coastlines, on tsunami transformation and runup processes. This case study improves our understanding of tsunamis in tropical island environment and validates the modeling capability to predict their impacts for hazard mitigation and emergency management.

GEOSIM: A numerical model for geophysical fluid flow simulation

NASA Technical Reports Server (NTRS)

Butler, Karen A.; Miller, Timothy L.; Lu, Huei-Iin

1991-01-01

A numerical model which simulates geophysical fluid flow in a wide range of problems is described in detail, and comparisons of some of the model's results are made with previous experimental and numerical studies. The model is based upon the Boussinesq Navier-Stokes equations in spherical coordinates, which can be reduced to a cylindrical system when latitudinal walls are used near the pole and the ratio of latitudinal length to the radius of the sphere is small. The equations are approximated by finite differences in the meridional plane and spectral decomposition in the azimuthal direction. The user can specify a variety of boundary and initial conditions, and there are five different spectral truncation options. The results of five validation cases are presented: (1) the transition between axisymmetric flow and baroclinic wave flow in the side heated annulus; (2) the steady baroclinic wave of the side heated annulus; (3) the wave amplitude vacillation of the side heated annulus; (4) transition to baroclinic wave flow in a bottom heated annulus; and (5) the Spacelab Geophysical Fluid Flow Cell (spherical) experiment.

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

NASA Astrophysics Data System (ADS)

Reiter, Paul; Ziegelwanger, Harald

2017-12-01

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

Convergence of shock waves generated by underwater electrical explosion of cylindrical wire arrays between different boundary geometries

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

Yanuka, D.; Zinowits, H. E.; Krasik, Ya. E.

The results of experiments and numerical simulations of a shock wave propagating between either conical or parabolic bounding walls are presented. The shock wave was generated by a microsecond timescale underwater electrical explosion of a cylindrical wire array supplied by a current pulse having an amplitude of ∼230 kA and a rise time of ∼1 μs. It is shown that with the same energy density deposition into the exploding wire array, the shock wave converges faster between parabolic walls, and as a result, the pressure in the vicinity of convergence is ∼2.3 times higher than in the case of conical walls. Themore » results obtained are compared to those of earlier experiments [Antonov et al., Appl. Phys. Lett. 102, 124104 (2013)] with explosions of spherical wire arrays. It is shown that at a distance of ∼400 μm from the implosion origin the pressure obtained in the current experiments is higher than for the case of spherical wire arrays.« less

The self-similarly expanding Eshelby ellipsoidal inclusion: II. The Dynamic Eshelby Tensor for the expanding sphere

NASA Astrophysics Data System (ADS)

Ni, Luqun; Markenscoff, Xanthippi

2016-11-01

The field solution of a self-similarly (subsonically) expanding Eshelby ellipsoidal inclusion obtained in Part I is evaluated for the case of the expanding spherical inclusion under general uniform eigenstrain ɛij* in self-similar motion R = υt, starting from zero dimension. The particle velocity in the interior domain vanishes and the displacement gradient is constant exhibiting the Eshelby property in the self-similar dynamic case. All components of the interior and exterior Dynamic Eshelby Tensor are obtained for the sphere, with the interior ones depending on the wave speeds and the expansion speed of the inclusion, while the exterior ones depend, in addition, on the variable of self-similarity r / t and the direction of the field point. By a limiting procedure the static Eshelby tensor both interior and exterior is retrieved, thus making the static inclusion a special limit of the dynamic self-similarly expanding one. The jump of the particle velocity across the moving inclusion boundary is obtained, and it depends only on the wave and expansion speeds and the direction of the normal.

X ray microscope assembly and alignment support and advanced x ray microscope design and analysis

NASA Technical Reports Server (NTRS)

Shealy, David L.

1991-01-01

Considerable efforts have been devoted recently to the design, analysis, fabrication, and testing of spherical Schwarzschild microscopes for soft x ray application in microscopy and projection lithography. The spherical Schwarzschild microscope consists of two concentric spherical mirrors configured such that the third order spherical aberration and coma are zero. Since multilayers are used on the mirror substrates for x ray applications, it is desirable to have only two reflecting surfaces in a microscope. In order to reduce microscope aberrations and increase the field of view, generalized mirror surface profiles have been considered in this investigation. Based on incoherent and sine wave modulation transfer function (MTF) calculations, the object plane resolution of a microscope has been analyzed as a function of the object height and numerical aperture (NA) of the primary for several spherical Schwarzschild, conic, and aspherical head reflecting two mirror microscope configurations.

Nanocomposite and method of making thereof

DOEpatents

Tangirala, Ravisubhash; Milliron, Delia J.; Llordes, Anna

2016-03-15

An embodiment of an inorganic nanocomposite includes a nanoparticle phase and a matrix phase. The nanoparticle phase includes nanoparticles that are arranged in a repeating structure. In an embodiment, the nanoparticles have a spherical or pseudo-spherical shape and are incompatible with hydrazine. In another embodiment, the nanoparticles have neither a spherical nor pseudo-spherical shape. The matrix phase lies between the nanoparticles of the nanoparticle phase. An embodiment of a method of making an inorganic nanocomposite of the present invention includes forming a nanoparticle superlattice on a substrate. The nanoparticle superlattice includes nanoparticles. Each nanoparticle has organic ligands attached to a surface of the nanoparticle. The organic ligands separate adjacent nanoparticles within the nanoparticle superlattice. The method also includes forming a solution that includes an inorganic precursor. The nanoparticle superlattice is placed in the solution for a sufficient time for the inorganic precursor to replace the organic ligands.

SUNIST Microwave Power System

NASA Astrophysics Data System (ADS)

Feng, Songlin; Yang, Xuanzong; Feng, Chunhua; Wang, Long; Rao, Jun; Feng, Kecheng

2005-06-01

Experiments on the start-up and formation of spherical tokamak plasmas by electron cyclotron heating alone without ohmic heating and electrode discharge assisted electron cyclotron wave current start-up will be carried out on the SUNIST (Sino United Spherical Tokamak) device. The 2.45 GHz/100kW/30 ms microwave power system and 1000 V/50 A power supply for electrode discharge are ready for experiments with non-inductive current drive.

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.

Modeling micromechanical measurements of depth-varying properties with scanning acoustic microscopy

NASA Astrophysics Data System (ADS)

Marangos, Orestes; Misra, Anil

2018-02-01

Scanning acoustic microscopy (SAM) has been applied to measure the near-surface elastic properties of materials. For many substrates, the near-surface property is not constant but varies with depth. In this paper, we aim to interpret the SAM data from such substrates by modeling the interaction of the focused ultrasonic field with a substrate having a near-surface graded layer. The focused ultrasonic field solutions were represented as spherical harmonic expansions while the substrate solutions were represented as plane wave expansions. The bridging of the two solutions was achieved through the decomposition of the ultrasonic pressure fields in their angular spectra. Parametric studies were performed, which showed that near-surface graded layers exhibit distinctive frequency dependence of their reflectance functions. This behavior is characteristic to the material property gradation profile as well as the extent of the property gradation. The developed model was used to explain the frequency-dependent reflection coefficients measured from an acid-etched dentin substrate. Based on the model calculations, the elastic property variations of the acid-etched dentin near-surface indicate that the topmost part of the etched layer is very soft (3-6 GPa) and transitions to the native dentin through a depth of 27 and 36 microns.

Generalized transformations and coordinates for static spherically symmetric general relativity

NASA Astrophysics Data System (ADS)

Hill, James M.; O'Leary, Joseph

2018-04-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

Generalized transformations and coordinates for static spherically symmetric general relativity.

PubMed

Hill, James M; O'Leary, Joseph

2018-04-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

Generalized transformations and coordinates for static spherically symmetric general relativity

PubMed Central

2018-01-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington–Finkelstein transformation and the Kruskal–Szekeres coordinates. PMID:29765624

Computerized ultrasound risk evaluation system

DOEpatents

Duric, Nebojsa; Littrup, Peter J.; Holsapple, III, Earle; Barter, Robert Henry; Moore, Thomas L.; Azevedo, Stephen G.; Ferguson, Sidney W.

2007-10-23

A method and system for examining tissue are provided in which the tissue is maintained in a position so that it may be insonified with a plurality of pulsed spherical or cylindrical acoustic waves. The insonifying acoustic waves are scattered by the tissue so that scattered acoustic radiation including a mix of reflected and transmitted acoustic waves is received. A representation of a portion of the tissue is then derived from the received scattered acoustic radiation.

Faraday Wave Turbulence on a Spherical Liquid Shell

NASA Technical Reports Server (NTRS)

Holt, R. Glynn; Trinh, Eugene H.

1996-01-01

Millimeter-radius liquid shells are acoustically levitated in an ultrasonic field. Capillary waves are observed on the shells. At low energies (minimal acoustic amplitude, thick shell) a resonance is observed between the symmetric and antisymmetric thin film oscillation modes. At high energies (high acoustic pressure, thin shell) the shell becomes fully covered with high-amplitude waves. Temporal spectra of scattered light from the shell in this regime exhibit a power-law decay indicative of turbulence.

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

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

Mandel, Ilya

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

General Wahlquist metrics in all dimensions

NASA Astrophysics Data System (ADS)

Hinoue, Kazuki; Houri, Tsuyoshi; Rugina, Christina; Yasui, Yukinori

2014-07-01

It is shown that the Wahlquist metric, which is a stationary, axially symmetric perfect fluid solution with ρ +3p=const, admits a rank-2 generalized closed conformal Killing-Yano tensor with a skew-symmetric torsion. Taking advantage of the presence of such a tensor, we obtain a higher-dimensional generalization of the Wahlquist metric in arbitrary dimensions, including a family of vacuum black hole solutions with spherical horizon topology such as Schwarzschild-Tangherlini, Myers-Perry and higher-dimensional Kerr-NUT-(A)dS metrics and a family of static, spherically symmetric perfect fluid solutions in higher dimensions.

Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity

NASA Astrophysics Data System (ADS)

Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb

2017-03-01

A set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass \\wp function and the Kleinian σ function. Using conserved energy and angular momentum we can characterize the different orbits. Also, considering parametric diagrams and effective potentials, we plot some possible orbits. Moreover, with the help of analytical solutions, we investigate the light deflection for such an escape orbit. Finally, by using periastron advance we get to an upper bound for magnitude of γ.

Spin flip statistics and spin wave interference patterns in Ising ferromagnetic films: A Monte Carlo study.

PubMed

Acharyya, Muktish

2017-07-01

The spin wave interference is studied in two dimensional Ising ferromagnet driven by two coherent spherical magnetic field waves by Monte Carlo simulation. The spin waves are found to propagate and interfere according to the classic rule of interference pattern generated by two point sources. The interference pattern of spin wave is observed in one boundary of the lattice. The interference pattern is detected and studied by spin flip statistics at high and low temperatures. The destructive interference is manifested as the large number of spin flips and vice versa.

Solution of the mean spherical approximation for polydisperse multi-Yukawa hard-sphere fluid mixture using orthogonal polynomial expansions

NASA Astrophysics Data System (ADS)

Kalyuzhnyi, Yurij V.; Cummings, Peter T.

2006-03-01

The Blum-Høye [J. Stat. Phys. 19 317 (1978)] solution of the mean spherical approximation for a multicomponent multi-Yukawa hard-sphere fluid is extended to a polydisperse multi-Yukawa hard-sphere fluid. Our extension is based on the application of the orthogonal polynomial expansion method of Lado [Phys. Rev. E 54, 4411 (1996)]. Closed form analytical expressions for the structural and thermodynamic properties of the model are presented. They are given in terms of the parameters that follow directly from the solution. By way of illustration the method of solution is applied to describe the thermodynamic properties of the one- and two-Yukawa versions of the model.

Wave aberrations in rhesus monkeys with vision-induced ametropias

PubMed Central

Ramamirtham, Ramkumar; Kee, Chea-su; Hung, Li-Fang; Qiao-Grider, Ying; Huang, Juan; Roorda, Austin; Smith, Earl L.

2007-01-01

The purpose of this study was to investigate the relationship between refractive errors and high-order aberrations in infant rhesus monkeys. Specifically, we compared the monochromatic wave aberrations measured with a Shack-Hartman wavefront sensor between normal monkeys and monkeys with vision-induced refractive errors. Shortly after birth, both normal monkeys and treated monkeys reared with optically induced defocus or form deprivation showed a decrease in the magnitude of high-order aberrations with age. However, the decrease in aberrations was typically smaller in the treated animals. Thus, at the end of the lens-rearing period, higher than normal amounts of aberrations were observed in treated eyes, both hyperopic and myopic eyes and treated eyes that developed astigmatism, but not spherical ametropias. The total RMS wavefront error increased with the degree of spherical refractive error, but was not correlated with the degree of astigmatism. Both myopic and hyperopic treated eyes showed elevated amounts of coma and trefoil and the degree of trefoil increased with the degree of spherical ametropia. Myopic eyes also exhibited a much higher prevalence of positive spherical aberration than normal or treated hyperopic eyes. Following the onset of unrestricted vision, the amount of high-order aberrations decreased in the treated monkeys that also recovered from the experimentally induced refractive errors. Our results demonstrate that high-order aberrations are influenced by visual experience in young primates and that the increase in high-order aberrations in our treated monkeys appears to be an optical byproduct of the vision-induced alterations in ocular growth that underlie changes in refractive error. The results from our study suggest that the higher amounts of wave aberrations observed in ametropic humans are likely to be a consequence, rather than a cause, of abnormal refractive development. PMID:17825347

Scattering of massless scalar waves by magnetically charged black holes in Einstein-Yang-Mills-Higgs theory

NASA Astrophysics Data System (ADS)

Gußmann, Alexander

2017-03-01

The existence of the classical black hole solutions of the Einstein-Yang-Mills-Higgs equations with non-Abelian Yang-Mills-Higgs hair implies that not all classical stationary magnetically charged black holes can be uniquely described by their asymptotic characteristics. In fact, in a certain domain of parameters, there exist different spherically-symmetric, non-rotating and asymptotically-flat classical black hole solutions of the Einstein-Yang-Mills-Higgs equations which have the same ADM mass and the same magnetic charge but significantly different geometries in the near-horizon regions. (These are black hole solutions which are described by a Reissner-Nordström metric on the one hand and the black hole solutions with non-Abelian Yang-Mills-Higgs hair which are described by a metric which is not of Reissner-Nordström form on the other hand). One can experimentally distinguish such black holes with the same asymptotic characteristics but different near-horizon geometries classically by probing the near-horizon regions of the black holes. We argue that one way to probe the near-horizon region of a black hole which allows one to distinguish magnetically charged black holes with the same asymptotic characteristics but different near-horizon geometries is by classical scattering of waves. Using the example of a minimally-coupled massless probe scalar field scattered by magnetically charged black holes which can be obtained as solutions of the Einstein-Yang-Mills-Higgs equations with a Higgs triplet and gauge group SU(2) in the limit of an infinite Higgs self-coupling constant we show how, in this case, the scattering cross sections differ for the magnetically charged black holes with different near-horizon geometries but the same asymptotic characteristics. We find in particular that the characteristic glory peaks in the cross sections are located at different scattering angles.

EEG-distributed inverse solutions for a spherical head model

NASA Astrophysics Data System (ADS)

Riera, J. J.; Fuentes, M. E.; Valdés, P. A.; Ohárriz, Y.

1998-08-01

The theoretical study of the minimum norm solution to the MEG inverse problem has been carried out in previous papers for the particular case of spherical symmetry. However, a similar study for the EEG is remarkably more difficult due to the very complicated nature of the expression relating the voltage differences on the scalp to the primary current density (PCD) even for this simple symmetry. This paper introduces the use of the electric lead field (ELF) on the dyadic formalism in the spherical coordinate system to overcome such a drawback using an expansion of the ELF in terms of longitudinal and orthogonal vector fields. This approach allows us to represent EEG Fourier coefficients on a 2-sphere in terms of a current multipole expansion. The choice of a suitable basis for the Hilbert space of the PCDs on the brain region allows the current multipole moments to be related by spatial transfer functions to the PCD spectral coefficients. Properties of the most used distributed inverse solutions are explored on the basis of these results. Also, a part of the ELF null space is completely characterized and those spherical components of the PCD which are possible silent candidates are discussed.

Spherical nitroguanidine process

DOEpatents

Sanchez, John A.; Roemer, Edward L.; Stretz, Lawrence A.

1990-01-01

A process of preparing spherical high bulk density nitroguanidine by dissing low bulk density nitroguanidine in N-methyl pyrrolidone at elevated temperatures and then cooling the solution to lower temperatures as a liquid characterized as a nonsolvent for the nitroguanidine is provided. The process is enhanced by inclusion in the solution of from about 1 ppm up to about 250 ppm of a metal salt such as nickel nitrate, zinc nitrate or chromium nitrate, preferably from about 20 to about 50 ppm.

The pulsar force-free magnetosphere linked to its striped wind: time-dependent pseudo-spectral simulations

NASA Astrophysics Data System (ADS)

Pétri, J.

2012-07-01

Pulsar activity and its related radiation mechanism are usually explained by invoking some plasma processes occurring inside the magnetosphere, be it polar caps, outer/slot gaps or the transition region between the quasi-static magnetic dipole regime and the wave zone, like the striped wind. Despite many detailed local investigations, the global electrodynamics around those neutron stars remains poorly described with only little quantitative studies on the largest scales, i.e. of several light-cylinder radii rL. A better understanding of these compact objects requires a deep and accurate knowledge of their immediate electromagnetic surrounding within the magnetosphere and its link to the relativistic pulsar wind. This is compulsory to make any reliable predictions about the whole electric circuit, energy losses, sites of particle acceleration and the possibly associated emission mechanisms. The aim of this work is to present accurate solutions to the nearly stationary force-free pulsar magnetosphere and its link to the striped wind, for various spin periods and arbitrary inclination. To this end, the time-dependent Maxwell equations are solved in spherical geometry in the force-free approximation using a vector spherical harmonic expansion of the electromagnetic field. An exact analytical enforcement of the divergencelessness of the magnetic part is obtained by a projection method. Special care has been given to designing an algorithm able to look deeply into the magnetosphere with physically realistic ratios of stellar R* to light-cylinder rL radius. However, currently available computational resources allow us only to set R*/rL= 10-1 corresponding to pulsars with a period of 2 ms. The spherical geometry permits a proper and mathematically well-posed imposition of self-consistent physical boundary conditions on the stellar crust. We checked our code against several analytical solutions, like the Deutsch vacuum rotator solution and the Michel monopole field. We also retrieve energy losses comparable to the magnetodipole radiation formula and consistent with previous similar works. Finally, for arbitrary obliquity, we give an expression for the total electric charge of the system. It does not vanish except for the perpendicular rotator. This is due to the often ignored point charge located at the centre of the neutron star. It is questionable if such solutions with huge electric charges could exist in reality except for configurations close to an orthogonal rotator. The charge spread over the stellar crust is not a tunable parameter as often hypothesized.

Spherically symmetric conformal gravity and ''gravitational bubbles''

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

Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@inr.ac.ru

2016-01-01

The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ''gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-timesmore » (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ''nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.« less

Asymptotically flat black holes in Horndeski theory and beyond

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

Babichev, E.; Charmousis, C.; Lehébel, A., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr

We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for a pure quartic Lagrangian, the metric of which ismore » Schwarzschild. We show that under two requirements on the theory in question, any vacuum GR solution is also solution to the quartic theory. As an example, we show that a Kerr black hole with a non-trivial scalar field is an exact solution to these theories.« less

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

PubMed

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

2017-04-01

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

Dispersion in Spherical Water Drops.

ERIC Educational Resources Information Center

Eliason, John C., Jr.

1989-01-01

Discusses a laboratory exercise simulating the paths of light rays through spherical water drops by applying principles of ray optics and geometry. Describes four parts: determining the output angles, computer simulation, explorations, model testing, and solutions. Provides a computer program and some diagrams. (YP)

On mass transport in magmatic porosity waves

NASA Astrophysics Data System (ADS)

Jordan, J.; Hesse, M. A.; Rudge, J. F.

2017-12-01

Geochemical analyses of oceanic basalts indicate the mantle is lithologically heterogenous and subject to partial melting. Here we show that porosity waves-which arise naturally in models of buoyancy driven melt migration-transport mass and preserve geochemical signatures, at least partially. Prior studies of tracer transport in one dimensional porosity waves conclude that porosity waves do not transfer mass. However, it is well known that one-dimensional porosity waves are unstable in two and three dimensions and break up into sets of cylindrical or spherical porosity waves. We show that tracer transport in higher dimensional porosity waves is dramatically different than in one dimension. Lateral melt focusing into these high porosity regions leads to melt recirculating in the center of the wave. Melt focusing and recirculation are not resolvable in one dimension where no sustained transport is observed in numerical experiments of solitary porosity waves. In two and three dimensions, the recirculating melt is separated from the background melt-flow field by a circular or spherical dividing streamline and transported with the phase velocity of the porosity wave. The amount of melt focusing that occurs within any given porosity wave, and thus, the extent of the dividing streamline, and resultant volume of transported melt is extremely sensitive to the selection of porosity-permeability and porosity-rheology relationships. Therefore, we present a regime diagram spanning common parameterizations that illustrates the minimum amplitude and phase velocity required for a solitary porosity wave to transport mass as a function of material properties and common parameters used in magma dynamics and mid-ocean ridge models. The realization that solitary waves are capable of sustaining melt transport may require the reinterpretation of previous studies. For example, transport in porosity waves may allow melts that originated from the partial melting of fertile heterogeneities to retain their incompatible trace element signatures as they rise through the mantle. Porosity waves may also provide a mechanism for mixing melts derived from heterogeneities with ambient melts derived from different depths in the mantle.

Switch-on Shock and Nonlinear Kink Alfvén Waves in Solar Polar Jets

NASA Astrophysics Data System (ADS)

DeVore, C. Richard; Karpen, Judith T.; Antiochos, Spiro K.; Uritsky, Vadim

2016-05-01

It is widely accepted that solar polar jets are produced by fast magnetic reconnection in the low corona, whether driven directly by flux emergence from below or indirectly by instability onset above the photosphere. In either scenario, twisted flux on closed magnetic field lines reconnects with untwisted flux on nearby open field lines. Part of the twist is inherited by the newly reconnected open flux, which rapidly relaxes due to magnetic tension forces that transmit the twist impulsively into the outer corona and heliosphere. We propose that this transfer of twist launches switch-on MHD shock waves, which propagate parallel to the ambient coronal magnetic field ahead of the shock and convect a perpendicular component of magnetic field behind the shock. In the frame moving with the shock front, the post-shock flow is precisely Alfvénic in all three directions, whereas the pre-shock flow is super-Alfvénic along the ambient magnetic field, yielding a density enhancement at the shock front. Nonlinear kink Alfvén waves are exact solutions of the time-dependent MHD equations in the post-shock region when the ambient corona is uniform and the magnetic field is straight. We have performed and analyzed 3D Cartesian and spherical simulations of polar jets driven by instability onset in the corona. The results of both simulations are consistent with the generation of MHD switch-on shocks trailed predominantly by incompressible kink Alfvén waves. It is noteworthy that the kink waves are irrotational, in sharp contrast to the vorticity-bearing torsional waves reported from previous numerical studies. We will discuss the implications of the results for understanding solar polar jets and predicting their heliospheric signatures. Our research was supported by NASA’s LWS TR&T and H-SR programs.

Shock waves from non-spherically collapsing cavitation bubbles

NASA Astrophysics Data System (ADS)

Supponen, Outi; Obreschkow, Danail; Farhat, Mohamed

2017-11-01

Combining simultaneous high-speed imaging and hydrophone measurements, we uncover details of the multiple shock wave emission from laser-induced cavitation bubbles collapsing in a non-spherical way. For strongly deformed bubbles collapsing near a free surface, we identify the distinct shock waves caused by the jet impact onto the opposite bubble wall and by the individual collapses of the remaining bubble segments. The energy carried by each of these shocks depends on the level of bubble deformation, quantified by the anisotropy parameter ζ, the dimensionless equivalent of the Kelvin impulse. For jetting bubbles, at ζ < 0.01 , the jet impact hammer pressure is found to be the most energetic shock. Through statistical analysis of the experimental data and theoretical derivations, and by comparing bubbles deformed by different sources (variable gravity achieved on parabolic flights, and neighboring free and rigid surfaces), we find that the shock peak pressure may be approximated as the jet impact-induced water hammer as ph = 0.45 (ρc2 Δp) 1 / 2ζ-1 .

Acoustic-to-Seismic Coupling Over Porous Ground Surfaces.

DTIC Science & Technology

1984-01-01

of sound into the ground is predicted for both spherical and plane acoustic waves incident upon two models of the ground viz i) a rigid porous solid...and soils of above-ground acoustic disturbances. Furthermore it is found possible to predict the results of model measurements using continuous and...saddle point 2.4 The geometrical wave 2.5 The lateral wave 2.6 Special cases 3. POINT TO POINT PROPAGATION MEASUREMENTS USING ACOUSTIC MODELLING " 3.0

Atomic collisions in the presence of laser radiation - Time dependence and the asymptotic wave function

NASA Technical Reports Server (NTRS)

Devries, P. L.; George, T. F.

1982-01-01

A time-dependent, wave-packet description of atomic collisions in the presence of laser radiation is extracted from the more conventional time-independent, stationary-state description. This approach resolves certain difficulties of interpretation in the time-independent approach which arise in the case of asymptotic near resonance. In the two-state model investigated, the approach predicts the existence of three spherically scattered waves in this asymptotically near-resonant case.

Spherically symmetric solutions and gravitational collapse in brane-worlds

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

Heydari-Fard, Malihe; Sepangi, Hamid R., E-mail: heydarifard@qom.ac.ir, E-mail: hr-sepangi@sbu.ac.ir

2009-02-15

We consider spherically symmetric solutions within the context of brane-world theory without mirror symmetry or any form of junction conditions. For a constant curvature bulk, we obtain the modified Tolman-Oppenheimer-Volkoff (TOV) interior solutions in two cases where one is matched to a schwarzschild-de Sitter exterior while the other is consistent with an exterior solution whose structure can be used to explain the galaxy rotation curves without postulating dark matter. We also find the upper bound to the mass of a static brane-world star and show that the influence of the bulk effects on the interior solutions is small. Finally, wemore » investigate the gravitational collapse on the brane and show that the exterior of a collapsing star can be static in this scenario.« less

Integral Equations and Scattering Solutions for a Square-Well Potential.

ERIC Educational Resources Information Center

Bagchi, B.; Seyler, R. G.

1979-01-01

Derives Green's functions and integral equations for scattering solutions subject to a variety of boundary conditions. Exact solutions are obtained for the case of a finite spherical square-well potential, and properties of these solutions are discussed. (Author/HM)

Time-Dependent Simulations of Fast-Wave Heated High-Non-Inductive-Fraction H-Mode Plasmas in the National Spherical Torus Experiment Upgrade

NASA Astrophysics Data System (ADS)

Taylor, Gary; Bertelli, Nicola; Gerhardt, Stefan P.; Hosea, Joel C.; Mueller, Dennis; Perkins, Rory J.; Poli, Francesca M.; Wilson, James R.; Raman, Roger

2017-10-01

30 MHz fast-wave heating may be an effective tool for non-inductively ramping low-current plasmas to a level suitable for initiating up to 12 MW of neutral beam injection on the National Spherical Tokamak Experiment Upgrade (NSTX-U). Previously on NSTX 30 MHz fast wave heating was shown to efficiently and rapidly heat electrons; at the NSTX maximum axial toroidal magnetic field (BT(0)) of 0.55 T, 1.4 MW of 30 MHz heating increased the central electron temperature from 0.2 to 2 keV in 30 ms and generated an H-mode plasma with a non-inductive fraction (fNI) ˜ 0.7 at a plasma current (Ip) of 300 kA. NSTX-U will operate at BT(0) up to 1 T, with up to 4 MW of 30 MHz power (Prf). Predictive TRANSP free boundary transport simulations, using the TORIC full wave spectral code to calculate the fast-wave heating and current drive, have been run for NSTX-U Ip = 300 kA H-mode plasmas. Favorable scaling of fNI with 30 MHz heating power is predicted, with fNI ≥ 1 for Prf ≥ 2 MW.

Numerical investigation of interactions of multiple spherical shock waves between themselves and with the underlying surface

NASA Astrophysics Data System (ADS)

Andrushchenko, V. A.; Murashkin, I. V.; Shevelev, Yu. D.

2016-06-01

Within the investigation of various aspects of asteroid and comet danger and, in particular, the explosion of several fragments of meteoroids in the atmosphere above the Earth surface, the toy problem about four point explosions in the case of their special arrangement above the underlying surface is numerically solved. Complex interactions of primary and secondary shock waves between themselves, with the hard surface, and with tangential discontinuities are examined. The structure of flow inside gas regions disturbed by the explosions—the occurrence of eddy structures in them and the influence of reflected shocks waves on them—are investigated. The tendency of the external wave fronts of each explosion to form a unified front and the tendency of their internal hot domains to merge into a joined configuration (where the second process proceeds a little later than the first one) is revealed. This unified front and joined configuration are qualitatively identical to the external internal structure for the solitary explosion. The specially arranged explosions are chosen because the effects of multiple diffraction, interference, and, the main thing, cumulation of spherical waves are manifested more clearly in this caseTwo variants with different altitude of the explosions above the surface are calculated.

Scanning dimensional measurement using laser-trapped microsphere with optical standing-wave scale

NASA Astrophysics Data System (ADS)

Michihata, Masaki; Ueda, Shin-ichi; Takahashi, Satoru; Takamasu, Kiyoshi; Takaya, Yasuhiro

2017-06-01

We propose a laser trapping-based scanning dimensional measurement method for free-form surfaces. We previously developed a laser trapping-based microprobe for three-dimensional coordinate metrology. This probe performs two types of measurements: a tactile coordinate and a scanning measurement in the same coordinate system. The proposed scanning measurement exploits optical interference. A standing-wave field is generated between the laser-trapped microsphere and the measured surface because of the interference from the retroreflected light. The standing-wave field produces an effective length scale, and the trapped microsphere acts as a sensor to read this scale. A horizontal scan of the trapped microsphere produces a phase shift of the standing wave according to the surface topography. This shift can be measured from the change in the microsphere position. The dynamics of the trapped microsphere within the standing-wave field was estimated using a harmonic model, from which the measured surface can be reconstructed. A spherical lens was measured experimentally, yielding a radius of curvature of 2.59 mm, in agreement with the nominal specification (2.60 mm). The difference between the measured points and a spherical fitted curve was 96 nm, which demonstrates the scanning function of the laser trapping-based microprobe for free-form surfaces.

Theory of wave propagation in partially saturated double-porosity rocks: a triple-layer patchy model

NASA Astrophysics Data System (ADS)

Sun, Weitao; Ba, Jing; Carcione, José M.

2016-04-01

Wave-induced local fluid flow is known as a key mechanism to explain the intrinsic wave dissipation in fluid-saturated rocks. Understanding the relationship between the acoustic properties of rocks and fluid patch distributions is important to interpret the observed seismic wave phenomena. A triple-layer patchy (TLP) model is proposed to describe the P-wave dissipation process in a double-porosity media saturated with two immiscible fluids. The double-porosity rock consists of a solid matrix with unique host porosity and inclusions which contain the second type of pores. Two immiscible fluids are considered in concentric spherical patches, where the inner pocket and the outer sphere are saturated with different fluids. The kinetic and dissipation energy functions of local fluid flow (LFF) in the inner pocket are formulated through oscillations in spherical coordinates. The wave propagation equations of the TLP model are based on Biot's theory and the corresponding Lagrangian equations. The P-wave dispersion and attenuation caused by the Biot friction mechanism and the local fluid flow (related to the pore structure and the fluid distribution) are obtained by a plane-wave analysis from the Christoffel equations. Numerical examples and laboratory measurements indicate that P-wave dispersion and attenuation are significantly influenced by the spatial distributions of both, the solid heterogeneity and the fluid saturation distribution. The TLP model is in reasonably good agreement with White's and Johnson's models. However, differences in phase velocity suggest that the heterogeneities associated with double-porosity and dual-fluid distribution should be taken into account when describing the P-wave dispersion and attenuation in partially saturated rocks.

Topics in viscous potential flow of two-phase systems

NASA Astrophysics Data System (ADS)

Padrino Inciarte, Juan Carlos

Two-phase flows are ubiquitous, from natural and domestic environments to industrial settings. However, due to their complexity, modeling these fluid systems remains a challenge from both the perspective of fundamental questions on the dynamics of an individual, smooth interface, and the perspective of integral analyses, which involve averaging of the conservation laws over large domains, thereby missing local details of the flow. In this work, we consider a set of five problems concerning the linear and non-linear dynamics of an interface or free surface and the study of cavitation inception. Analyses are carried out by assuming the fluid motion to be irrotational, that is, with zero vorticity, and the fluids to be viscous, although results from rotational analyses are presented for the purpose of comparison. The problems considered here are the following: First, we analyze the non-linear deformation and break-up of a bubble or drop immersed in a uniaxial extensional flow of an incompressible viscous fluid. The method of viscous potential flow, in which the flow field is irrotational and viscosity enters through the balance of normal stresses at the interface, is used in the analysis. The governing equations are solved numerically to track the motion of the interface by coupling a boundary element method with a time-integration routine. When break-up occurs, the break-up time computed here is compared with results obtained elsewhere from numerical simulations of the Navier.Stokes equations, which thus keeps vorticity in the analysis, for several combinations of the relevant dimensionless parameters of the problem. For the bubble, for Weber numbers 3 ≤ We ≤ 6, predictions from viscous potential flow shows good agreement with the results from the Navier.Stokes equations for the bubble break-up time, whereas for larger We, the former underpredicts the results given by the latter. Including viscosity increases the break-up time with respect to the inviscid case. For the drop, as expected, increasing the viscous effects of the irrotational motion produces large, elongated drops that take longer to break up in comparison with results for inviscid fluids. In the second problem, we compute the force acting on a spherical bubble of variable radius moving within a liquid with an outer spherical boundary. Viscous potential flow and the dissipation method, which is another purely irrotational approach stemming from the mechanical energy equation, are both systematically implemented. This exposes the role of the choice of the outer boundary condition for the stress on the drag, an issue not explained in the literature known to us. By means of the well-known "cell-model" analysis, the results for the drag are then applied to the case of a swarm of rising bubbles having a certain void fraction. Computations from the dissipation method for the drag coefficient and rise velocity for a bubble swarm agree with numerical solutions; evaluation against experimental data for high Reynolds and low Weber numbers shows that all the models considered, including those given in the literature, overpredict the bubble swarm rise velocity. In the next two problems, we apply the analysis of viscous potential flow and the dissipation method to study the linear dynamics of waves of "small" amplitude acting either on a plane or on a spherical interface separating a liquid from a dynamically inactive fluid. It is shown that the viscous irrational theories exhibit the features of the wave dynamics by comparing with the exact solution. The range of parameters for which good agreement with the exact solution exists is presented. The general trend shows that for long waves the dissipation method results in the best approximation, whereas for short waves, even for very viscous liquids, viscous potential flow demonstrates better agreement. Finally, the problem of cavitation inception for the flow of a viscous liquid past a stationary sphere is studied by means of the theory of stress-induced cavitation. The flow field for a single phase needed in the analysis is found from three different methods, namely, the numerical solution of the Navier--Stokes equations, the irrotational motion of a viscous fluid, and, in the limit of no inertia, the Stokes flow formulation. The new predictions are then compared with those obtained from the classical pressure criterion. The main finding is that at a fixed cavitation number more viscous liquids are at greater risk to cavitation.

Bubbles with shock waves and ultrasound: a review.

PubMed

Ohl, Siew-Wan; Klaseboer, Evert; Khoo, Boo Cheong

2015-10-06

The study of the interaction of bubbles with shock waves and ultrasound is sometimes termed 'acoustic cavitation'. It is of importance in many biomedical applications where sound waves are applied. The use of shock waves and ultrasound in medical treatments is appealing because of their non-invasiveness. In this review, we present a variety of acoustics-bubble interactions, with a focus on shock wave-bubble interaction and bubble cloud phenomena. The dynamics of a single spherically oscillating bubble is rather well understood. However, when there is a nearby surface, the bubble often collapses non-spherically with a high-speed jet. The direction of the jet depends on the 'resistance' of the boundary: the bubble jets towards a rigid boundary, splits up near an elastic boundary, and jets away from a free surface. The presence of a shock wave complicates the bubble dynamics further. We shall discuss both experimental studies using high-speed photography and numerical simulations involving shock wave-bubble interaction. In biomedical applications, instead of a single bubble, often clouds of bubbles appear (consisting of many individual bubbles). The dynamics of such a bubble cloud is even more complex. We shall show some of the phenomena observed in a high-intensity focused ultrasound (HIFU) field. The nonlinear nature of the sound field and the complex inter-bubble interaction in a cloud present challenges to a comprehensive understanding of the physics of the bubble cloud in HIFU. We conclude the article with some comments on the challenges ahead.

Solution of Eshelby's inclusion problem with a bounded domain and Eshelby's tensor for a spherical inclusion in a finite spherical matrix based on a simplified strain gradient elasticity theory

NASA Astrophysics Data System (ADS)

Gao, X.-L.; Ma, H. M.

2010-05-01

A solution for Eshelby's inclusion problem of a finite homogeneous isotropic elastic body containing an inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). An extended Betti's reciprocal theorem and an extended Somigliana's identity based on the SSGET are proposed and utilized to solve the finite-domain inclusion problem. The solution for the disturbed displacement field is expressed in terms of the Green's function for an infinite three-dimensional elastic body in the SSGET. It contains a volume integral term and a surface integral term. The former is the same as that for the infinite-domain inclusion problem based on the SSGET, while the latter represents the boundary effect. The solution reduces to that of the infinite-domain inclusion problem when the boundary effect is not considered. The problem of a spherical inclusion embedded concentrically in a finite spherical elastic body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. This Eshelby tensor depends on the position, inclusion size, matrix size, and material length scale parameter, and, as a result, can capture the inclusion size and boundary effects, unlike existing Eshelby tensors. It reduces to the classical Eshelby tensor for the spherical inclusion in an infinite matrix if both the strain gradient and boundary effects are suppressed. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high. However, the inclusion size effect is diminishing as the inclusion becomes large enough, and the boundary effect is vanishing as the inclusion volume fraction gets sufficiently low.

Analytic Description of Critical Point Nuclei in a Spherical-Axially Deformed Shape Phase Transition

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

Iachello, F.

2001-07-30

An approximate solution at the critical point of the spherical to axially deformed shape phase transition in nuclei is presented. The eigenvalues of the Hamiltonian are expressed in terms of zeros of Bessel functions of irrational order.

Plasma instability in fast spherical discharge induced by a preionization

NASA Astrophysics Data System (ADS)

Antsiferov, P. S.; Dorokhin, L. A.

2015-04-01

As it was shown earlier, fast discharge (dI/dt ˜ 1012 A/s and Imax ≈ 40 kA) in a spherical cavity (Al2O3, inner diameter 11 mm, 4 mm apertures for the current supply) filled with working gas (Ar and Xe, pressure 80 Pa), results in the formation of a plasma with the form close to spherical. The physical mechanism can be the cumulation of a convergent shock wave, which was originated near the inner surface of the discharge cavity. It was also shown for the cylindrical fast discharge that the preionization influences the dynamics of the cylindrical convergent shock wave, its evolutions becomes faster. The present work is devoted to the study of the influence of the preionization on the plasma formation in the fast discharge with spherical geometry (Ar, 80 Pa). The inductive storage with plasma erosion opening switch was used as a current driver. The spatial structure of the discharge plasma was studied by means of a pin-hole camera with the microchannel plate (MCP) detector with time gate of 5 ns. The extreme ultra violet spectra were studied by means of the grazing incidence spectrometer with the same MCP detector with time gate of 20 ns. Beside the expected effects (reduction of the spherical plasma formation time and some increase of the electron temperature), the preionization of the discharge by the current 500 A results also in the development of the plasma instabilities and destruction of the compact plasma ball in several tens of nanoseconds. Possible mechanism of the instability is discussed.

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

Suzuki, Akihiro; Maeda, Keiichi; Shigeyama, Toshikazu

A two-dimensional special relativistic radiation-hydrodynamics code is developed and applied to numerical simulations of supernova shock breakout in bipolar explosions of a blue supergiant. Our calculations successfully simulate the dynamical evolution of a blast wave in the star and its emergence from the surface. Results of the model with spherical energy deposition show a good agreement with previous simulations. Furthermore, we calculate several models with bipolar energy deposition and compare their results with the spherically symmetric model. The bolometric light curves of the shock breakout emission are calculated by a ray-tracing method. Our radiation-hydrodynamic models indicate that the early partmore » of the shock breakout emission can be used to probe the geometry of the blast wave produced as a result of the gravitational collapse of the iron core.« less

Effect of anisotropy on intensity fluctuations in oceanic turbulence

NASA Astrophysics Data System (ADS)

Baykal, Yahya

2018-04-01

For an optical spherical wave propagating in an oceanic turbulent medium, the effect of anisotropy on the received intensity fluctuations is investigated. For different anisotropy factors, the variations of the scintillation index vs. the ratio that determines the relative strength of temperature and salinity in the index fluctuations, the rate of dissipation of the mean squared temperature, the rate of dissipation of the turbulent kinetic energy, viscosity, link length and the wavelength are plotted. It is found that, for all the oceanic turbulence and the link parameters of interest, as the medium becomes more anisotropic, the intensity of the optical spherical wave fluctuates less. It is concluded that the performance of an optical wireless communication systems (OWCS) operating in anisotropic oceanic turbulence is better than the performance of OWCS operating in isotropic oceanic turbulence.

Numerical simulations of bistable flows in precessing spheroidal shells

NASA Astrophysics Data System (ADS)

Vormann, J.; Hansen, U.

2018-05-01

Precession of the rotation axis is an often neglected mechanical driving mechanism for flows in planetary interiors, through viscous coupling at the boundaries and topographic forcing in non-spherical geometries. We investigate precession-driven flows in spheroidal shells over a wide range of parameters and test the results against theoretical predictions. For Ekman numbers down to 8.0 × 10-7, we see a good accordance with the work of Busse, who assumed the precession-driven flow to be dominated by a rigid rotation component that is tilted to the main rotation axis. The velocity fields show localized small-scale structures for lower Ekman numbers and clear signals of inertial waves for some parameters. For the case of moderate viscosity and strong deformation, we report the realization of multiple solutions at the same parameter combination, depending on the initial condition.

The Space-Wise Global Gravity Model from GOCE Nominal Mission Data

NASA Astrophysics Data System (ADS)

Gatti, A.; Migliaccio, F.; Reguzzoni, M.; Sampietro, D.; Sanso, F.

2011-12-01

In the framework of the GOCE data analysis, the space-wise approach implements a multi-step collocation solution for the estimation of a global geopotential model in terms of spherical harmonic coefficients and their error covariance matrix. The main idea is to use the collocation technique to exploit the spatial correlation of the gravity field in the GOCE data reduction. In particular the method consists of an along-track Wiener filter, a collocation gridding at satellite altitude and a spherical harmonic analysis by integration. All these steps are iterated, also to account for the rotation between local orbital and gradiometer reference frame. Error covariances are computed by Montecarlo simulations. The first release of the space-wise approach was presented at the ESA Living Planet Symposium in July 2010. This model was based on only two months of GOCE data and partially contained a priori information coming from other existing gravity models, especially at low degrees and low orders. A second release was distributed after the 4th International GOCE User Workshop in May 2011. In this solution, based on eight months of GOCE data, all the dependencies from external gravity information were removed thus giving rise to a GOCE-only space-wise model. However this model showed an over-regularization at the highest degrees of the spherical harmonic expansion due to the combination technique of intermediate solutions (based on about two months of data). In this work a new space-wise solution is presented. It is based on all nominal mission data from November 2009 to mid April 2011, and its main novelty is that the intermediate solutions are now computed in such a way to avoid over-regularization in the final solution. Beyond the spherical harmonic coefficients of the global model and their error covariance matrix, the space-wise approach is able to deliver as by-products a set of spherical grids of potential and of its second derivatives at mean satellite altitude. These grids have an information content that is very similar to the original along-orbit data, but they are much easier to handle. In addition they are estimated by local least-squares collocation and therefore, although computed by a unique global covariance function, they could yield more information at local level than the spherical harmonic coefficients of the global model. For this reason these grids seem to be useful for local geophysical investigations. The estimated grids with their estimated errors are presented in this work together with proposals on possible future improvements. A test to compare the different information contents of the along-orbit data, the gridded data and the spherical harmonic coefficients is also shown.

Relativistic scattered-wave theory. II - Normalization and symmetrization. [of Dirac wavefunctions

NASA Technical Reports Server (NTRS)

Yang, C. Y.

1978-01-01

Formalisms for normalization and symmetrization of one-electron Dirac scattered-wave wavefunctions are presented. The normalization integral consists of one-dimensional radial integrals for the spherical regions and an analytic expression for the intersphere region. Symmetrization drastically reduces the size of the secular matrix to be solved. Examples for planar Pb2Se2 and tetrahedral Pd4 are discussed.

Three-Dimensional Visualization of Wave Functions for Rotating Molecule: Plot of Spherical Harmonics

ERIC Educational Resources Information Center

Nagaoka, Shin-ichi; Teramae, Hiroyuki; Nagashima, Umpei

2013-01-01

At an early stage of learning quantum chemistry, undergraduate students usually encounter the concepts of the particle in a box, the harmonic oscillator, and then the particle on a sphere. Rotational levels of a diatomic molecule can be well approximated by the energy levels of the particle on a sphere. Wave functions for the particle in a…

Helical localized wave solutions of the scalar wave equation.

PubMed

Overfelt, P L

2001-08-01

A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch.

On the stability of soliton and hairy black hole solutions of 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant

NASA Astrophysics Data System (ADS)

Baxter, J. Erik; Winstanley, Elizabeth

2016-02-01

We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant Λ. These solutions are described by N - 1 magnetic gauge field functions ωj. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any N, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions ωj have no zeros and satisfy a set of N - 1 inequalities. In the gravitational sector, we prove that there are solutions which have no instabilities in a neighbourhood of stable embedded 𝔰𝔲(2) solutions, provided the magnitude of the cosmological constant |" separators=" Λ | is sufficiently large.

Global solutions to physical vacuum problem of non-isentropic viscous gaseous stars and nonlinear asymptotic stability of stationary solutions

NASA Astrophysics Data System (ADS)

Hong, Guangyi; Luo, Tao; Zhu, Changjiang

2018-07-01

This paper is concerned with spherically symmetric motions of non-isentropic viscous gaseous stars with self-gravitation. When the stationary entropy S ‾ (x) is spherically symmetric and satisfies a suitable smallness condition, the existence and properties of the stationary solutions are obtained for 6/5 < γ < 2 with weaker constraints upon S ‾ (x) compared with the one in [26], where γ is the adiabatic exponent. The global existence of strong solutions capturing the physical vacuum singularity that the sound speed is C 1/2 -Hölder continuous across the vacuum boundary to a simplified system for non-isentropic viscous flow with self-gravitation and the nonlinear asymptotic stability of the stationary solution are proved when 4/3 < γ < 2 with the detailed convergence rates, motivated by the results and analysis of the nonlinear asymptotic stability of Lane-Emden solutions for isentropic flows in [29,30].

Torsional Alfvén Waves in a Dipolar Magnetic Field

NASA Astrophysics Data System (ADS)

Nataf, H. C.; Tigrine, Z.; Cardin, P.; Schaeffer, N.

2017-12-01

The discovery of torsional Alfvén waves in the Earth's core (Gillet et al, 2010) is a strong motivation for investigating the properties of these waves. Here, we report on the first experimental study of such waves. Alfvén waves are difficult to excite and observe in liquid metals because of their high magnetic diffusivity. Nevertheless, we obtained clear signatures of such diffusive waves in our DTS experiment. In this setup, some 40 liters of liquid sodium are contained between a ro = 210 mm-radius stainless steel outer shell, and a ri = 74 mm-radius copper inner sphere. Both spherical boundaries can rotate independently around a common vertical axis. The inner sphere shells a strong permanent magnet, which produces a nearly dipolar magnetic field whose intensity falls from 175 mT at ri to 8 mT at ro in the equatorial plane. We excite Alfvén waves in the liquid sodium by applying a sudden jerk of the inner sphere. To study the effect of global rotation, which leads to the formation of geostrophic torsional Alfvén waves, we spin the experiment at rotation rates fo = fi up to 15 Hz. The Alfvén wave produces a clear azimuthal magnetic signal on magnetometers installed in a sleeve inside the fluid. We also probe the associated azimuthal velocity field using ultrasound Doppler velocimetry. Electric potentials at the surface of the outer sphere turn out to be very revealing as well. In parallel, we use the XSHELLS magnetohydrodynamics spherical code to model torsional Alfvén waves in the experimental conditions, and beyond. We explore both linear and non-linear regimes. We observe a strong excitation of inertial waves in the equatorial plane, where the wave transits from a region of strong magnetic field to a region dominated by rotation (see figure of meridian map of azimuthal velocity). These novel observations should help deciphering the dynamics of Alfvén waves in planetary cores.

Caustics for spherical waves

DOE PAGES

de Rham, Claudia; Motohashi, Hayato

2017-03-07

We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an S O ( p ) -symmetry in an arbitrary number of space dimensions. We show that the pure Galileon, the DBI–Galileon, and the extreme-relativistic Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple S O ( p ) -waves and the existence of either a global Galilean symmetry or a global (extreme-)relativistic Galilean symmetry.

Spherical harmonic results for the 3D Kobayashi Benchmark suite

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

Brown, P N; Chang, B; Hanebutte, U R

1999-03-02

Spherical harmonic solutions are presented for the Kobayashi benchmark suite. The results were obtained with Ardra, a scalable, parallel neutron transport code developed at Lawrence Livermore National Laboratory (LLNL). The calculations were performed on the IBM ASCI Blue-Pacific computer at LLNL.

Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry

NASA Astrophysics Data System (ADS)

Kitzmann, D.; Bolte, J.; Patzer, A. B. C.

2016-11-01

The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case owing to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.

Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

Analytical solution for the transient wave propagation of a buried cylindrical P-wave line source in a semi-infinite elastic medium with a fluid surface layer

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng

2018-02-01

This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.

Changes in divergence-free grid turbulence interacting with a weak spherical shock wave

NASA Astrophysics Data System (ADS)

Kitamura, T.; Nagata, K.; Sakai, Y.; Sasoh, A.; Ito, Y.

2017-06-01

The characteristics of divergence-free grid turbulence interacting with a weak spherical shock wave with a Mach number of 1.05 are experimentally investigated. Turbulence-generating grids are used to generate nearly isotropic, divergence-free turbulence. The turbulent Reynolds number based on the Taylor microscale R eλ and the turbulent Mach number Mt are 49 ≤R eλ≤159 and 0.709 × 1 0-3≤Mt≤2.803 ×1 0-3, respectively. A spherical shock wave is generated by a diaphragmless shock tube. The instantaneous streamwise velocity before and after the interaction is measured by a hot wire probe. The results show that the root-mean-square value of streamwise velocity fluctuations (r.m.s velocity) increases and the streamwise integral length scale decreases after the interaction. The changes in the r.m.s velocity become small with the increase in R eλ and Mt for the same strength of the shock wave. This tendency is similar to that of the streamwise integral length scale. The continuous wavelet analysis shows that high intensity appears mainly in the low-frequency region and positive and negative wavelet coefficients appear periodically in time before the interaction, whereas such high intensity appears in both the low- and high-frequency regions after the interaction. The spectral analysis reveals that the energy at high wavenumbers increases after the interaction. The change in turbulence after the interaction is explained from the viewpoint of the initial turbulent Mach number. It is suggested that the change is more significant for initial divergence-free turbulence than for curl-free turbulence.

Penetration of steady fluid motions into an outer stable layer excited by MHD thermal convection in rotating spherical shells

NASA Astrophysics Data System (ADS)

Takehiro, Shin-ichi; Sasaki, Youhei

2018-03-01

Penetration of steady magneto-hydrodynamic (MHD) disturbances into an upper strongly stratified stable layer excited by MHD thermal convection in rotating spherical shells is investigated. The theoretical model proposed by Takehiro (2015) is reexamined in the case of steady fluid motion below the bottom boundary. Steady disturbances penetrate into a density stratified MHD fluid existing in the semi-infinite region in the vertical direction. The axis of rotation of the system is tilted with respect to the vertical. The basic magnetic field is uniform and may be tilted with respect to the vertical and the rotation axis. Linear dispersion relation shows that the penetration distance with zero frequency depends on the amplitude of Alfvén wave speed. When Alfvén wave speed is small, viscous diffusion becomes dominant and penetration distance is similar to the horizontal scale of the disturbance at the lower boundary. In contrast, when Alfvén wave speed becomes larger, disturbance can penetrate deeper, and penetration distance becomes proportional to the Alfvén wave speed and inversely proportional to the geometric average of viscous and magnetic diffusion coefficients and to the total horizontal wavenumber. The analytic expression of penetration distance is in good agreement with the extent of penetration of mean zonal flow induced by finite amplitude convection in a rotating spherical shell with an upper stably stratified layer embedded in an axially uniform basic magnetic field. The theory expects that the stable layer suggested in the upper part of the outer core of the earth could be penetrated completely by mean zonal flows excited by thermal/compositional convection developing below the stable layer.

The Bargmann-Wigner equations in spherical space

NASA Astrophysics Data System (ADS)

McKeon, D. G. C.; Sherry, T. N.

2006-01-01

The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of the parameters characterizing them. For spheres embedded in three, four, and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second-order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two-point function is shown to vanish at the one-loop order.

Theoretical and experimental design studies for the Atmospheric General Circulation Experiment

NASA Technical Reports Server (NTRS)

Fowlis, W. W.; Hathaway, D. H.; Miller, T. L.; Roberts, G. O.; Kopecky, K. J.

1985-01-01

The major criterion for the Atmospheric General Circulation Experiment (AGCE) design is that it be possible to realize strong baroclinic instability in the spherical configuration chosen. A configuration was selected in which a hemispherical shell of fluid is subjected to latitudinal temperature gradients on its spherical boundaries and the latitudinal boundaries are insulators. Work in the laboratory with a cylindrical version of this configuration revealed more instabilities than baroclinic instability. Since researchers fully expect these additional instabilities to appear in the spherical configuration also, they decided to continue the laboratory cylindrical annulus studies. Four flow regimes were identified: an axisymmetric Hadley circulation, boundary layer convection, baroclinic waves and deep thermal convection. Regime diagrams were prepared.

Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Jia, Shu-Liang; Huang, Qian-Min; Lan, Zhong-Zhou

2016-11-01

In this paper, a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation is investigated, which has been presented as a model for the shallow water wave in fluids or the electrostatic wave potential in plasmas. By virtue of the binary Bell polynomials, the bilinear form of this equation is obtained. With the aid of the bilinear form, N -soliton solutions are obtained by the Hirota method, periodic wave solutions are constructed via the Riemann theta function, and breather wave solutions are obtained according to the extended homoclinic test approach. Travelling waves are constructed by the polynomial expansion method as well. Then, the relations between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure. Furthermore, we obtain some new solutions of this equation by the standard extended homoclinic test approach. Finally, we give a generalized form of this equation, and find that similar analytical solutions can be obtained from the generalized equation with arbitrary coefficients.

Simulation of wave propagation in three-dimensional random media

NASA Astrophysics Data System (ADS)

Coles, Wm. A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1995-04-01

Quantitative error analyses for the simulation of wave propagation in three-dimensional random media, when narrow angular scattering is assumed, are presented for plane-wave and spherical-wave geometry. This includes the errors that result from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive indices of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared with the spatial spectra of

Stimulated Raman scattering of sub-millimeter waves in bismuth

NASA Astrophysics Data System (ADS)

Kumar, Pawan; Tripathi, V. K.

2007-12-01

A high-power sub-millimeter wave propagating through bismuth, a semimetal with non-spherical energy surfaces, parametrically excites a space-charge mode and a back-scattered electromagnetic wave. The free carrier density perturbation associated with the space-charge wave couples with the oscillatory velocity due to the pump to derive the scattered wave. The scattered and pump waves exert a pondermotive force on electrons and holes, driving the space-charge wave. The collisional damping of the decay waves determines the threshold for the parametric instability. The threshold intensity for 20 μm wavelength pump turns out to be ˜2×1012 W/cm2. Above the threshold, the growth rate scales increase with ωo, attain a maximum around ωo=6.5ωp, and, after this, falls off.

Static models with conformal symmetry

NASA Astrophysics Data System (ADS)

Manjonjo, A. M.; Maharaj, S. D.; Moopanar, S.

2018-02-01

We study static spherically symmetric spacetimes with a spherical conformal symmetry and a nonstatic conformal factor associated with the conformal Killing field. With these assumptions we find an explicit relationship relating two metric components of the metric tensor field. This leads to the general solution of the Einstein field equations with a conformal symmetry in a static spherically symmetric spacetime. For perfect fluids we can find all metrics explicitly and show that the models always admit a barotropic equation of state. Contained within this class of spacetimes are the well known metrics of (interior) Schwarzschild, Tolman, Kuchowicz, Korkina and Orlyanskii, Patwardhan and Vaidya, and Buchdahl and Land. The isothermal metric of Saslaw et al also admits a conformal symmetry. For imperfect fluids an infinite family of exact solutions to the field equations can be generated.

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

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

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

Euclidean, Spherical, and Hyperbolic Shadows

ERIC Educational Resources Information Center

Hoban, Ryan

2013-01-01

Many classical problems in elementary calculus use Euclidean geometry. This article takes such a problem and solves it in hyperbolic and in spherical geometry instead. The solution requires only the ability to compute distances and intersections of points in these geometries. The dramatically different results we obtain illustrate the effect…

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

PubMed

Liu, Wei; Zhang, Jing; Li, Xiliang

2018-01-01

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

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

PubMed Central

Zhang, Jing; Li, Xiliang

2018-01-01

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

Finite-difference numerical simulations of underground explosion cavity decoupling

NASA Astrophysics Data System (ADS)

Aldridge, D. F.; Preston, L. A.; Jensen, R. P.

2012-12-01

Earth models containing a significant portion of ideal fluid (e.g., air and/or water) are of increasing interest in seismic wave propagation simulations. Examples include a marine model with a thick water layer, and a land model with air overlying a rugged topographic surface. The atmospheric infrasound community is currently interested in coupled seismic-acoustic propagation of low-frequency signals over long ranges (~tens to ~hundreds of kilometers). Also, accurate and efficient numerical treatment of models containing underground air-filled voids (caves, caverns, tunnels, subterranean man-made facilities) is essential. In support of the Source Physics Experiment (SPE) conducted at the Nevada National Security Site (NNSS), we are developing a numerical algorithm for simulating coupled seismic and acoustic wave propagation in mixed solid/fluid media. Solution methodology involves explicit, time-domain, finite-differencing of the elastodynamic velocity-stress partial differential system on a three-dimensional staggered spatial grid. Conditional logic is used to avoid shear stress updating within the fluid zones; this approach leads to computational efficiency gains for models containing a significant proportion of ideal fluid. Numerical stability and accuracy are maintained at air/rock interfaces (where the contrast in mass density is on the order of 1 to 2000) via a finite-difference operator "order switching" formalism. The fourth-order spatial FD operator used throughout the bulk of the earth model is reduced to second-order in the immediate vicinity of a high-contrast interface. Current modeling efforts are oriented toward quantifying the amount of atmospheric infrasound energy generated by various underground seismic sources (explosions and earthquakes). Source depth and orientation, and surface topography play obvious roles. The cavity decoupling problem, where an explosion is detonated within an air-filled void, is of special interest. A point explosion source located at the center of a spherical cavity generates only diverging compressional waves. However, we find that shear waves are generated by an off-center source, or by a non-spherical cavity (e.g. a tunnel). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Gravitational Wave Experiments - Proceedings of the First Edoardo Amaldi Conference

NASA Astrophysics Data System (ADS)

Coccia, E.; Pizzella, G.; Ronga, F.

1995-07-01

The Table of Contents for the full book PDF is as follows: * Foreword * Notes on Edoardo Amaldi's Life and Activity * PART I. INVITED LECTURES * Sources and Telescopes * Sources of Gravitational Radiation for Detectors of the 21st Century * Neutrino Telescopes * γ-Ray Bursts * Space Detectors * LISA — Laser Interferometer Space Antenna for Gravitational Wave Measurements * Search for Massive Coalescing Binaries with the Spacecraft ULYSSES * Interferometers * The LIGO Project: Progress and Prospects * The VIRGO Experiment: Status of the Art * GEO 600 — A 600-m Laser Interferometric Gravitational Wave Antenna * 300-m Laser Interferometer Gravitational Wave Detector (TAMA300) in Japan * Resonant Detectors * Search for Continuous Gravitational Wave from Pulsars with Resonant Detector * Operation of the ALLEGRO Detector at LSU * Preliminary Results of the New Run of Measurements with the Resonant Antenna EXPLORER * Operation of the Perth Cryogenic Resonant-Bar Gravitational Wave Detector * The NAUTILUS Experiment * Status of the AURIGA Gravitational Wave Antenna and Perspectives for the Gravitational Waves Search with Ultracryogenic Resonant Detectors * Ultralow Temperature Resonant-Mass Gravitational Radiation Detectors: Current Status of the Stanford Program * Electromechanical Transducers and Bandwidth of Resonant-Mass Gravitational-Wave Detectors * Fully Numerical Data Analysis for Resonant Gravitational Wave Detectors: Optimal Filter and Available Information * PART II. CONTRIBUTED PAPERS * Sources and Telescopes * The Local Supernova Production * Periodic Gravitational Signals from Galactic Pulsars * On a Possibility of Scalar Gravitational Wave Detection from the Binary Pulsars PSR 1913+16 * Kazan Gravitational Wave Detector “Dulkyn”: General Concept and Prospects of Construction * Hierarchical Approach to the Theory of Detection of Periodic Gravitational Radiation * Application of Gravitational Antennae for Fundamental Geophysical Problems * On Production of Gravitational Radiation by Particle Accelerators and by High Power Lasers * NESTOR: An Underwater Cerenkov Detector for Neutrino Astronomy * A Cosmic-Ray Veto System for the Gravitational Wave Detector NAUTLUS * Interferometers * Development of a 20m Prototype Laser Interferometric Gravitational Wave Detector at NAO * Production of Higher-Order Light Modes by High Quality Optical Components * Vibration Isolation and Suspension Systems for Laser Interferometer Gravitational Wave Detectors * Quality Factors of Stainless Steel Pendulum Wires * Reduction of Suspension Thermal Noises in Laser Free Masses Gravitational Antenna by Correlation of the Output with Additional Optical Signal * Resonant Detectors * Regeneration Effects in a Resonant Gravitational Wave Detector * A Cryogenic Sapphire Transducer with Double Frequency Pumping for Resonant Mass GW Detectors * Effect of Parametric Instability of Gravitational Wave Antenna with Microwave Cavity Transducer * Resonators of Novel Geometry for Large Mass Resonant Transducers * Measurements on the Gravitational Wave Antenna ALTAIR Equipped with a BAE Transducer * The Rome BAE Transducer: Perspectives of its Application to Ultracryogenic Gravitational Wave Antennas * Behavior of a de SQUID Tightly Coupled to a High-Q Resonant Transducer * High Q-Factor LC Resonators for Optimal Coupling * Comparison Between Different Data Analysis Procedures for Gravitational Wave Pulse Detection * Supernova 1987A Rome Maryland Gravitational Radiation Antenna Observations * Analysis of the Data Recorded by the Maryland and Rome Gravitational-Wave Detectors and the Seismic Data from Moscow and Obninsk Station during SN1987A * Multitransducer Resonant Gravitational Antennas * Local Array of High Frequency Antennas * Interaction Cross-Sections for Spherical Resonant GW Antennae * Signal-To-Noise Analysis for a Spherical Gravitational Wave Antenna Instrumented with Multiple Transducers * On the Design of Ultralow Temperature Spherical Gravitational Wave Detectors * List of Participants

On the propagation and multiple reflections of a blast wave travelling through a dusty gas in a closed box

NASA Astrophysics Data System (ADS)

Lappa, Marcello; Drikakis, Dimitris; Kokkinakis, Ioannis

2017-03-01

This paper concerns the propagation of shock waves in an enclosure filled with dusty gas. The main motivation for this problem is to probe the effect on such dynamics of solid particles dispersed in the fluid medium. This subject, which has attracted so much attention over recent years given its important implications in the study of the structural stability of systems exposed to high-energy internal detonations, is approached here in the framework of a hybrid numerical two-way coupled Eulerian-Lagrangian methodology. In particular, insights are sought by considering a relatively simple archetypal setting corresponding to a shock wave originating from a small spherical region initialized on the basis of available analytic solutions. The response of the system is explored numerically with respect to several parameters, including the blast intensity (via the related value of the initial shock Mach number), the solid mass fraction (mass load), and the particle size (Stokes number). Results are presented in terms of pressure-load diagrams. Beyond practical applications, it is shown that a kaleidoscope of fascinating patterns is produced by the "triadic" relationships among multiple shock reflection events and particle-fluid and particle-wall interaction dynamics. These would be of great interest to researchers and scientists interested in fundamental problems relating to the general theory of pattern formation in complex nonlinear multiphase systems.

Numerical estimates of seismic effects after collisions of small bodies with the Earth atmosphere

NASA Astrophysics Data System (ADS)

Svetsov, Vladimir; Shuvalov, Valery

Small bodies - meteoroids, asteroids or cometary objects of moderate size (10 - 100 m) every so often do not survive the entry through the planetary atmosphere and release their energy at some altitudes. Then the aerial blast waves reach the ground and generate Rayleigh seismic surface waves. The magnitude of the following earthquake can be significant as in the cases of the Tunguska event of 30 June 1908 or the Chelyabinsk airburst of 15 February 2013. If the pressure on the ground is known as a function of coordinates and time, the energy of seismic waves can be calculated using a solution of Lamb’s problem of the response to vertical load acting on the surface of an elastic half-space. The numerical procedure includes calculations of pressure spectra and integrals which are proportional to the energy of seismic waves. The final formula for the calculation of earthquake magnitudes was calibrated using published results of measurements made during nuclear tests on Novaya Zemlya in 1961 - 1962. We carried out numerical simulations of the aerial shock waves in Chelyabinsk event of 15 February 2013, using hydrodynamic codes. The energy input along the atmospheric trajectory inclined at 19° to the Earth surface was assumed to be proportional to the radiation intensity derived from numerous video records. The calculated magnitude of the seismic source proved to be 3.85 on the assumption that the initial kinetic energy of the asteroid was 300 kt TNT. For the energy of 500 kt TNT the magnitude was 4.0. These values are in agreement with the results of magnitude records within the measurement errors. We also calculated the magnitudes of earthquakes caused by spherical explosions with the energies from 30 kt to 30 Mt TNT (bodies from ~7 to 70 m in size) at altitudes from 5 to 45 km. The earthquake magnitude of the Chelyabinsk event corresponds to a spherical explosion at an altitude of about 35 km. For the Tunguska event of 1908, we obtained the earthquake magnitudes from 4.8 to 5.0, assuming that the body energy was from 7 to 18 Mt. Furthermore, we determined the energy of the Chulym bolide of 26 February 1984 which caused an earthquake with a magnitude of about 3.4. The calculated energy is 35 Mt TNT. The work was partly supported by the Russian Foundation for Basic Research, grant no. 13-05-00309-a

Paraboloid-aspheric lenses free of spherical aberration

NASA Astrophysics Data System (ADS)

Lozano-Rincón, Ninfa del C.; Valencia-Estrada, Juan Camilo

2017-07-01

A method to design singlet paraboloid-aspheric lenses free of all orders of spherical aberration with maximum aperture is described. This work includes all parametric formulas to describe paraboloid-aspheric or aspheric-paraboloid lenses for any finite conjugated planes. It also includes the Schwarzchilds approximations (which can be used to calculate one rigorous propagation of light waves in physic optics) to design convex paraboloid-aspheric lenses for imaging an object at infinity, with explicit formulas to calculate thicknesses easily. The results were verified with software through ray tracing.

Propagation of diffuse light in a turbid medium with multiple spherical inhomogeneities.

PubMed

Pustovit, Vitaliy N; Markel, Vadim A

2004-01-01

We develop a fast and accurate solver for the forward problem of diffusion tomography in the case of several spherical inhomogeneities. The approach allows one to take into account multiple scattering of diffuse waves between different inhomogeneities. Theoretical results are illustrated with numerical examples; excellent numerical convergence and efficiency are demonstrated. The method is generalized for the case of additional planar diffuse-nondiffuse interfaces and is therefore applicable to the half-space and slab imaging geometries.

A reflective optical transport system for ultraviolet Thomson scattering from electron plasma waves on OMEGA.

PubMed

Katz, J; Boni, R; Sorce, C; Follett, R; Shoup, M J; Froula, D H

2012-10-01

A reflective optical transport system has been designed for the OMEGA Thomson-scattering diagnostic. A Schwarzschild objective that uses two concentric spherical mirrors coupled to a Pfund objective provides diffraction-limited imaging across all reflected wavelengths. This enables the operator to perform Thomson-scattering measurements of ultraviolet (0.263 μm) light scattered from electron plasma waves.

Extended optical theorem in isotropic solids and its application to the elastic radiation force

NASA Astrophysics Data System (ADS)

Leão-Neto, J. P.; Lopes, J. H.; Silva, G. T.

2017-04-01

In this article, we derive the extended optical theorem for the elastic-wave scattering by a spherical inclusion (with and without absorption) in a solid matrix. This theorem expresses the extinction cross-section, i.e., the time-averaged power extracted from the incoming beam per its intensity, regarding the partial-wave expansion coefficients of the incident and scattered waves. We also establish the connection between the optical theorem and the elastic radiation force by a plane wave in a linear and isotropic solid. We obtain the absorption, scattering, and extinction efficiencies (the corresponding power per characteristic incident intensity per sphere cross-section area) for a plane wave and a spherically focused beam. We discuss to which extent the radiation force theory for plane waves can be used to the focused beam case. Considering an iron sphere embedded in an aluminum matrix, we numerically compute the scattering and elastic radiation force efficiencies. The radiation force on a stainless steel sphere embedded in a tissue-like medium (soft solid) is also computed. In this case, resonances are observed in the force as a function of the sphere size parameter (the wavenumber times the sphere radius). Remarkably, the relative difference between our findings and previous lossless liquid models is about 100% in the long-wavelength limit. Regarding some applications, the obtained results have a direct impact on ultrasound-based elastography techniques and ultrasonic nondestructive testing, as well as implantable devices activated by ultrasound.

Blowup Phenomenon of Solutions for the IBVP of the Compressible Euler Equations in Spherical Symmetry

PubMed Central

Cheung, Ka Luen; Wong, Sen

2016-01-01

The blowup phenomenon of solutions is investigated for the initial-boundary value problem (IBVP) of the N-dimensional Euler equations with spherical symmetry. We first show that there are only trivial solutions when the velocity is of the form c(t)|x|α−1 x + b(t)(x/|x|) for any value of α ≠ 1 or any positive integer N ≠ 1. Then, we show that blowup phenomenon occurs when α = N = 1 and c2(0)+c˙(0)<0. As a corollary, the blowup properties of solutions with velocity of the form (a˙t/at)x+b(t)(x/x) are obtained. Our analysis includes both the isentropic case (γ > 1) and the isothermal case (γ = 1). PMID:27066528

Generalizations of the Toda molecule

NASA Astrophysics Data System (ADS)

Van Velthoven, W. P. G.; Bais, F. A.

1986-12-01

Finite-energy monopole solutions are constructed for the self-dual equations with spherical symmetry in an arbitrary integer graded Lie algebra. The constraint of spherical symmetry in a complex noncoordinate basis leads to a dimensional reduction. The resulting two-dimensional ( r, t) equations are of second order and furnish new generalizations of the Toda molecule equations. These are then solved by a technique which is due to Leznov and Saveliev. For time-independent solutions a further reduction is made, leading to an ansatz for all SU(2) embeddings of the Lie algebra. The regularity condition at the origin for the solutions, needed to ensure finite energy, is also solved for a special class of nonmaximal embeddings. Explicit solutions are given for the groups SU(2), SO(4), Sp(4) and SU(4).

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

NASA Astrophysics Data System (ADS)

Crittenden, P. E.; Balachandar, S.

2018-07-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+-up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

The impact of the form of the Euler equations for radial flow in cylindrical and spherical coordinates on numerical conservation and accuracy

NASA Astrophysics Data System (ADS)

Crittenden, P. E.; Balachandar, S.

2018-03-01

The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+ -up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.

Analytical and exact solutions of the spherical and cylindrical diodes of Langmuir-Blodgett law

NASA Astrophysics Data System (ADS)

Torres-Cordoba, Rafael; Martinez-Garcia, Edgar

2017-10-01

This paper discloses the exact solutions of a mathematical model that describes the cylindrical and spherical electron current emissions within the context of a physics approximation method. The solution involves analyzing the 1D nonlinear Poisson equation, for the radial component. Although an asymptotic solution has been previously obtained, we present a theoretical solution that satisfies arbitrary boundary conditions. The solution is found in its parametric form (i.e., φ(r )=φ(r (τ)) ) and is valid when the electric field at the cathode surface is non-zero. Furthermore, the non-stationary spatial solution of the electric potential between the anode and the cathode is also presented. In this work, the particle-beam interface is considered to be at the end of the plasma sheath as described by Sutherland et al. [Phys. Plasmas 12, 033103 2005]. Three regimes of space charge effects—no space charge saturation, space charge limited, and space charge saturation—are also considered.

Efficient molecular density functional theory using generalized spherical harmonics expansions.

PubMed

Ding, Lu; Levesque, Maximilien; Borgis, Daniel; Belloni, Luc

2017-09-07

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.

Fully non-inductive second harmonic electron cyclotron plasma ramp-up in the QUEST spherical tokamak

NASA Astrophysics Data System (ADS)

Idei, H.; Kariya, T.; Imai, T.; Mishra, K.; Onchi, T.; Watanabe, O.; Zushi, H.; Hanada, K.; Qian, J.; Ejiri, A.; Alam, M. M.; Nakamura, K.; Fujisawa, A.; Nagashima, Y.; Hasegawa, M.; Matsuoka, K.; Fukuyama, A.; Kubo, S.; Shimozuma, T.; Yoshikawa, M.; Sakamoto, M.; Kawasaki, S.; Nakashima, H.; Higashijima, A.; Ide, S.; Maekawa, T.; Takase, Y.; Toi, K.

2017-12-01

Fully non-inductive second (2nd) harmonic electron cyclotron (EC) plasma current ramp-up was demonstrated with a newlly developed 28 GHz system in the QUEST spherical tokamak. A high plasma current of 54 kA was non-inductively ramped up and sustained stably for 0.9 s with a 270 kW 28 GHz wave. A higher plasma current of 66 kA was also non-inductively achieved with a slow ramp-up of the vertical field. We have achieved a significantly higher plasma current than those achieved previously with the 2nd harmonic EC waves. This fully non-inductive 2nd harmonic EC plasma ramp-up method might be useful for future burning plasma devices and fusion reactors, in particular for operations at half magnetic field with the same EC heating equipment.

The effects of electron thermal radiation on laser ablative shock waves from aluminum plasma into ambient air

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

Sai Shiva, S.; Leela, Ch.; Prem Kiran, P., E-mail: premkiranuoh@gmail.com, E-mail: prem@uohyd.ac.in

2016-05-15

The effect of electron thermal radiation on 7 ns laser ablative shock waves from aluminum (Al) plasma into an ambient atmospheric air has been numerically investigated using a one-dimensional, three-temperature (electron, ion, and radiation) radiation hydrodynamic code MULTI. The governing equations in Lagrangian form are solved using an implicit scheme for planar, cylindrical, and spherical geometries. The shockwave velocities (V{sub sw}) obtained numerically are compared with our experimental values obtained over the intensity range of 2.0 × 10{sup 10} to 1.4 × 10{sup 11 }W/cm{sup 2}. It is observed that the numerically obtained V{sub sw} is significantly influenced by the thermal radiation effects which are foundmore » to be dominant in the initial stage up to 2 μs depending on the input laser energy. Also, the results are found to be sensitive to the co-ordinate geometry used in the simulation (planar, cylindrical, and spherical). Moreover, it is revealed that shock wave undergoes geometrical transitions from planar to cylindrical nature and from cylindrical to spherical nature with time during its propagation into an ambient atmospheric air. It is also observed that the spatio-temporal evolution of plasma electron and ion parameters such as temperature, specific energy, pressure, electron number density, and mass density were found to be modified significantly due to the effects of electron thermal radiation.« less

Enhanced control of light and sound trajectories with three-dimensional gradient index lenses

NASA Astrophysics Data System (ADS)

Chang, T. M.; Dupont, G.; Enoch, S.; Guenneau, S.

2012-03-01

We numerically study the focusing and bending effects of light and sound waves through heterogeneous isotropic cylindrical and spherical devices. We first point out that transformation optics and acoustics show that the control of light requires spatially varying anisotropic permittivity and permeability, while the control of sound is achieved via spatially anisotropic density and isotropic compressibility. Moreover, homogenization theory applied to electromagnetic and acoustic periodic structures leads to such artificial (although not spatially varying) anisotropic permittivity, permeability and density. We stress that homogenization is thus a natural mathematical tool for the design of structured metamaterials. To illustrate the two-step geometric transform-homogenization approach, we consider the design of cylindrical and spherical electromagnetic and acoustic lenses displaying some artificial anisotropy along their optical axis (direction of periodicity of the structural elements). Applications are sought in the design of Eaton and Luneburg lenses bending light at angles ranging from 90° to 360°, or mimicking a Schwartzchild metric, i.e. a black hole. All of these spherical metamaterials are characterized by a refractive index varying inversely with the radius which is approximated by concentric layers of homogeneous material. We finally propose some structured cylindrical metamaterials consisting of infinitely conducting or rigid toroidal channels in a homogeneous bulk material focusing light or sound waves. The functionality of these metamaterials is demonstrated via full-wave three-dimensional computations using nodal elements in the context of acoustics, and finite edge-elements in electromagnetics.

An Exact Solution of Einstein-Maxwell Gravity Coupled to a Scalar Field

NASA Technical Reports Server (NTRS)

Turyshev, S. G.

1995-01-01

The general solution to low-energy string theory representing static spherically symmetric solution of the Einstein-Maxwell gravity with a massless scalar field has been found. Some of the partial cases appear to coincide with known solutions to black holes, naked singularities, and gravity and electromagnetic fields.

Wavenumber-extended high-order oscillation control finite volume schemes for multi-dimensional aeroacoustic computations

NASA Astrophysics Data System (ADS)

Kim, Sungtae; Lee, Soogab; Kim, Kyu Hong

2008-04-01

A new numerical method toward accurate and efficient aeroacoustic computations of multi-dimensional compressible flows has been developed. The core idea of the developed scheme is to unite the advantages of the wavenumber-extended optimized scheme and M-AUSMPW+/MLP schemes by predicting a physical distribution of flow variables more accurately in multi-space dimensions. The wavenumber-extended optimization procedure for the finite volume approach based on the conservative requirement is newly proposed for accuracy enhancement, which is required to capture the acoustic portion of the solution in the smooth region. Furthermore, the new distinguishing mechanism which is based on the Gibbs phenomenon in discontinuity, between continuous and discontinuous regions is introduced to eliminate the excessive numerical dissipation in the continuous region by the restricted application of MLP according to the decision of the distinguishing function. To investigate the effectiveness of the developed method, a sequence of benchmark simulations such as spherical wave propagation, nonlinear wave propagation, shock tube problem and vortex preservation test problem are executed. Also, throughout more realistic shock-vortex interaction and muzzle blast flow problems, the utility of the new method for aeroacoustic applications is verified by comparing with the previous numerical or experimental results.

Ion absorption of the high harmonic fast wave in the National Spherical Torus Experiment

NASA Astrophysics Data System (ADS)

Rosenberg, Adam Lewis

Ion absorption of the high harmonic fast wave in a spherical torus is of critical importance to assessing the viability of the wave as a means of heating and driving current. Analysis of recent NSTX shots has revealed that under some conditions when neutral beam and RF power are injected into the plasma simultaneously, a fast ion population with energy above the beam injection energy is sustained by the wave. In agreement with modeling, these experiments find the RF-induced fast ion tail strength and neutron rate at lower B-fields to be less enhanced, likely due to a larger β profile, which promotes greater off-axis absorption where the fast ion population is small. Ion loss codes find the increased loss fraction with decreased B insufficient to account for the changes in tail strength, providing further evidence that this is an RF interaction effect. Though greater ion absorption is predicted with lower k∥, surprisingly little variation in the tail was observed, along with a neutron rate enhancement with higher k∥. Data from the neutral particle analyzer, neutron detectors, x-ray crystal spectrometer, and Thomson scattering is presented, along with results from the TRANSP transport analysis code, ray-tracing codes HPRT and CURRAY, full-wave code and AORSA, quasilinear code CQL3D, and ion loss codes EIGOL and CONBEAM.

A vectorized Poisson solver over a spherical shell and its application to the quasi-geostrophic omega-equation

NASA Technical Reports Server (NTRS)

Mullenmeister, Paul

1988-01-01

The quasi-geostrophic omega-equation in flux form is developed as an example of a Poisson problem over a spherical shell. Solutions of this equation are obtained by applying a two-parameter Chebyshev solver in vector layout for CDC 200 series computers. The performance of this vectorized algorithm greatly exceeds the performance of its scalar analog. The algorithm generates solutions of the omega-equation which are compared with the omega fields calculated with the aid of the mass continuity equation.

Flow design and simulation of a gas compression system for hydrogen fusion energy production

NASA Astrophysics Data System (ADS)

Avital, E. J.; Salvatore, E.; Munjiza, A.; Suponitsky, V.; Plant, D.; Laberge, M.

2017-08-01

An innovative gas compression system is proposed and computationally researched to achieve a short time response as needed in engineering applications such as hydrogen fusion energy reactors and high speed hammers. The system consists of a reservoir containing high pressure gas connected to a straight tube which in turn is connected to a spherical duct, where at the sphere’s centre plasma resides in the case of a fusion reactor. Diaphragm located inside the straight tube separates the reservoir’s high pressure gas from the rest of the plenum. Once the diaphragm is breached the high pressure gas enters the plenum to drive pistons located on the inner wall of the spherical duct that will eventually end compressing the plasma. Quasi-1D and axisymmetric flow formulations are used to design and analyse the flow dynamics. A spike is designed for the interface between the straight tube and the spherical duct to provide a smooth geometry transition for the flow. Flow simulations show high supersonic flow hitting the end of the spherical duct, generating a return shock wave propagating upstream and raising the pressure above the reservoir pressure as in the hammer wave problem, potentially giving temporary pressure boost to the pistons. Good agreement is revealed between the two flow formulations pointing to the usefulness of the quasi-1D formulation as a rapid solver. Nevertheless, a mild time delay in the axisymmetric flow simulation occurred due to moderate two-dimensionality effects. The compression system is settled down in a few milliseconds for a spherical duct of 0.8 m diameter using Helium gas and a uniform duct cross-section area. Various system geometries are analysed using instantaneous and time history flow plots.

The Thermal Phase Curve Offset on Tidally and Nontidally Locked Exoplanets: A Shallow Water Model

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

Penn, James; Vallis, Geoffrey K, E-mail: jp492@exeter.ac.uk, E-mail: g.vallis@exeter.ac.uk

2017-06-20

Using a shallow water model with time-dependent forcing, we show that the peak of an exoplanet thermal phase curve is, in general, offset from the secondary eclipse when the planet is rotating. That is, the planetary hot spot is offset from the point of maximal heating (the substellar point) and may lead or lag the forcing; the extent and sign of the offset are functions of both the rotation rate and orbital period of the planet. We also find that the system reaches a steady state in the reference frame of the moving forcing. The model is an extension ofmore » the well-studied Matsuno–Gill model into a full spherical geometry and with a planetary-scale translating forcing representing the insolation received on an exoplanet from a host star. The speed of the gravity waves in the model is shown to be a key metric in evaluating the phase curve offset. If the velocity of the substellar point (relative to the planet’s surface) exceeds that of the gravity waves, then the hot spot will lag the substellar point, as might be expected by consideration of forced gravity wave dynamics. However, when the substellar point is moving slower than the internal wave speed of the system, the hottest point may lead the passage of the forcing. We provide an interpretation of this result by consideration of the Rossby and Kelvin wave dynamics, as well as, in the very slowly rotating case, a one-dimensional model that yields an analytic solution. Finally, we consider the inverse problem of constraining planetary rotation rate from an observed phase curve.« less

Converging shock wave focusing and interaction with a target

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

Nitishinskiy, M.; Efimov, S.; Antonov, O.

2016-04-15

Converging shock waves in liquids can be used efficiently in the research of the extreme state of matter and in various applications. In this paper, the recent results related to the interaction of a shock wave with plasma preliminarily formed in the vicinity of the shock wave convergence are presented. The shock wave is produced by the underwater electrical explosion of a spherical wire array. The plasma is generated prior to the shock wave's arrival by a low-pressure gas discharge inside a quartz capillary placed at the equatorial plane of the array. Analysis of the Stark broadening of H{sub α}more » and H{sub β} spectral lines and line-to-continuum ratio, combined with the ratio of the relative intensities of carbon C III/C II and silicon Si III/Si II lines, were used to determine the plasma density and temperature evolution. It was found that during the first ∼200 ns with respect to the beginning of the plasma compression by the shock wave and when the spectral lines are resolved, the plasma density increases from 2 × 10{sup 17 }cm{sup −3} to 5 × 10{sup 17 }cm{sup −3}, while the temperature remains at the same value of 3–4 eV. Further, following the model of an adiabatically imploding capillary, the plasma density increases >10{sup 19 }cm{sup −3}, leading to the continuum spectra obtained experimentally, and the plasma temperature >30 eV at radii of compression of ≤20 μm. The data obtained indicate that the shock wave generated by the underwater electrical explosion of a spherical wire array retains its uniformity during the main part of its convergence.« less

Dynamic transverse shear modulus for a heterogeneous fluid-filled porous solid containing cylindrical inclusions

NASA Astrophysics Data System (ADS)

Song, Yongjia; Hu, Hengshan; Rudnicki, John W.; Duan, Yunda

2016-09-01

An exact analytical solution is presented for the effective dynamic transverse shear modulus in a heterogeneous fluid-filled porous solid containing cylindrical inclusions. The complex and frequency-dependent properties of the dynamic shear modulus are caused by the physical mechanism of mesoscopic-scale wave-induced fluid flow whose scale is smaller than wavelength but larger than the size of pores. Our model consists of three phases: a long cylindrical inclusion, a cylindrical shell of poroelastic matrix material with different mechanical and/or hydraulic properties than the inclusion and an outer region of effective homogeneous medium of laterally infinite extent. The behavior of both the inclusion and the matrix is described by Biot's consolidation equations, whereas the surrounding effective medium which is used to describe the effective transverse shear properties of the inner poroelastic composite is assumed to be a viscoelastic solid whose complex transverse shear modulus needs to be determined. The determined effective transverse shear modulus is used to quantify the S-wave attenuation and velocity dispersion in heterogeneous fluid-filled poroelastic rocks. The calculation shows the relaxation frequency and relative position of various fluid saturation dispersion curves predicted by this study exhibit very good agreement with those of a previous 2-D finite-element simulation. For the double-porosity model (inclusions having a different solid frame than the matrix but the same pore fluid as the matrix) the effective shear modulus also exhibits a size-dependent characteristic that the relaxation frequency moves to lower frequencies by two orders of magnitude if the radius of the cylindrical poroelastic composite increases by one order of magnitude. For the patchy-saturation model (inclusions having the same solid frame as the matrix but with a different pore fluid from the matrix), the heterogeneity in pore fluid cannot cause any attenuation in the transverse shear modulus at all. A comparison with the case of spherical inclusions illustrates that the transverse shear modulus for the cylindrical inclusion exhibits more S-wave attenuation than spherical inclusions.

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

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.

PubMed

Hu, Xiao-Rui; Lou, Sen-Yue; Chen, Yong

2012-05-01

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions.

Bopp-Podolsky black holes and the no-hair theorem

NASA Astrophysics Data System (ADS)

Cuzinatto, R. R.; de Melo, C. A. M.; Medeiros, L. G.; Pimentel, B. M.; Pompeia, P. J.

2018-01-01

Bopp-Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are analyzed using Bekenstein's method. It is shown that the solutions split up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp-Podolsky black holes, the non-homogeneous solutions are found to be Maxwell's solutions leading to a Reissner-Nordström black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwell one. Thus, in the light of the energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp-Podolsky fields in spherically symmetric space-times.

Integration of the Rotation of an Earth-like Body as a Perturbed Spherical Rotor

NASA Astrophysics Data System (ADS)

Ferrer, Sebastián; Lara, Martin

2010-05-01

For rigid bodies close to a sphere, we propose an analytical solution that is free from elliptic integrals and functions, and can be fundamental for application to perturbed problems. After reordering the Hamiltonian as a perturbed spherical rotor, the Lie-series solution is generated up to an arbitrary order. Using the inertia parameters of different solar system bodies, the comparison of the approximate series solution with the exact analytical one shows that the precision reached with relatively low orders is at the same level of the observational accuracy for the Earth and Mars. Thus, for instance, the periodic errors of the mathematical solution are confined to the microarcsecond level with a simple second-order truncation for the Earth. On the contrary, higher orders are required for the mathematical solution to reach a precision at the expected level of accuracy of proposed new theories for the rotational dynamics of the Moon.

Two space scatterer formalism calculation of bulk parameters of thunderclouds

NASA Technical Reports Server (NTRS)

Phanord, Dieudonne D.

1994-01-01

In a previous study, we used a modified two-space scatterer formalism of Twersky to establish for a cloud modeled as a statistically homogeneous distribution of spherical water droplets, the dispersion relations that determine its bulk propagation numbers and bulk indexes of refraction in terms of the vector equivalent scattering amplitude and the dyadic scattering amplitude of the single water droplet in isolation. The results were specialized to the forward direction of scattering while demanding that the scatterers preserve the incident polarization. We apply this approach to obtain specific numerical values for the macroscopic parameters of the cloud. We work with a cloud of density rho = 100 cm(exp -3), a wavelength lambda = 0.7774 microns, and with spherical water droplets of common radius alpha = 10 microns. In addition, the scattering medium is divided into three parts, the medium outside the cloud, moist air (the medium inside the cloud but outside the droplets), and the medium inside the spherical water droplets. The results of this report are applicable to a cloud of any geometry since the boundary does not interfere with the calculations. Also, it is important to notice the plane wave nature of the incidence wave in the moist atmosphere.

Numerical modeling of lower hybrid current drive in fully non-inductive plasma start-up experiments on TST-2

NASA Astrophysics Data System (ADS)

Tsujii, N.; Takase, Y.; Ejiri, A.; Shinya, T.; Togashi, H.; Yajima, S.; Yamazaki, H.; Moeller, C. P.; Roidl, B.; Sonehara, M.; Takahashi, W.; Toida, K.; Yoshida, Y.

2017-12-01

Non-inductive plasma start-up is a critical issue for spherical tokamaks since there is not enough room to provide neutron shielding for the center solenoid. Start-up using lower hybrid (LH) waves has been studied on the TST-2 spherical tokamak. Because of the low magnetic field of a spherical tokamak, the plasma density needs to be kept at a very low value during the plasma current ramp-up so that the plasma core remains accessible to the LH waves. However, we have found that higher density was required to sustain larger plasma current. The achievable plasma current was limited by the maximum operational toroidal field of TST-2. The existence of an optimum density for LH current drive and its toroidal field dependence is explained through a numerical simulation based on a ray tracing code and a Fokker-Planck solver. In order to access higher density at the same magnetic field, a top-launch antenna was recently installed in addition to the existing outboard-launch antenna. Increase in the density limit was observed when the power was launched from the top antenna, consistently with the numerical predictions.

Fully non-inductive plasma start-up with lower-hybrid waves using the outboard-launch and top-launch antennas on the TST-2 spherical tokamak

NASA Astrophysics Data System (ADS)

Tsujii, Naoto; Takase, Yuichi; Ejiri, Akira; Shinya, Takahiro; Yajima, Satoru; Yamazaki, Hibiki; Togashi, Hiro; Moeller, Charles P.; Roidl, Benedikt; Takahashi, Wataru; Toida, Kazuya; Yoshida, Yusuke

2017-10-01

Removal of the central solenoid is essential to realize an economical spherical tokamak fusion reactor, but non-inductive plasma start-up is a challenge. On the TST-2 spherical tokamak, non-inductive plasma start-up using lower-hybrid (LH) waves has been investigated. Using the capacitively-coupled combline (CCC) antenna installed at the outboard midplane, fully non-inductive plasma current ramp-up up to a quarter of that of the typical Ohmic discharges has been achieved. Although it was desirable to keep the density low during the plasma current ramp-up to avoid the LH density limit, it was recognized that there was a maximum current density that could be carried by a given electron density. Since the density needed to increase as the plasma current was ramped-up, the achievable plasma current was limited by the maximum operational toroidal field of TST-2. The top-launch CCC antenna was installed to access higher density with up-shift of the parallel index of refraction. Numerical analysis of LH current drive with the outboard-launch and top-launch antennas was performed and the results were qualitatively consistent with the experimental observations.

Signatures of Nonlinear Waves in Coronal Plumes and Holes

NASA Technical Reports Server (NTRS)

Ofman, Leon

1999-01-01

In recent Ultraviolet Coronagraph Spectrometer/Solar and Heliospheric Observatory (UVCS/SOHO) White Light Channel (WLC) observations we found quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes at heliocentric distances of 1.9-2.45 solar radii. The motivation for the observation is the 2.5D Magnetohydrodynamics (MHD) model of solar wind acceleration by nonlinear waves, that predicts compressive fluctuations in coronal holes. To help identify the waves observed with the UVCS/WLC we model the propagation and dissipation of slow magnetosonic waves in polar plumes using 1D MHD code in spherical geometry, We find that the slow waves nonlinearly steepen in the gravitationally stratified plumes. The nonlinear steepening of the waves leads to enhanced dissipation due to compressive viscosity at the wave-fronts.

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

Li Jibin; Qiao Zhijun

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

Generation of extreme state of water by spherical wire array underwater electrical explosion

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

Antonov, O.; Gilburd, L.; Efimov, S.

2012-10-15

The results of the first experiments on the underwater electrical explosion of a spherical wire array generating a converging strong shock wave are reported. Using a moderate pulse power generator with a stored energy of {<=}6 kJ and discharge current of {<=}500 kA with a rise-time of {approx}300 ns, explosions of Cu and Al wire arrays of different diameters and with a different number and diameter of wires were tested. Electrical, optical, and destruction diagnostics were used to determine the energy deposited into the array, the time-of-flight of the shock wave to the origin of the implosion, and the parametersmore » of water at that location. The experimental and numerical simulation results indicate that the convergence of the shock wave leads to the formation of an extreme state of water in the vicinity of the implosion origin that is characterized by pressure, temperature, and compression factors of (2 {+-} 0.2) Multiplication-Sign 10{sup 12} Pa, 8 {+-} 0.5 eV, and 7 {+-} 0.5, respectively.« less

Amplitude-modulated acoustic radiation force experienced by elastic and viscoelastic spherical shells in progressive waves.

PubMed

Mitri, F G; Fellah, Z E A

2006-07-01

The dynamic acoustic radiation force resulting from a dual-frequency beam incident on spherical shells immersed in an inviscid fluid is examined theoretically in relation to their thickness and the contents of their interior hollow regions. The theory is modified to include a hysteresis type of absorption inside the shells' material. The results of numerical calculations are presented for stainless steel and absorbing lucite (PolyMethyMethacrylAte) shells with the hollow region filled with water or air. Significant differences occur when the interior fluid inside the hollow region is changed from water to air. It is shown that the dynamic radiation force function Yd deviates from the static radiation force function Yp when the modulation size parameter deltax = mid R:x2 - x1mid R: (x1 = k1a, x2 = k2a, k1 and k2 are the wave vectors of the incident ultrasound waves, and a is the outer radius of the shell) starts to exceed the width of the resonance peaks in the Yp curves.

Nonparaxial wave beams and packets with general astigmatism

NASA Astrophysics Data System (ADS)

Kiselev, A. P.; Plachenov, A. B.; Chamorro-Posada, P.

2012-04-01

We present exact solutions of the wave equation involving an arbitrary wave form with a phase closely similar to the general astigmatic phase of paraxial wave optics. Special choices of the wave form allow general astigmatic beamlike and pulselike waves with a Gaussian-type unrestricted localization in space and time. These solutions are generalizations of the known Bateman-type waves obtained from the connection existing between beamlike solutions of the paraxial parabolic equation and relatively undistorted wave solutions of the wave equation. As a technical tool, we present a full description of parametrizations of 2×2 symmetric matrices with positive imaginary part, which arise in the theory of Gaussian beams.

Morphological Control of Metal Oxide-Doped Zinc Oxide and Application to Cosmetics

NASA Astrophysics Data System (ADS)

Goto, Takehiro; Yin, Shu; Sato, Tsugio; Tanaka, Takumi

2012-06-01

Zinc oxide shows excellent transparency and ultraviolet radiation shielding ability, and is used for various cosmetics.1-3 However, it possesses high catalytic activity and lower dispersibility. Therefore, spherical particles of zinc oxide have been synthesized by soft solution reaction using zinc nitrate, ethylene glycol, sodium hydroxide and triethanolamine as starting materials. After dissolving these compounds in water, the solution was heated at 90°C for 1 h to form almost mono-dispersed spherical zinc oxide particles. The particle size changed depending on zinc ion concentration, ethylene glycol concentration and so on. Furthermore, with doping some metal ions, the phtocatalytic activity could be decreased. The obtained monodispersed metal ion-doped spherical zinc oxides showed excellent UV shielding ability and low photocatalytic activity. Therefore, they are expected to be used as cosmetics ingredients.

Tests and applications of nonlinear force-free field extrapolations in spherical geometry

NASA Astrophysics Data System (ADS)

Guo, Y.; Ding, M. D.

2013-07-01

We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry with an analytical solution from Low and Lou. The potential field source surface (PFSS) model is served as the initial and boundary conditions where observed data are not available. The analytical solution can be well recovered if the boundary and initial conditions are properly handled. Next, we discuss the preprocessing procedure for the noisy bottom boundary data, and find that preprocessing is necessary for NLFFF extrapolations when we use the observed photospheric magnetic field as bottom boundaries. Finally, we apply the NLFFF model to a solar area where four active regions interacting with each other. An M8.7 flare occurred in one active region. NLFFF modeling in spherical geometry simultaneously constructs the small and large scale magnetic field configurations better than the PFSS model does.

Spherical D-brane by tachyon condensation

NASA Astrophysics Data System (ADS)

Asakawa, Tsuguhiko; Matsuura, So

2018-03-01

We find a novel tachyon condensation which provides a D-brane system with spherical worldvolume in the flat spacetime. The tachyon profile is a deformation of a known D0-brane solution on non-BPS D3-branes in type IIA superstring theory, which realizes a bound state of a spherical D2-brane and a D0-brane. The D0-brane is resolved into the sphere as a U(1) monopole flux of the unit magnetic charge. We show that the system has the correct tension and the RR-coupling. Although the low-energy effective action of the system is the same as that of the dual description of the fuzzy sphere solution of multiple D0-branes, our system cannot be equivalent to the fuzzy sphere. The use of projective modules in describing the tachyon condensation is emphasized.

The theory of nonstationary thermophoresis of a solid spherical particle

NASA Astrophysics Data System (ADS)

Kuzmin, M. K.; Yalamov, Yu. I.

2007-06-01

The theory of nonstationary thermophoresis of a solid spherical particle in a viscous gaseous medium is presented. The theory is constructed on the solutions of fluid-dynamics and thermal problems, each of which is split into stationary and strictly nonstationary parts. The solution of the stationary parts of the problems gives the final formula for determining the stationary component of the thermophoretic velocity of this particle. To determine the nonstationary component of the thermophoretic velocity of the particle, the corresponding formula in the space of Laplace transforms is derived. The limiting value theorems from operational calculus are used for obtaining the dependence of the nonstationary component of the thermophoretic velocity of the spherical particle on the strictly nonstationary temperature gradient for large and small values of time. The factors determining the thermophoretic velocity of the particle under investigation are determined.

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

PubMed

Ankiewicz, A; Akhmediev, N

2017-07-01

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions. We also present several examples of exact solutions of second-order rogue waves, including rogue wave triplets.

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Escape of gravitational radiation from the field of massive bodies

NASA Technical Reports Server (NTRS)

Price, Richard H.; Pullin, Jorge; Kundu, Prasun K.

1993-01-01

We consider a compact source of gravitational waves of frequency omega in or near a massive spherically symmetric distribution of matter or a black hole. Recent calculations have led to apparently contradictory results for the influence of the massive body on the propagation of the waves. We show here that the results are in fact consistent and in agreement with the 'standard' viewpoint in which the high-frequency compact source produces the radiation as if in a flat background, and the background curvature affects the propagation of these waves.

Underscreening in ionic liquids: a first principles analysis.

PubMed

Rotenberg, Benjamin; Bernard, Olivier; Hansen, Jean-Pierre

2018-02-07

An attempt is made to understand the underscreening effect, observed in concentrated electrolyte solutions or melts, on the basis of simple, admittedly crude models involving charged (for the ions) and neutral (for the solvent molecules) hard spheres. The thermodynamic and structural properties of these 'primitive' and 'semi-primitive' models are calculated within mean spherical approximation, which provides the basic input required to determine the partial density response functions. The screening length [Formula: see text], which is unambiguously defined in terms of the wave-number-dependent response functions, exhibits a cross-over from a low density, Debye-like regime, to a regime where [Formula: see text] increases with density beyond a critical density at which the Debye length [Formula: see text] becomes comparable to the ion diameter. In this high density regime the ratio [Formula: see text] increases according to a power law, in qualitative agreement with experimental measurements, albeit at a much slower rate.

Underscreening in ionic liquids: a first principles analysis

NASA Astrophysics Data System (ADS)

Rotenberg, Benjamin; Bernard, Olivier; Hansen, Jean-Pierre

2018-02-01

An attempt is made to understand the underscreening effect, observed in concentrated electrolyte solutions or melts, on the basis of simple, admittedly crude models involving charged (for the ions) and neutral (for the solvent molecules) hard spheres. The thermodynamic and structural properties of these ‘primitive’ and ‘semi-primitive’ models are calculated within mean spherical approximation, which provides the basic input required to determine the partial density response functions. The screening length λS , which is unambiguously defined in terms of the wave-number-dependent response functions, exhibits a cross-over from a low density, Debye-like regime, to a regime where λS increases with density beyond a critical density at which the Debye length λD becomes comparable to the ion diameter. In this high density regime the ratio λ_S/λD increases according to a power law, in qualitative agreement with experimental measurements, albeit at a much slower rate.

Quantum Black Hole Model and HAWKING’S Radiation

NASA Astrophysics Data System (ADS)

Berezin, Victor

The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schroedinger-type equation for such a model is derived. This equation appeared to be a finite differences equation. A theory of such an equation is developed and general solution is found and investigated in details. The discrete spectrum of the bound state energy levels is obtained. All the eigenvalues appeared to be infinitely degenerate. The ground state wave functions are evaluated explicitly. The quantum black hole states are selected and investigated. It is shown that the obtained black hole mass spectrum is compatible with the existence of Hawking’s radiation in the limit of low temperatures both for large and nearly extreme Reissner-Nordstrom black holes. The above mentioned infinite degeneracy of the mass (energy) eigenvalues may appeared helpful in resolving the well known information paradox in the black hole physics.

Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere

NASA Astrophysics Data System (ADS)

Lukin, Igor P.

2017-11-01

In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.

Minimum change in spherical aberration that can be perceived

PubMed Central

Manzanera, Silvestre; Artal, Pablo

2016-01-01

It is important to know the visual sensitivity to optical blur from both a basic science perspective and a practical point of view. Of particular interest is the sensitivity to blur induced by spherical aberration because it is being used to increase depth of focus as a component of a presbyopic solution. Using a flicker detection-based procedure implemented on an adaptive optics visual simulator, we measured the spherical aberration thresholds that produce just-noticeable differences in perceived image quality. The thresholds were measured for positive and negative values of spherical aberration, for best focus and + 0.5 D and + 1.0 D of defocus. At best focus, the SA thresholds were 0.20 ± 0.01 µm and −0.17 ± 0.03 µm for positive and negative spherical aberration respectively (referred to a 6-mm pupil). These experimental values may be useful in setting spherical aberration permissible levels in different ophthalmic techniques. PMID:27699113

Processes for making dense, spherical active materials for lithium-ion cells

DOEpatents

Kang, Sun-Ho [Naperville, IL; Amine, Khalil [Downers Grove, IL

2011-11-22

Processes are provided for making dense, spherical mixed-metal carbonate or phosphate precursors that are particularly well suited for the production of active materials for electrochemical devices such as lithium ion secondary batteries. Exemplified methods include precipitating dense, spherical particles of metal carbonates or metal phosphates from a combined aqueous solution using a precipitating agent such as ammonium hydrogen carbonate, sodium hydrogen carbonate, or a mixture that includes sodium hydrogen carbonate. Other exemplified methods include precipitating dense, spherical particles of metal phosphates using a precipitating agent such as ammonium hydrogen phosphate, ammonium dihydrogen phosphate, sodium phosphate, sodium hydrogen phosphate, sodium dihydrogen phosphate, or a mixture of any two or more thereof. Further provided are compositions of and methods of making dense, spherical metal oxides and metal phosphates using the dense, spherical metal precursors. Still further provided are electrodes and batteries using the same.

From Panoramic Photos to a Low-Cost Photogrammetric Workflow for Cultural Heritage 3d Documentation

NASA Astrophysics Data System (ADS)

D'Annibale, E.; Tassetti, A. N.; Malinverni, E. S.

2013-07-01

The research aims to optimize a workflow of architecture documentation: starting from panoramic photos, tackling available instruments and technologies to propose an integrated, quick and low-cost solution of Virtual Architecture. The broader research background shows how to use spherical panoramic images for the architectural metric survey. The input data (oriented panoramic photos), the level of reliability and Image-based Modeling methods constitute an integrated and flexible 3D reconstruction approach: from the professional survey of cultural heritage to its communication in virtual museum. The proposed work results from the integration and implementation of different techniques (Multi-Image Spherical Photogrammetry, Structure from Motion, Imagebased Modeling) with the aim to achieve high metric accuracy and photorealistic performance. Different documentation chances are possible within the proposed workflow: from the virtual navigation of spherical panoramas to complex solutions of simulation and virtual reconstruction. VR tools make for the integration of different technologies and the development of new solutions for virtual navigation. Image-based Modeling techniques allow 3D model reconstruction with photo realistic and high-resolution texture. High resolution of panoramic photo and algorithms of panorama orientation and photogrammetric restitution vouch high accuracy and high-resolution texture. Automated techniques and their following integration are subject of this research. Data, advisably processed and integrated, provide different levels of analysis and virtual reconstruction joining the photogrammetric accuracy to the photorealistic performance of the shaped surfaces. Lastly, a new solution of virtual navigation is tested. Inside the same environment, it proposes the chance to interact with high resolution oriented spherical panorama and 3D reconstructed model at once.

Modeling the Effects of Transbasin Nonlinear Internal Waves Through the South China Sea Basin

DTIC Science & Technology

2013-06-01

sound propagation through the SCS needs to be developed to help maintain tactical superiority. This model will provide valuable information for...METHODOLOGY A. ACOUSTIC MODEL 1. Ray Trace Theory Modeling of sound propagation through the ocean requires solving the governing spherical wave equation...arrival structure simulation code. The model permits the study of the physics and phenomenology of sound propagation though the SCS

Diagnostic Analysis Of Ultrasound Data

DOEpatents

Chambers, David H.; Mast, Jeffrey; Azevedo, Stephen G.; Wuebbeling, Frank; Natterer, Frank; Duric, Neb; Littrup, Peter J.; Holsapple, Earle

2006-01-10

A method and apparatus are provided for investigating tissue in which acoustic data are derived from scattering a plurality of pulsed spherical or cylindrical acoustic waves from a plurality of transmission elements through the tissue to a plurality of receiving elements. The acoustic data, which include a mix of reflected and transmitted acoustic waves, are received and digitized, and a representation of a portion of the tissue is generated from the digitized acoustic data.

Sound wave generation by a spherically symmetric outburst and AGN feedback in galaxy clusters II: impact of thermal conduction.

NASA Astrophysics Data System (ADS)

Tang, Xiaping; Churazov, Eugene

2018-04-01

We analyze the impact of thermal conduction on the appearance of a shock-heated gas shell which is produced when a spherically symmetric outburst of a supermassive black hole inflates bubbles of relativistic plasma at the center of a galaxy cluster. The presence of the hot and low-density shell can be used as an ancillary indicator for a high rate of energy release during the outburst, which is required to drive strong shocks into the gas. Here we show that conduction can effectively erase such shell, unless the diffusion of electrons is heavily suppressed. We conclude that a more robust proxy to the energy release rate is the ratio between the shock radius and bubble radius. We also revisited the issue of sound waves dissipation induced by thermal conduction in a scenario, where characteristic wavelength of the sound wave is set by the total energy of the outburst. For a fiducial short outburst model, the dissipation length does not exceed the cooling radius in a typical cluster, provided that the conduction is suppressed by a factor not larger than ˜100. For quasi-continuous energy injection neither the shock-heated shell nor the outgoing sound wave are important and the role of conduction is subdominant.

Fully- and weakly-nonlinear biperiodic traveling waves in shallow water

NASA Astrophysics Data System (ADS)

Hirakawa, Tomoaki; Okamura, Makoto

2018-04-01

We directly calculate fully nonlinear traveling waves that are periodic in two independent horizontal directions (biperiodic) in shallow water. Based on the Riemann theta function, we also calculate exact periodic solutions to the Kadomtsev-Petviashvili (KP) equation, which can be obtained by assuming weakly-nonlinear, weakly-dispersive, weakly-two-dimensional waves. To clarify how the accuracy of the biperiodic KP solution is affected when some of the KP approximations are not satisfied, we compare the fully- and weakly-nonlinear periodic traveling waves of various wave amplitudes, wave depths, and interaction angles. As the interaction angle θ decreases, the wave frequency and the maximum wave height of the biperiodic KP solution both increase, and the central peak sharpens and grows beyond the height of the corresponding direct numerical solutions, indicating that the biperiodic KP solution cannot qualitatively model direct numerical solutions for θ ≲ 45^\\circ . To remedy the weak two-dimensionality approximation, we apply the correction of Yeh et al (2010 Eur. Phys. J. Spec. Top. 185 97-111) to the biperiodic KP solution, which substantially improves the solution accuracy and results in wave profiles that are indistinguishable from most other cases.

Correlations among the parameters of the spherical model for eclipsing binaries

NASA Technical Reports Server (NTRS)

Sobieski, S.; White, J. E.

1971-01-01

Correlation coefficients were computed to investigate the parameters for describing the spherical model of an eclipsing binary system. Regions in parameter hyperspace were identified where strong correlations exist and, by implication, the solution determinacy is low. The results are presented in tabular form for a large number of system configurations.

Three-Dimensional Profiles Using a Spherical Cutting Bit: Problem Solving in Practice

ERIC Educational Resources Information Center

Ollerton, Richard L.; Iskov, Grant H.; Shannon, Anthony G.

2002-01-01

An engineering problem concerned with relating the coordinates of the centre of a spherical cutting tool to the actual cutting surface leads to a potentially rich example of problem-solving techniques. Basic calculus, Lagrange multipliers and vector calculus techniques are employed to produce solutions that may be compared to better understand…

Dyons and dyonic black holes in su (N ) Einstein-Yang-Mills theory in anti-de Sitter spacetime

NASA Astrophysics Data System (ADS)

Shepherd, Ben L.; Winstanley, Elizabeth

2016-03-01

We present new spherically symmetric, dyonic soliton and black hole solutions of the su (N ) Einstein-Yang-Mills equations in four-dimensional asymptotically anti-de Sitter spacetime. The gauge field has nontrivial electric and magnetic components and is described by N -1 magnetic gauge field functions and N -1 electric gauge field functions. We explore the phase space of solutions in detail for su (2 ) and su (3 ) gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.

Static black hole solutions with a self-interacting conformally coupled scalar field

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

Dotti, Gustavo; Gleiser, Reinaldo J.; Martinez, Cristian

2008-05-15

We study static, spherically symmetric black hole solutions of the Einstein equations with a positive cosmological constant and a conformally coupled self-interacting scalar field. Exact solutions for this model found by Martinez, Troncoso, and Zanelli were subsequently shown to be unstable under linear gravitational perturbations, with modes that diverge arbitrarily fast. We find that the moduli space of static, spherically symmetric solutions that have a regular horizon--and satisfy the weak and dominant energy conditions outside the horizon--is a singular subset of a two-dimensional space parametrized by the horizon radius and the value of the scalar field at the horizon. Themore » singularity of this space of solutions provides an explanation for the instability of the Martinez, Troncoso, and Zanelli spacetimes and leads to the conclusion that, if we include stability as a criterion, there are no physically acceptable black hole solutions for this system that contain a cosmological horizon in the exterior of its event horizon.« less

Fundamental solutions to the bioheat equation and their application to magnetic fluid hyperthermia.

PubMed

Giordano, Mauricio A; Gutierrez, Gustavo; Rinaldi, Carlos

2010-01-01

Methods of predicting temperature profiles during local hyperthermia treatment are very important to avoid damage to healthy tissue. With this aim, fundamental solutions of Pennes' bioheat equation are derived in rectangular, cylindrical, and spherical coordinates. The medium is idealised as isotropic with effective thermal properties. Temperature distributions due to space- and time-dependent heat sources are obtained by the solution method presented. Applications of the fundamental solutions are addressed with emphasis on a particular problem of Magnetic Fluid Hyperthermia (MFH) consisting of a thin shell of magnetic nanoparticles in the outer surface of a spherical solid tumour. It is observed from the solution of this particular problem that the temperature profiles are strongly dependent on the distribution of the magnetic nanoparticles within the tissue. An almost uniform temperature profile is obtained inside the tumour with little penetration of therapeutic temperatures to the outer region of healthy tissue. The fundamental solutions obtained can be used to develop boundary element methods to predict temperature profiles with more complicated geometries.

Analytic solution of magnetic induction distribution of ideal hollow spherical field sources

NASA Astrophysics Data System (ADS)

Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min

2017-12-01

The Halbach type hollow spherical permanent magnet arrays (HSPMA) are volume compacted, energy efficient field sources, and capable of producing multi-Tesla field in the cavity of the array, which have attracted intense interests in many practical applications. Here, we present analytical solutions of magnetic induction to the ideal HSPMA in entire space, outside of array, within the cavity of array, and in the interior of the magnet. We obtain solutions using concept of magnetic charge to solve the Poisson's and Laplace's equations for the HSPMA. Using these analytical field expressions inside the material, a scalar demagnetization function is defined to approximately indicate the regions of magnetization reversal, partial demagnetization, and inverse magnetic saturation. The analytical field solution provides deeper insight into the nature of HSPMA and offer guidance in designing optimized one.

The sagitta and lens thickness: the exact solution and a matrix approximation for lenses with toric, spherical, and cylindrical surfaces.

PubMed

Harris, W F

1989-03-01

The exact equation for sagitta of spherical surfaces is generalized to toric surfaces which include spherical and cylindrical surfaces as special cases. Lens thickness, therefore, can be calculated accurately anywhere on a lens even in cases of extreme spherical and cylindrical powers and large diameters. The sagittae of tire- and barrel-form toric surfaces differ off the principal meridians, as is shown by a numerical example. The same holds for pulley- and capstan-form toric surfaces. A general expression is given for thickness at an arbitrary point on a toric lens. Approximate expressions are derived and re-expressed in terms of matrices. The matrix provides an elegant means of generalizing equations for spherical surfaces and lenses to toric surfaces and lenses.

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

A new spherical model for computing the radiation field available for photolysis and heating at twilight

NASA Technical Reports Server (NTRS)

Dahlback, Arne; Stamnes, Knut

1991-01-01

Accurate computation of atmospheric photodissociation and heating rates is needed in photochemical models. These quantities are proportional to the mean intensity of the solar radiation penetrating to various levels in the atmosphere. For large solar zenith angles a solution of the radiative transfer equation valid for a spherical atmosphere is required in order to obtain accurate values of the mean intensity. Such a solution based on a perturbation technique combined with the discrete ordinate method is presented. Mean intensity calculations are carried out for various solar zenith angles. These results are compared with calculations from a plane parallel radiative transfer model in order to assess the importance of using correct geometry around sunrise and sunset. This comparison shows, in agreement with previous investigations, that for solar zenith angles less than 90 deg adequate solutions are obtained for plane parallel geometry as long as spherical geometry is used to compute the direct beam attenuation; but for solar zenith angles greater than 90 deg this pseudospherical plane parallel approximation overstimates the mean intensity.

METHOD FOR PREPARATION OF SPHERICAL UO$sub 4$

DOEpatents

Gregory, J.F. Jr.; Levey, R.P. Jr.

1962-06-01

A method is given for continuously precipitating ura nium peroxide in the form of spherical particles. Seed crystals are formed in a first reaction zone by introducing an acidified aqueous uranyl nitrate solution and an aqueous hydrogen peroxide solution at a ratio of 5 to 20 per cent of the stoichiometric amount required for complete precipitation. After a mean residence time of 2 to 5 minutes in the first reaction zone, the resulting mixture is introduced into a second reaction zone, together with a large excess of hydrogen peroxide solution. The resulting UO4 is rapidly separated from the mother liquor after an over-all residence time of 5 to 11 minutes. The first reaction is maintained at a temperature of 85 to 90 deg C and the second zone above 50 deg C. Additional reaction zones may be employed for further crystal growth. The UO/sub 4/ is converted to U/sub 3/O/sub 8/ or UO/sub 2/ by heating in air or hydrogen atmosphere. This method is particularly useful for the preparation of spherical UO/sub 2/ particles 10 to 25 microns in diameter. (AEC)

Nucleation and evolution of spherical crystals with allowance for their unsteady-state growth rates

NASA Astrophysics Data System (ADS)

Alexandrov, D. V.

2018-02-01

The growth dynamics of a spherical crystal in a metastable liquid is analyzed theoretically. The unsteady-state contributions to the crystal radius and its growth rate are found as explicit functions of metastability level Δ and time t. It is shown that the fundamental contribution to the growth rate represents the time independent solution of a similar temperature conductivity problem (Alexandrov and Malygin 2013 J. Phys. A: Math. Theor. 46 455101) whereas the next unsteady-state contribution is proportional to Δ2 t . On the basis of these explicit unsteady-state solutions, the process of transient nucleation and growth of spherical crystals in a metastable system is theoretically studied at the intermediate stage of phase transformation. A complete analytical solution for the particle-radius distribution function and metastability level is constructed with allowance for the Weber-Volmer-Frenkel-Zel’dovich and Meirs kinetic mechanisms. It is shown that the obtained unsteady-state contribution to the crystal growth rate plays an important role in the nucleation process and drastically changes the particle-radius distribution function.

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

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

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

Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach.

PubMed

Geng, Xiaolong; Boufadel, Michel C; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L; Miller, Richard S

2014-09-01

A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies. Copyright © 2014 Elsevier B.V. All rights reserved.

Model Scaling of Hydrokinetic Ocean Renewable Energy Systems

NASA Astrophysics Data System (ADS)

von Ellenrieder, Karl; Valentine, William

2013-11-01

Numerical simulations are performed to validate a non-dimensional dynamic scaling procedure that can be applied to subsurface and deeply moored systems, such as hydrokinetic ocean renewable energy devices. The prototype systems are moored in water 400 m deep and include: subsurface spherical buoys moored in a shear current and excited by waves; an ocean current turbine excited by waves; and a deeply submerged spherical buoy in a shear current excited by strong current fluctuations. The corresponding model systems, which are scaled based on relative water depths of 10 m and 40 m, are also studied. For each case examined, the response of the model system closely matches the scaled response of the corresponding full-sized prototype system. The results suggest that laboratory-scale testing of complete ocean current renewable energy systems moored in a current is possible. This work was supported by the U.S. Southeast National Marine Renewable Energy Center (SNMREC).

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle.

PubMed

Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu

2006-07-10

The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.

Acoustically mediated long-range interaction among multiple spherical particles exposed to a plane standing wave

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.

Benchmark solution of the dynamic response of a spherical shell at finite strain

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

Versino, Daniele; Brock, Jerry S.

2016-09-28

Our paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. Furthermore, the equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge–Kutta schemes. Finally, we evaluate accuracy and convergence of the proposed method bymore » means of numerical examples with finite deformations and material non-linearities and inelasticity.« less

Vacuum solutions around spherically symmetric and static objects in the Starobinsky model

NASA Astrophysics Data System (ADS)

ćıkıntoǧlu, Sercan

2018-02-01

The vacuum solutions around a spherically symmetric and static object in the Starobinsky model are studied with a perturbative approach. The differential equations for the components of the metric and the Ricci scalar are obtained and solved by using the method of matched asymptotic expansions. The presence of higher order terms in this gravity model leads to the formation of a boundary layer near the surface of the star allowing the accommodation of the extra boundary conditions on the Ricci scalar. Accordingly, the metric can be different from the Schwarzschild solution near the star depending on the value of the Ricci scalar at the surface of the star while matching the Schwarzschild metric far from the star.

Generalization of the Euler-type solution to the wave equation

NASA Astrophysics Data System (ADS)

Borisov, Victor V.

2001-08-01

Generalization of the Euler-type solution to the wave equation is given. Peculiarities of the space-time structure of obtained waves are considered. For some particular cases interpretation of these waves as `subliminal' and `superluminal' is discussed. The possibility of description of electromagnetic waves by means of the scalar solutions is shown.

Plasticity solutions for soil behaviour around contracting cavities and tunnels

NASA Astrophysics Data System (ADS)

Yu, H. S.; Rowe, R. K.

1999-10-01

The action of tunnel excavation reduces the in-situ stresses along the excavated circumference and can therefore be simulated by unloading of cavities from the in-situ stress state. Increasing evidence suggests that soil behavior in the plane perpendicular to the tunnel axis can be modelled reasonably by a contracting cylindrical cavity, while movements ahead of an advancing tunnel heading can be better predicted by spherical cavity contraction theory. In the past, solutions for unloading of cavities from in-situ stresses in cohesive-frictional soils have mainly concentrated on the small strain, cylindrical cavity model. Large strain spherical cavity contraction solutions with a non-associated Mohr-Coulomb model do not seem to be widely available for tunnel applications. Also, cavity unloading solutions in undrained clays have been developed only in terms of total stresses with a linear elastic-perfectly plastic soil model. The total stress analyses do not account for the effects of strain hardening/softening, variable soil stiffness, and soil stress history (OCR). The effect of these simplifying assumptions on the predicted soil behavior around tunnels is not known.In this paper, analytical and semi-analytical solutions are presented for unloading of both cylindrical and spherical cavities from in-situ state of stresses under both drained and undrained conditions. The non-associated Mohr-Coulomb model and various critical state theories are used respectively to describe the drained and undrained stress-strain behaviors of the soils. The analytical solutions presented in this paper are developed in terms of large strain formulations. These solutions can be used to serve two main purposes: (1) to provide models for predicting soil behavior around tunnels; (2) to provide valuable benchmark solutions for verifying various numerical methods involving both Mohr-Coulomb and critical state plasticity models.

Effect of acoustic field parameters on arc acoustic binding during ultrasonic wave-assisted arc welding.

PubMed

Xie, Weifeng; Fan, Chenglei; Yang, Chunli; Lin, Sanbao

2016-03-01

As a newly developed arc welding method, power ultrasound has been successfully introduced into arc and weld pool during ultrasonic wave-assisted arc welding process. The advanced process for molten metals can be realized by utilizing additional ultrasonic field. Under the action of the acoustic wave, the plasma arc as weld heat source is regulated and its characteristics make an obvious change. Compared with the conventional arc, the ultrasonic wave-assisted arc plasma is bound significantly and becomes brighter. To reveal the dependence of the acoustic binding force on acoustic field parameters, a two-dimensional acoustic field model for ultrasonic wave-assisted arc welding device is established. The influences of the radiator height, the central pore radius, the radiator radius, and curvature radius or depth of concave radiator surface are discussed using the boundary element method. Then the authors analyze the resonant mode by this relationship curve between acoustic radiation power and radiator height. Furthermore, the best acoustic binding ability is obtained by optimizing the geometric parameters of acoustic radiator. In addition, three concave radiator surfaces including spherical cap surface, paraboloid of revolution, and rotating single curved surface are investigated systematically. Finally, both the calculation and experiment suggest that, to obtain the best acoustic binding ability, the ultrasonic wave-assisted arc welding setup should be operated under the first resonant mode using a radiator with a spherical cap surface, a small central pore, a large section radius and an appropriate curvature radius. Copyright © 2015 Elsevier B.V. All rights reserved.

New 2D dilaton gravity for nonsingular black holes

NASA Astrophysics Data System (ADS)

Kunstatter, Gabor; Maeda, Hideki; Taves, Tim

2016-05-01

We construct a two-dimensional action that is an extension of spherically symmetric Einstein-Lanczos-Lovelock (ELL) gravity. The action contains arbitrary functions of the areal radius and the norm squared of its gradient, but the field equations are second order and obey Birkhoff’s theorem. In complete analogy with spherically symmetric ELL gravity, the field equations admit the generalized Misner-Sharp mass as the first integral that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of interesting nonsingular black hole spacetimes than previously available.

Total Internal Reflection Ultrasonic Sensor for Detection of Subsurface Flaws: Proof of Concept

DTIC Science & Technology

2010-01-01

34 Tv001 Ve group (ray) velocity of the elastic wave X1, X2, X3 crystallographic coordinates x, y, z Descartes ’ coordinates tied to the transducer y0...TeO2 prism. 1.2.1. Orientation of directions and planes of interest with respect to Descartes ’ and Spherical coordinates. 1.2.2. Reflection of the...spect to Descartes ’ and Spherical coordi- nates. , (1.2.1) lili uuv Γ=ρ 2 where ρ is the crystal density and the symmetrical second rank Christoffel

Numerical simulation of MHD turbulence in three dimensions

NASA Technical Reports Server (NTRS)

Goldstein, M. L.; Roberts, D. A.; Deane, A.

1997-01-01

The evolution of Alfvenic turbulence in 3D spherical geometry can now be studied. In simulations, a fast stream is sandwiched between two slower streams. The inflow is both supersonic and superAlfvenic. Alfven waves entering the box are convected into the medium and interact nonlinearly with the velocity shear and with any structures (i.e., flux tubes) that might be present. These initial simulations suggest that velocity shear, even in spherical geometry, is able to drive a turbulent cascade which results in approximately Kolmogoroff-like power spectra.

Dynamics of Inhomogeneous Shell Systems Under Non-Stationary Loading (Survey)

NASA Astrophysics Data System (ADS)

Lugovoi, P. Z.; Meish, V. F.

2017-09-01

Experimental works on the determination of dynamics of smooth and stiffened cylindrical shells contacting with a soil medium under various non-stationary loading are reviewed. The results of studying three-layer shells of revolution whose motion equations are obtained within the framework of the hypotheses of the Timoshenko geometrically nonlinear theory are stated. The numerical results for shells with a piecewise or discrete filler enable the analysis of estimation of the influence of geometrical and physical-mechanical parameters of structures on their dynamics and reveal new mechanical effects. Basing on the classical theory of shells and rods, the effect of the discrete arrangement of ribs and coefficients of the Winkler or Pasternak elastic foundation on the normal frequencies and modes of rectangular planar cylindrical and spherical shells is studied. The number and shape of dispersion curves for longitudinal harmonic waves in a stiffened cylindrical shell are determined. The equations of vibrations of ribbed shells of revolution on Winkler or Pasternak elastic foundation are obtained using the geometrically nonlinear theory and the Timoshenko hypotheses. On applying the integral-interpolational method, numerical algorithms are developed and the corresponding non-stationary problems are solved. The special attention is paid to the statement and solution of coupled problems on the dynamical interaction of cylindrical or spherical shells with the soil water-saturated medium of different structure.

Quasinormal acoustic oscillations in the Michel flow

NASA Astrophysics Data System (ADS)

Chaverra, Eliana; Morales, Manuel D.; Sarbach, Olivier

2015-05-01

We study spherical and nonspherical linear acoustic perturbations of the Michel flow, which describes the steady radial accretion of a perfect fluid into a nonrotating black hole. The dynamics of such perturbations are governed by a scalar wave equation on an effective curved background geometry determined by the acoustic metric, which is constructed from the spacetime metric and the particle density and four-velocity of the fluid. For the problem under consideration in this paper the acoustic metric has the same qualitative features as an asymptotically flat, static and spherically symmetric black hole, and thus it represents a natural astrophysical analogue black hole. As for the case of a scalar field propagating on a Schwarzschild background, we show that acoustic perturbations of the Michel flow exhibit quasinormal oscillations. Based on a new numerical method for determining the solutions of the radial mode equation, we compute the associated frequencies and analyze their dependency on the mass of the black hole, the radius of the sonic horizon and the angular momentum number. Our results for the fundamental frequencies are compared to those obtained from an independent numerical Cauchy evolution, finding good agreement between the two approaches. When the radius of the sonic horizon is large compared to the event horizon radius, we find that the quasinormal frequencies scale approximately like the surface gravity associated with the sonic horizon.

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

NASA Astrophysics Data System (ADS)

Sun, Baonan; Wazwaz, Abdul-Majid

2018-11-01

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

Global evaluation of new GRACE mascon products for hydrologic applications

NASA Astrophysics Data System (ADS)

Scanlon, Bridget R.; Zhang, Zizhan; Save, Himanshu; Wiese, David N.; Landerer, Felix W.; Long, Di; Longuevergne, Laurent; Chen, Jianli

2016-12-01

Recent developments in mascon (mass concentration) solutions for GRACE (Gravity Recovery and Climate Experiment) satellite data have significantly increased the spatial localization and amplitude of recovered terrestrial Total Water Storage anomalies (TWSA); however, land hydrology applications have been limited. Here we compare TWSA from April 2002 through March 2015 from (1) newly released GRACE mascons from the Center for Space Research (CSR-M) with (2) NASA JPL mascons (JPL-M), and with (3) CSR Tellus gridded spherical harmonics rescaled (sf) (CSRT-GSH.sf) in 176 river basins, ˜60% of the global land area. Time series in TWSA mascons (CSR-M and JPL-M) and spherical harmonics are highly correlated (rank correlation coefficients mostly >0.9). The signal from long-term trends (up to ±20 mm/yr) is much less than that from seasonal amplitudes (up to 250 mm). Net long-term trends, summed over all 176 basins, are similar for CSR and JPL mascons (66-69 km3/yr) but are lower for spherical harmonics (˜14 km3/yr). Long-term TWSA declines are found mostly in irrigated basins (-41 to -69 km3/yr). Seasonal amplitudes agree among GRACE solutions, increasing confidence in GRACE-based seasonal fluctuations. Rescaling spherical harmonics significantly increases agreement with mascons for seasonal fluctuations, but less for long-term trends. Mascons provide advantages relative to spherical harmonics, including (1) reduced leakage from land to ocean increasing signal amplitude, and (2) application of geophysical data constraints during processing with little empirical postprocessing requirements, making it easier for nongeodetic users. Results of this product intercomparison should allow hydrologists to better select suitable GRACE solutions for hydrologic applications.

Ion-ion correlation, solvent excluded volume and pH effects on physicochemical properties of spherical oxide nanoparticles.

PubMed

Ovanesyan, Zaven; Aljzmi, Amal; Almusaynid, Manal; Khan, Asrar; Valderrama, Esteban; Nash, Kelly L; Marucho, Marcelo

2016-01-15

One major source of complexity in the implementation of nanoparticles in aqueous electrolytes arises from the strong influence that biological environments has on their physicochemical properties. A key parameter for understanding the molecular mechanisms governing the physicochemical properties of nanoparticles is the formation of the surface charge density. In this article, we present an efficient and accurate approach that combines a recently introduced classical solvation density functional theory for spherical electrical double layers with a surface complexation model to account for ion-ion correlation and excluded volume effects on the surface titration of spherical nanoparticles. We apply the proposed computational approach to account for the charge-regulated mechanisms on the surface chemistry of spherical silica (SiO2) nanoparticles. We analyze the effects of the nanoparticle size, as well as pH level and electrolyte concentration of the aqueous solution on the nanoparticle's surface charge density and Zeta potential. We validate our predictions for 580Å and 200Å nanoparticles immersed in acid, neutral and alkaline mono-valent aqueous electrolyte solutions against experimental data. Our results on mono-valent electrolyte show that the excluded volume and ion-ion correlations contribute significantly to the surface charge density and Zeta potential of the nanoparticle at high electrolyte concentration and pH levels, where the solvent crowding effects and electrostatic screening have shown a profound influence on the protonation/deprotonation reactions at the liquid/solute interface. The success of this approach in describing physicochemical properties of silica nanoparticles supports its broader application to study other spherical metal oxide nanoparticles. Copyright © 2015 Elsevier Inc. All rights reserved.

No hair theorem in quasi-dilaton massive gravity

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

Wu, De-Jun; Zhou, Shuang-Yong

We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential are fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter ormore » de Sitter asymptotics. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).« less

No hair theorem in quasi-dilaton massive gravity

DOE PAGES

Wu, De-Jun; Zhou, Shuang-Yong

2016-04-11

We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential are fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter ormore » de Sitter asymptotics. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).« less

Elastic properties of spherically anisotropic piezoelectric composites

NASA Astrophysics Data System (ADS)

Wei, En-Bo; Gu, Guo-Qing; Poon, Ying-Ming

2010-09-01

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.