Showing papers on "Plane wave published in 2006"
TL;DR: The techniques developed in this work can be used to design lattices with a desired band structure and the observed spatial filtering effects due to anisotropy at high frequencies (short wavelengths) of wave propagation are consistent with the lattice symmetries.
Abstract: Plane wave propagation in infinite two-dimensional periodic lattices is investigated using Floquet-Bloch principles. Frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies: hexagonal honeycomb, Kagome lattice, triangular honeycomb, and the square honeycomb. These topologies exhibit dramatic differences in their long-wavelength deformation properties. Long-wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices. The slenderness ratio of the constituent beams of the lattice (or relative density) has a significant influence on the band structure. The techniques developed in this work can be used to design lattices with a desired band structure. The observed spatial filtering effects due to anisotropy at high frequencies (short wavelengths) of wave propagation are consistent with the lattice symmetries.
593 citations
TL;DR: In this article, a pseudopotential plane-wave scheme is modified at the Poisson solver part with the help of the Green's function technique to screen the excess surface charge.
Abstract: A new first-principles computational approach to a charged surface/interface is presented. The surface is modeled as a slab imposed with boundary conditions to screen the excess surface charge. To treat this model, which is nonperiodic in the surface normal direction, a standard pseudopotential plane-wave scheme is modified at the Poisson solver part with the help of the Green's function technique. Benchmark calculations are done for $\mathrm{Al}∕\mathrm{Si}(111)$ with the bias voltage applied between the surface and the model scanning tunneling microscopy (STM) tip, the model back gate, or the model solution. The calculations are found to be efficient and stable, and their implementation is found to be easy. Because of the flexibility, the scheme is considered to be applicable to more general experimental situations.
551 citations
TL;DR: It is shown that the introduction of a second plane wave, propagating in a different direction, can result in an increase in the instability growth rates and enlargement of the instability region.
Abstract: Here we consider a simple weakly nonlinear model that describes the interaction of two-wave systems in deep water with two different directions of propagation. Under the hypothesis that both sea systems are narrow banded, we derive from the Zakharov equation two coupled nonlinear Schrodinger equations. Given a single unstable plane wave, here we show that the introduction of a second plane wave, propagating in a different direction, can result in an increase of the instability growth rates and enlargement of the instability region. We discuss these results in the context of the formation of rogue waves.
299 citations
TL;DR: An expression is derived for the radiation force on a sphere placed on the axis of an ideal acoustic Bessel beam propagating in an inviscid fluid using the partial-wave coefficients found in the analysis of the scattering when the sphere is placed in a plane wave traveling in the same external fluid.
Abstract: An expression is derived for the radiation force on a sphere placed on the axis of an ideal acoustic Bessel beam propagating in an inviscid fluid The expression uses the partial-wave coefficients found in the analysis of the scattering when the sphere is placed in a plane wave traveling in the same external fluid The Bessel beam is characterized by the cone angle β of its plane wave components where β=0 gives the limiting case of an ordinary plane wave Examples are found for fluid spheres where the radiation force reverses in direction so the force is opposite the direction of the beam propagation Negative axial forces are found to be correlated with conditions giving reduced backscattering by the beam This condition may also be helpful in the design of acoustic tweezers for biophysical applications Other potential applications include the manipulation of objects in microgravity Islands in the (ka,β) parameter plane having a negative radiation force are calculated for the case of a hexane drop in w
237 citations
TL;DR: The extended theory of high-frame rate imaging theory is extended to include explicitly various transmission schemes such as multiple limited-diffraction array beams and steered plane waves, and shows that image resolution and contrast are increased over a large field of view.
Abstract: Fast three-dimensional (3-D) ultrasound imaging is a technical challenge. Previously, a high-frame rate (HFR) imaging theory was developed in which a pulsed plane wave was used in transmission, and limited-diffraction array beam weightings were applied to received echo signals to produce a spatial Fourier transform of object function for 3-D image reconstruction. In this paper, the theory is extended to include explicitly various transmission schemes such as multiple limited-diffraction array beams and steered plane waves. A relationship between the limited-diffraction array beam weighting of received echo signals and a 2-D Fourier transform of the same signals over a transducer aperture is established. To verify the extended theory, computer simulations, in vitro experiments on phantoms, and in vivo experiments on the human kidney and heart were performed. Results show that image resolution and contrast are increased over a large field of view as more and more limited-diffraction array beams with different parameters or plane waves steered at different angles are used in transmissions. Thus, the method provides a continuous compromise between image quality and image frame rate that is inversely proportional to the number of transmissions used to obtain a single frame of image. From both simulations and experiments, the extended theory holds a great promise for future HFR 3-D imaging
181 citations
TL;DR: In this article, the authors developed a consistent analytic treatment of plane-wave properties for transversely isotropic (TI) media with attenuation anisotropy, assuming that the real and imaginary parts of the wave vector are parallel to one another.
Abstract: Directionally dependent attenuation in transversely isotropic (TI) media can influence significantly the body-wave amplitudes and distort the results of the AVO (amplitude variation with offset) analysis. Here, we develop a consistent analytic treatment of plane-wave properties for TI media with attenuation anisotropy. We use the concept of homogeneous wave propagation, assuming that in weakly attenuative media the real and imaginary parts of the wave vector are parallel to one another. The anisotropic quality factor can be described by matrix elements Qij , defined as the ratios of the real and imaginary parts of the corresponding stiffness coefficients. To characterize TI attenuation, we follow the idea of the Thomsen notation for velocity anisotropy and replace the components Qij by two reference isotropic quantities and
150 citations
TL;DR: This work illustrates patterns numerically and experimentally and explains the three-, four- and five-wave topologies with a phasor argument.
Abstract: When three or more plane waves overlap in space, complete destructive interference occurs on nodal lines, also called phase singularities or optical vortices. For super positions of three plane waves, the vortices are straight, parallel lines. For four plane waves the vortices form an array of closed or open loops. For five or more plane waves the loops are irregular. We illustrate these patterns numerically and experimentally and explain the three-, four- and five-wave topologies with a phasor argument.
140 citations
TL;DR: In this article, it was shown that a sound-hard polyhedral scatterer in R N (N 2 ) is uniquely determined by N far-field measurements corresponding to N incident plane waves given by a fixed wave number and linearly independent incident directions.
Abstract: This paper addresses the uniqueness for an inverse acoustic obstacle scattering problem. It is proved that a general sound-hard polyhedral scatterer in R N (N 2), possibly consisting of finitely many solid polyhedra and subsets of (N − 1)-dimensional hyperplanes, is uniquely determined by N far-field measurements corresponding to N incident plane waves given by a fixed wave number and N linearly independent incident directions. A simple proof, which is quite different from that in Alessandrini and Rondi (2005 Proc. Am. Math. Soc. 6 1685–91), is also provided for the unique determination of a general sound-soft polyhedral scatterer by a single incoming wave.
136 citations
TL;DR: A quantitative estimate for realistic experimental conditions of the ellipticity and the rotation of the main polarization plane acquired by the x-ray probe after the interaction shows that the implementation of such vacuum effects is feasible with future X-ray Free Electron Laser light.
Abstract: The nonlinear quantum interaction of a linearly polarized x-ray probe beam with a focused intense standing laser wave is studied theoretically. Because of the tight focusing of the standing laser pulse, diffraction effects arise for the probe beam as opposed to the corresponding plane wave scenario. A quantitative estimate for realistic experimental conditions of the ellipticity and the rotation of the main polarization plane acquired by the x-ray probe after the interaction shows that the implementation of such vacuum effects is feasible with future X-ray Free Electron Laser light.
133 citations
TL;DR: In this paper, the authors reported first principles self-consistent electronic structure calculations using the full-potential linearized augmented plane wave method using X-ray photoelectron spectroscopy data.
Abstract: We report first principles self-consistent electronic structure calculations of $\mathrm{Ru}{\mathrm{O}}_{2}$ and $\mathrm{Ir}{\mathrm{O}}_{2}$ using the full-potential linearized augmented plane wave method. Our electronic properties are in good agreement with x-ray photoelectron spectroscopy data regarding the bandwidths and peak positions. Additionally, we probe our electronic structures by calculating the dielectric functions and comparing them with optical measurements. Our calculations show that intraband transitions play an important role to describe properly the optical response of $\mathrm{Ru}{\mathrm{O}}_{2}$ and $\mathrm{Ir}{\mathrm{O}}_{2}$. We find that these materials are good absorbers at low energies where the dielectric functions exhibit a Drude like behavior. At higher energies, the optical features are due to electronic transitions from oxygen $2p$ to metal $d$ bands. Our results for the dielectric functions and energy loss spectra show a good agreement with optical measurements.
117 citations
TL;DR: In this paper, the simulated plane wave section method was used to separate specular reflections and diffraction events and to suppress specular events resulting in plane-wave sections of diffractions.
Abstract: Summary We use the simulated plane wave section method to separate specular reflections and diffraction events. We show that plane wave sections naturally separate specular and diffracted events and allow us to use plane-wave distruction filters to suppress specular events resulting in plane-wave sections of diffractions. A synthetic example demonstrates the effectiveness of our method in imaging faults and small-scale discontinuities.
TL;DR: This work demonstrates that total reflection is not the only possible outcome of the incident wave, and can appear in the form of a frozen mode with very large diverging amplitude and either zero, or purely tangential energy flux.
Abstract: Consider a plane monochromatic wave incident on a semi-infinite periodic structure. What happens if the normal component of the transmitted wave group velocity vanishes? At first sight, zero normal component of the transmitted wave group velocity simply implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possible outcome. Instead, the transmitted wave can appear in the form of a frozen mode with very large diverging amplitude and either zero, or purely tangential energy flux. The field amplitude in the transmitted wave can exceed that of the incident wave by several orders of magnitude. There are two qualitatively different kinds of frozen mode regime. The first one is associated with a stationary inflection point of electromagnetic dispersion relation. This phenomenon has been analyzed in our previous papers. Now, our focus is on the frozen mode regime related to a degenerate photonic band edge. An advantage of this phenomenon is that it can occur in much simpler periodic structures. This spectacular effect is extremely sensitive to the frequency and direction of propagation of the incident plane wave. These features can be very attractive in a variety of practical applications, such as higher harmonic generation and wave mixing, light amplification and lasing, highly efficient superprizms, etc.
TL;DR: In this article, a wavelet-based method is developed to calculate elastic band gaps of two-dimensional phononic crystals, where the wave field is expanded in the wavelet basis and an equivalent eigenvalue problem is derived in a matrix form involving the adaptive computation of integrals of the wavelets.
Abstract: A wavelet-based method is developed to calculate elastic band gaps of two-dimensional phononic crystals. The wave field is expanded in the wavelet basis and an equivalent eigenvalue problem is derived in a matrix form involving the adaptive computation of integrals of the wavelets. The method is applied to a binary system. We first compute the band gaps of Au cylinders in an epoxy host. The advantages of the wavelet-based method are discussed in regard with the well-known plane-wave expansion method. Then the method is used to compute the band gaps of Au cylinders in a soft rubber with elastic constant ${10}^{6}$ times lower than that of Au. The convergence tests show that the wavelet-based method can reduce the Gibbs effect to a certain extent. These advantages make it possible for easy calculations of band structures of mixed solid-fluid phononic crystals where the traditional plane wave method encounters difficulties. In addition, the adaptability of wavelets makes the method possible for efficient band gap computations of more complex phononic structures.
TL;DR: In this paper, a general plane wave decomposition procedure that determines both the wave amplitudes (or the reflection coefficient) and the wavenumbers is proposed for in-duct measurements.
TL;DR: In this paper, it was proved that the continuity of the tangential components of the average electric and magnetic fields is insufficient to describe the reflection of plane waves by a set of thin parallel wires embedded in a dielectric host using a homogenization approach.
Abstract: In this paper, it is proved that the continuity of the tangential components of the average electric and magnetic fields is insufficient to describe the reflection of plane waves by a set of thin parallel wires embedded in a dielectric host using a homogenization approach. Based on physical arguments a new boundary condition is proposed to characterize the scattering of waves by the homogenized wire medium. In order to further support the proposed theory, the problem of reflection of a plane wave by a set of semi-infinite parallel wires is solved analytically within the thin-wire approximation. Extensive numerical simulations demonstrate that when the additional boundary condition is considered the agreement between full wave results and homogenization theory is very good even for wavelengths comparable with the lattice constant.
TL;DR: In this paper, the propagation of harmonic plane waves in media described by the two-temperature theory of thermoelasticity (2TT) is investigated, and exact dispersion relation solutions are determined and several characterizations of the wave field are examined.
TL;DR: A semianalytical model that quantitatively predicts the scattering of light by a single subwavelength slit in a thick metal screen is presented and is shown to provide accurate formulas for the plasmonic generation strength coefficients, even for metals with a low conductivity.
Abstract: We present a semianalytical model that quantitatively predicts the scattering of light by a single subwavelength slit in a thick metal screen. In contrast to previous theoretical works related to the transmission properties of the slit, the analysis emphasizes the generation of surface plasmons at the slit apertures. The model relies on a two-stage scattering mechanism, a purely geometric diffraction problem in the immediate vicinity of the slit aperture followed by the launching of a bounded surface-plasmon wave on the flat interfaces surrounding the aperture. By comparison with a full electromagnetic treatment, the model is shown to provide accurate formulas for the plasmonic generation strength coefficients, even for metals with a low conductivity. Limitations are outlined for large slit widths (>λ) or oblique incidence (>30°) when the slit is illuminated by a plane wave.
TL;DR: In this article, the energy flow during the scattering of a plane wave by a small homogeneous cylinder in the vicinity of surface-plasmon resonance is analyzed, where the anomalous light scattering possesses a variety of unusual features, such as an inverse hierarchy of optical resonances and a complicated near field structure, which may include optical vortexes, optical whirlpools, and other peculiarities in nanoscale area.
Abstract: We analyze the energy flow during the scattering of a plane wave by a small homogeneous cylinder in the vicinity of surface-plasmon resonance, where ${\ensuremath{\epsilon}}^{\ensuremath{'}}=\mathrm{Re}\phantom{\rule{0.2em}{0ex}}\ensuremath{\epsilon}=\ensuremath{-}1$ ($\ensuremath{\epsilon}$ stands for permittivity). For the case of small dissipation, ${\ensuremath{\epsilon}}^{\ensuremath{''}}=\mathrm{Im}\phantom{\rule{0.2em}{0ex}}\ensuremath{\epsilon}ll1$, this scattering can strongly deviate from the classical dipole approximation (Rayleigh scattering). In certain specified cases, the Rayleigh scattering is replaced with an anomalous light scattering regardless the wire smallness. The phenomenon is based on interplay of the usual dissipative and radiative damping, where the latter is related to inverse transformation of localized resonant plasmons into scattered light. The anomalous light scattering possesses a variety of unusual features, such as an inverse hierarchy of optical resonances and a complicated near-field structure, which may include optical vortexes, optical whirlpools, and other peculiarities in nanoscale area.
TL;DR: In this article, the authors studied the long time interaction of envelope solitary gravity waves propagating at the surface of a two-dimensional deep fluid in potential flow and showed that three large wave events are formed during the evolution.
Abstract: This paper concerns long time interaction of envelope solitary gravity waves propagating at the surface of a two-dimensional deep fluid in potential flow. Fully nonlinear numerical simulations show how an initially long wave group slowly splits into a number of solitary wave groups. In the example presented, three large wave events are formed during the evolution. They occur during a time scale that is beyond the time range of validity of simplified equations like the nonlinear Schrodinger (NLS) equation or modifications of this equation. A Fourier analysis shows that these large wave events are caused by significant transfer to side-band modes of the carrier waves. Temporary downshiftings of the dominant wavenumber of the spectrum coincide with the formation large wave events. The wave slope at maximal amplifications is about three times higher than the initial wave slope. The results show how interacting solitary wave groups that emerge from a long wave packet can produce freak wave events. Our reference numerical simulation are performed with the fully nonlinear model of Clamond and Grue [D. Clamond, J. Grue, A fast method for fully nonlinear water wave computations, J. Fluid Mech. 447 (2001) 337–355]. The results of this model are compared with that of two weakly nonlinear models, the NLS equation and its higher-order extension derived by Trulsen et al. [K. Trulsen, I. Kliakhandler, K.B. Dysthe, M.G. Velarde, On weakly nonlinear modulation of waves on deep water, Phys. Fluids 12 (10) (2000) 2432–2437]. They are also compared with the results obtained with a high-order spectral method (HOSM) based on the formulation of West et al. [B.J. West, K.A. Brueckner, R.S. Janda, A method of studying nonlinear random field of surface gravity waves by direct numerical simulation, J. Geophys. Res. 92 (C11) (1987) 11 803–11 824]. An important issue concerning the representation and the treatment of the vertical velocity in the HOSM formulation is highlighted here for the study of long-time evolutions.
TL;DR: The existence of band gaps for low-order Lamb wave modes is demonstrated in the systems made of alternating strips of tungsten materials and silicon resin in this article, where the finite element method is employed to calculate the transmitted power spectra, in good agreement with the results by plane wave exposition.
Abstract: We study theoretically the propagation of lower-order Lamb waves in one-dimensional composite thin plates. The dispersion curves of Lamb modes propagating parallel to the surfaces of the thin plates in the periodic direction are calculated based on the plane wave expansion method. The existence of band gaps for low-order Lamb wave modes is demonstrated in the systems made of alternating strips of tungsten materials and silicon resin. The finite element method is employed to calculate the transmitted power spectra, which is in good agreement with the results by plane wave exposition. A crucial parameter, i.e., the ratio of the plate thickness $(L)$ to the lattice spacing $(D)$, is discussed in detail for the influence of formation of band gaps.
TL;DR: In this paper, a discontinuous Galerkin finite element method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of Helmholtz problems in the mid-frequency regime.
Abstract: Recently, a discontinuous Galerkin finite element method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of Helmholtz problems in the mid-frequency regime. In this paper, this method is extended to three dimensions and several new elements are proposed. Computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher-order Galerkin method.
TL;DR: This Letter proposes a new trapping regime based on the equilibrium between a scattering force and optical binding forces only, which is efficient at trapping multiple free particles.
Abstract: Various trapping configurations have been realized so far, either based on the scattering force or the gradient force. In this Letter, we propose a new trapping regime based on the equilibrium between a scattering force and optical binding forces only. The trap is realized from the interaction between a single plane wave and a series of fixed small particles, and is efficient at trapping multiple free particles. The effects are demonstrated analytically upon computing the exact scattering from a collection of cylindrical particles and calculating the Lorentz force on each free particle via the Maxwell stress tensor.
TL;DR: Analytical expressions containing a hypergeometric function are derived to describe the Fresnel and Fraunhofer diffraction of a plane wave of circular and ringlike cross section by a spiral phase plate (SPP) of an arbitrary integer order.
Abstract: We derive analytical expressions containing a hypergeometric function to describe the Fresnel and Fraunhofer diffraction of a plane wave of circular and ringlike cross section by a spiral phase plate (SPP) of an arbitrary integer order. Experimental diffraction patterns generated by an SPP fabricated in resist through direct e-beam writing are in good agreement with the theoretical intensity distribution.
TL;DR: It is found, that the isofrequency surfaces of the plane extraordinary waves have a hyperbolic shape which allows the propagation of waves with infinitely long wave vectors.
Abstract: The dispersion relation for plane waves in uniaxial metamaterials with indefinite dielectric tensors and scalar positive permeability is theoretically investigated. It is found, that the isofrequency surfaces of the plane extraordinary waves have a hyperbolic shape which allows the propagation of waves with infinitely long wave vectors. As an example a metallodielectric multilayer was considered and the dispersion relations were determined using an effective medium approximation and an analytically exact Bloch wave calculation. The extraordinary waves in this structure are identified as multilayer plasmons and the validity of the effective medium approximation is examined.
TL;DR: In this article, a spectral finite-difference time domain (SFDTD) method was proposed to calculate the reflection coefficient for the plane wave incident on planar periodic structures.
Abstract: This paper introduces a new technique which calculates the reflection coefficient for the plane wave incident on planar periodic structures. The method referred to as spectral finite-difference time-domain (SFDTD) replaces the conventional single-angle incident wave, with a constant transverse wavenumber (CTW) wave. Because the transverse wavenumbers are constant, the fields have no delay in the transverse plane (x-y plane), and PBC (periodic boundary condition) can be directly implemented in the time domain for both oblique and normal incident waves. The stability criterion for this new FDTD technique is angle-independent and therefore this method works well for incident angles close to grazing (/spl theta/=90/spl deg/) as well as normal incident (/spl theta/=0/spl deg/). This shows the efficiency of the method compared to other available FDTD techniques for the same purpose that force a more restricted stability criterion as angles turns to grazing. The validity of this method is verified by comparing the reflection coefficient calculated by this method with the analytical results of a grounded slab. The results of this technique are also compared with method of moments for a periodic array of metallic patches and a good agreement is observed. A periodic array of metallic patches above a PEC plate is analyzed and the reflection coefficient is calculated over a wide frequency band for angles varying from 0/spl deg/ to close to 90/spl deg/.
TL;DR: By using the method of modal expansions of the independent transverse fields, a formula of vector plane wave spectrum (VPWS) of an arbitrary polarized electromagnetic wave in a homogenous medium is derived, where the amplitude and unit polarized direction of every plane wave are separable.
Abstract: By using the method of modal expansions of the independent transverse fields, a formula of vector plane wave spectrum (VPWS) of an arbitrary polarized electromagnetic wave in a homogenous medium is derived. In this formula VPWS is composed of TM- and TE-mode plane wave spectrum, where the amplitude and unit polarized direction of every plane wave are separable, which has more obviously physical meaning and is more convenient to apply in some cases compared to previous formula of VPWS. As an example, the formula of VPWS is applied to the well-known radially and azimuthally polarized beam. In addition, vector Fourier-Bessel transform pairs of an arbitrary polarized electromagnetic wave with circular symmetry are also derived.
TL;DR: In this article, the effect of rotation and magnetic field on the plane harmonic waves of a rotating semi-infinite elastic solid nearby a vacuum under Green and Naghdi theory was investigated.
Abstract: In this paper reflection of magneto-thermoelastic waves is employed to study the effect of rotation and the magnetic field on the plane harmonic waves of a rotating semi-infinite elastic solid nearby a vacuum under Green and Naghdi theory. The expressions for the reflection coefficients, which are the ratios of the amplitudes of the reflected waves to the amplitude of the incident wave, are obtained. The effect of rotation, the magnetic field, coupling parameter and frequency on the reflection ratios are illustrated graphically. Comparisons are made with the results predicted by GN theory of type II in the presence and absence of rotation and magnetic field. A comparison is also made with the results predicted by GN theory of types II and III in the presence of the magnetic field and rotation.
TL;DR: In this paper, the propagation of plane waves in a fiber-reinforced, anisotropic, generalized thermoelastic media is discussed, and the governing equations in x-y plane are solved to obtain a cubic equation in phase velocity.
Abstract: The propagation of plane waves in a fibre-reinforced, anisotropic, generalized thermoelastic media is discussed. The governing equations in x–y plane are solved to obtain a cubic equation in phase velocity. Three coupled waves, namely quasi-P, quasi-SV and quasi-thermal waves are shown to exist. The propagation of Rayleigh waves in stress free thermally insulated and transversely isotropic fibre-reinforced thermoelastic solid half-space is also investigated. The frequency equation is obtained for these waves. The velocities of the plane waves are shown graphically with the angle of propagation. The numerical results are also compared to those without thermal disturbances and anisotropy parameters.
TL;DR: In this paper, the characteristics of impulse waves generated in reservoirs by the impact of variable density mass flows were assessed using two-dimensional model experimentation using particle image velocimetry (PIV) and seven successive capacitance wave gages.
Abstract: The characteristics of impulse waves generated in reservoirs by the impact of variable density mass flows were assessed using two-dimensional model experimentation. Particle image velocimetry (PIV) was applied within the wave generation area at the slide impact location and the water wave profiles were measured by seven successive capacitance wave gages. The maximum relative wave amplitude and the normalized wave amplitude of the propagating wave train were correlated with the dimensionless slide quantities and the relative propagation distance, respectively. The impact Froude number was identified as the dominant parameter for slow impacting slides, whereas the water depth and the slide thickness governed the maximum possible wave amplitude for large impact Froude numbers. Four wave types were distinguished due to three different levels of wave nonlinearity associated with variable impact Froude numbers, relative slide densities, and characteristic slide geometries: nonlinear transient bore, transition wave, oscillatory wave, and nonbreaking solitary wave. Moreover, the density effect on the wave generation process was investigated with small impact Froude numbers using sequential PIV velocity vector fields.
TL;DR: In this paper, the authors study theories with SU(2|4) symmetry, which include the plane wave matrix model, 2+1 SYM on R? S2 and = 4 SYM ON R?S3/Zk, and show that these theories possess many vacua.
Abstract: We study theories with SU(2|4) symmetry, which include the plane wave matrix model, 2+1 SYM on R ? S2 and = 4 SYM on R ? S3/Zk. All these theories possess many vacua. From Lin-Maldacena's method which gives the gravity dual of each vacuum, it is predicted that the theory around each vacuum of 2+1 SYM on R ? S2 and = 4 SYM on R ? S3/Zk is embedded in the plane wave matrix model. We show this directly on the gauge theory side. We clearly reveal relationships among the spherical harmonics on S3, the monopole harmonics and the harmonics on fuzzy spheres. We extend the compactification (the T-duality) in matrix models a la Taylor to that on spheres.