Showing papers on "Plane wave published in 2009"

Rogue waves and rational solutions of the nonlinear Schrödinger equation

Abstract: We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear Schrodinger equation and present explicit forms for these solutions from first to fourth order. We also explain their relation to the highest amplitude part of a field that starts with a plane wave perturbed by random small amplitude radiation waves. Our work can elucidate the appearance of rogue waves in the deep ocean and can be applied to the observation of rogue light pulse waves in optical fibers.

Practical issues in reverse time migration: true amplitude gathers, noise removal and harmonic source encoding

Abstract: Reverse time migration (RTM) is the method of choice for imaging complex subsurface structures. In this paper, we show that slightly modifying the conventional formulation, plus implementing an appropriate imaging condition, yields a true amplitude version of RTM that provides the correct amplitude-versus-angle relation. We also discuss different ways to suppress the migration artifacts and show how noise attenuation can be handled naturally in the common reflection angle domain. Finally, we introduce a harmonic source phase-encoding method to allow a relatively efficient delayed shot or plane wave reverse time migration. Taken together, these techniques yield a powerful true amplitude migration method that uses the complete two-way acoustic wave equation to image complex structures.

A synthetic Schlieren method for the measurement of the topography of a liquid interface

Abstract: An optical method for the measurement of the instantaneous topography of the interface between two transparent fluids, named free-surface synthetic Schlieren (FS-SS), is characterised. This method is based on the analysis of the refracted image of a random dot pattern visualized through the interface. The apparent displacement field between the refracted image and a reference image obtained when the surface is flat is determined using a digital image correlation (DIC) algorithm. A numerical integration of this displacement field, based on a least square inversion of the gradient operator, is used for the reconstruction of the instantaneous surface height, allowing for an excellent spatial resolution with a low computational cost. The main limitation of the method, namely the ray crossing (caustics) due to strong curvature and/or large surface-pattern distance, is discussed. Validation experiments using a transparent solid model with a wavy surface or plane waves at a water–air interface are presented, and some additional time-resolved measurements of circular waves generated by a water drop impact are discussed.

Analysis of ambient noise energy distribution and phase velocity bias in ambient noise tomography, with application to SE Tibet

Abstract: SUMMARY Green’s functions (GFs) of surface wave propagation between two receivers can be estimated from the cross-correlation of ambient noise under the assumption of diffuse wavefields or energy equipartitioning. Interferometric GF reconstruction is generally incomplete, however, because the distribution of noise sources is neither isotropic nor stationary and the wavefields considered in the cross-correlation are generally non-diffuse. Furthermore, medium complexity can affect the empirical Green’s function (EGF) from the cross-correlation if noise sources are all far away (i.e. approximately plane-wave sources), which makes the problem non-linear. We analyse the effect of uneven ambient noise distribution and medium heterogeneity and azimuthal anisotropy on phase velocities measured from EGFs with an asymptotic plane wave (far-field) approximation (which underlies most constructions of phase velocity maps). Phase velocity bias due to uneven noise distribution can be determined (and corrected) if the noise energy distribution and the velocity model are known. We estimate the (normalized) azimuthal distribution of ambient noise energy directly from the cross-correlation functions obtained through ambient noise interferometry. The (smaller, second order) bias due to non-linearity can be reduced iteratively, for instance by using the tomographic model that results from the inversion of uncorrected data. We illustrate our method for noise energy estimation, phase velocity bias suppression, and ambient noise tomography (including azimuthal anisotropy) with data from a seismic array (26 stations) in SE Tibet. We show that the phase velocity bias due to uneven noise energy distribution (and medium complexity) in SE Tibet has a small effect (<1 per cent) on the isotropic part phase velocities (for T = 10–30 s) and the azimuthal anisotropy obtained before and after bias correction shows very similar pattern and magnitude.

Second-order Møller-Plesset perturbation theory applied to extended systems. I. Within the projector-augmented-wave formalism using a plane wave basis set.

Abstract: We present an implementation of the canonical formulation of second-order Moller-Plesset (MP2) perturbation theory within the projector-augmented-wave method under periodic boundary conditions using a plane wave basis set. To demonstrate the accuracy of our approach we show that our result for the atomization energy of a LiH molecule at the Hartree-Fock+MP2 level is in excellent agreement with well converged Gaussian-type-orbital calculations. To establish the feasibility of employing MP2 perturbation theory in its canonical form to systems that are periodic in three dimensions we calculated the cohesive energy of bulk LiH.

A heterogeneous nonlinear attenuating full- wave model of ultrasound

Abstract: A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). Three-dimensional solutions of the equation are verified with water tank measurements of a commercial diagnostic ultrasound transducer and are shown to be in excellent agreement in terms of the fundamental and harmonic acoustic fields and the power spectrum at the focus. The linear and nonlinear components of the algorithm are also verified independently. In the linear nonattenuating regime solutions match results from Field II, a well established software package used in transducer modeling, to within 0.3 dB. Nonlinear plane wave propagation is shown to closely match results from the Galerkin method up to 4 times the fundamental frequency. In addition to thermoviscous attenuation we present a numerical solution of the relaxation attenuation laws that allows modeling of arbitrary frequency dependent attenuation, such as that observed in tissue. A perfectly matched layer (PML) is implemented at the boundaries with a numerical implementation that allows the PML to be used with high-order discretizations. A -78 dB reduction in the reflected amplitude is demonstrated. The numerical algorithm is used to simulate a diagnostic ultrasound pulse propagating through a histologically measured representation of human abdominal wall with spatial variation in the speed of sound, attenuation, nonlinearity, and density. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beam-forming algorithm to generate a images. The resulting harmonic image exhibits characteristic improvement in lesion boundary definition and contrast when compared with the fundamental image. We demonstrate a mechanism of harmonic image quality improvement by showing that the harmonic point spread function is less sensitive to reverberation clutter.

PLANE WAVE DISCONTINUOUS GALERKIN METHODS: ANALYSIS OF THE h-VERSION ∗, ∗∗

Abstract: We are concerned with a finite element approximation for time-harmonic wave propagation governed by the Helmholtz equation. The usually oscillatory behavior of solutions, along with numerical dispersion, render standard finite element methods grossly inefficient already in medium-frequency regimes. As an alternative, methods that incorporate information about the solution in the form of plane waves have been proposed. We focus on a class of Trefftz-type discontinuous Galerkin methods that employs trial and test spaces spanned by local plane waves. In this paper we give ap riori convergence estimates for the h-version of these plane wave discontinuous Galerkin methods in two dimensions. To that end, we develop new inverse and approximation estimates for plane waves and use these in the context of duality techniques. Asymptotic optimality of the method in a mesh dependent norm can be established. However, the estimates require a minimal resolution of the mesh beyond what it takes to resolve the wavelength. We give numerical evidence that this requirement cannot be dispensed with. It reflects the presence of numerical dispersion.

Observation of electronic structure minima in high-harmonic generation.

Abstract: We report detailed measurements of the high-harmonic spectra generated from argon atoms. The spectra exhibit a deep minimum that is shown to be independent of the laser intensity, and is thus a clear measure of the electronic structure of the atom. We show that exact field-free continuum wave functions reproduce the minimum, but plane wave and Coulomb wave functions do not. This remarkable observation suggests that electronic structure can be accurately determined in high-harmonic experiments despite the presence of the strong laser field. Our results clarify the relation between high-harmonic generation and photoelectron spectroscopy. The use of exact continuum functions also resolves the ambiguity associated with the choice of the dispersion relation.

The Pseudo-analytical Method: Application of Pseudo-Laplacians to Acoustic And Acoustic Anisotropic Wave Propagation

Abstract: Summary We generalize the pseudo-spectral method for the acoustic wave equation to create analytical solutions to the constant velocity acoustic wave equation in an arbitrary number of space dimensions. We accomplish this by modifying the Fourier Transform of the Laplacian operator so that it compensates exactly for the error due to the second-order finite-difference time marching scheme used in the conventional pseudo-spectral method. Of more practical interest, we show that this modified or pseudo-Laplacian is a smoothly varying function of the parameters of the acoustic wave equation (velocity most importantly) and thus can be further generalized to create near-analyticallyaccurate solutions for the variable velocity case. We call this new method the pseudo-analytical method. We further show that by applying this approach to the concept of acoustic anisotropic wave propagation, we can create scalar-mode VTI and TTI wave equations that overcome the disadvantages of previously published methods for acoustic anisotropic wave propagation. These methods should be ideal for forward modeling and reverse time migration applications.

The Dynamics of Modulated Wave Trains

Abstract: The authors of this title investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg - Landau equation, they establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, they show that the viscous shock profiles in the Burgers equation for the wave number can be found as genuine modulated waves in the underlying reaction-diffusion system. In other words, they establish the existence and stability of waves that are time-periodic in appropriately moving coordinate frames which separate regions in physical space that are occupied by wave trains of different, but almost identical, wave number. The speed of these shocks is determined by the Rankine - Hugoniot condition where the flux is given by the nonlinear dispersion relation of the wave trains. The group velocities of the wave trains in a frame moving with the interface are directed toward the interface. Using pulse-interaction theory, the authors also consider similar shock profiles for wave trains with large wave number, that is, for an infinite sequence of widely separated pulses. The results presented here are applied to the FitzHugh - Nagumo equation and to hydrodynamic stability problems.

Anomalous properties of the acoustic excitations in glasses on the mesoscopic length scale

Abstract: The low-temperature thermal properties of dielectric crystals are governed by acoustic excitations with large wavelengths that are well described by plane waves. This is the Debye model, which rests on the assumption that the medium is an elastic continuum, holds true for acoustic wavelengths large on the microscopic scale fixed by the interatomic spacing, and gradually breaks down on approaching it. Glasses are characterized as well by universal low-temperature thermal properties that are, however, anomalous with respect to those of the corresponding crystalline phases. Related universal anomalies also appear in the low-frequency vibrational density of states and, despite a longstanding debate, remain poorly understood. By using molecular dynamics simulations of a model monatomic glass of extremely large size, we show that in glasses the structural disorder undermines the Debye model in a subtle way: The elastic continuum approximation for the acoustic excitations breaks down abruptly on the mesoscopic, medium-range-order length scale of ≈10 interatomic spacings, where it still works well for the corresponding crystalline systems. On this scale, the sound velocity shows a marked reduction with respect to the macroscopic value. This reduction turns out to be closely related to the universal excess over the Debye model prediction found in glasses at frequencies of ≈1 THz in the vibrational density of states or at temperatures of ≈10 K in the specific heat.

Electromagnetic boundary and its realization with anisotropic metamaterial.

Abstract: A set of boundary conditions requiring vanishing of the normal components of the D and B vectors at the boundary surface is introduced and labeled as that of DB boundary Basic properties of the DB boundary are studied in this paper Reflection of an arbitrary plane wave, incident with a complex propagation vector, is analyzed for the planar DB boundary It is shown that waves polarized transverse electric (TE) and transverse magnetic (TM) with respect to the normal of the boundary are reflected as from respective perfect electric conductor and perfect magnetic conductor planes The basic problem of current source above the planar DB boundary is solved by applying TE and TM decomposition for the source Realization of the DB boundary in terms of an interface of uniaxially anisotropic metamaterial half-space with zero axial medium parameters is considered It is also shown that such a medium with small axial parameters acts as a spatial filter for waves incident at the interface which could be used for narrowing the beam of a directive antenna Application of DB boundary as an isotropic soft surface with low interaction between antenna apertures also appears possible

Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ϵ ( t )

Abstract: We present a theoretical description of the response of a dynamic slab, with time-periodic dielectric function $ϵ(t)$, to a normally incident monochromatic plane wave of frequency ${\ensuremath{\omega}}_{o}$. As a consequence of the interaction of this incoming wave with the dynamic slab, the reflected and transmitted waves contain harmonics of the modulating frequency $\ensuremath{\Omega}$, namely, the slab itself becomes a polychromatic source of frequencies ${\ensuremath{\omega}}_{o}\ensuremath{-}n\ensuremath{\Omega}(n=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2,\dots{})$. We establish a general formalism to quantify the reflected and transmitted fields for any periodic variation in the dielectric function. To achieve this, a description of wave propagation in a dynamic bulk is needed. A theoretical framework to treat such propagation, based on the concept of a temporal photonic crystal, is developed. As a consequence of the Bloch-Floquet theorem, the dispersion relation is a band structure that is periodic with frequency and exhibits forbidden wave vector gaps. The Poynting vectors of the transmitted and reflected fields are analyzed in detail. Our theory is applied to the case in which the dielectric function is modulated sinusoidally. We calculate numerically the magnitudes and phases of the reflection and transmission coefficients for several harmonics ${\ensuremath{\omega}}_{o}\ensuremath{-}n\ensuremath{\Omega}$ and slab thicknesses. Three modulation regimes are considered: weak, moderate, and strong. The response in the weak regime is similar to that of a Fabry-Perot etalon---the strengths of the harmonics are weak. For the strong-modulation regime, the strengths of reflection and transmission coefficients of the harmonics become large; they can even exceed one due to the openness of the system in which an external modulating agent can provide part of the invested energy. Dynamic variation in the dielectric properties of materials can give rise to new effects in wave propagation and to novel optical applications and is readily attainable with present-day technology.

Evolution of a Random Directional Wave and Freak Wave Occurrence

Abstract: The evolution of a random directional wave in deep water was studied in a laboratory wave tank (50 m long, 10 m wide, 5 m deep) utilizing a directional wave generator. A number of experiments were conducted, changing the various spectral parameters (wave steepness 0.05 < e < 0.11, with directional spreading up to 36° and frequency bandwidth 0.2 < δk/k < 0.6). The wave evolution was studied by an array of wave wires distributed down the tank. As the spectral parameters were altered, the wave height statistics change. Without any wave directionality, the occurrence of waves exceeding twice the significant wave height (the freak wave) increases as the frequency bandwidth narrows and steepness increases, due to quasi-resonant wave–wave interaction. However, the probability of an extreme wave rapidly reduces as the directional bandwidth broadens. The effective Benjamin–Feir index (BFIeff) is introduced, extending the BFI (the relative magnitude of nonlinearity and dispersion) to incorporate the effect...

Properties of the Lattice-Boltzmann Method for Acoustics

Abstract: Numerical simulations are performed to investigate the fundamental acoustics properties of the Lattice–Boltzmann method. The propagation of planar acoustic waves is studied to determine the resolution dependence of numerical dissipation and dispersion. The two setups considered correspond to the temporal decay of a standing plane wave in a periodic domain, and the spatial decay of a propagating planar acoustic pulse of Gaussian shape. Theoretical dispersion relations are obtained from the corresponding temporal and spatial analyses of the linearized Navier–Stokes equations. Comparison of theoretical and numerical predictions show good agreement and demonstrate the low dispersive and dissipative capabilities the Lattice–Boltzmann method. The analysis is performed with and without turbulence modeling, and the changes in dissipation and dispersion are discussed. Overall, the results show that the Lattice–Boltzmann method can accurately reproduce time-explicit acoustic phenomena.

Properties of dayside outer zone chorus during HILDCAA events: Loss of energetic electrons

Abstract: [1] The dayside outer zone (DOZ) portion of the magnetosphere is a region where chorus intensities are statistically found to be the most intense. In this study, DOZ chorus have been examined using OGO-5 plasma wave and GEOTAIL plasma wave, magnetic field and energetic particle data. Dayside chorus is noted to be composed of ∼0.1 to 0.5 s rising-tone emissions called “elements.” The duration of the elements and their frequency-time characteristics are repeatable throughout the chorus event (lasting from tens of minutes to hours), but may differ from event to event. Chorus is a right-hand, circularly polarized electromagnetic plane wave. Waves are detected propagating from along the ambient magnetic field, Bo, to oblique angles near the Gendrin angle, θGendrin. All waves, independent of wave direction of propagation relative to Bo, are found to be circularly polarized, to first order. Chorus rising-tone elements are composed of coherent “subelements” or “packets” with durations of ∼5 to 10 ms. Consecutive subelements/packets step in frequency with time to form the elements. The peak amplitudes within a packet can be ∼0.2 nT or greater. The subelement or packet amplitudes are at least an order of magnitude larger than previously estimated chorus amplitudes obtained by power spectral measurements. This discrepancy is due to the presence of interspacings between chorus elements, the interspacings between subelements/packets within an element, and the different frequencies of subelements/packets within a rising-tone. DOZ chorus studied here were found to be consistent with generation via the loss cone instability of substorm-injected temperature-anisotropic (/ > 1) E = 5 to 40 keV electrons drifting from the midnight sector to the DOZ region. Using a large amplitude subelement/packet wave magnetic field amplitude of ∼0.2 nT, it is shown that the instantaneous Kennel-Petschek pitch angle diffusion rate Dαα is ∼5 × 10−2 s−1. This latter quantity is based on incoherent waves. If energetic electrons stay in cyclotron resonance throughout their interaction with a coherent subelement of duration 10 ms, they may be “pitch angle transported” by ∼5°. Therefore electrons within 5° of the loss cone can be lost in a single wave-particle interaction. Several such interactions as the electrons traverse the wave region can lead to much larger pitch angle transport angles. The similar time-scales of chorus elements and bremsstrahlung X-ray microbursts (∼0.5 s) can be explained by the “pitch angle transport” mechanism described above. Increasing and decreasing pitch angle transport via this mechanism will lead to much higher pitch angle diffusion or “super diffusion” rates. Isotropic unpolarized noise of ∼20 pT peak amplitude has also been detected. The noise is well above instrument noise levels and is speculated to be remnants of chorus or hiss.

Gravity Wave Instability Dynamics at High Reynolds Numbers. Part I: Wave Field Evolution at Large Amplitudes and High Frequencies

Abstract: Direct numerical simulations are employed to examine gravity wave instability dynamics at a high intrinsic frequency, wave amplitudes both above and below nominal convective instability, and a Reynolds number sufficiently high to allow a fully developed turbulence spectrum Assumptions include no mean shear, uniform stratification, and a monochromatic gravity wave to isolate fluxes due to gravity wave and turbulence structures from those arising from environmental shears or varying wave amplitudes The results reveal strong wave breaking for both wave amplitudes, severe primary wave amplitude reductions within ∼1 or 2 wave periods, an extended turbulence inertial range, significant excitation of additional wave motions exhibiting upward and downward propagation, and a net positive vertical potential temperature flux due to the primary wave motion, with secondary waves and turbulence contributing variable and negative potential temperature fluxes, respectively Turbulence maximizes within ∼1 buoya

An Introduction to Soil Dynamics

Abstract: 1. Vibrating Systems 1.1 Single mass system 1.2 Characterization of viscosity 1.3 Free Vibrations 1.4 Forced Vibrations 1.5 Equivalent spring and damping 1.6 Solution by Laplace transform method 1.7 Hysteretic damping 2. Waves in Piles 2.1 One-dimensional wave equation 2.2 Solution by Laplace transform method 2.3 Separation of variables 2.4 Solution by characteristics 2.5 Reflection and transmission 2.6 The influence of friction 2.7 Numerical solution 2.8 Modeling a pile with friction 3. Earthquakes in Soft Layers 3.1 Earthquake parameters 3.2 Horizontal vibrations 3.3 Shear waves in a Gibson material 3.4 Hysteretic damping 3.5 Numerical solution 4. Theory of Consolidation 4.1 Consolidation 4.2 Conservation of mass 4.3 Darcy's law 4.4 Equilibrium equations 4.5 Drained deformations 4.6 Un-drained deformations 4.7 Cryer's problem 4.8 Uncoupled consolidation 4.9 Terzaghi's problem 5. Plane Waves in Porous Media 5.1 Dynamics of porous media 5.2 The basic differential equations 5.3 Special cases 5.4 Analytical solution 5.5 Numerical solution 5.6 Conclusion 6. Cylindrical Waves 6.1 Static problems 6.2 Dynamic problems 6.3 Propagation of a shock wave 6.4 Radial propagation of shear waves 7. Spherical Waves 7.1 Static problems 7.2 Dynamic problems 7.3 Propagation of a shock wave 8. Elastostatics of a Half Space 8.1 Basic equations of elastostatics 8.2 Boussinesq problems 8.3 Fourier transforms 8.4 Axially symmetric problems 8.5 Mixed boundary value problems 8.6 Confined elastostatics 9. Elastodynamics of a Half Space 9.1 Basic equations of elastodynamics 9.2Compression waves 9.3 Shear waves 9.4 Rayleigh waves 9.5 Love waves 10. Confined Elastodynamics 10.1 Line load on half space 10.2 Line pulse on half space 10.3 Point load on half space 10.4 Periodic load on half space 11. Line Load on Elastic Half Space 11.1 Line pulse 11.2 Constant line load 12. Strip Load on Elastic Half Space 12.1 The strip pulse problem 12.2 The strip load problem 13. Point Load on Elastic Half Space 13.1 Problem 13.2 Solution 14. Moving Loads on Elastic Half Space 14.1 Moving wave 14.2 Moving strip load 15. Foundation Vibrations 15.1 Foundation response 15.2 Equivalent spring and damping 15.3 Soil properties 15.4 Propagation of vibrations 15.5 Design criteria Appendix A. Integral Transforms A.1 Laplace transforms A.2 Fourier transforms A.3 Hankel transforms A.4 De Hoop's inversion method Appendix B. Dual Integral Equations Appendix C. Bateman-Pekeris Theorem References Author Index Index CD-ROM included A CD-ROM accompanies this book containing programs for waves in piles, propagation of earthquakes in soils, waves in a half space generated by a line load, a point load, a strip load, or a moving load, and the propagation of a shock wave in a saturated elastic porous material

Experiments on high-performance beam-scanning antennas made of gradient-index metamaterials

Abstract: A planar lens made of gradient index metamaterials can transform cylindrical waves to plane waves, and the beam direction of plane waves is controlled by adjusting the refractive-index distributions of the lens. Based on such properties, we present high-performance beam-scanning antennas experimentally using the gradient-index planar lens and horn antenna. The lens is carefully designed with metamaterials to achieve different refractive indices and good matching of impedance. The near-field distributions of antennas are measured using a two-dimensional near-field microwave scanning apparatus, and the radiation patterns are presented to show the high directivity and low sidelobe.

Generalized Lorenz-Mie theories, the third decade: A perspective

Abstract: During the year 2008, we have been commemorating, in several places, the hundredth anniversary of the famous 1908-paper by Mie describing the interaction between an electromagnetic plane wave and a homogeneous sphere defined by its diameter d and its complex refractive index m . Due to the existence of a prior version by Lorenz, Mie's theory may also be named as Lorenz–Mie theory (LMT). The generalized Lorenz–Mie theory (GLMT) stricto sensu deals with the more general case when the illuminating wave is an arbitrary shaped beam (say: a laser beam) still interacting with a homogeneous sphere defined by its diameter d and its complex refractive index m . The name “GLMTs” is generically used to designate various variants for other particle shapes when the method of separation of variables is used. The present paper provides a review of the work accomplished in this generalized field during the last decade (the third decade). As a convenient selection criterion, only papers citing the work of the group of Rouen have been essentially used, with ISIweb of knowledge providing a database.

Calculation of Body Waves, for Caustics and Tunnelling in Core Phases

Abstract: Summary The known failure of classical ray theory at caustics has led to a reconsideration of displacement (in the frequency domain), expressed as an integral over ray parameter p. The integrand contains saddle-points on the real p-axis which correspond to rays for the associated physical problem, and it is shown here that direct computation of the complex integral is still straightforward, even when two saddle-points (rays) have coalesced to form a caustic. WKBJ theory is still usable for the vertical wave-functions, but one may avoid both the Taylor series expansion for the phase, and the steepest-descents approximation. Attention is first directed towards the PKKP caustic near 119°, to calculations of both amplitude and the phase slowness (dT/dδ) as a function of frequency, and to a criticism of some uses of plane wave reflection coefficients across the core-mantle boundary. It is then shown that short-period P-wave energy is efficiently tunnelled into and out of the Earth'score, from body waves having their turning point just above the core-mantle boundary. This provides an explanation for observations of multiply reflected core phases, PmKP with m > 2, which are found usually at distances beyond the cutoff one would expect from requiring real angles of incidence (∼ 90°) from mantle to core. To obtain body wave pulse shapes in the time domain, a method is described which appears to offer some strong advantages over Cagniard-de Hoop inversion.

Core-level spectroscopy calculation and the plane wave pseudopotential method

Abstract: A plane wave based method for the calculation of core-level spectra is presented. We provide details of the implementation of the method in the pseudopotential density functional code CASTEP, including technical issues concerning the calculations, and discuss the applicability and accuracy of the method. A number of examples are provided for comparing the results to both experiment and other density functional theory techniques.

Comparison of two wave element methods for the Helmholtz problem

Abstract: In comparison with low-order finite element methods (FEMs), the use of oscillatory basis functions has been shown to reduce the computational complexity associated with the numerical approximation of Helmholtz problems at high wave numbers. We compare two different wave element methods for the 2D Helmholtz problems. The methods chosen for this study are the partition of unity FEM (PUFEM) and the ultra-weak variational formulation (UWVF). In both methods, the local approximation of wave field is computed using a set of plane waves for constructing the basis functions. However, the methods are based on different variational formulations; the PUFEM basis also includes a polynomial component, whereas the UWVF basis consists purely of plane waves. As model problems we investigate propagating and evanescent wave modes in a duct with rigid walls and singular eigenmodes in an L-shaped domain. Results show a good performance of both methods for the modes in the duct, but only a satisfactory accuracy was obtained in the case of the singular field. On the other hand, both the methods can suffer from the ill-conditioning of the resulting matrix system.

On spherical vs. plane wave modeling of line-of-sight MIMO channels

Abstract: In this paper we consider pure line-of-sight multiple-input multiple-output (MIMO) channels employing uniform linear antenna arrays. We investigate the influence of exact spherical wave propagation modeling versus approximate plane wave propagation modeling on the properties of the MIMO channel matrix. When the transmission distance increases, the properties of the singular values of the MIMO channel matrix given by the spherical wave model approach the properties given by the simpler plane wave model. We investigate this transition between the two channel models, which results in a new tool giving us analytical expressions describing when spherical wave modeling is necessary and when plane wave modeling gives sufficient modeling accuracy. The parameters of interest are the transmission distance, the frequency, the array orientation, and the array size. The tool introduced is general, in the sense that it supports different performance measures when deciding on the transition between the two models. As an example, we investigate underestimation of the mutual information in this paper. The results show that the spherical wave model should be applied e.g. in some practical WLAN scenarios where plane wave modeling is commonly applied today.

Intermolecular shielding contributions studied by modeling the 13 C chemical-shift tensors of organic single crystals with plane waves

Abstract: In order to predict accurately the chemical shift of NMR-active nuclei in solid phase systems, magnetic shielding calculations must be capable of considering the complete lattice structure. Here we assess the accuracy of the density functional theory gauge-including projector augmented wave method, which uses pseudopotentials to approximate the nodal structure of the core electrons, to determine the magnetic properties of crystals by predicting the full chemical-shift tensors of all (13)C nuclides in 14 organic single crystals from which experimental tensors have previously been reported. Plane-wave methods use periodic boundary conditions to incorporate the lattice structure, providing a substantial improvement for modeling the chemical shifts in hydrogen-bonded systems. Principal tensor components can now be predicted to an accuracy that approaches the typical experimental uncertainty. Moreover, methods that include the full solid-phase structure enable geometry optimizations to be performed on the input structures prior to calculation of the shielding. Improvement after optimization is noted here even when neutron diffraction data are used for determining the initial structures. After geometry optimization, the isotropic shift can be predicted to within 1 ppm.