Nearfield broadband array design using a radially invariant modal expansion

This paper introduces an efficient parameterization for the nearfield broadband beamforming problem with a single parameter to focus the beamformer to a desired operating radius and another set of parameters to control the actual broadband beampattern shape. The parameterization is based on an orthogonal basis set of elementary beampatterns by which an arbitrary beampattern can be constructed. A set of elementary beamformers are then designed for each elementary beampattern and the desired beamformer is constructed by summing the elementary beamformers with frequency and source-array distance dependent weights. An important consequence of our result is that the beamformer can be factored into three levels of filtering: (i) beampattern independent elementary beamformers; (ii) beampattern shape dependent filters; and (iii) radial focusing filters where a single parameter can be adjusted to focus the array to a desired radial distance from the array origin. As an illustration the method is applied to the problem of producing a practical array design that achieves a frequency invariant beampattern over the frequency range of 1:10 (which is suitable for speech acquisition using a microphone array), and with the array focused either to farfield or nearfield where at the lowest frequency the radial distance to the source is only three wavelengths.     

Spectral radial basis functions for full sphere computations

The singularity of cylindrical or spherical coordinate systems at the origin imposes certain regularity conditions on the spectral expansion of any infinitely differentiable function. There are two efficient choices of a set of radial basis functions suitable for discretising the solution of a partial differential equation posed in either such geometry. One choice is methods based on standard Chebyshev polynomials; although these may be efficiently computed using fast transforms, differentiability to all orders of the obtained solution at the origin is not guaranteed. The second is the so-called one-sided Jacobi polynomials that explicitly satisfy the required behavioural conditions. In this paper, we compare these two approaches in their accuracy, differentiability and computational speed. We find that the most accurate and concise representation is in terms of one-sided Jacobi polynomials. However, due to the lack of a competitive fast transform, Chebyshev methods may be a better choice for some computationally intensive timestepping problems and indeed will yield sufficiently (although not infinitely) differentiable solutions provided they are adequately converged.     

Spectral radial basis functions for full sphere computations

The singularity of cylindrical or spherical coordinate systems at the origin imposes certain regularity conditions on the spectral expansion of any infinitely differentiable function. There are two efficient choices of a set of radial basis functions suitable for discretising the solution of a partial differential equation posed in either such geometry. One choice is methods based on standard Chebyshev polynomials; although these may be efficiently computed using fast transforms, differentiability to all orders of the obtained solution at the origin is not guaranteed. The second is the so-called one-sided Jacobi polynomials that explicitly satisfy the required behavioural conditions. In this paper, we compare these two approaches in their accuracy, differentiability and computational speed. We find that the most accurate and concise representation is in terms of one-sided Jacobi polynomials. However, due to the lack of a competitive fast transform, Chebyshev methods may be a better choice for some computationally intensive timestepping problems and indeed will yield sufficiently (although not infinitely) differentiable solutions provided they are adequately converged.     

Bound Dirac states,different Lorentz-type couplings of central potentials and the non-relativistic limit

The analysis of bound radial Dirac states is shown to simplify for problems with an equal mixture of Lorentz vector and Lorentz scalar potentials, thus satisfying a so-called spin symmetry of the energy spectrum. Typical relativistic restrictions on potentials that are singular at the origin then disappear. Such potentials may even be strongly singular at the origin like the well known Lennard-Jones potentials modelling many atom-atom interactions, and they reduce to non-relativistic potentials of identical form. Bound state energies for potentials with equal vector- and scalar couplings are compared with those of a pure vector coupling of the same radial (attractive screened and unscreened Coulomb) shapes, and with non-relativistic results.     

VIS/NIR imaging application for honey floral origin determination

Nondestructive methods are of utmost importance for honey characterization. This study investigates the potential application of VIS-NIR hyperspectral imaging for detection of honey flower origin using machine learning techniques. Hyperspectral images of 52 honey samples were taken in transmittance mode in the visible/near infrared (VIS-NIR) range (400–1000 nm). Three different machine learning algorithms were implemented to predict honey floral origin using honey spectral images. These methods, included radial basis function (RBF) network, support vector machine (SVM), and random forest (RF). Principal component analysis (PCA) was also exploited for dimensionality reduction. According to the obtained results, the best classifier (RBF) achieved a precision of 94% in a fivefold cross validation experiment using only the first two PCs. Mapping of the classifier results to the test set images showed 90% accuracy for honey images. Three types of honey including buckwheat, rapeseed and heather were classified with 100% accuracy. The proposed approach has great potential for honey floral origin detection. As some other honey properties can also be predicted using image features, in addition to floral origin detection, this method may be applied to predict other honey characteristics.     

ON THE HERMITIAN OF THE HAMILTONIAN OF RADIAL EQUATION

The Hamiltonian of a radial equation is defined on a half-line,and there is a close relation between its hermitian and the boundary condition of the wave functions at the origin.If the wave functions are nonvanishing and convergent at the origin,the Hamiltonian has a one-parameter family of self-adjoint extensions which are related with the vanishness of the radial probability current at the origin.In this paper the problem on the hermitian of the Hamiltonian of a radial equation is studied systematically.Some methods for determining the parameter for the fermion moving in the magnetic monopole field are discussed.     

Localization of Dirac-like excitations in graphene in the presence of smooth inhomogeneous magnetic fields

The present paper discusses magnetic confinement of the Dirac excitations in graphene in the presence of inhomogeneous magnetic fields. In the first case a magnetic field directed along the z axis whose magnitude is proportional to 1/r is chosen. In the next case we choose a more realistic magnetic field which does not blow up at the origin and gradually fades away from the origin. The magnetic fields chosen do not have any finite/infinite discontinuity for finite values of the radial coordinate. The novelty of the two magnetic fields is related to the equations which are used to find the excited spectra of the excitations. It turns out that the bound state solutions of the two-dimensional hydrogen atom problem are related to the spectra of graphene excitations in the presence of the 1/r (inverse-radial) magnetic field. For the other magnetic field profile one can use the knowledge of the bound state spectrum of a two-dimensional cutoff Coulomb potential to dictate the excitation spectra of graphene. The spectrum of the graphene excitations in the presence of the inverse-radial magnetic field can be exactly solved while the other case cannot be. In the later case we give the localized solutions of the zero-energy states in graphene.     

Anomalous enhancement in the infrared phonon intensity of a one-dimensional uneven peanut-shaped C60 polymer

A one-dimensional (1D) uneven peanut-shaped C(60) polymer formed from electron-beam (EB)-induced polymerization of C(60) molecules showed an anomalous increase in two characteristic infrared (IR) peak intensities, which are respectively due to the radial and tangential motion of the 1D polymer, when compared to the IR peaks of pristine C(60) films. This anomaly was analyzed on the basis of the vibrational van Hove singularity (VHS), using an extended thin-shell elastic model fully considering the effects of periodic radius modulation inherent to the 1D uneven peanut-shaped C(60) polymer. We succeeded in explaining the enhancement in the tangential peak intensity by VHS, whereas the origin to cause that in the radial peak intensity is still unclear.     

Spin 3/2 Field Equation: Separation and Solution in a Class of Lema?tre–Tolman–Bondi Cosmologies

The spin 3/2 field equation is studied in the general Lema?tre–Tolman–Bondi (LTB) space-time. The equation is separated by variable separation. The angular dependence factors out at the level of the general LTB metric. Due to spherical symmetry the separated angular equations coincide with those, previously integrated, relative to the Robertson–Walker and Schwarzschild metric. Separation of time and radial dependence is possible within a class of LTB cosmological models for which the physical radius is a product of a time and a radial function, the last one being further selected by the consistency condition of the radial equations. The separated time dependence, that can be integrated by series, results essentially unique. Instead the radial dependence can be reduced to two independent second order ordinary differential equations that still depend on an arbitrary radial function that is an integration function of the cosmological model. The generalization of the scheme to arbitrary spin field equation is suggested.     

Spherically Symmetric Solutions of Einstein's Vacuum Equations in Five Dimensions

Multi-dimensional spherically symmetric spacetimes are of interest in the study of higher-dimensional black holes (and solitons) and higher-dimensional cosmological models. In this paper we shall present a comprehensive investigation of solutions of the five-dimensional spherically symmetric vacuum Einstein field equations subject only to the condition of separability in the radial coordinate (but not necessarily in the remaining two coordinates). A variety of new solutions are found which generalize a number of previous results. The properties of these solutions are discussed with particular attention being paid to their possible astrophysical and cosmological applications. In addition, the four-dimensional properties of matter can be regarded as geometrical in origin by a reduction of the five-dimensional vacuum field equations to Einstein's four-dimensional theory with a non-zero energy-momentum tensor constituting the material source; we shall also be interested in the induced matter associated with the new five-dimensional solutions obtained.     

Properties of $$\boldsymbol{B}_{\boldsymbol{c}}$$ Mesons and Variational Constraints on Their Masses

Physics of Atomic Nuclei - Spectrum, radii, radial wave functions at origin, decay constants, and momentum widths for radial and orbital excited $$B_{c}$$ mesons are derived within non-relativistic...     

Classification of Static, Spherically Symmetric Solutions of the Einstein-Yang-Mills Theory with Positive Cosmological Constant

We give a complete classification of all static, spherically symmetric solutions of the SU(2) Einstein-Yang-Mills theory with a positive cosmological constant. Our classification proceeds in two steps. We first extend solutions of the radial field equations to their maximal interval of existence. In a second step we determine the Carter-Penrose diagrams of all 4-dimensional space-times constructible from such radial pieces. Based on numerical studies we sketch a complete phase space picture of all solutions with a regular origin.     

Search for the origin of double-peak structure at RHIC by AMPT model with triggered di-jet

With a multi-phase transport (AMPT) model,a γ-jet with known production point and momentum is triggered to search for the origin of double-peak structure in di-hadron azimuthal correlation in central Au+Au collisions at RHIC energy.The different configurations of triggered γ-jet produce different shapes of medium responses.The key of the double-peak structure is found to be a strong shadowing effect of dense core,which is related to transverse expansion and radial flow of partonic matter.     

Higher order JWKB expressions for the energy levels and the wavefunction at the origin

We derive an exact quantization condition for the energy levels of a particle in a radial potential assumed finite at the origin. This is used to derive corrections to the semiclassical JWKB quantization condition. We further relate the normalization integral of the wavefunction to the energy derivative of wavefunction at origin and use this expression to derive the corrections to the semiclassical JWKB expressions for the wavefunction at origin. An application to upsilon leptonic decay width is also given.     

CO2激光局域辐照对熔石英损伤特性的影响

研究了CO₂激光局域辐照对熔石英损伤特性的影响, 发现当辐照中心温度较低时(1139 K), 辐照对损伤阈值没有明显影响, 但辐照中心温度较高时(1638 K), 辐照对损伤阈值有明显的影响, 损伤阈值随距离辐照中心间距的增大而减小, 在残余应力产生光程差最大处附近, 损伤阈值降到最小, 随着与辐照中心间距的进一步增加, 损伤阈值略有上升. 对导致此现象的原因做了分析. 由于残余应力的存在, 在辐照中心发生再损伤产生的裂纹后, 裂纹先沿径向扩展, 在残余应力产生光程差最大处附近, 裂纹转而向切向扩展, 这可能与径向和环向张应力随半径的变化有关. 在采用热处理炉退火消除残余应力时, 必须注意元件的洁净处理, 否则退火会出现析晶现象, 对损伤阈值和透射率造成不良影响. 关键词： 2激光局域辐照')" href="#">CO₂激光局域辐照 熔石英 损伤特性     

Exact partial wave expansion of optical beams with respect to an arbitrary origin

Using an analytical expression for an integral involving Bessel and Legendre functions, we succeed in obtaining the partial wave decomposition of a general optical beam at an arbitrary location relative to the origin. We also showed that solid angle integration will eliminate the radial dependence of the expansion coefficients. The beam shape coefficients obtained are given by an exact expression in terms of single or double integrals. These integrals can be evaluated numerically on a short time scale. We present the results for the case of a linear-polarized Gaussian beam.     

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Radial imaging techniques, such as projection-reconstruction （PR）, are used in magnetic resonance imaging （MRI） for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function （PSF）. In this paper, a shaking projection （SP） k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. ASP trajectory has the same aliasing character when using half sampling frequency （or half data） for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling recon- struction. Furthermore, this method can be applied to three-dimensional （3D） hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.     

Self-gravitating fluid systems and galactic dark matter

We study gravitational collapse with anisotropic pressures, whose end stage can mimic space–times that are seeded by galactic dark matter. To this end, we identify a class of space–times (with conical defects) that can arise out of such a collapse process, and admit stable circular orbits at all radial distances. These have a naked singularity at the origin. An example of such a space–time is seen to be the Bertrand space–time discovered by Perlick, that admits closed, stable orbits at all radii. Using relativistic two-fluid models, we show that our galactic space–times might indicate exotic matter, i.e one of the component fluids may have negative pressure for a certain asymptotic fall off of the associated mass density, in the Newtonian limit. We complement this analysis by studying some simple examples of Newtonian two-fluid systems, and compare this with the Newtonian limit of the relativistic systems considered.     

Radial asymptotics of Lemaître–Tolman–Bondi dust models

We examine the radial asymptotic behavior of spherically symmetric Lemaître–Tolman–Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length ?, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing quasi-local scalars defined as integral functions along the rays, we obtain a complete and covariant representation of the models, leading to an initial value parametrization in which all scalars can be given by scaling laws depending on two metric scale factors and two basic initial value functions. Considering regular “open” LTB models whose space slices allow for a diverging ?, we provide the conditions on the radial coordinate so that its asymptotic limit corresponds to the limit as ? → ∞. The “asymptotic state” is then defined as this limit, together with asymptotic series expansion around it, evaluated for all metric functions, covariant scalars (local and quasi-local) and their fluctuations. By looking at different sets of initial conditions, we examine and classify the asymptotic states of parabolic, hyperbolic and open elliptic models admitting a symmetry center. We show that in the radial direction the models can be asymptotic to any one of the following spacetimes: FLRW dust cosmologies with zero or negative spatial curvature, sections of Minkowski flat space (including Milne’s space), sections of the Schwarzschild–Kruskal manifold or self-similar dust solutions.