Spherical gravitational waves and quasi-spherical waves scattered from black string in massive gravity

Spherical gravitational wave is strictly forbidden in vacuum space in frame of general relativity by the Birkhoff theorem. We prove that spherical gravitational waves do exist in non-linear massive gravity, and find the exact solution with a special singular reference metric. Further more, we find exact gravitational wave solution with a singular string by meticulous studies of familiar equation, in which the horizon becomes non-compact. We analyze the properties of the congruence of graviton rays of these wave solution. We clarify subtle points of dispersion relation, velocity and mass of graviton in massive gravity with linear perturbations. We find that the graviton ray can be null in massive gravity by considering full back reaction of the massive gravitational waves to the metric. We demonstrate that massive gravity has deep and fundamental discrepancy from general relativity, for whatever a tiny mass of the graviton.

Experimental realization of a Fresnel hologram as a super spectral resolution optical element

A highly dispersive, diffractive optical element is designed and realized for an extremely high spectral resolution spectroscopy for exoplanet telescope application. Our design uses an annular Fresnel hologram to transform incident starlight directly into a spectrogram. The recording of the hologram is accomplished using two spherical waves of different radius of curvature. The resultant hologram consists of an annular grating structure with a gradually shrinking period as a function of increasing radius. The variable period not only could bring the incoming star-light into focus, but also exhibits a large on-axis chromatic behavior. We demonstrate a dispersion of wavelength 430–700 nm over 190 mm on-axis distance, leading to a super fine spectral resolution 0.0266 nm at wavelength 515 nm for a detector size of 20 µm.

Inward and outward dust acoustic cylindrical and spherical waves interaction in four-component dusty plasma with nonthermal ions

A theoretical investigation by an all-inclusive adaptation of the PLK strategy is carried out in order to study the inward and outward interaction between two cylindrical and spherical dust acoustic solitary waves (DASWs) in an unmagnetized dusty plasma consisting of nonthermal distributed ions, negatively and positively charged dust grains along with electrons featuring Boltzmann’s distribution. The interactions and collisions between two cylindrical and spherical geometries at different time scales are studied. Also the combined effects of the nonthermality of ions, ion to electron temperature ratio as well as mass ratio of positive to negative dust grains have been studied in detail on the phase shifts raised due to collision. It has been seen that the properties of the cooperation of DASWs in cylindrical and spherical shaped are distinct.

Newton and Knowledge of the Universe

Like Bacon, Descartes, and Galileo, Newton identified method as the key to discovering truths about the world, and like theirs, Newton’s method conflated induction and deduction in making claims about reality. Against Robert Hooke, Newton claimed that data spoke for themselves, as in his claim that his prism experiments directly proved that sunlight really was a combination of colors. In his theory of light, Newton claimed that his data allowed him to “deduce” that light was made up of corpuscles, against Christiaan Huygens’ claim that light was composed of spherical waves. In Newton’s mechanics, which became the cornerstone of modern mathematical physics, neither his definitions of space, time, matter, and motion nor his famous three laws of motion were deduced from experimental data. In his dismissal of Descartes’ method of reasoning and in his battles with Leibniz over the nature of reality, Newton was forced to confront the logical weakness of his ontological claims.

Energy-Band Theory

Various methods to calculate energy bands and the electronic structure of solids are described in detail. Although the emphasis lies on linear methods well known for their transparency and high numerical speed, traditional methods are described to supply historical background and to point the way to modern methods. After introducing Bloch electrons and the reciprocal space, plane waves, orthogonalized plane waves, and pseudopotentials are discussed, followed by the important augmented plane wave method (APW). Multiple scattering theory defines scattering phase shifts encoding atomic properties and the structure constants that describe the crystal lattice. Linear combination of atomic orbitals (LCAO) and linear combination of muffin-tin orbitals (LMTO) result in efficient and fast methods as does the related augmented spherical waves (ASW) method. The treatment of arbitrary spin configurations using the ASW method and the formulation of incommensurate spiral structures on the basis of the unitary SU(2) group are developed in detail.

Gain Enhancement Planar Lens Antenna based on Wideband Focusing Gradient Meta-surface

A three-layered transmitting focusing gradient meta-surface (FGMS) has been proposed, which can achieve broadband gain enhancement from 8.2 GHz to 10 GHz. The element of broadband transmitting FGMS has high transmitting efficiencies that over 0.7 and achieve [0, 2π] phase range with a flat and linear trend in the operating band. The FGMS can transform the spherical waves into plane waves. Three patch antennas working at 8.2 GHz, 9.1 GHz, and 10 GHz respectively are placed the focus of broadband FGMS as the spherical-wave source to build a broadband planar lens antenna system. It achieves a simulation gain of 15.44 dBi which is 7.51dB higher than that of the bare patch antenna at 10 GHz with satisfying SLLs and beamwidths. However, it enhanced the gain of the bare patch antenna in a wide operating band. Finally, the FGMS and the patch antenna are fabricated and measured. The measured results are in good agreement with the simulations.

Resolution Enhancement of Spherical Wave-Based Holographic Stereogram with Large Depth Range

The resolution-priority holographic stereogram uses spherical waves focusing on the central depth plane (CDP) to reconstruct 3D images. The image resolution near the CDP can be easily enhanced by modifying three parameters: the capturing depth, the pixel size of elemental image and the focal length of lens array. However, the depth range may decrease as a result. In this paper, the resolution characteristics were analyzed in a geometrical imaging model, and three corresponding methods were proposed: a numerical method was proposed to find the proper capturing depth; a partial aperture filtering technique was proposed after reducing pixel size; the moving array lenslet technique was introduced after increasing focal length and partial aperture filtering. Each method can enhance resolution within the total depth range. Simulation and optical experiments were performed to verify the proposed methods.

Wavefront Modulation and Beam Shaping into Arbitrary Three-Dimensional Intensity Distributions

In this study the methods of three-dimensional (3D) wavefront intensity modulation by employing contrast-inverted holography, previously introduced as Gabor inverted holography, are further investigated. The present study provides the recipes for creating 3D wavefront intensity modulations using phase-only and amplitude-only modulators and compares the results. The 3D wavefront modulation using spherical waves is also demonstrated, and the miniaturization of 3D intensity beams is discussed; it is shown that both the resolution and the size of the created 3D structures are ultimately given by the wavelength of the employed radiation. The manuscript also addresses the quality of the formed 3D intensity curves and determines the parameters that provide the best smooth appearance of the 3D curves. The presented methods of 3D intensity wavefront modulation can be realized for all kinds of waves: light, X-ray, electron, etc, provided the modulator can be manufactured for the corresponding wavelength. The methods of 3D intensity wavefront modulation can be applied in various techniques: lithography, micro-robotics, particle trapping, etc.