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《Expositiones Mathematicae》2020,38(2):202-216
We give a transparent algebraic formulation of our pictorial approach to the reflection positivity (RP), that we introduced in a previous paper. We apply this quantization to the Levin–Wen model to obtain anyonic/quantum spin chain theory on the boundary, possibly entangled in the bulk. The reflection positivity property has played a central role in both mathematics and physics, as well as providing a crucial link between the two subjects. In a previous paper we gave a new geometric approach to understanding reflection positivity in terms of pictures. Here we give a transparent algebraic formulation of our pictorial approach. We use insights from this translation to establish the reflection positivity property for the fashionable Levin–Wen models with respect both to vacuum and to bulk excitations. We believe these methods will be useful for understanding a variety of other problems. 相似文献
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Summary In this paper, the reflection and refraction of a plane wave at an interface between two half-spaces composed of triclinic crystalline material is considered. It is shown that due to incidence of plane wave three types of waves, namely quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH), will be generated governed by the propagation condition involving the acoustic tensor. A simple procedure has been presented for the calculation of all the three phase velocities of the quasi waves. It has been established that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation. Relations are established between directions of motion and propagation, respectively. The expressions for reflection and refraction coefficients of qP, qSV and qSH waves are obtained. Numerical results of reflection and refraction coefficients are presented for different types of anisotropic media and for different types of incident waves. Graphical representations have been made for incident qP waves, and for incident qSV and qSH waves numerical data are presented in tables.The work was completed while the author was visiting the University of Kaiserslautern, Department of Geomathematics as Visiting Professor. The Author is grateful to Professor Dr. W. Freeden for providing DAAD fellowship and all the facilities for conducting research, as well as to Dr. V.Michel for various discussions about the research work and also for all kinds of help during his stay at Kaiserslautern, Germany. This award is very gratefully acknowledged. 相似文献
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《Current Applied Physics》2020,20(5):638-642
A series of bio-silica incorporated barium-ferrite-composites with the composition of (x)Bio-SiO2:(80-x)γ-Fe2O3:(20)BaO, where x = 0, 1, 2, and 3 wt% were prepared using the modified solid-state reaction method. The influence of different bio-silica (extricated from sintered rice husk) contents on the surface morphologies, structures, and magnetic characteristics of these composites were assessed. The relative complex permittivity and permeability were resolved using the Nicholson-Ross-Weir strategy in the frequency range of 8–13 GHz. Meanwhile, the reflection loss was estimated through the transmission/reflection line theory to assess the MW absorption properties of the composites. Incorporation of the bio-silica in the barium ferrite composites generated a new hexagonal phase (Ba3Fe32O51) and a tetragonal phase (BaFeSi4O10) which led to a decrease in the saturation magnetization and significant shift in the MW frequency absorption peak positions. 相似文献
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《Wave Motion》2020
Three problems for a discrete analog of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: (1) the problem with a point source on an entire plane; (2) the problem of diffraction by a Dirichlet half-line; (3) the problem of diffraction by a Dirichlet right angle. It is shown that the total field can be represented as an integral of an algebraic function over a contour drawn on some manifold. The latter is a torus. As a result, explicit solutions are obtained in terms of recursive relations (for the Green’s function), algebraic functions (for the half-line problem), or elliptic functions (for the right angle problem). 相似文献
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Mechanical problems involving an interphase between two well-defined, and eventually different, materials are of interest. The aim of this paper is to present a simplified model that, for low frequency regime, is appropriate for this situation: an interface model with elastic and inertial properties. We present, together with the equations of motion, an identification procedure that is valid for any mass density profile along the thickness of the interphase. For evaluating the accuracy of the model, computations of the reflection coefficients in some relevant cases are shown. Besides, a finite element method is used as a benchmark for both the high and low frequency regimes. It is worth to be noted that the numerical test has been inspired by the problem of the interphase that is formed at the bone-implant boundary. 相似文献
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The propagation of plane harmonic waves are studied in a microstretch fluid medium. It is found that five basic waves can propagate at distinct speeds in an infinite linear homogeneous isotropic microstretch fluid. Out of these five waves, one is a longitudinal micro-rotational wave, two are coupled longitudinal waves and remaining two are coupled transverse waves. The longitudinal micro-rotational wave travels independently and is not influenced by the microstretching of the medium, while the coupled longitudinal waves arise due to the presence of microstretching and coupled transverse waves arise due to the presence of micro-rotation in the medium. Speed of propagation of all the waves are found to be complex valued and dispersive at low frequency, but almost non-dispersive at high frequency. Due to complex valued speeds of propagation, all the waves are attenuating but differently. Coupled sets of longitudinal waves reduce to a longitudinal wave of micropolar fluid in the absence of microstretching. Reflection phenomena of a set of coupled longitudinal waves incident obliquely at the free surface of a microstretch fluid half-space has been investigated. Closed formulae for the reflection coefficients are presented and computed numerically for a particular medium. The real and imaginary parts of the complex speeds of all the waves and their corresponding attenuation coefficients have also been studied numerically and depicted graphically against frequency parameter. 相似文献
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Qiumin Yang Jie Zhao Min Guan Chao Liu Lijie Cui Dejun HanYiping Zeng 《Applied Surface Science》2011,257(21):9038-9043
CdSe thin films have been grown on GaAs (0 0 1) substrates by molecular beam epitaxy (MBE). The effects of substrate temperature and annealing treatment on the structural properties of CdSe layers were investigated. The growth rate slightly decreases due to the accelerated desorption of Cd from CdSe surface with an increase in the temperature. The sample grown at 260 °C shows a polycrystalline structure with rough surface. As the temperature increases over 300 °C, crystalline CdSe (0 0 1) epilayers with zinc-blende structure are achieved and the structural quality is improved remarkably. The epilayer grown at 340 °C displays the narrowest full-width at half-maximum (FWHM) from (0 0 4) reflection in double-crystal X-ray rocking curve (DCXRC) and the smallest root-mean-square (RMS) roughness of 0.816 nm. Additionally, samples fabricated at 320 °C were annealed in air for 30 min to study the films’ thermal stability. X-ray diffraction (XRD) results indicate that the zinc-blende structure remains unchanged when the annealing temperature is elevated to 460 °C, meaning a good thermal stability of the cubic CdSe epilayers. 相似文献