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This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as \"the amplitude equation\", is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions $u^{\\varepsilon} $ to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength $\\varepsilon $, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to $u^{\\varepsilon}$ on a time interval independent of $\\varepsilon $. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.

In Measuring Shadows, Raz Chen-Morris demonstrates that a close study of Kepler's Optics is essential to understanding his astronomical work and his scientific epistemology. He explores Kepler's radical break from scientific and epistemological traditions and shows how the seventeenth-century astronomer posited new ways to view scientific truth and knowledge. Chen-Morris reveals how Kepler's ideas about the formation of images on the retina and the geometrics of the camera obscura, as well as his astronomical observations, advanced the argument that physical reality could only be described through artificially produced shadows, reflections, and refractions. Breaking from medieval and Renaissance traditions that insisted upon direct sensory perception, Kepler advocated for instruments as mediators between the eye and physical reality, and for mathematical language to describe motion. It was only through this kind of knowledge, he argued, that observation could produce certainty about the heavens. Not only was this conception of visibility crucial to advancing the early modern understanding of vision and the retina, but it affected how people during that period approached and understood the world around them.

In this study, we used a research tool for measuring students’ conceptual understanding in optics, the Geometrical Optics Conceptual Understanding Test-2 (GOCUT-2), to evaluate the impact of supplementing classroom instruction with laboratory experiments, PhET simulations, or YouTube videos. This study involved students from public, urban secondary schools in Rwanda. Preliminary findings from the study indicate that these instructional resources did impact student conceptual understanding, and this impact is not uniform across all topics covered in geometric optics. A MANOVA demonstrated that learning outcomes were best for students who combined traditional physics labs with digital tools. This analysis also indicates that schools, where physics laboratories were most used, were more likely to exhibit greater conceptual understanding. We observed similar increases when PhET simulations and YouTube video resources were used together. In each case, students still showed some gaps related to drawing and interpreting images formed by lenses. We recommend that teachers supplement the geometric optics curriculum with open educational resources (OERs), including PhET simulations and YouTube videos.

Traditionally, the study of quantum key distribution (QKD) assumes an omnipotent eavesdropper that is only limited by the laws of physics. However, this is not the case for specific application scenarios such as the QKD over a free-space link. In this invited paper, we introduce the geometrical optics restricted eavesdropping model for secret key distillation security analysis and apply to a few scenarios common in satellite-to-satellite applications.

Diffractive sail components may be used in part or whole for in-space propulsion and attitude control. A sun-facing hybrid diffractive solar sail having reflective front facets and transmissive side facets is described. This hybrid design seeks to minimize the undesirable scattering from side facets. Predictions of radiation pressure are compared for analytical geometrical optics and numerical finite difference time domain approaches. Our calculations across a spectral irradiance band from 0.5 to 3 μm suggest the transverse force in a sun facing configuration reaches 48% when the refractive index of the sail material is 1.5. Diffraction measurements at a representative optical wavelength of 633 nm support our predictions.

The preponderance of laser beam shapes cannot be ruled out during the implementation of an optical experiment nor during the formulation of its theoretical background. The present work elucidates the role of Gaussian and top-hat beam shapes in generating and analysing the photothermal beam deflection (PBD) signals. The complex geometrical optics models encompassing the perturbations in the phase and amplitude of the probe beam with one-dimensional (1D) and two-dimensional (2D) approaches is employed to curve fit the PBD signal and are compared. From the fitted curve, the thermal diffusivity and conductivity of the sample are calculated with the 1D and 2D models. A uniform intensity distribution over the sample, like a top-hat beam, is achieved using an optical lens system and verified using a beam profiler. When the phase and amplitude of the PBD signal are fitted at different positions of the lens, i.e., in focussed and defocussed conditions, it is observed that difference in the measured thermal characteristics is about 30% for the Gaussian pump beam profile, whereas it is only <4% for top-hat beam. Even though the fitting accuracy and sum of residues estimated for the 2D model are better than 1D, the ease of computation with the 1D model employing top-hat excitation suggests the application of the top-hat profile in photothermal experiments.

5G (fifth generation) signals have small coverage and poor stability, and 5G channels are prone to loss in substations densely populated with metal equipment. Due to the particularity of the spatial layout in the substation, traditional physical or statistical channel models cannot accurately calculate the 5G channel loss in the substation. Therefore, this paper introduces the basic idea of ray tracing algorithm for studying ray propagation. Based on the geometric optics theory of ray propagation, the effective channel path of 5G signal in substation is found. Through the electromagnetic reflection theory and consistent diffraction theory, the energy loss caused by signal reflection and diffraction is calculated. Combined with the relationship between the free space loss of 5G signal on the transceiver path and the change of electric field, the solution method of 5G channel loss in substation is deduced. According to this method, (the influence of signal receiver height, 5G antenna height and its spatial position in horizontal and vertical directions on 5G channel loss of substation is studied in turn. By optimizing the layout of communication facilities according to the influence law, the reliability of 5G channel in substation can be realized).

In this work, the analytical solutions are constructed that describe the Green function for the equation of internal gravity waves in a stratified medium with variable buoyancy frequency. An asymptotical method for constructing solutions is proposed using the method of geometric optics; the method applies explicit analytical solutions for a semi-infinite stratified medium with linear distribution of the square of the buoyancy frequency. It is shown that the proposed algorithm for building the asymptotic of the Green function can be generalized to the case of horizontally inhomogeneous stratified media, when the buoyancy frequency depends not only on the vertical coordinate, but also on the horizontal coordinates.

In this work, the wave dynamics of far fields of internal gravity waves in stratified media of variable depth is studied. One of the most difficult questions is considered arising in investigating the wave dynamics by means of the geometric optics methods: the problem of constructing the asymptotics near singular spatial curves and surfaces—caustics. The asymptotic representations built in this work in the most general form allow describing the far field of internal gravity waves excited by a source moving over a slowly changing bottom. The uniform asymptotic expressions of the solution are obtained that reflect the main peculiarities of the wave fields near caustics and wave fronts. Universal character of the proposed asymptotic methods and approaches allows efficiently computing the wave fields at large distances from the source moving in a stratified medium of variable depth. The obtained analytical results enable analyzing the wave patterns in their entirety, which is important for both the correct formulation of the mathematical models of wave dynamics and estimation calculations at field measurements of wave fields in the ocean.

— The concept of Alfvén waves, introduced into science 80 years ago, played an important role in the formation and development of cosmic electrodynamics. Alfvén waves differ in that at each point in space the group velocity vector and the vector of the external magnetic field are collinear to each other, due to which the waves can carry momentum, energy, and information over long distances. In memory of the outstanding event, we briefly describe two Alfvén resonators, one of which is located high above the Earth, in the radiation belt, and the second, in the ionospheric layers. Both resonators have a discrete spectrum in the upper part of the range of ultralow frequency oscillations of natural origin (approximately from 0.2 Hz to 7 Hz). The close connection between the concept of Alfvén waves and the current problems of the electrodynamics of geophysical media is especially emphasized.