Physics

Reconfigurable intelligent surfaces (RISs) are an emerging field of research in wireless communications. A fundamental component for analyzing and optimizing RIS-empowered wireless networks is the development of simple but sufficiently accurate models for the power scattered by an RIS. By leveraging the general scalar theory of diffraction and the Huygens-Fresnel principle, we introduce simple formulas for the electric field scattered by an RIS that is modeled as a sheet of electromagnetic material of negligible thickness. The proposed approach allows us to identify the conditions under which an RIS of finite size can or cannot be approximated as an anomalous mirror. Numerical results are illustrated to confirm the proposed approach.

A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account. The quadratic law for the resistance force is used. An analytic approach applies for the investigation. Equations of the projectile motion are solved analytically for an arbitrarily large period of time. The constructed analytical solutions are universal. As a limit case of motion, the vertical asymptote formula is obtained. The value of the vertical asymptote is calculated directly from the initial conditions of motion. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball, a tennis ball and shuttlecock of badminton are presented as examples.

Graphic statics is undergoing a renaissance, with computerized visual representation becoming both easier and more spectacular as time passes. While methods of the past are revived and tweaked, little emphasis has been placed on studying the details of these methods. Due to the considerable advances of our mathematical understanding since the birth of graphic statics, we can learn many interesting and beautiful things by examining these old methods from a more modern viewpoint. As such, this work shows the mathematical fabric joining different aspects of graphic statics, like dualities, reciprocal diagrams and discontinous stress functions.

Ground-based astro-geodetic observations and atmospheric occultations, are two examples of observational techniques requiring a scrutiny analysis of atmospheric refraction. In both cases, the measured changes in observables are geometrically related to changes in the photon path and the light time of the received electromagnetic signal. In the context of geometrical optics, the change in the physical properties of the signal are related to the refractive profile of the crossed medium. Therefore, having a clear knowledge of how the refractivity governs the photon path and the light time evolution is of prime importance to clearly understand observational features. Analytical studies usually focused on spherically symmetric atmospheres and only few aimed at exploring the effect of the non-spherical symmetry on the observables. In this paper, we analytically perform the integration of the photon path and the light time of rays traveling across a planetary atmosphere. We do not restrict our attention to spherically symmetric atmospheres and introduce a comprehensive mathematical framework which allows to handle any kind of analytical studies in the context of geometrical optics. To highlight the capabilities of this new formalism, we carry out five realistic applications for which we derive analytical solutions. The accuracy of the method of integration is assessed by comparing our results to a numerical integration of the equations of geometrical optics in the presence of a quadrupolar moment J 2 . This shows that the analytical solution leads to the determination of the light time and the refractive bending with relative errors at the level of one part in 10 8 and one part in 10 5 , for typical values of the refractivity and the J 2 parameter at levels of 10 −4 and 10 −2 , respectively.

Laplace's equation appears frequently in physical applications involving conservable quantities. Among these applications, miniaturized devices have been of interest, in particular those using interdigitated arrays. Therefore, we solved the two-dimensional Laplace's equation for a shallow or finite domain consisting of interdigitated boundaries. We achieved this by using Jacobian elliptic functions to conformally transform the interdigitated domain into a parallel plates domain. The obtained expressions for potential distribution, flux density and flux allow for arbitrary domain height, different band widths and asymmetric potentials at the interdigitated array, besides considering fringing effects at both ends of the array. All these expressions depend only on relative dimensions, instead of absolute ones. With these results we showed that the behavior in shallow or finite domains approaches that of a semi-infinite domain, when its height is greater than the separation between the centers of consecutive bands. We also found that, for any desired but fixed flux, bands of equal width minimize the total surface of the interdigitated array. Finally, we present approximate expressions for the flux, based on elementary functions, which can be applied to ease the calculation of currents (faradaic or non-faradaic), capacitances and resistances among other possible applications.

To draw conclusions as regards the stability and modelling limits of the investigated continuum, we consider a family of infinitesimal isotropic generalized continuum models (Mindlin-Eringen micromorphic, relaxed micromorphic continuum, Cosserat, micropolar, microstretch, microstrain, microvoid, indeterminate couple stress, second gradient elasticity, etc.) and solve analytically the simple shear problem of an infinite stripe. A qualitative measure characterizing the different generalized continuum moduli is given by the shear stiffness μ ∗ . This stiffness is in general length-scale dependent. Interesting limit cases are highlighted, which allow to interpret some of the appearing material parameter of the investigated continua.

We derive a general condition for angle-independent bianisotropic nongyrotropic metasurfaces and present two applications corresponding to particular cases: an angle-independent absorber/amplifier and an angle-independent spatial gyrator.

Some recent papers have argued that frequency should have the dimensions of angle/time, with the consequences that 1 Hz = 2? rad/s instead of 1 s ?? , and also that ν=? and h=??. This letter puts the case that this argument redefines the quantity frequency and then draws conclusions from equations that rely on the standard definition being used. The problems that this redefinition is designed to address arise from the widespread unstated adoption of the Radian Convention, which treats the radian as a dimensionless quantity equal to the number 1, in effect making the radian a hidden unit. This convention is currently built-in to the SI, when it should be separable from it. The unhelpful status of angles in the SI can be remedied with minimal disruption by (1) changing the definition of the radian from a radian equals 1 m/m to e.g. a right angle equals ?/2 radians, and (2) acknowledging that the adoption of the Radian Convention is acceptable, when made explicit. The standard definitions of frequency and the hertz should remain unchanged.

This paper concerns anisotropic two-dimensional and planar elasticity models within the frameworks of classical linear elasticity and the bond-based peridynamic theory of solid mechanics. We begin by reviewing corresponding models from the classical theory of linear elasticity. This review includes a new elementary and self-contained proof that there are exactly four material symmetry classes of the elasticity tensor in two dimensions. We also summarize classical plane strain and plane stress linear elastic models and explore their connections to the pure two-dimensional linear elastic model, relying on the definitions of the engineering constants. We then provide a novel formulation for pure two-dimensional anisotropic bond-based linear peridynamic models, which accommodates all four material symmetry classes. We further present innovative formulations for peridynamic plane strain and plane stress, which are obtained using direct analogies of the classical planar elasticity assumptions, and we specialize these formulations to a variety of material symmetry classes. The presented anisotropic peridynamic models are constrained by Cauchy's relations, which are an intrinsic property of bond-based peridynamic models. The uniqueness of the presented peridynamic plane strain and plane stress formulations in this work is that we directly reduce three-dimensional models to two-dimensional formulations, as opposed to matching two-dimensional peridynamic models to classical plane strain and plane stress formulations. This results in significant computational savings, while retaining the dynamics of the original three-dimensional bond-based peridynamic problems under suitable assumptions.

This work investigates anomalous transmission effects in periodic dissipative media, which is identified as an acoustic analogue of the Borrmann effect. For this, the scattering of acoustic waves on a set of equidistant resistive sheets is considered. It is shown both theoretically and experimentally that at the Bragg frequency of the system, the transmission coefficient is significantly higher than at other frequencies. The optimal conditions are identified: one needs a large number of sheets, which induce a very narrow peak, and the resistive sheets must be very thin compared to the wavelength, which gives the highest maximal transmission. Using the transfer matrix formalism, it is shown that this effect occurs when the two eigenvalues of the transfer matrix coalesce, i.e. at an exceptional point. Exploiting this algebraic condition, it is possible to obtain similar anomalous transmission peaks in more general periodic media. In particular, the system can be tuned to show a peak at an arbitrary long wavelength.