Physics

We analyse the stability of virus-carrying particles in air at equilibrium after the dissipation of the initial turbulent process produced by sneezing, coughing, breathing or speaking. Because the viruses are expelled mainly attached to small droplets, with diverse sizes and weights, and the external environmental conditions can also be diverse, the subsequent motion spannes different spatial and temporal scales. For droplet sizes larger than 100μm , computing the time of decay to the ground and the distance travelled with a simple free fall model with empirical data extracted from the literature, we obtain distances in the range between 1 to 3 meters from the emitter, with a falling time of less than 1s , similar to known recommendations for safe social distancing. For droplets sizes less than 100μm a simple model of motion in a viscous medium predicts that isolated viruses could remain suspended in quiet air for more than a month, while small droplets of 1μm in size can remain suspended for several hours, in agreement with recent experimental results on virus stability in aerosols. These results give solid background for the discussion of prevention strategies, like the use of masks in closed environments.

We present here how a coherent perfect absorber-laser (CPAL) enabled by parity-time ( PT )-symmetry breaking may be exploited to build monochromatic amplifying devices for flexural waves. The fourth order partial differential equation governing the propagation of flexural waves leads to four by four transfer matrices, and this results in physical properties of the PT -symmetry specific to elastic plate systems. We thus demonstrate the possibility of using CPAL for such systems and we argue the possibility of using this concept to detect extremely small-scale vibration perturbations with important outcomes in surface science (imaging of nanometer vibration) and geophysics (improving seismic sensors like velocimeters). The device can also generate finite signals using very low exciting intensities. The system can alternatively be used as a perfect absorber for flexural energy by tailoring the left and right incident wave for energy harvesting applications.

It is demonstrated in this paper that the propagation of the electric wave field in a heterogeneous medium in 3D can sometimes be governed well by a single PDE, which is derived from the Maxwell's equations. The corresponding component of the electric field dominates two other components. This justifies some past results of the second author with coauthors about numerical solutions of coefficient inverse problems with experimental electromagnetic data. In addition, since it is simpler to work in applications with a single PDE rather than with the complete Maxwell's system, then the result of this paper might be useful to researchers working on applied issues of the propagation of electromagnetic waves in inhomogeneous media.

In our analysis, we extend the capstan equation to noncircular geometries. We derive a closed from solution for a membrane with a zero-Poisson's ratio (or a string with an arbitrary Poisson's ratio) supported by a rigid prism, and then a rigid cone, at limiting-equilibrium. As a comparison, we extend Kikuchi and Oden's model for Coulomb's law of static friction to curvilinear coordinates. We also conduct numerical experiments to see how close Coulomb's law of static friction is to the ordinary friction law implied by our generalised capstan equation, in curvilinear coordinates. Our numerical results indicate that increasing the curvature, the Poisson's ratio and the thickness of the elastic body increases the frictional force, for a constant coefficient of friction, and incompressible materials such as rubber can have a high frictional forces, even under low coefficients of friction. Our analysis implies that the coefficient of friction is model dependent.

A new model for calculating the Casimir-Lifshitz force per unit length for two dielectric rods is proposed, based on the Green function method of classical electrodynamics and the Lorentz model for permittivity.

During the evolution of coupled nonlinear oscillators on a lattice, with dynamics dictated by the discrete nonlinear Schrödinger equation (DNLSE systems), two quantities are conserved: system energy (Hamiltonian) and system density (number of particles). If the number of system oscillators is large enough, a significant portion of the array can be considered to be an "open system", in intimate energy and density contact with a "bath" - the rest of the array. Thus, as indicated in previous works, the grand canonical formulation can be exploited in order to determine equilibrium statistical properties of thermalized DNLSE systems. In this work, given the values of the two conserved quantities, we have calculated the necessary values of the two Lagrange parameters (typically designated β,μ ) associated with the grand canonical partition function in two different ways. One is numerical and the other is analytic, based on a published approximate entropy expression. In addition we have accessed a purposely-derived approximate PDF expression of site-densities. Applying these mathematical tools we have generated maps of temperatures, chemical potentials, and field correlations for DNLSE systems over the entire thermalization zone of the DNLSE phase diagram, subjected to all system-nonlinearity levels. The end result is a rather complete picture, characterizing equilibrated large DNLSE systems.

Knots have been put forward to explain various physical phenomena because of their topological stability. Nevertheless, few works have reported on the exotic symmetry properties that certain knots possess. Here we reveal an exceptional form of symmetry for a family of knots that are both chiral and three-dimensional (3-D) rotationally symmetric about every axis of a standard Cartesian coordinate system. We call these unique knotted structures chiral balls. To demonstrate the unprecedented physical characteristics exhibited by these unique structures, we study the electromagnetic scattering properties of a representative conductive chiral ball. In particular, a characteristic mode analysis is performed to investigate the intrinsic scattering properties of this chiral ball. With both chirality and 3-D rotational symmetry, the chiral ball is shown to exhibit an extraordinary isotropic circularly polarized scattering property, which has not been previously reported for any known electromagnetic structures. Because of their unique properties, chiral balls are expected to not only have a profound impact on the fields of electromagnetics and optics but also far beyond.

The transmission of linearly and circularly polarized waves are studied both theoretically and experimentally for chiral metasurfaces formed by arrays of metallic square helices. The helical particles of the metasurfaces are constructed of rectangular bars manufactured by direct three-dimensional printing in solid metal. The transmittance of the metasurface is found to depend critically on the number of bars forming the square helical particles. In the case of an even number of bars, the chiral metasurface exhibits identical co-polarized transmittance of orthogonal linearly polarized waves, which are characterized by a dual-band asymmetric transmission. For an odd number of bars, the metasurface provides the same cross-polarization conversion for any polarization orientation of the incident field and thus serves as a polarization-independent twist polarizer. Finally, the transmittance of this polarizer is investigated with respect to the dimensions of the square helices. The investigated chiral metasurfaces are characterized by strong broadband circular dichroism regardless of the number of bars in the helical particles. The wide variety of transmission properties observed in the metasurfaces makes them particularly attractive for use in polarization conversion and separation devices.

This paper provides a mathematical approach to study chromatic aberration in metalenses. It is shown that radiation of a given wavelength is refracted according to a generalized Snell's law which together with the notion of envelope yields the existence of phase discontinuities. This is then used to establish a quantitative measure of dispersion in metalenses concluding that in the visible spectrum it has the same order of magnitude as for standard lenses.

In this work we obtain Planck's blackbody spectrum from the thermal scalar radiation contained in a resonant cavity of volume V in the context of classical mechanics, which provides the classical zero-point electromagnetic radiation in terms of a scale parameter that depends on geometric properties of the enclosure and electrical magnitudes. The scale parameter of the classical zero-point electromagnetic radiation is associated to experimental measurements of Casimir forces, but we show that theoretically its value for known radiant cavities that approach a blackbody has a numerical value of the order of Planck's constant.