Physics

The forced-vibration response of a simply-supported isotropic thick-walled hollow elastic circular cylinder subjected to two-dimensional harmonic standing-wave excitations on its curved surfaces is studied within the framework of linear elastodynamics. Exact semi-analytical solutions for the steady-state displacement field of the cylinder are constructed using recently-published parametric solutions to the Navier-Lamé equation. Formal application of the standing-wave boundary conditions generates three parameter-dependent 6×6 linear systems, each of which can be numerically solved in order to determine the parametric response of the cylinder's displacement field under various conditions. The method of solution is direct and demonstrates a general approach that can be applied to solve many other elastodynamic forced-response problems involving isotropic elastic cylinders. As an application, and considering several examples, the obtained solution is used to compute the steady-state frequency response in a few specific low-order excitation cases. In each case, the solution generates a series of resonances that are in exact correspondence with a unique subset of the natural frequencies of the simply-supported cylinder. The considered problem is of general theoretical interest in structural mechanics and acoustics and more practically serves as a benchmark forced-vibration problem involving a thick-walled hollow elastic cylinder.

An extension of the Helmholtz theorem is proved, which states that two retarded vector fields F 1 and F 2 satisfying appropriate initial and boundary conditions are uniquely determined by specifying their divergences ∇⋅ F 1 and ∇⋅ F 2 and their coupled curls −∇× F 1 −∂ F 2 /∂t and ∇× F 2 −(1/ c 2 )∂ F 1 /∂t , where c is the propagation speed of the fields. When a corollary of this theorem is applied to Maxwell's equations, the retarded electric and magnetic fields are directly obtained. The proof of the theorem relies on a novel demonstration of the uniqueness of the solutions of the vector wave equation.

It is proven, without using the microscopic reversibility argument of Onsager, that lossy reciprocal systems have a hidden time-reversal symmetry. The key idea is that the dissipation channels of lossy dielectrics can be mimicked by a distributed network of lossless transmission lines. It is highlighted that the reciprocity of lossy dielectrics is fundamentally rooted on the hidden time-reversal invariance and on linearity of the materials. Furthermore, it is demonstrated that the upper-half plane response of dissipative materials can be approximated as much as desired by the response of some lossless material.

The tight connection between mass and energy unveiled by Special Relativity, summarized by the iconic formula E=m c 2 , has revolutionized our understanding of nature and even shaped our political world over the past century through its military application. It is certainly one of the most exhaustively-tested and well-known equations of modern science. Although we have become used to its most obvious implication -- mass-energy equivalence --, it is surprising that one of its subtle -- yet, inevitable -- consequences is still a matter of confusion: the so-called hidden momentum. Often considered as a peculiar feature of specific systems or as an artifact to avoid paradoxal situations, here we present a new relativistic "paradox" which exposes the true nature and ubiquity of hidden momentum. We also show that hidden momentum can be forced to reveal itself through observable effects, hopefully putting an end to decades of controversy about its reality.

You have a rocket in a high circular orbit around a massive central body (a planet, or the Sun) and wish to escape with the fastest possible speed at infinity for a given amount of fuel.

In systems with non-local potentials or other kinds of non-locality, the Landauer-Büttiker formula of quantum transport leads to replace the usual gauge-invariant current density J with a current J ext which has a non-local part and coincides with the current of the extended Aharonov-Bohm electrodynamics. It follows that the electromagnetic field generated by this current can have some peculiar properties, and in particular the electric field of an oscillating dipole can have a long-range longitudinal component. The calculation is complex because it requires the evaluation of double-retarded integrals. We report the outcome of some numerical integrations with specific parameters for the source: dipole length ∼ 10 −7 cm, frequency 10 GHz. The resulting longitudinal field E L turns out to be of the order of 10 2 to 10 3 times larger than the transverse component (only for the non-local part of the current). Possible applications concern the radiation field generated by Josephson tunnelling in thick SNS junctions in YBCO and by current flow in molecular nano-devices.

Inspired by complete graph theory, we demonstrate that a metallic claw "meta-atom" structure can carry a high number of nearly degenerate resonant modes. A photonic meta-crystal composing of a lattice of such meta-atoms exhibits a large number of flat bands that are squeezed into a narrow frequency window, and these flat bands can be designed to locate in a wide complete 3D bandgap. The degeneracy dimension (Nf) of the flat bands is determined by the number of branches (Nb) of the metallic claw with Nf=Nb-3, which is geometrically related to the complete graph theory. Different from those flat bands emerging from special lattice arrangements (e.g., Kagome lattice), the isolated flat bands here are insensitive to lattice perturbations. The proposed mechanism offers a new platform for realizing various dispersion-less phenomena and a new paradigm to realize high density of states and spectra compressing.

In this work, we present the computational realization of holographic metasurfaces to generation of the non-diffracting waves. These holographic metasurfaces (HMS) are simulated by modeling a periodic lattice of metallic patches on dielectric substrates with sub-wavelength dimensions, where each one of those unit cells alter the phase of the incoming wave. We use the surface impedance (Z) to control the phase of the electromagnetic wave through the metasurface in each unit cell. The sub-wavelength dimensions guarantees that the effective medium theory is fulfilled. The metasurfaces are designed by the holographic technique and the computer-generated holograms (CGHs) of non-diffracting waves are generated and reproduced using such HMS in the microwave regime. The results is according to the theoretically predicted by non-diffracting wave theory. These results are important given the possibilities of applications of these types of electromagnetic waves in several areas of telecommunications and bioengineering.

We report on the experimental investigation of the dependence of the elastic enhancement, i.e., enhancement of scattering in backward direction over scattering in other directions of a wave-chaotic system with partially violated time-reversal (T ) invariance on its openness. The elastic enhancement factor is a characteristic of quantum chaotic scattering which is of particular importance in experiments, like compound-nuclear reactions, where only cross sections, i.e., the moduli of the associated scattering matrix elements are accessible. In the experiment a quantum billiard with the shape of a quarter bow-tie, which generates a chaotic dynamics, is emulated by a flat microwave cavity. Partial T-invariance violation of varying strength 0 < xi < 1 is induced by two magnetized ferrites. The openness is controlled by increasing the number M of open channels, 2 < M < 9, while keeping the internal absorption unchanged. We investigate the elastic enhancement as function of xi and find that for a fixed M it decreases with increasing time-reversal invariance violation, whereas it increases with increasing openness beyond a certain value of xi > 0.2. The latter result is surprising because it is opposite to that observed in systems with preserved T invariance (xi = 0). We come to the conclusion that the effect of T -invariance violation on the elastic enhancement then dominates over the openness, which is crucial for experiments which rely on enhanced backscattering, since, generally, a decrease of the openness is unfeasible. Motivated by these experimental results we, furthermore, performed theoretical investigations based on random matrix theory which confirm our findings.

Is flipping a coin a deterministic process or a random one? We do not allow bounces. If we know the initial velocity and the spin given to the coin, mechanics should predict the face it lands on. However, the coin toss has been everyone's introduction to probability and has been assumed to be the hallmark random process. So, what's going on here? This article discusses the problem first brought up by Keller in 1986 using a perspective tangential to the one used by Keller which leads us to new insight about the probability of getting heads.