Physics

Nonreciprocity has been introduced to various fields to realize asymmetric, nonlinear, and/or time non-revisal physical systems. By virtue of the Maxwell-Betti reciprocal theorem, breaking the time-reversal symmetry of dynamic mechanical systems is only possible using nonlinear materials. Nonetheless, nonlinear materials should be accompanied by geometrical asymmetries to achieve nonreciprocity in static systems. Here, we further investigate this and demonstrate a novel nonreciprocal elasticity concept. We show that the nonreciprocity of static mechanical systems can be achieved only and only if the material exhibits nonreciprocal elasticity. We experimentally demonstrate linear and nonlinear materials with nonreciprocal elasticities. By means of topological mechanics, we demonstrate that the mechanical nonreciprocity requires nonreciprocal elasticity no matter what the material is linear or nonlinear elastic. We show that linear materials with nonreciprocal elasticity can realize nonreciprocal-topological systems. The nonreciprocal elasticity developed here will open new venues of the design of mechanical systems with effective nonreciprocity.

We introduce the concept of nonreciprocal nongyrotropic phase gradient metasurfaces. Such metasurfaces are based on bianisotropic phase shifting unit cells, with the required nonreciprocal and nongyrotropic characteristics. Moreover, we present a transistor-based implementation of a nonreciprocal phase shifting subwavelength unit cell. Finally, we demonstrate the concept with a simulation of a 6-port spatial circulator application.

In the paper \cite{carati95} it was shown that, for motions on a line under the action of a potential barrier, the third-order Abraham-Lorentz-Dirac equation presents the phenomenon of nonuniqueness of nonrunaway solutions. Namely, at least for a sufficiently steep barrier, the physical solutions of the equation are not determined by the "mechanical state" of position and velocity, and knowledge of the initial acceleration too is required. Due to recent experiments, both in course and planned, on the interactions between strong laser pulses and ultra relativistic electrons, it becomes interesting to establish whether such a nonuniqueness phenomenon extends to the latter case, and for which ranges of the parameters. In the present work we will consider just the simplest model, i.e., the case of an electromagnetic plane wave, and moreover for the Abraham-Lorentz-Dirac equation dealt with in the nonrelativistic approximation. The result we found is that the nonuniqueness phenomenon occurs if, at a given frequency of the incoming wave, the field intensity is sufficiently large. An analytic estimate of such a threshold is also given. At the moment it is unclear whether such a phenomenon applies also in the full relativistic case, which is the one of physical interest.

Being a general wave phenomenon, bound states in the continuum (BICs) appear in acoustic, hydrodynamic, and photonic systems of various dimensionalities. Here, we report the first experimental observation of an accidental electromagnetic BIC in a one-dimensional periodic chain of coaxial ceramic disks. We show that the accidental BIC manifests itself as a narrow peak in the transmission spectra of the chain placed between two loop antennas. We demonstrate a linear growth of the radiative quality factor of the BICs with the number of disks that is well-described with a tight-binding model. We estimate the number of the disks when the radiation losses become negligible in comparison to material absorption and, therefore, the chain can be considered practically as infinite. The presented analysis is supported by near-field measurements of the BIC profile. The obtained results provide useful guidelines for practical implementations of structures with BICs opening new horizons for the development of radio-frequency and optical metadevices.

In this work, we experimentally report the acoustic realization the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model in a simple network of air channels. We analytically study the steady state dynamics of the system using a set of discrete equations for the acoustic pressure, leading to the 2D SSH Hamiltonian matrix without using tight binding approximation. By building an acoustic network operating in audible regime, we experimentally demonstrate the existence of topological band gap. More supremely, within this band gap we observe the associated edge waves even though the system is open to free space. Our results not only experimentally demonstrate topological edge waves in a zero Berry curvature system but also provide a flexible platform for the study of topological properties of sound waves.

A fractional variational principle was derived in order to be used with lagrangians containing fractional derivatives of order 1/2. By forcing the action associated to this type of lagrangian to be stationary, a modified fractional Euler-Lagrange equation was obtained. This was shown to reproduce the equations of motion of two basic 1-dimensional energy-dissipative systems: a spring-mass system damped by friction, and a RLC circuit connected in series. Finally, by using the fractional Euler-Lagrange equation, the Drude relationship for electrons in metals was recovered when a fractional kinetic energy was taken into consideration in the electron's associated energies.

In this paper, we investigate a transition from an elastica to a piece-wised elastica whose connected point defines the hinge angle ϕ 0 ; we refer the piece-wised elastica Λ ϕ 0 -elastica or Λ -elastica. The transition appears in the bending beam experiment; we compress elastic beams gradually and then suddenly due the rupture, the shapes of Λ -elastica appear. We construct a mathematical theory to describe the phenomena and represent the Λ -elastica in terms of the elliptic ζ -function completely. Using the mathematical theory, we discuss the experimental results from an energetic viewpoint and numerically show the explicit shape of Λ -elastica. It means that this paper provides a novel investigation on elastica theory with rupture.

Continuum mechanics can be formulated in the Lagrangian frame (addressing motion of individual continuum particles) or in the Eulerian frame (addressing evolution of fields in an inertial frame). There is a canonical Hamiltonian structure in the Lagrangian frame. By transformation to the Eulerian frame we find the Poisson bracket for Eulerian continuum mechanics with deformation gradient (or the related distortion matrix). Both Lagrangian and Eulerian Hamiltonian structures are then discussed from the perspective of space-time variational formulation and by means of semidirect products and Lie algebras. Finally, we discuss the importance of the Jacobi identity in continuum mechanics and approaches to prove hyperbolicity of the evolution equations and their gauge invariance.

Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the canonical commutation relations and hence quantum mechanics at the Planck scale. The corresponding modification of classical mechanics is usually considered by replacing modified quantum commutators by Poisson brackets suitably modified in such a way that they retain their main properties (antisymmetry, linearity, Leibniz rule and Jacobi identity). We indicate that there exists an alternative interesting possibility. Koopman-Von Neumann's Hilbert space formulation of classical mechanics allows, as Sudarshan remarked, to consider the classical mechanics as a hidden variable quantum system. Then the Planck scale modification of this quantum system naturally induces the corresponding modification of dynamics in the classical substrate. Interestingly, it seems this induced modification in fact destroys the classicality: classical position and momentum operators cease to be commuting and hidden variables do appear in their evolution equations.

In this paper we consider a nonlinear generalization of the isotonic oscillator in the same spirit as one considers the generalization of the harmonic oscillator with a truly nonlinear restoring force. The corresponding potential being asymmetric we invoke the symmetrization principle and construct a symmetric potential in which the period function has the same value as in the original asymmetric potential. The period function is amplitude dependent and expressible in terms of the hypergeometric function and reduces to 2π when α=1 , i.e., corresponding to the special case of an isotonic oscillator.