经典物理
Mirror symmetry of a wave system imposes corresponding even or odd parity on its eigenmodes. For a discrete system, eigenmode parity on a specific subset of sites may also originate from so-called latent symmetry. This symmetry is hidden,…
Multi-layer structures are ubiquitous in constructing metamaterial devices to realise various frontier applications including super-resolution imaging and invisibility cloaking. In this paper, we develop a general mathematical framework for…
Textbook treatments of classical mechanics typically assume that the Lagrangian is nonsingular. That is, the matrix of second derivatives of the Lagrangian with respect to the velocities is invertible. This assumption insures that (i)…
Though commonly used to calculate Q-factor and fractional bandwidth, the energy stored by radiating systems (antennas) is a subtle and challenging concept that has perplexed researchers for over half a century. Here, the obstacles in…
The topic of a photon mass has received justified attention over the years with strong theoretical reasoning for its existence. We derive a full description of mode solutions in step-index optical fibres on the basis of Proca's equation as…
A wave propagating through a scattering medium typically yields a complex temporal field distribution. Over the years, a number of procedures have emerged to shape the temporal profile of the field in order to temporally focus its energy on…
Dispersion curves of elastic waveguides exhibit points where the group velocity vanishes while the wavenumber remains finite. These are the so-called zero-group-velocity (ZGV) points. As the elastodynamic energy at these points remains…
The amplitude of a pulse that propagates in a homogeneous material whose properties are instantaneously changed periodically in time will undergo an exponential increase, due to the interference between the reflected and transmitted pulses…
We revisit in this note the H\'enon's isochrone problem. By using the standard Abel inversion technique for one-dimensional motion, we recover in a simple way the H\'enon's parabolae and get all isochrone central potentials under mild…
A complete treatment regarding frustrated total internal reflection (FTIR) of ultrasonic waves is presented and validated against experiments, providing a theoretical explanation for the physics behind this phenomenon. Two different…
An asymptotically exact two-dimensional theory of functionally graded piezoelectric shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application,…
What is the fate of an oscillator when its inductance and capacitance are varied while its frequency is kept constant? Inspired by this question, we propose a protocol to implement parity-time (PT) symmetry in a lone oscillator. Different…
This letter gives a condition for the existence of the pure TE and TM modes in the metallic waveguide filled with a homogeneous, fully anisotropic and lossless medium. The condition is a relation between the permittivity and permeability…
Periodicity is usually assumed to be the necessary and sufficient condition for the formation of band gaps, i.e., energy bands with a suppressed density of states. Here, we check this premise by analyzing the band gap properties of three…
The article shows how the factorization of an arbitrary Lorentz transformation is performed. That is, representation of an arbitrary Lorentz transformation as a sequence of spatial rotation and boost or boost and spatial rotation. Relations…
A detailed set of experiments are described that capture over a 1000 different instances of the bounce of a golf ball. Video analysis is used to capture velocity and spin immediately prior to and subsequent to each bounce for a wide variety…
When a Hamiltonian system undergoes a stochastic, time-dependent anharmonic perturbation, the values of its adiabatic invariants as a function of time follow a distribution whose shape obeys a Fokker-Planck equation. The effective dynamics…
We that show two body gravitational orbits may be plotted using a radial reference frame rather than the customary Newtonian rectilinear inertial frame. Infinitesimal calculus cofounder and continental contemporary of Newton, Leibniz…
The present paper is devoted to the group classification of magnetogasdynamics equations in which dependent variables in Euler coordinates depend on time and two spatial coordinates. It is assumed that the continuum is inviscid and…
A cornerstone of physics, Maxwell's theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and self-mass of an electron of finite extension do not obey Einstein's famous…