Classical Physics
The van der Pauw method for two-dimensional samples of arbitrary shape with an isolated hole is considered. Correlations between extreme values of the resistances allow one to determine the specific resistivity of the sample and the…
An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.
We experimentally demonstrate that a Duraluminium thin plate with a thickness profile varying radially in a piecewise constant fashion as h(r)=h(0)(1+(r/Rmax)), with h(0)=0.5 mm, h(Rmax)=2 mm and Rmax=10 cm behaves in many ways as Maxwell's…
We consider a simple model of a one dimensional universe embedded in the Euclidean plane. In this model, a circle travelling at constant speed intersects the line in a pair of points which first separate and then rejoin. We interpret this…
Though sufficient for local conservation of charge, we show that Maxwells displacement current is not necessary. An alternative to the Ampere Maxwell equation is exhibited and the alternative s electric and magnetic fields and scalar and…
A class of generally nonlinear dynamical systems is considered, for which the Lagrangian is represented as a sum of homogeneous functions of the displacements and their derivatives. It is shown that an energy partition as a single relation…
The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…
We exhibit two symmetries of one-dimensional Newtonian mechanics whereby a solution is built from the history of another solution via a generally nonlinear and complex potential-dependent transformation of the time. One symmetry intertwines…
Calculating the electromagnetic field of a uniformly accelerated charged particle is a surprisingly subtle problem that has been long discussed in the literature. While the correct field has been obtained many times and through various…
We demonstrate that mechanical waves traveling in a torsional, mechanical wave machine exhibit dispersion due to gravity and the discreteness of the medium. We also show that although the dispersion due to discreteness is negligible, the…
In this paper we propose a new lattice structure having macroscopic Poisson's ratio arbitrarily close to the stability limit -1. We tested experimentally the effective Poisson's ratio of the micro-structured medium; the uniaxial test has…
This paper derives a finite-strain plate theory consistent with the principle of stationary three-dimensional (3-D) potential energy under general loadings with a third-order error. Staring from the 3-D nonlinear elasticity (with both…
In this paper, we present an approach to ultrasonic beam-forming and beam-steering in structures based on the concept of embedded non-resonant acoustic metamaterial lenses. The lens design exploits the principle of acoustic drop-channel…
We have discovered a new, forerunning mode transition as the periodic transition wave propagating in a uniform continuous waveguide. The latter is represented by an elastic beam separating from the elastic foundation under the action of…
We employ metamaterial beam-wave interaction structures for tuning the gain and bandwidth of short traveling wave tubes. The interaction structures are made from metal rings of uniform cross section, which are periodically deployed along…
The effect of nonzero extent of an electric charge is considered within the assumption that the structure of the charge at rest is spherically-symmetric and the current vector is linear in the acceleration.
We develop a compact perturbative series for accoustic wave propagation in a medium with a non Gaussian stochastic speed of sound. We use Martin - Siggia and Rose auxiliary field techniques to render the classical wave propagation problem…
In this paper, we show how the electromagnetic phenomena in moving magnetodielectric media can be emulated using artificial composite structures at rest. In particular, we introduce nonreciprocal periodically loaded transmission lines which…
A particle in hyperbolic motion produces electric fields that appear to terminate in mid-air, violating Gauss's law. The resolution to this paradox has been known for sixty years, but exactly why the naive approach fails is not so clear.
In past years, triggered by their successful realizations in electromagnetics, invisible cloaks have experienced rapid development and have been widely pursued in many different fields, though so far only for a single physical system. In…