Classical Physics
The time evolution of an oscillator coupled to an infinite string with a discontinuous mass density is investigated. It is shown that the equation of motion of the oscillator leads to a nonlinear characteristic equation due to the…
One of the goals that physicists have been pursuing is to get the same explanation from different angles for the same phenomenon, so as to realize the unity of basic physical laws. Geometry, classical mechanics and classical thermodynamics…
A method is given for evaluating electromagnetic scattering by an irregular surface with spatially-varying impedance. This uses an operator expansion with respect to impedance variation and allows examination of its effects and the…
This paper presents a study of transmission through arrays of periodic sub-wavelength apertures. Fundamental limitations for this phenomenon are formulated as a sum rule, relating the transmission coefficient over a bandwidth to the static…
Hawking-Unruh thermal state of warm surrounding field encountered in non-inertial frames is shown to be a real phenomenon, a marker of nonstationary dynamic evolutions. In accelerated motion of a charged particle it is shown that the…
This paper is a theoretical and numerical study of the uniform growth of a repeating sinusoidal imperfection in the line of a strut on a nonlinear elastic Winkler type foundation. The imperfection is introduced by considering an initially…
In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from $1$ to $k$ as the beam deflection increases. Periodic equilibrium solutions are found analytically and are in…
This paper describes energy distribution in a block medium simulated by a one-dimensional chain of masses joined by springs and dampers. Equations describing the motion of masses are solved by the methods of the theory of ordinary…
In 19th century Maxwell derived Maxwell equations from the knowledge of three experimental physical laws: the Coulomb's law, the Ampere's force law and Faraday's law of induction. However, theoretical basis for Ampere's force law and…
IPMCs consist of a Nafion(R) ionic polymer film coated on both sides with a thin layer of metallic electrodes. The polymer completely dissociates when it is saturated with water, releasing small cations while anions remain bound to the…
In the standard Lagrangian and Hamiltonian approach to Maxwell's theory the potentials $A^{\mu}$ are taken as the dynamical variables. In this paper I take the electric field $\vec{E}$ and the magnetic field $\vec{B}$ as the the dynamical…
In this comment it is argued that the argument for a unique determination of the electromagnetic potentials in classical electrodynamics in [1] is flawed. To the contrary the "gauge freedom" of the electromagnetic potentials has proven as…
Radiation force in Abraham-Lorentz-Dirac equation is revisited for possible signature of irreversible action in the dynamics. The analysis shows that the classical electron can dissipate out a certain fraction of field energy that…
In our analysis, we show that Howell et al.'s nonlinear beam theory does not depict a representation of the Euler-Bernoulli beam equation, nonlinear or otherwise. The authors' nonlinear beam theory implies that one can bend a beam in to a…
Objective: The brain operates via generation, transmission and integration of neuronal signals and most neurological disorders are related to perturbation of these processes. Neurostimulation by Focused Ultrasound (FUS) is a promising…
In the article, hyperelastic material models which state consistent polynomial expansions of the stored energy function are discussed. The approach follows from the muliplicative decomposition of the deformation gradient. Some advantages of…
A classical system, which is analogous to the quantum one with a backflow of probability, is proposed. The system consists of a chain of masses interconnected by springs, as well attached by other springs to fixed supports. Thanks to the…
We present simple expressions for load required to indent a layer of arbitrary thickness with a conical, paraboloidal or cylindrical punch. A rigid substrate underneath the sample leads to an increase of load required for indentation. This…
We study scalar field theory as a generalization of point particle mechanics using the Polyakov action, and demonstrate how to extend Lorentzian and Riemannian Eisenhart lifts to the theory in a similar manner. Then we explore extension of…
The dynamics of a simple pencil with a tip laid on a rough table and set free to fall under the action of gravity is scrutinized as a pedagogic case study. The full inquiry is anticipated by a review of three other simplified movements…