Classical Physics
This review article revisits and outlines the perfectly matched layer (PML) method and its various formulations developed over the past 25 years for the numerical modeling and simulation of wave propagation in unbounded media. Based on the…
We provide an elementary proof that the action for the physical trajectory of the one-dimensional harmonic oscillator is guaranteed to be a minimum if and only if $\tau < \pi/\omega$, where $\tau$ is the elapsed time and $\omega$ is the…
The current state of the art for analytical and computational modelling of deformation in nonlinear electroelastic and magnetoelastic membranes is reviewed. A general framework and a list of methods to model large deformation and associated…
We present here how a coherent perfect absorber-laser (CPAL) enabled by parity-time ($\mathcal{PT}$)-symmetry breaking may be exploited to build monochromatic amplifying devices for flexural waves. The fourth order partial differential…
The strange visual appearance of objects is one of the puzzling predictions of Einstein's relativity. This is mainly due to the distinction between measuring and seeing, where the former is described by the Lorentz Transformation and the…
The aim of this paper is to estimate the damage of railway carriage wheels caused by lock-up braking. First, we investigate the typical characteristics of wheel-rail contact including the parameters of contact patch, longitudinal creep and…
The analogy between self-similar time series with given Hurst exponent H and Markovian, Gaussian stochastic processes with multiplicative noise and entropic index q (Borland, PRE 57, 6, 6634-6642, 1998) allows us to explain the empirical…
We present exact closed-form expressions and complete asymptotic expansions for the electrostatic force between two charged conducting spheres of arbitrary sizes. Using asymptotic expansions of the force we confirm that even like-charged…
The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (non-integrable) discrete nonlinear Schr{\"o}dinger (DNLS) one. The competition of local on-site nonlinearity…
We recently introduced a new family of processes which describe particles which only can move at the speed of light c in the ordinary 3D physical space. The velocity, which randomly changes direction, can be represented as a point on the…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…
Methods for finding the optimal choices of the applied remote loads -- the applied normal force, moment, shear force and remote bulk stresses -- needed to solve frictional contact problems in partial-slip using half-plane theory are derived…
We consider the dynamics of a classical charge in flat spacetime of six dimensions. The mass shell relation of a free charge admits nonlinear oscillations. Having analyzed the problem of on eigenvalues and eigenvectors of Faraday tensor, we…
A theory for analyzing the radiative and reactive energies for pulse radiators in free space is presented. With the proposed definition of reactive energies and radiative energies, power balance at arbitrarily chosen observation surfaces…
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…
In classical mechanics, the motion of an object is described with Newton's three laws of motion, which means that the motion of the material elements composing a continuum can be described with the particle model. However, this viewpoint is…
The peridynamic stress tensor proposed by Lehoucq and Silling (2008) is cumbersome to implement in numerical computations. In this note, we show that the peridynamic stress tensor has the mathematical expression of a weighted static Virial…
Floquet-Bloch wave asymptotics is used to homogenize the in-plane mechanical response of a periodic grillage of elastic Rayleigh rods, possessing a distributed mass density, together with rotational inertia. The grid is subject to…
We analyze the points of total collision of the Newtonian gravitational system on shape space (the relational configuration space of the system). While the Newtonian equations of motion, formulated with respect to absolute space and time,…
The piezoelectricity law is a constitutive model that describes how mechanical andelectric fields are coupled within a material. In its linear formulation this law comprises threeconstitutive tensors of increasing order: the second order…