Classical Physics
A specialized high-precision numerical search for equal-mass collisionless three-body periodic free-fall orbits with central symmetry is conducted. The search is based on Newton's method with initial approximations obtained by the…
This article delves into the intricate dynamics of Rayleigh wave propagation within a nonlocal orthotropic medium, where the presence of void and diffusion adds an intriguing layer to the analysis. Grounded in Eringen nonlocal elasticity…
Noether's theorem is a cornerstone of analytical mechanics, making the link between symmetries and conserved quantities. In this article, I propose a simple, geometric derivation of this theorem that circumvents the usual difficulties that…
Overcoming the diffraction limit, meaning focusing waves on a sub-wavelength scale, has received considerable attention for applications involving light and acoustics. Indeed, the intense focusing achieved enhances the interactions between…
We study how a charged particle moving in a uniform magnetic field along its standard circular path (cyclotron motion) reacts to a short-duration, homogeneous, uniform electric field pulse injected in the plane perpendicular to the magnetic…
The rotations of rigid bodies in Euclidean space are characterized by their instantaneous angular velocity and angular momentum. In an arbitrary number of spatial dimensions, these quantities are represented by bivectors (antisymmetric…
Electric fields are commonly visualized with field line diagrams, which only unambiguously specify the field's direction. We consider two simple questions. First, can one deduce if an electric field is conservative, as required e.g. in…
We study the precession of a Foucault pendulum using a new approach. We characterize the support anisotropy by the difference between the maximum and minimum periods of the pendulum along the principal axes of the support. Then we compute…
An analytical model describing the action of a rigid beam under shear forces to the quasi-crystalline half-space is analyzed. The elasticity theory of quasicrystals and the method of complex variables is used. Graphs of stresses and…
The lowest notes produced by string instruments are typically limited by the fundamental vibration of the strings. However, precise control of bow pressure can lead to the production of even lower notes. Despite significant interest in this…
The present paper introduces the notion of chiral gravitational elastic waves and explores their connections to equatorial and planetary waves. The analysis of the gravity-induced waveforms in gyroscopic systems composed of gyropendulums…
The least action principle played a central role in the development of modern physics. A major drawback of the principle is that its applicability is limited to holonomic constraints. In the present work, we investigate the energy lost by…
Topological wave structures, such as vortices and skyrmions, appear in a variety of quantum and classical wave fields, including optics and acoustics. In particular, optical vortices have found numerous applications ranging from quantum…
In this work, the paraxial approximation of the free Dirac equation is examined. The results are first obtained by constructing superpositions of exact solutions with suitable profiles, which are borrowed from paraxial optics. In this…
In the classical model of atomic polarizability, atomic charges are displaced by an applied electric field, assuming the electron cloud remains spherically symmetric but with its center shifted from the nucleus, thereby inducing an electric…
A new method to calculate the electric field inside a spherical shell with surface charge in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical…
The present work is aimed at formulating equivalent boundary conditions for the electromagnetic field on the surface of a periodic grating of resistive strips valid for arbitrary incident fields. It is assumed that the period of the grating…
We use a simple effective model, obtained through the application of high-frequency homogenisation, to tackle the fundamental question of how the choice of gradient function affects the performance of a graded metamaterial. This approach…
The Breakthrough Starshot project aims to send a tiny 2 gram spacecraft to Proxima Centauri propelled by a light sail and powerful Earth-based lasers. We provide two derivations of the laser energy required to propel the spacecraft and give…
Statistical fluctuations of local tensorial fields beyond the mean are relevant to predict localized failure or overall behavior of the inelastic composites. The expression for second moments of the local fields can be established using the…