Classical Physics
Newton's Principia is famous for its investigations of the inverse square force law for gravity. But in this book Newton also did something that remained little-known until fairly recently. He figured out what kind of central force exerted…
Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, non-holonomic systems --…
Determination of the electric potential of insulated conducting objects is an important problem both theoretically and practically. For an insulated conducting object in the presence of external charges or charges distributed on the object…
The linear and nonlinear motions of a damped rigid planar pendulum, driven by vibrating its pivot sinusoidally, are reexamined. The pendulum is known to exhibit periodic, quasiperiodic, and chaotic motions. Floquet analysis identifies…
Two different frameworks are developed to model the wave field generated by a transducer and propagating through one or more interfaces, and a Quasi-Monte Carlo (QMC) integration scheme is used to numerically evaluate their results. The…
Dynamic room acoustic simulation aims to render the acoustic effects of an environment in real time while accounting for potentially moving sources and receivers. In this context, the efficient synthesis of the long-term room response, also…
We study unidirectional transverse scattering in a two-dimensional acoustic dimer composed of two isotropic subwavelength scatterers. Using a coupled multipole model, we show that inter-particle coupling enables effective monopole-dipole…
This study investigates the elastic response of a two-dimensional semi-infinite medium subjected to a moving surface load with a prescribed displacement profile. As a fundamental step, we derive analytical Green's functions for the…
A slightly tilted permanent magnet rotating at high speed can induce a magnetic field capable of trapping another permanent magnet in a gravity independent levitated bound state, bypassing Earnshaw's theorem. During levitation, the floater…
This paper examines the theory of electron magnetic dipole moment interactions with magnetic fields or other electrons in classical and quantum electrodynamics. We show that these interactions may be described by a version of the Poynting…
Two equal and opposite distributed dead loads are applied orthogonally to the axis of an elastic rod in its rectilinear reference configuration, one at the extrados and the other at the intrados, such that the resultant applied force per…
We investigate the generation of standing waves in the model provided by the inhomogeneous telegraph equation under different forcing conditions. We show that sustained standing waves arise only for a specific forcing that is spatially…
This study utilizes the variational-asymptotic method to establish a one-dimensional theory for functionally graded rods characterized by general anisotropy from the three-dimensional elasticity theory. A distinctive feature of this…
We review, critique, and extend results related to the problem of closed loop shape equilibria of a string shooter, a type of catenary consisting of steady, axially moving configurations of an inertial, inextensible, perfectly flexible…
The optical theorem is a powerful tool of scattering theory that directly relates the extinction cross section of a scatterer to its forward scattering amplitude. While widely used in electromagnetism and optics, its application in…
Advances in the study of relativistic quantum phase space have established the set of Linear Canonical Transformations (LCTs) as a candidate for the fundamental symmetry group associated with relativistic quantum physics. In this framework,…
The complex relationship between Einstein's second postulate and the Maxwell electromagnetic theory is elucidated. A simple deduction of the main results of the Ignatowski approach to the theory of relativity is given. The peculiar status…
To describe the interactions in magnetically soft particle systems either numerical full-field methods or dipole models are used. Whereas the former are computationally challenging, simple dipole interactions are largely underestimating the…
We investigate the gravitational potentials generated by axisymmetric, razor-thin disks. Within certain limitations, the potential on one side of the disk is shown to be equivalent to the potential produced by a linear mass distribution…
Underground lifelines, such as pipelines and tunnels, are susceptible to ground vibrations from seismic events, traffic, and other dynamic sources. Accurate prediction of their response is essential for ensuring structural safety and…