Classical Physics
In this work, we present an analytical study of the electrostatic potential generated by a charged disk with a surface charge distribution that possesses radial axial symmetry. We express the potential in cylindrical coordinates and apply a…
Our previous study [1] has demonstrated that the gauge theory is a proper framework for characterizing the local temporal and spatial interactions in inhomogeneous elastic media. However, in that study temporal interactions were interpreted…
Causal nature of the acoustic response, for any materials or structures, dictates an inequality that relates the absorption spectrum of the sample to its thickness. We present a general recipe for constructing sound-absorbing structures…
This paper aims to show how to guide students with a familiar example to extract as much physics as possible before jumping into mathematical calculation. The period for a physical pendulum made up of a uniform rod is changed by attaching a…
In this paper we derive and discuss the time it takes for a force to turn a velocity. More precisely, we derive the formula for the time $\tau$ it takes a constant force that makes an angle $\alpha$ with the initial velocity $\vec{v}(0)$ to…
We present a pair-wise force law in a system of N particles that produces analytic solutions for arbitrary number of particles, masses, and initial conditions. Each pair of particles interacts via a force that is proportional to the product…
We present a manifestly covariant formulation of relativistic electromagnetism, focusing on the computation of electromagnetic fields from moving charges in a manifestly Lorentz-covariant manner. The electromagnetic field at a given…
An "upward-driven disk" is a novel mechanical device built from LEGO parts. A circular disk is suspended from the point where it is sandwiched between two wheels, making it free to oscillate as a pendulum, but the location of that…
In order to reconcile the entropy reduction of a system through external interventions that are linked to a measurement with the second law of thermodynamics, there are two main proposals: (i) The entropy reduction is compensated by the…
Inspired by Tokieda's work on mechanical insights in geometry, we explore a hydrostatic approach to classical geometric problems. Using principles of fluid statics, we derive two mathematical results regarding polygons. These results…
Building blocks containing strongly coupled posts offer new possibilities for advanced coaxial (comb-line) filter designs. Equivalent circuits based on the individual resonances of the posts cannot be used to reliably describe the behavior…
A generalized hydrodynamic theory that systematically incorporates elasticity and viscoelasticity had been derived about a quarter of a century ago. It is based on a strictly Euler point of view, as is natural for hydrodynamics. We used and…
We derive approximate expressions for the amplitude decay of harmonic oscillations weakly damped by the simultaneous action of three different damping forces: force of constant magnitude, force linear in velocity, and force quadratic in…
We propose a structural variational resolution of the Abraham-Lorentz-Dirac (ALD) pathologies. By deriving the Variational Kinematic Constraint (VKC) and the Variational Dynamics Constraint (VDC) from the particle's proper-time perspective,…
Bloch wavefunctions in crystals experience localization within the bulk when disorder is introduced, a phenomenon commonly known as Anderson localization. This effect is considered universal, being applicable to all types of waves, quantum…
Aeroelastic model testing is essential for evaluating the wind resistance performance of long-span suspension bridges. In these models, truss girders are commonly modelled by a discrete-stiffness system incorporating U-shaped springs to…
Semi-analytical methods for the modeling of guided waves in structures of constant cross-section lead to frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems for a range…
It is well-known that band gaps, in the frequency domain, can be achieved by using periodic metamaterials. However it has been challenging to design materials with broad band gaps or that have multiple overlapping band gaps. For periodic…
The well-known expressions for the Green's functions for the Helmholtz equation in polar coordinates with Dirichlet and Neumann boundary conditions are transformed. The slowly converging double series describing these Green's functions are…
In electromagnetic statics, the standard procedure to determine the electric scalar potential or magnetic vector potential in a bounded space is to solve Poisson's equation subject to certain boundary conditions. On the other hand, as a…