经典物理
Can a filament transmit the curvatures across the constituting modules and control them at one of its end? Inspired by the observation of protofilament - constituent biopolymer of microtubule - this question is addressed by a constructive…
Li'enard-Wiechert potentials have been derived for a moving and 'classically' spinning point-charge; assuming it to be a small rigid charged-sphere in combined non-relativistic translational and rotational motion, and subsequently reducing…
This paper aims to shed some more light on one of the best known phenomena in the field of physics, the Doppler effect, in particular, on its classical version. Although, as mentioned, it is a phenomenon already described more than 150…
We extend Kramers-Kronig relations beyond the optical approximation to dielectric functions that depend not only on frequency but on the wave number as well. This implies extending the notion of causality commonly used in the theory of…
These lecture notes in geometric mechanics are meant to convey insight through clear definitions and workable examples. The lecture format adopted here is intended to convey the immediacy of the taught course and to be useful as a basis for…
Understanding degrees of freedom in classical mechanics is fundamental to characterizing physical systems. Counting them is usually easy, especially if we can assign them a clear meaning. However, the precise definition of a degree of…
This paper presents the 3D soundfield synthesis of the pressure field radiated by directional acoustic sources using both the multimodal method and higher-order ambisonics (HOA). Ambisonics is a technique for encoding and reproducing…
Information is everywhere in nature which is very uncertain and unpredictable. But information, in itself, is a very ambiguous term. In this cursory write-up, we attempt to understand the formal meaning of information by quantifying…
The current study explores the analysis of crack in initially stressed, rotating material strips, drawing insights from singular integral equations. In this work, a self-reinforced material strip with finite thickness and infinite extent,…
In mechanics, common energy principles are based on fixed boundary conditions. However, in bridge engineering structures, it is usually necessary to adjust the boundary conditions to make the structure's internal force reasonable and save…
Explicit formulae for the $4\times 4$ Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well-known. Significantly less well-known is the explicit formula for a general Lorentz…
The intrigue of waves on periodic lattices and gratings has resonated with physicists and mathematicians alike for decades. In-depth analysis has been devoted to the seemingly simplest array system: a one-dimensionally periodic lattice of…
A relationship is established between the effective Youngs modulus of a two-phase elastic composite and a known mathematical mean value. Specifically, the effective Youngs modulus of a composite obtained from repeated parallel and serial…
In this work, we introduce the Law of Closest Approach which is derived from the properties of conic orbits and can be considered an addendum to the laws of Kepler. It states that on the closest approach, the distance between the objects is…
Exceptional points (EPs) are spectral singularities in non-Hermitian systems where eigenvalues and their corresponding eigenstates coalesce simultaneously. In this study, we calculate scattering poles in an open spherical solid and propose…
This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy…
This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional…
The paper gives an introduction to rate equations in nonlinear continuum mechanics which should obey specific transformation rules. Emphasis is placed on the geometrical nature of the operations involved in order to clarify the different…
It is shown that when the well-known minimal complementary energy variational principle in linear elastostatics is written in a different form with the strain tensor as an independent variable and the constitutive relation as one of the…
Electromagnetic quantities at a spacetime point have tensor Lorentz transformations between relatively-moving inertial frames. However, since the Lorentz transformation of time between inertial frames depends upon both the time and space…