经典物理
We present a general formalism for the analysis of mechanical lattices with microstructure using the concept of effective mass. We first revisit a classical case of microstructure being modeled by a spring-interconnected mass-in-mass cell.…
Starting from a new factorization of the frequencydomain modal expansion coefficients, we generate analytical expressions in time-domain for the various quantities of interest of a biconical antenna of arbitrary length and cone angle. In…
The Aharonov-Bohm phase shift in a particle interference pattern when electrons pass a long solenoid is identical in form with the optical interference pattern shift when a piece of retarding glass is introduced into one path of a two-beam…
Microwave remote sensing is significantly altered when passing through clouds or dense ice. This phenomenon isn't unique to microwaves; for instance, ultrasound is also disrupted when traversing through heterogeneous tissues. Understanding…
We give a geometrical interpretation for the principle of stationary action in classical Lagrangian particle mechanics. In a nutshell, the difference of the action along a path and its variation effectively ``counts'' the possible…
Elastic angular momentum is an emerging field, with some controversies on the correct field-theory expressions and the decomposition of longitudinal and transverse components. Motivated by the recent two papers [Phys.Rev.Lett. 128,…
We present the results of linear stability of a damped coplanar double pendulum and its non-linear motion, when the point of suspension is vibrated sinusoidally in the vertical direction with amplitude $a$ and frequency $\omega $. A double…
We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate…
As one of the most important topics studied in creep fracture mechanics, mechanics fields at three-dimensional (3D) sharp V-notches and crack tip have drawn tremendous attentions. With many years efforts on constraint theory developed in…
There are several ways to derive Einstein's celebrated formula for the energy of a massive particle at rest, $E=mc^2$. Noether's theorem applied to the relativistic Lagrange function provides an unambiguous and straightforward access to…
We analyze the non-Fourier dual-phase-lag heat conduction process in a three-dimensional medium heated by a moving circular or annular laser beam, which is modeled by a set of point heat sources in the cross-section. In order to solve the…
An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…
I discuss the influence of adding the air resistance and the kinetic friction to the classical mechanics homework-problem: finding the motion of a body sliding down a hemispherical hill. For a physically realistic ($\propto v^2$) form of…
The Debye-Falkenhagen differential equation is commonly used as a mean-field macroscopic model for describing electrochemical ionic drift and diffusion in dilute binary electrolytes when subjected to a suddenly applied potential smaller…
This paper examines the details of an inelastic collision when a bullet shoots a block vertically upward from below. With the assumption of constant interaction force between them, we obtain quantities of interest including the displacement…
A charged particle which is allowed to accelerate must have relativistic behavior because it is coupled to electromagnetic radiation which propagates at the speed of light. We treat the simple steady-state situation of a charged particle…
We drop a circular disk magnet through a thin coil of wire, record the induced voltage, and compare the results to an analytic model based on the dipole approximation and Faraday's law, which predicts that the difference between the voltage…
In this paper we show for the first time the phenomenon of negative reflection in a simple mechanical structure. The latter is a grating of fixed inclusions embedded in a linear elastic matrix. Numerical analyses for out-of-plane shear…
Considering interatomic potential $U({\mathbf q})$ where ${\mathbf q} = [{\mathbf q}_1, {\mathbf q}_2, \dots, {\mathbf q}_N] \in {\mathbb R}^{3N}$ is a vector describing positions, $\mathbf{q}_i \in {\mathbb R}^3$, it is shown that $U$ can…
Finding an optimum strategy to reach a certain destination by swimming in a background flow is an interesting question which leads to non-trivial results and swimming paths. Here we consider different strategies for various types of surface…