Classical Physics
We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…
The status of classical stability in higher-derivative systems is still subject to discussions. In this note, we argue that, contrary to general belief, many higher-derivative systems are classically stable. The main tool to see this…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
I present two toy models for the motion of a tank car as fluid drains out of an off-center opening, based on replacing the fluid with particles. No knowledge beyond simple Lagrangian mechanics is required. The first toy model is solved…
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…
Recent static experiments on twist effects in chiral three-dimensional mechanical metamaterials have been discussed in the context of micropolar Eringen continuum mechanics, which is a generalization of Cauchy elasticity. For cubic…
This paper outlines the issues related to RF MEMS packaging and low actuation voltage. An original approach is presented concerning the modeling of capacitive contacts using multiphysics simulation and advanced characterization. A similar…
The 42nd Scandinavian Symposium on Physical Acoustics was held at Geilo, Norway from January 27 to January 30, 2019. It was arranged by the Acoustics and Optics group of the Norwegian Physical Society, and was coordinated by Geir Pedersen…
A myth of antiquity is explained with modern science in the context of an ancient naval battle. A legend was invoked by the admiral Pliny the Elder to explain the defeat of Antony and Cleopatra against Octavian at the naval battle of…
This paper concerns anisotropic two-dimensional and planar elasticity models within the frameworks of classical linear elasticity and the bond-based peridynamic theory of solid mechanics. We begin by reviewing corresponding models from the…
An application of variational principle to bifurcation of periodic solution in Lagrangian mechanics is shown. A few higher derivatives of the action integral at a periodic solution reveals the behaviour of the action in function space near…
The present paper gives an interaction of electromagnetic waves with a smooth convex tri-angular obstacle and its adjacent wedge regions. We attempt to find the power of groove fields under Dirichlet conditions associated with axisymmetric…
A paper by Ye, Berdichevsky and Yu features a set of formulas for effective stiffnesses of corrugated plates. Without elaborating on said authors' actual approach leading to such formulas, we shall focus on the fact that they can be brought…
In an extension of speculations that physical space-time is a fractal which might itself be embedded in a high-dimensional continuum, it is hypothesized to "compensate" for local variations of the fractal dimension by instead varying the…
We solve the problem of determining basic topological properties of flat samples by performing measurements on their outer edge. The global maximum of four probe resistances shows a characteristic behaviour, which is dependent on the genus…
We analyze spin and orbital angular momenta in monochromatic acoustic wave fields in a homogeneous medium. Despite being purely longitudinal (curl-free), inhomogeneous acoustic waves generically possess nonzero spin angular momentum density…
It is proven, without using the microscopic reversibility argument of Onsager, that lossy reciprocal systems have a hidden time-reversal symmetry. The key idea is that the dissipation channels of lossy dielectrics can be mimicked by a…
A conceptually simple physical interpretation of a conserved Hamiltonian $\mathcal{H}$ for a mechanical system with a time-dependent constraint is given. For the case of a bead on a vertical hoop forced to rotate with constant angular…
This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are…
We examine physical aspects for the electric version of a recently proposed logarithmic electrodynamics, for which the electric field of a point-like charge is finite at the origin. It is shown that this electrodynamics displays the vacuum…