经典物理
It is well known that the three-body problem has few analytical solutions in certain symmetrical constraints; the Lagrangian triangular solution is one of them. This triangular solution has been revisited by R.Broucke and H.Lass in 1971,…
Due to the mirror symmetry breaking, chiral structures show fantastic electromagnetic (EM) properties involving negative refraction, giant optical activity, and asymmetric transmission. Aligned electric and magnetic dipoles excited in…
We study here the behaviour of solutions for conjugated (antipodal) points in the $2$-body problem on the two-dimensional sphere $\mathbb{M}^2_R$. We use a slight modification of the classical potential used commonly in \cite{Borisov},…
The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a…
The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem…
Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature…
Effective medium theory aims to describe a complex inhomogeneous material in terms of a few important macroscopic parameters. To characterise wave propagation through an inhomogeneous material, the most crucial parameter is the effective…
In this paper, we completely eliminate all numerical integrations needed to compute the far-field envelope cross-correlation (ECC) in multiple-input-multiple-output (MIMO) systems by deriving accurate and efficient analytical expressions…
Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input…
For over 70 years it has been assumed that scalar wave propagation in (ensemble-averaged) random particulate materials can be characterised by a single effective wavenumber. Here, however, we show that there exist many effective…
Knots have been put forward to explain various physical phenomena because of their topological stability. Nevertheless, few works have reported on the exotic symmetry properties that certain knots possess. Here we reveal an exceptional form…
Small axial and flexural oscillations are analyzed for a periodic and infinite structure, constrained by sliding sleeves and composed of elastic beams. A nested Bloch-Floquet technique is introduced to treat the non-linear coupling between…
At a boundary between two transparent, linear, isotropic, homogeneous materials, derivations of the electromagnetic boundary conditions and the Fresnel relations typically proceed from the Minkowski {E,B,D,H} representation of the…
Positive definiteness and symmetry of the constitutive tensors describing a second-gradient elastic (SGE) material, which is energetically equivalent to a hexagonal planar lattice made up of axially deformable bars, are analyzed by…
A second-gradient elastic (SGE) material is identified as the homogeneous solid equivalent to a periodic planar lattice characterized by a hexagonal unit cell, which is made up of three different linear elastic bars ordered in a way that…
Recently, it was shown that surface electromagnetic waves at interfaces between continuous homogeneous media (e.g., surface plasmon-polaritons at metal-dielectric interfaces) have a topological origin [K. Y. Bliokh et al., Nat. Commun. 10,…
Electromagnetic (EM) scattering systems widely exist in EM engineering domain. For a certain objective scattering system, all of its working modes constitute a linear space, i.e. modal space. Characteristic mode theory (CMT) can effectively…
With the rich dynamics studies of single-state processes, the two-state processes attract more and more interests of people, since they are widely observed in complex system and have effective applications in diverse fields, say, foraging…
A folded chain, with one end fixed at the ceiling and the other end released from the same elevation, is commonly modeled as an energy-conserving system in one-dimension. However, the analytical paradigms in previous literature is…
Superradiant gain is the process in which waves are amplified via their interaction with a rotating body, examples including evaporation of a spinning black hole and electromagnetic emission from a rotating metal sphere. In this paper we…