Related papers: Conserved geometric phase and group velocity
For hyperbolic systems of conservation laws in one space dimension with a mathematical entropy, we define the notion of entropy velocity. Then we give sufficient conditions for such a system to be covariant under the action of a group of…
We consider the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel dielectric cylinders embedded a uniform medium. The frequency band structure is computed using the standard plane-wave expansion method,…
The group velocity of a plasmonic guided mode can be written as the ratio of the flux of the Poynting to the integral of the energy density along the profile of the mode. This theorem, linking the way energy propagates in metals to the…
We analyse the motion of the spinning body (in the pole-dipole approximation) in the gravitational and electromagnetic fields described by the Mathisson-Papapetrou-Dixon-Souriau equations. First, we define a novel spin condition for the…
For a particle moves on a 2D surface f(x)=0 embedded in 3D Euclidean space, the geometric momentum and potential are simultaneously admissible within the Dirac canonical quantization scheme for constrained motion. In our approach, not the…
The derivation of a new condition for characterizing isotropic dielectric-magnetic materials exhibiting negative phase velocity, and the equivalence of that condition with previously derived conditions, are presented.
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
A new theory on gas-liquid phase transition is given. The new idea is that the total intermolecular potential energy for a classical system in equilibrium is relative with the average distance of molecules. A new space homogeneity…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
Under certain circumstances, the group velocity in a homogenized composite medium (HCM) can exceed the group velocity in its component material phases. We explore this phenomenon for a uniaxial dielectric HCM comprising isotropic component…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
We recall the systematic formulation of Eulerian mechanics in terms of Lie derivatives along the vector field of the material points. Using the abstract properties of Lie derivatives we show that the transport via Lie derivatives generates…
Statistical theory of the dielectric susceptibility of polar liquid crystals is proposed. The molecules are not uniaxial but similar to cones. It is assumed that the permanent dipole moment of a molecule is parallel to the axis of the…
This paper is concerned with geometric exponential energy-preserving integrators for solving charged-particle dynamics in a magnetic field from normal to strong regimes. We firstly formulate the scheme of the methods for the system in a…
In this second paper we complete the classical description of an isolated system of "charged positive-energy particles, with Grassmann-valued electric charges and mutual Coulomb interaction, plus a transverse electro-magnetic field" in the…
We provide an improved definition of new conserved quantities derived from the energy-momentum tensor in curved spacetime by introducing an additional scalar function. We find that the conserved current and the associated conserved charge…
The equations of motion of a charged ideal fluid, respectively the superconductivity equation (both in a given magnetic field) are showed to be geodesic equations on a general, respectively central extension of the group of volume…
We adopt the continuum limit of a linear, isotropic, homogeneous, transparent, dispersion-negligible dielectric of refractive index $n$ and examine the consequences of the effective speed of light in a stationary dielectric, $c/n$, for…
We derive a closed-form expression of the magnetic field of a finite-size current sheet and use it to calculate the field of permanent magnets, which are modeled through their surface current densities. We illustrate the method by…
We propose a geometric perspective to describe the motion of self-propelled particles moving at constant speed in d dimensions. We exploit the fact that the vector that conveys the direction of motion of the particle performs a random walk…