Periodic structure in nuclear matter

The properties of nuclear matter are studied in the framework of quantum hadrodynamics. Assuming an ω-meson field, periodic in space, a self-consistent set of equations is derived in the mean-field approximation for the description of nucleons interacting via σ-meson and ω-meson fields. Solutions of these self-consistent equations have been found: The baryon density is constant in space, however, the baryon current density is periodic. This high density phase of nuclear matter can be produced by anisotropic external pressure, occurring, e.g., in relativistic heavy ion reactions. The self-consistent fields developing beyond the instability limit have a special screw symmetry. In the presence of such an ω field, the energy spectrum of the relativistic nucleons exhibits allowed and forbidden bands, similar to the energy spectrum of the electrons in solids

Casimir Effect under Quasi-Periodic Boundary Condition Inspired by Nanotubes

When one studies the Casimir effect, the periodic (anti-periodic) boundary condition is usually taken to mimic a periodic (anti-periodic) structure for a scalar field living in a flat space with a non-Euclidean topology. However, there could be an arbitrary phase difference between the value of the scalar field on one endpoint of the unit structure and that on the other endpoint, such as the structure of nanotubes. Then, in this paper, a periodic condition on the ends of the system with an additional phase factor, which is called the ``quasi-periodic" condition, is imposed to investigate the corresponding Casimir effect. And an attractive or repulsive Casimir force is found, whose properties depend on the phase angle value. Especially, the Casimir effect disappears when the phase angle takes a particular value. High dimensional space-time case is also investigated.Comment: 8 pages, 1 figure, accepted by MPL

Outline of nguetseng's approach to non-periodic homogenization

Classical homogenization theory developed for modeling heterogeneous media with regular ne structure is based on the assumption that the structure is periodic. Since the structure of real materials is not perfectly periodic, several approaches were proposed. The approach proposed by Gabriel Nguetseng in 2003 seems to be the most general deterministic approach, it covers periodic, almost periodic and other structures. It is based on the notion of Banach algebra spectrum. The aim of this survey paper is to give a brief self-contained outline of this rather complicated approach described in many-page papers

Statistical properties of periodic orbits in 4-disk billiard system: pruning-proof property

Periodic orbit theory for classical hyperbolic system is very significant matter of how we can interpret spectral statistics in terms of semiclassical theory. Although pruning is significant and generic property for almost all hyperbolic systems, pruning-proof property for the correlation among the periodic orbits which gains a resurgence of second term of the random matrix form factor remains open problem. In the light of the semiclassical form factor, our attention is paid to statistics for the pairs of periodic orbits. Also in the context of pruning, we investigated statistical properties of the "actual" periodic orbits in 4-disk billiard system. This analysis presents some universality for pair-orbits' statistics. That is, even if the pruning progresses, there remains the periodic peak structure in the statistics for periodic orbit pairs. From that property, we claim that if the periodic peak structure contributes to the correlation, namely the off-diagonal part of the semiclassical form factor, then the correlation must remain while pruning progresse.Comment: 30 pages, 58 figure

Periodic paths on the pentagon, double pentagon and golden L

We give a tree structure on the set of all periodic directions on the golden L, which gives an associated tree structure on the set of periodic directions for the pentagon billiard table and double pentagon surface. We use this to give the periods of periodic directions on the pentagon and double pentagon. We also show examples of many periodic billiard trajectories on the pentagon, which are strikingly beautiful, and we describe some of their properties. Finally, we give conjectures and future directions based on experimental computer evidence.Comment: 29 pages, 20 figures, 1 appendix; Sage code in .tex fil

POLICRYPS-based electrically switchable Bragg reflector

The formation and characterization of a switchable volume reflective element fabricated from a polymer liquid crystal (LC) polymer slice (POLICRYPS) structure by holographic photopolymerization at high temperature (65 °C) using a photosensitive/nematic liquid crystal prepolymer mixture is reported. The submicron Bragg structure formed consists of periodic continuous polymeric walls separated by periodic LC channels. The phase separated NLC self-aligns in a homeotropic alignment between the polymer walls as indicated by polarizing optical microscopy analysis (Maltese cross). The resulting periodic grating structure results in a Bragg reflection notch upon illumination with white light due to the periodic variation in refractive index. Electro-optical experiments realized through in-plane electrodes and temperature experiments confirm that the multilayer structure acts as a Bragg mirror whose reflection efficiency can be controlled by either a small (∼3V/μm) electric field or temperature

Chaotic Spiral Galaxies

We study the role of asymptotic curves in supporting the spiral structure of a N-body model simulating a barred spiral galaxy. Chaotic orbits with initial conditions on the unstable asymptotic curves of the main unstable periodic orbits follow the shape of the periodic orbits for an initial interval of time and then they are diffused outwards supporting the spiral structure of the galaxy. Chaotic orbits having small deviations from the unstable periodic orbits, stay close and along the corresponding unstable asymptotic manifolds, supporting the spiral structure for more than 10 rotations of the bar. Chaotic orbits of different Jacobi constants support different parts of the spiral structure. We also study the diffusion rate of chaotic orbits outwards and find that chaotic orbits that support the outer parts of the galaxy are diffused outwards more slowly than the orbits supporting the inner parts of the spiral structure.Comment: 14 pages, 11 figure

Electronic structure of periodic curved surfaces -- topological band structure

Electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface characterized completely in terms of "navels") but represent the topology of real systems such as zeolites and negative-curvature fullerene. The band structure turns out to be primarily determined by the topology of the surface, i.e., how the wavefunction interferes on a multiply-connected surface, so that the bands are little affected by the way in which we confine the electrons on the surface (thin-slab limit or zero thickness from the outset). Another curiosity is that different minimal surfaces connected by the Bonnet transformation (such as Schwarz's P- and D-surfaces) possess one-to-one correspondence in their band energies at Brillouin zone boundaries.Comment: 6 pages, 8 figures, eps files will be sent on request to [email protected]