Extended phase diagram of the Lorenz model

The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz model equations for thermal convection in Rayleigh-B\'enard flow is studied. Its bifurcation structure has commonly been investigated as a function of r, the normalized Rayleigh number, at fixed Prandtl number \sigma. The present work extends the analysis to the entire (r,\sigma) parameter plane. An onion like periodic pattern is found which is due to the alternating stability of symmetric and non-symmetric periodic orbits. This periodic pattern is explained by considering non-trivial limits of large r and \sigma. In addition to the limit which was previously analyzed by Sparrow, we identify two more distinct asymptotic regimes in which either \sigma/r or \sigma^2/r is constant. In both limits the dynamics is approximately described by Airy functions whence the periodicity in parameter space can be calculated analytically. Furthermore, some observations about sequences of bifurcations and coexistence of attractors, periodic as well as chaotic, are reported.Comment: 36 pages, 20 figure

Influence of thickness on properties of plasticized oat starch films.

The aim of this study was to investigate the effect of thickness (between 80 and 120 µm) on apparent opacity, water vapor permeability and mechanical properties (tensile and puncture) of oat starch films plasticized with glycerol, sorbitol, glycerol:sorbitol mixture, urea and sucrose. Films were stored under 11, 57, 76 and 90% relative humidity (RH) to study the mechanical properties. It was observed that the higher the thickness, the higher was the opacity values. Films without the plasticizer were more opaque in comparison with the plasticized ones. Glycerol:sorbitol films presented increased elongation with increasing thickness at all RH. Puncture force showed a strong dependence on the film thickness, except for the films plasticized with sucrose. In general, thickness did not affect the water permeability

Visualization of Coherent Destruction of Tunneling in an Optical Double Well System

We report on a direct visualization of coherent destruction of tunneling (CDT) of light waves in a double well system which provides an optical analog of quantum CDT as originally proposed by Grossmann, Dittrich, Jung, and Hanggi [Phys. Rev. Lett. {\bf 67}, 516 (1991)]. The driven double well, realized by two periodically-curved waveguides in an Er:Yb-doped glass, is designed so that spatial light propagation exactly mimics the coherent space-time dynamics of matter waves in a driven double-well potential governed by the Schr\"{o}dinger equation. The fluorescence of Er ions is exploited to image the spatial evolution of light in the two wells, clearly demonstrating suppression of light tunneling for special ratios between frequency and amplitude of the driving field.Comment: final versio

Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose-systems in power law traps within a semi-analytic approach with a continuous one-particle density of states $\Omega(E)\sim E^{d-1}$ for different values of $d$ and to a three dimensional harmonically confined ideal Bose-gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.Comment: 7 pages, 9 eps-figures, For recent information on physics of small systems see "http://www.smallsystems.de

Heisenberg Evolution WKB and Symplectic Area Phases

The Schrodinger and Heisenberg evolution operators are represented in quantum phase space by their Weyl symbols. Their semiclassical approximations are constructed in the short and long time regimes. For both evolution problems, the WKB representation is purely geometrical: the amplitudes are functions of a Poisson bracket and the phase is the symplectic area of a region in phase space bounded by trajectories and chords. A unified approach to the Schrodinger and Heisenberg semiclassical evolutions is developed by introducing an extended phase space. In this setting Maslov's pseudodifferential operator version of WKB analysis applies and represents these two problems via a common higher dimensional Schrodinger evolution, but with different extended Hamiltonians. The evolution of a Lagrangian manifold in the extended phase space, defined by initial data, controls the phase, amplitude and caustic behavior. The symplectic area phases arise as a solution of a boundary condition problem. Various applications and examples are considered.Comment: 32 pages, 7 figure

Confinement in the Deconfined Phase: A numerical study with a cluster algorithm

We have previously found analytically a very unusual and unexpected form of confinement in SU(3) Yang-Mills theory. This confinement occurs in the deconfined phase of the theory. The free energy of a single static test quark diverges, even though it is contained in deconfined bulk phase and there is no QCD string present. This phenomenon occurs in cylindrical volumes with a certain choice of spatial boundary conditions. We examine numerically an effective model for the Yang-Mills theory and, using a cluster algorithm, we observe this unusual confinement. We also find a new way to determine the interface tension of domain walls separating distinct bulk phases.Comment: LaTex, 14 pages, 4 figure

Dynamics of an electron in finite and infinite one dimensional systems in presence of electric field

We study,numerically, the dynamical behavior of an electron in a two site nonlinear system driven by dc and ac electric field separately. We also study, numerically, the effect of electric field on single static impurity and antidimeric dynamical impurity in an infinite 1D chain to find the strength of the impurities. Analytical arguments for this system have also been given.Comment: File Latex, 8 Figures available on reques

Bose-Einstein Condensation in a Harmonic Potential

We examine several features of Bose-Einstein condensation (BEC) in an external harmonic potential well. In the thermodynamic limit, there is a phase transition to a spatial Bose-Einstein condensed state for dimension D greater than or equal to 2. The thermodynamic limit requires maintaining constant average density by weakening the potential while increasing the particle number N to infinity, while of course in real experiments the potential is fixed and N stays finite. For such finite ideal harmonic systems we show that a BEC still occurs, although without a true phase transition, below a certain ``pseudo-critical'' temperature, even for D=1. We study the momentum-space condensate fraction and find that it vanishes as 1/N^(1/2) in any number of dimensions in the thermodynamic limit. In D less than or equal to 2 the lack of a momentum condensation is in accord with the Hohenberg theorem, but must be reconciled with the existence of a spatial BEC in D=2. For finite systems we derive the N-dependence of the spatial and momentum condensate fractions and the transition temperatures, features that may be experimentally testable. We show that the N-dependence of the 2D ideal-gas transition temperature for a finite system cannot persist in the interacting case because it violates a theorem due to Chester, Penrose, and Onsager.Comment: 34 pages, LaTeX, 6 Postscript figures, Submitted to Jour. Low Temp. Phy