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

Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Benard convection in glycerol

We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number (Ra) up to $10^8$ (for fixed temperature difference between the top and bottom plates) and as functions of "non-Oberbeck-Boussinesqness'' or "NOBness'' ($\Delta$) up to 50 K (for fixed Ra). For this large NOBness the center temperature $T_c$ is more than 5 K larger than the arithmetic mean temperature $T_m$ between top and bottom plate and only weakly depends on Ra. To physically account for the NOB deviations of the Nusselt numbers from its Oberbeck-Boussinesq values, we apply the decomposition of $Nu_{NOB}/Nu_{OB}$ into the product of two effects, namely first the change in the sum of the top and bottom thermal BL thicknesses, and second the shift of the center temperature $T_c$ as compared to $T_m$. While for water the origin of the $Nu$ deviation is totally dominated by the second effect (cf. Ahlers et al., J. Fluid Mech. 569, pp. 409 (2006)) for glycerol the first effect is dominating, in spite of the large increase of $T_c$ as compared to $T_m$.Comment: 6 pages, 7 figure

Molecular hydrogen as baryonic dark matter

High-angular resolution CO observations of small-area molecular structures (SAMS) are presented. The feature-less structures seen in the single-dish measurements break up into several smaller clumps in the interferometer map. At an adopted distance of 100pc their sizes are of order a few hundred AU, some of which are still unresolved at an angular resolution of about 3". The clumps have a fractal structure with a fractal index between 1.7 and 2.0. Their kinetic temperature is between 7K and 18K. Adopting standard conversion factors masses are about 1/10 Jupiter-masses for individual clumps and densities are higher than 20000cm^{-3}. The clumps are highly overpressured and it is unknown what creates or maintains such structures.Comment: 8 pages, 1 figure, accepted by Astrophysical Journal Letter

Body-Soul Discussion: Historical Matters and Hermeneutical Principles

This feature article is based on a paper given during the 1991 Spring Ministers\u27 Conference at Dordt College under the theme To Belong Body and Soul...

Attachment working models as unconscious structures: An experimental test

Internal working models of attachment (IWMs) are presumed to be largely unconscious representations of childhood attachment experiences. Several instruments have been developed to assess IWMs; some of them are based on self-report and others on narrative interview techniques. This study investigated the capacity of a self-report measure, the Inventory of Parent and Peer Attachment (IPPA; Armsden & Greenberg, 1987), and of a narrative interview method, the Adult Attachment Interview (AAI; George, Kaplan, & Main, 1985), to measure unconscious attachment models. We compared scores on the two attachment instruments to response latencies in an attachment priming task. It was shown that attachment organisation assessed by the AAI correlates with priming effects, whereas the IPPA scales were inversely or not related to priming. The results are interpreted as support for the assumption that the AAI assesses, to a certain degree, unconscious working models of attachment

Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems

We address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer linear relaxation of the bilinear problem. Besides showing that it can provide tighter bounds than a commercial global optimization solver within a given computational time, we propose to also take advantage of the relaxed formulation for contracting the variables domain and further reduce the optimality gap. Through the solution of a real-life case study from a hydroelectric power system, we show that this can be an efficient approach depending on the problem size. The relaxed formulation from multiparametric formulation is provided for a generic numeric representation system featuring a base between 2 (binary) and 10 (decimal)

Aging and intermittency in a p-spin model of a glass

We numerically analyze the statistics of the heat flow between an aging system and its thermal bath, following a method proposed and tested for a spin-glass model in a recent Letter (P. Sibani and H.J. Jensen, Europhys. Lett.69, 563 (2005)). The present system, which lacks quenched randomness, consists of Ising spins located on a cubic lattice, with each plaquette contributing to the total energy the product of the four spins located at its corners. Similarly to our previous findings, energy leaves the system in rare but large, so called intermittent, bursts which are embedded in reversible and equilibrium-like fluctuations of zero average. The intermittent bursts, or quakes, dissipate the excess energy trapped in the initial state at a rate which falls off with the inverse of the age. This strongly heterogeneous dynamical picture is explained using the idea that quakes are triggered by energy fluctuations of record size, which occur independently within a number of thermalized domains. From the temperature dependence of the width of the reversible heat fluctuations we surmise that these domains have an exponential density of states. Finally, we show that the heat flow consists of a temperature independent term and a term with an Arrhenius temperature dependence. Microscopic dynamical and structural information can thus be extracted from numerical intermittency data. This type of analysis seems now within the reach of time resolved micro-calorimetry techniques.Comment: 9 pages, 6 figures, europhysics letter style, to appear in Physical Review

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

Tunneling in a cavity

The mechanism of coherent destruction of tunneling found by Grossmann et al. [Phys. Rev. Lett. 67, 516 (1991)] is studied from the viewpoint of quantum optics by considering the photon statistics of a single mode cavity field which is strongly coupled to a two-level tunneling system (TS). As a function of the interaction time between TS and cavity the photon statistics displays the tunneling dynamics. In the semi-classical limit of high photon occupation number $n$, coherent destruction of tunneling is exhibited in a slowing down of an amplitude modulation for certain parameter ratios of the field. The phenomenon is explained as arising from interference between displaced number states in phase space which survives the large $n$ limit due to identical $n^{-1/2}$ scaling between orbit width and displacement.Comment: 4 pages Revtex, 2 PS-figures, appears in The Physical Review