Logarithmic temperature profiles in the ultimate regime of thermal convection

We report on the theory of logarithmic temperature profiles in very strongly developed thermal convection in the geometry of a Rayleigh-Benard cell with aspect ratio one and discuss the degree of agreement with the recently measured profiles in the ultimate state of very large Rayleigh number flow. The parameters of the log-profile are calculated and compared with the measure ones. Their physical interpretation as well as their dependence on the radial position are discussed.Comment: 14 pages, no figur

Spectra of Harmonium in a magnetic field using an initial value representation of the semiclassical propagator

For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the propagator lead to eigenvalues of the same accuracy as WKB calculations with Langer correction. The latter are restricted to integrable systems, however, whereas the time-dependent initial value approach allows for applications to high-dimensional, possibly chaotic dynamics and is extendable to arbitrary shapes of the potential.Comment: 11 pages, 1 figur

Velocity profiles in strongly turbulent Taylor-Couette flow

We derive the velocity profiles in strongly turbulent Taylor-Couette flow for the general case of independently rotating cylinders. The theory is based on the Navier-Stokes equations in the appropriate (cylinder) geometry. In particular, we derive the axial and the angular velocity profiles as functions of distance from the cylinder walls and find that both follow a logarithmic profile, with downwards-bending curvature corrections, which are more pronounced for the angular velocity profile as compared to the axial velocity profile, and which strongly increase with decreasing ratio $\eta$ between inner and outer cylinder radius. In contrast, the azimuthal velocity does not follow a log-law. We then compare the angular and azimuthal velocity profiles with the recently measured profiles in the ultimate state of (very) large Taylor numbers. Though the {\em qualitative} trends are the same -- down-bending for large wall distances and (properly shifted and non-dimensionalized) angular velocity profile $\omega^+(r)$ being closer to a log-law than (properly shifted and non-dimensionalized) azimuthal velocity profile $u^+_{\varphi}(r)$ -- {\em quantitative} deviations are found for large wall distances. We attribute these differences to the Taylor rolls and the height dependence of the profiles, neither of which are considered in the theoretical approach

Hidden Extra U(1) at the Electroweak/TeV Scale

We propose a simple extension of the Standard Model (SM) by adding an extra U(1) symmetry which is hidden from the SM sector. Such a hidden U(1) has not been considered before, and its existence at the TeV scale can be explored at the LHC. This hidden U(1) does not couple directly to the SM particles, and couples only to new SU(2)_L singlet exotic quarks and singlet Higgs bosons, and is broken at the TeV scale. The dominant signals at the high energy hadron colliders are multi lepton and multi b-jet final states with or without missing energy. We calculate the signal rates as well as the corresponding Standard Model background for these final states. A very distinctive signal is 6 high p_T b-jets in the final state with no missing energy. For a wide range of the exotic quarks masses the signals are observable above the background at the LHC.Comment: 19 pages, 5 figure

Finite size corrections to scaling in high Reynolds number turbulence

We study analytically and numerically the corrections to scaling in turbulence which arise due to the finite ratio of the outer scale $L$ of turbulence to the viscous scale $\eta$, i.e., they are due to finite size effects as anisotropic forcing or boundary conditions at large scales. We find that the deviations \dzm from the classical Kolmogorov scaling $\zeta_m = m/3$ of the velocity moments \langle |\u(\k)|^m\rangle \propto k^{-\zeta_m} decrease like $\delta\zeta_m (Re) =c_m Re^{-3/10}$. Our numerics employ a reduced wave vector set approximation for which the small scale structures are not fully resolved. Within this approximation we do not find $Re$ independent anomalous scaling within the inertial subrange. If anomalous scaling in the inertial subrange can be verified in the large $Re$ limit, this supports the suggestion that small scale structures should be responsible, originating from viscosity either in the bulk (vortex tubes or sheets) or from the boundary layers (plumes or swirls)

Maximum Resilience of Artificial Neural Networks

The deployment of Artificial Neural Networks (ANNs) in safety-critical applications poses a number of new verification and certification challenges. In particular, for ANN-enabled self-driving vehicles it is important to establish properties about the resilience of ANNs to noisy or even maliciously manipulated sensory input. We are addressing these challenges by defining resilience properties of ANN-based classifiers as the maximal amount of input or sensor perturbation which is still tolerated. This problem of computing maximal perturbation bounds for ANNs is then reduced to solving mixed integer optimization problems (MIP). A number of MIP encoding heuristics are developed for drastically reducing MIP-solver runtimes, and using parallelization of MIP-solvers results in an almost linear speed-up in the number (up to a certain limit) of computing cores in our experiments. We demonstrate the effectiveness and scalability of our approach by means of computing maximal resilience bounds for a number of ANN benchmark sets ranging from typical image recognition scenarios to the autonomous maneuvering of robots.Comment: Timestamp research work conducted in the project. version 2: fix some typos, rephrase the definition, and add some more existing wor

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

Universality in fully developed turbulence

We extend the numerical simulations of She et al. [Phys.\ Rev.\ Lett.\ 70, 3251 (1993)] of highly turbulent flow with $15 \le$ Taylor-Reynolds number $Re_\lambda\le 200$ up to $Re_\lambda \approx 45000$, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers $Re_\lambda$, the energy spectra as well as the higher moments -- when scaled by the spectral intensity at the wave number $k_p$ of peak dissipation -- can be described by {\it one universal} function of $k/k_p$ for all $Re_\lambda$. Second, the ISR scaling exponents $\zeta_m$ of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the large $Re_\lambda$ is), as is the $Re_\lambda$ dependence of $k_p$. Only around $k_p$ viscous damping leads to slight energy pileup in the spectra, as in the experimental data (bottleneck phenomenon).Comment: 14 pages, Latex, 5 figures (on request), 3 tables, submitted to Phys. Rev.

Dynamics of the Forest Sector: Problems and Policies

The dynamic behaviors of the forest sector are generated by the acting together of economic, ecological, social, and biological parts, characteristics and by geographical distribution such as of the forest industrial complexes, of the resources, and of the customers. These dynamics are influenced by and in turn are influencing factors such as wood availability, possible uses of wood, processing technologies, and economic activities. The first chapter of this paper deals with how to depict and how to evaluate such interrelationships and changes causing both problems and opportunities for the forest sector. In the discussion of the uncertainties in the future of the forest sector and of possible actions, it is necessary to specify different possible future dynamic developments for the above mentioned factors. This is done in some scenarios in the second chapter. The impacts of these factors and their future dynamics impacts can be evaluated with respect to cost competitiveness and wood availability for the individual company as well as for the structural change of the whole sector, for example, with respect to the location of the forest industry and the characteristics and distribution of the forest resources. A set of scenarios as a base for discussions with representatives of the sector can serve to find out the desirability of those developments and to help specify actions to change the undesired developments. At the end of the paper some actions are listed to deal with poor cost competitiveness and shortage of wood

Critical temperature of Bose-Einstein condensation in trapped atomic Bose-Fermi mixtures

We calculate the shift in the critical temperature of Bose-Einstein condensation for a dilute Bose-Fermi mixture confined by a harmonic potential to lowest order in both the Bose-Bose and Bose-Fermi coupling constants. The relative importance of the effect on the critical temperature of the boson-boson and boson-fermion interactions is investigated as a function of the parameters of the mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose-Fermi mixtures is discussed.Comment: 15 pages, 2 figures, submitted to J. Phys.