Dissipation Layers in Rayleigh-B\'{e}nard Convection: A Unifying View

Boundary layers play an important role in controlling convective heat transfer. Their nature varies considerably between different application areas characterized by different boundary conditions, which hampers a uniform treatment. Here, we argue that, independent from boundary conditions, systematic dissipation measurements in Rayleigh-B\'enard convection capture the relevant near-wall structures. By means of direct numerical simulations with varying Prandtl numbers, we demonstrate that such dissipation layers share central characteristics with classical boundary layers, but, in contrast to the latter, can be extended naturally to arbitrary boundary conditions. We validate our approach by explaining differences in scaling behavior observed for no-slip and stress-free boundaries, thus paving the way to an extension of scaling theories developed for laboratory convection to a broad class of natural systems

The tolerable windows approach: Theoretical and methodological foundations

The tolerable windows (TW) approach is presented as a novel scheme for integrated assessment of climate change. The TW approach is based on the specification of a set of guardrails for climate evolution which refer to various climate-related attributes. These constraints, which define what we call tolerable windows, can be purely systemic in nature - like critical thresholds for the North Atlantic Deep Water formation - or of a normative type - like minimum standards for per-capita food production worldwide. Starting from this catalogue of knock-out criteria and using appropriate modeling techniques, those policy strategies which are compatible with all the constraints specified are sought to be identified. In addition to the discussion of the basic elements and the general theory of the TW approach, a modeling exercise is carried out, based on simple models and assumptions adopted from the German Advisory Council on Global Change (WBGU). The analysis shows that if the global mean temperature is restricted to 2 degrees C beyond the preindustrial level, the cumulative emissions of CO2 are asymptotically limited to about 1550 Gt C. Yet the temporal distribution of these emissions is also determined by the climate and socio-economic constraints: using, for example, a maximal tolerable rate of temperature change of 0.2 degrees C/ dec and a smoothly varying emissions profile, we obtain the maximal cumulative emissions, amounting to 370 Gt C in 2050 and 585 Gt C in 2100

Butterfly-like spectra and collective modes of antidot superlattices in magnetic fields

We calculate the energy band structure for electrons in an external periodic potential combined with a perpendicular magnetic field. Electron-electron interactions are included within a Hartree approximation. The calculated energy spectra display a considerable degree of self-similarity, just as the ``Hofstadter butterfly.'' However, screening affects the butterfly, most importantly the bandwidths oscillate with magnetic field in a characteristic way. We also investigate the dynamic response of the electron system in the far-infrared (FIR) regime. Some of the peaks in the FIR absorption spectra can be interpreted mainly in semiclassical terms, while others originate from inter(sub)band transitions.Comment: 4 pages with 2 embeded eps figures. Uses revtex, multicol and graphicx styles. Accepted for publication in PRB Brief Report

Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?

We find that a 2D periodic potential with different modulation amplitudes in x- and y-direction and a perpendicular magnetic field may lead to a transition to electron transport along the direction of stronger modulation and to localization in the direction of weaker modulation. In the experimentally accessible regime we relate this new quantum transport phenomenon to avoided band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea

Hall conductance of Bloch electrons in a magnetic field

We study the energy spectrum and the quantized Hall conductance of electrons in a two-dimensional periodic potential with perpendicular magnetic field WITHOUT neglecting the coupling of the Landau bands. Remarkably, even for weak Landau band coupling significant changes in the Hall conductance compared to the one-band approximation of Hofstadter's butterfly are found. The principal deviations are the rearrangement of subbands and unexpected subband contributions to the Hall conductance.Comment: to appear in PRB; Revtex, 9 pages, 5 postscript figures; figures with better resolution may be obtained from http://www.chaos.gwdg.d

Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals

We investigate analytically and numerically the mean-field superconducting-normal phase boundaries of two-dimensional superconducting wire networks and Josephson junction arrays immersed in a transverse magnetic field. The geometries we consider include square, honeycomb, triangular, and kagome' lattices. Our approach is based on an analytical study of multiple-loop Aharonov-Bohm effects: the quantum interference between different electron closed paths where each one of them encloses a net magnetic flux. Specifically, we compute exactly the sums of magnetic phase factors, i.e., the lattice path integrals, on all closed lattice paths of different lengths. A very large number, e.g., up to $10^{81}$ for the square lattice, exact lattice path integrals are obtained. Analytic results of these lattice path integrals then enable us to obtain the resistive transition temperature as a continuous function of the field. In particular, we can analyze measurable effects on the superconducting transition temperature, $T_c(B)$, as a function of the magnetic filed $B$, originating from electron trajectories over loops of various lengths. In addition to systematically deriving previously observed features, and understanding the physical origin of the dips in $T_c(B)$ as a result of multiple-loop quantum interference effects, we also find novel results. In particular, we explicitly derive the self-similarity in the phase diagram of square networks. Our approach allows us to analyze the complex structure present in the phase boundaries from the viewpoint of quantum interference effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure

Integration of Case Studies on Global Change by Means of Artificial Intelligence

We present a novel methodology to integrate qualitative knowledge from different case studies on Global Change related issues into a single framework. The method is based on the concept of qualitative differential equations (QDEs) which represents a mathematically well-defined approach to investigate classes of ordinary differential equations (ODEs) used in conventional modeling exercises. These classes are defined by common qualitative features, e.g. monotonicity, signs, etc. Using the QSIMAlgorithm it is possible to derive the set of possible solutions of all ODEs in the class. Using this one can formulate a common, qualitatively specified cause-effect scheme valid for all case studies. The scheme is validated by testing it against the actually observed histories in the study regions with respect to their reconstruction by the corresponding QDE. The method is outlined theoretically and exemplary applied to the problem of land-use changes due to smallholders agriculture in de..

Statistical analysis of global wind dynamics in vigorous Rayleigh-Benard convection

Experimental and numerical studies of thermal convection have shown that sufficiently vigorous convective flows exhibit a large-scale thermal wind component sweeping along small-scale thermal boundary layer instabilities. A characteristic feature of these flows is an intermittent behavior in the form of irregular reversals in the orientation of the large-scale circulation. There have been several attempts toward a better understanding and description of the phenomenon of flow reversals, but so far most of these models are based on a statistical analysis of few-point measurements or on simplified theoretical assumptions. The analysis of long-term data sets (>5 × 105 turnover times τt = d/urms) obtained by numerical simulations of turbulent two-dimensional Rayleigh-Benard convection allows us to get a more comprehensive view of the spatio-temporal flow behavior. ´ By means of a global statistical analysis of the characteristic spatial modes of the flow we extract information about the stability of dominant large-scale modes as well as the reversal paths in state subspace. We examine probability density functions and drift vector fields of two-dimensional state subspaces spanned by different large-scale spatial modes. This also provides information about the coexistence of dominant modes

Convergence properties of the Kalman inverse filter

The Kalman filter has a long history of use in input deconvolution where it is desired to estimate structured inputs or disturbances to a plant from noisy output measurements. However, little attention has been given to the convergence properties of the deconvolved signal, in particular the conditions needed to estimate inputs and disturbances with zero bias. The paper draws on ideas from linear systems theory to understand the convergence properties of the Kalman filter when used for input deconvolution. The main result of the paper is to show that, in general, unbiased estimation of inputs using a Kalman filter requires both an exact model of the plant and an internal model of the input signal. We show that for unbiased estimation, an identified subblock of the Kalman filter that we term the plant model input generator (PMIG) must span all possible inputs to the plant and that the robustness of the estimator with respect to errors in model parameters depends on the eigenstructure of this subblock. We give estimates of the bias on the estimated inputs/disturbances when the model is in error. The results of this paper provide insightful guidance in the design of Kalman filters for input deconvolution