Kinetic Energy Transport in Rayleigh--B\'enard Convection

The kinetic energy balance in Rayleigh--B\'{e}nard convection is investigated for the Prandtl number range $0.01\le Pr \le 150$ and for fixed Rayleigh number $Ra=5\cdot10^{6}$. The kinetic energy balance is divided into a dissipation, a production and a flux term. We discuss profiles of all terms and find that the different contributions to the energy balance can be spatially separated into regions where kinetic energy is produced and where kinetic energy is dissipated. Analysing the Prandtl number dependence of the kinetic energy balance, we show that the height-dependence of the mean viscous dissipation is closely related to the flux of kinetic energy. We show that the flux of kinetic energy can be divided into four additive contributions, each representing a different elementary physical process (advection, buoyancy, normal viscous stresses and viscous shear stresses). The behaviour of these individual flux contributions is found to be surprisingly rich and exhibits a pronounced Prandtl number dependence. Different flux contributions dominate the kinetic energy transport at different depth, such that a comprehensive discussion requires a decomposition of the domain into a considerable number of sub-layers. On a less detailed level, our results reveal that advective kinetic energy fluxes play a key role in balancing the near-wall dissipation at low Prandtl number, whereas normal viscous stresses are particularly important at high Prandtl number. Finally, our work reveals that classical velocity boundary layers are deeply connected to the kinetic energy transport, but fail to correctly represent regions of enhanced viscous dissipation

The Hofstadter Energy Spectrum for an Interacting 2DEG

We study the effects of the Coulomb interactions between electrons on the Hofstadter butterfly, which characterizes the subband structure of the Landau levels of a two-dimensional electron gas in a perpendicular homogeneous magnetic field and a periodic lateral superlattice potential. The interactions essentially preserve the intricate gap structure of the Hofstadter spectra, but with a lower symmetry that depends on the filling of the Landau bands. For short enough periods and strong enough modulation the miniband structure can be resolved in the thermodynamic density of states.Comment: LaTeX 4 pages with 3 PostScript figures, Contribution to EP2DSXI Nottingham August 95 to appear in Surface Scienc

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 possibility of a metal insulator transition in antidot arrays induced by an external driving

It is shown that a family of models associated with the kicked Harper model is relevant for cyclotron resonance experiments in an antidot array. For this purpose a simplified model for electronic motion in a related model system in presence of a magnetic field and an AC electric field is developed. In the limit of strong magnetic field it reduces to a model similar to the kicked Harper model. This model is studied numerically and is found to be extremely sensitive to the strength of the electric field. In particular, as the strength of the electric field is varied a metal -- insulator transition may be found. The experimental conditions required for this transition are discussed.Comment: 6 files: kharp.tex, fig1.ps fig2.ps fi3.ps fig4.ps fig5.p

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

Manifestation of the Hofstadter butterfly in far-infrared absorption

The far-infrared absorption of a two-dimensional electron gas with a square-lattice modulation in a perpendicular constant magnetic field is calculated self-consistently within the Hartree approximation. For strong modulation and short period we obtain intra- and intersubband magnetoplasmon modes reflecting the subbands of the Hofstadter butterfly in two or more Landau bands. The character of the absorption and the correlation of the peaks to the number of flux quanta through each unit cell of the periodic potential depends strongly on the location of the chemical potential with respect to the subbands, or what is the same, on the density of electrons in the system.Comment: RevTeX file + 4 postscript figures, to be published Phys. Rev. B Rapid Com

Schrumpfung und Urban Sprawl - analytische und planerische Problemstellungen

Das vorliegende UFZ-Diskussionspapier ist die Dokumentation des Workshops Schrumpfung und Urban Sprawl, der am 3. November 2003 am UFZ stattfand. Es führt damit eine Diskussions- und Forschungslinie fort, die in den 1990er Jahren durch Forscher und Praktiker aus unterschiedlichen Einrichtungen der Region Halle-Leipzig begründet wurde. Im Arbeitskreis Suburbanisierung wurden unter Koordination des UFZ disziplinäre Zugänge und praktische Erfahrungen zusammengeführt und daraus Handlungsempfehlungen abgeleitet. Zwischenzeitlich hat der Suburbanisierungsdruck, der noch Ende der 1990er Jahre konstatiert wurde, deutlich abgenommen nicht nur in der Region, sondern in ganz Ostdeutschland. Nichtsdestoweniger ist Suburbanisierung ein zentraler Gegenstand von raumbezogener Politik und räumlicher Planung geblieben und hat im Zusammenhang mit dem Thema Stadtumbau neue Relevanz gewonnen. So ist davon auszugehen, dass auch in der Region Halle-Leipzig die intensive Beschäftigung mit dem Problem der Suburbanisierung anhalten wird allerdings unter veränderten Vorzeichen. Im Mittelpunkt steht nunmehr die Frage, welche Anforderungen sich aus der Situation von demographischer und städtischer Schrumpfung für die wissenschaftliche und praktische Auseinandersetzung mit Suburbanisierung ergeben. So gilt es, unter anderem, zu klären, ob sich die Richtung von Sprawl unter Schrumpfungsbedingungen umkehrt, ob das Zusammenspiel von Schrumpfung und Sprawl zu einer neuen Stadtstruktur führt oder ob sich durch diese spezifische Situation die Segregationsmuster verändern. Auf dem Workshop selbst wurden vor allem die Möglichkeiten der Steuerung von Suburbanisierung bzw. Sprawl unter Schrumpfungsbedingungen behandelt. Dazu wurden Überlegungen und Ergebnisse, die im EU-Projekt URBS PANDENS am Fallbeispiel Leipzig gewonnen wurden, vorgestellt, diskutiert und mit Erfahrungen aus der Praxis bzw. aus einer anderen Region konfrontiert. Neben der empirischen Analyse spielt dabei ein im Rahmen von URBS PANDENS entwickeltes qualitatives Modell des Urban Sprawl eine zentrale Rolle. --

Gauss map and Lyapunov exponents of interacting particles in a billiard

We show that the Lyapunov exponent (LE) of periodic orbits with Lebesgue measure zero from the Gauss map can be used to determine the main qualitative behavior of the LE of a Hamiltonian system. The Hamiltonian system is a one-dimensional box with two particles interacting via a Yukawa potential and does not possess Kolmogorov-Arnold-Moser (KAM) curves. In our case the Gauss map is applied to the mass ratio $\gamma = m_2/m_1$ between particles. Besides the main qualitative behavior, some unexpected peaks in the $\gamma$ dependence of the mean LE and the appearance of 'stickness' in phase space can also be understand via LE from the Gauss map. This shows a nice example of the relation between the "instability" of the continued fraction representation of a number with the stability of non-periodic curves (no KAM curves) from the physical model. Our results also confirm the intuition that pseudo-integrable systems with more complicated invariant surfaces of the flow (higher genus) should be more unstable under perturbation.Comment: 13 pages, 2 figure

O homem e a estética pessoal

Orientador: Marchetti, Renato ZancanMonografia (Especialização) - Universidade Federal do Paraná, Setor de Ciências Sociais Aplicadas, Curso de Especialização em Marketing Empresaria

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