Estimation of the Required Amount of Hydrological Exploration in Lignite Mining Areas on the Basis of Hypothetical Hydrogeological Models

Mine drainage is a necessary but very costly precaution for open-pit lignite mining in sandy aquifers. Consequently, the minimization of the number of drainage wells and their optimal operation become important tasks in designing mine drainage systems. Comprehensive groundwater flow models have to be used, both, for the design of drainage wells, and for the analysis of water management strategies in mining areas . The accuracy of computations with such models depends on the precision of the underlying hydrogeological informations. In order to get these informations detailed and costly hydrogeological explorations have to be done in the mining regions. The basic informations are obtained using exploration drilling. The cost for hydrogeological exploration are approximately a linear function of the number of exploration bore holes. Therefore the reduction of drilling gets a key role in reducing costs of exploration. This might be done by: increased use of geophysical exploration methods; complex analysis of exploration results using mathematical statistical methods; precise estimation of the required amount of hydrogeological informations. The paper describes a mathematical approach to support the complex decision making procedure of estimating the optimal amount of hydrogeological exploration with respect to a given mine drainage goal

Chaos in Quantum Dots: Dynamical Modulation of Coulomb Blockade Peak Heights

The electrostatic energy of an additional electron on a conducting grain blocks the flow of current through the grain, an effect known as the Coulomb blockade. Current can flow only if two charge states of the grain have the same energy; in this case the conductance has a peak. In a small grain with quantized electron states, referred to as a quantum dot, the magnitude of the conductance peak is directly related to the magnitude of the wavefunction near the contacts to the dot. Since dots are generally irregular in shape, the dynamics of the electrons is chaotic, and the characteristics of Coulomb blockade peaks reflects those of wavefunctions in chaotic systems. Previously, a statistical theory for the peaks was derived by assuming these wavefunctions to be completely random. Here we show that the specific internal dynamics of the dot, even though it is chaotic, modulates the peaks: because all systems have short-time features, chaos is not equivalent to randomness. Semiclassical results are derived for both chaotic and integrable dots, which are surprisingly similar, and compared to numerical calculations. We argue that this modulation, though unappreciated, has already been seen in experiments.Comment: 4 pages, 3 postscript figs included (2 color), uses epsf.st

Semiclassical Theory of Coulomb Blockade Peak Heights in Chaotic Quantum Dots

We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using Berry's conjecture, we calculate the peak height distributions and the correlation functions. We demonstrate that the corrections to the corresponding results of the standard statistical theory are non-universal and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The main effect is an oscillatory dependence of the peak heights on any parameter which is varied; it is substantial for both symmetric and asymmetric lead placement. Surprisingly, these dynamical effects do not influence the full distribution of peak heights, but are clearly seen in the correlation function or power spectrum. For non-zero temperature, the correlation function obtained theoretically is in good agreement with that measured experimentally.Comment: 5 color eps figure

Microwave study of quantum n-disk scattering

We describe a wave-mechanical implementation of classically chaotic n-disk scattering based on thin 2-D microwave cavities. Two, three, and four-disk scattering are investigated in detail. The experiments, which are able to probe the stationary Green's function of the system, yield both frequencies and widths of the low-lying quantum resonances. The observed spectra are found to be in good agreement with calculations based on semiclassical periodic orbit theory. Wave-vector autocorrelation functions are analyzed for various scattering geometries, the small wave-vector behavior allowing one to extract the escape rate from the quantum repeller. Quantitative agreement is found with the value predicted from classical scattering theory. For intermediate energies, non-universal oscillations are detected in the autocorrelation function, reflecting the presence of periodic orbits.Comment: 13 pages, 8 eps figures include

Approach to ergodicity in quantum wave functions

According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that relates the rate of approach to the decay of certain classical fluctuations. For uniformly hyperbolic systems we find that the variance of the quantum matrix elements is proportional to the variance of the integral of the associated classical operator over trajectory segments of length $T_H$, and inversely proportional to $T_H^2$, where $T_H=h\bar\rho$ is the Heisenberg time, $\bar\rho$ being the mean density of states. Since for these systems the classical variance increases linearly with $T_H$, the variance of the matrix elements decays like $1/T_H$. For non-hyperbolic systems, like Hamiltonians with a mixed phase space and the stadium billiard, our results predict a slower decay due to sticking in marginally unstable regions. Numerical computations supporting these conclusions are presented for the bakers map and the hydrogen atom in a magnetic field.Comment: 11 pages postscript and 4 figures in two files, tar-compressed and uuencoded using uufiles, to appear in Phys Rev E. For related papers, see http://www.icbm.uni-oldenburg.de/icbm/kosy/ag.htm

Resonances in a chaotic attractor crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle--Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises

Metagenomic binning of a marine sponge microbiome reveals unity in defense but metabolic specialization

Marine sponges are ancient metazoans that are populated by distinct and highly diverse microbial communities. In order to obtain deeper insights into the functional gene repertoire of the Mediterranean sponge Aplysina aerophoba, we combined Illumina short-read and PacBio long-read sequencing followed by un-targeted metagenomic binning. We identified a total of 37 high-quality bins representing 11 bacterial phyla and two candidate phyla. Statistical comparison of symbiont genomes with selected reference genomes revealed a significant enrichment of genes related to bacterial defense (restriction-modification systems, toxin-antitoxin systems) as well as genes involved in host colonization and extracellular matrix utilization in sponge symbionts. A within-symbionts genome comparison revealed a nutritional specialization of at least two symbiont guilds, where one appears to metabolize carnitine and the other sulfated polysaccharides, both of which are abundant molecules in the sponge extracellular matrix. A third guild of symbionts may be viewed as nutritional generalists that perform largely the same metabolic pathways but lack such extraordinary numbers of the relevant genes. This study characterizes the genomic repertoire of sponge symbionts at an unprecedented resolution and it provides greater insights into the molecular mechanisms underlying microbial-sponge symbiosis

Simulation von Stroemungs- und Transportprozessen fuer die Bewertung von Altlasten. T. 3: Erarbeitung eines public-domain software-pools zur Simulation von Stroemungs- und Transportprozessen fuer Fachbehoerden

Available from TIB Hannover: RN 8908(97-053,3) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEUmweltbundesamt, Berlin (Germany); Bundesministerium fuer Umwelt, Naturschutz und Reaktorsicherheit, Bonn (Germany)DEGerman

Simulation von Stroemungs- und Transportprozessen fuer die Bewertung von Altlasten. T. 1: Simulation von Grundwasserstroemungs- und transportprozessen fuer das Lockergestein im Rahmen der Altlastenbearbeitung

The paper describes the modelling of groundwater flow and quality problems in sand and gravel formations with influence of landfills and hazard industrial waste. Based on the theoretical background the paper describes the possibility of parameter identification and gives a classification of many computer programs by using in the different levels of landfill and hazard industrial waste management. The second chapter of the paper describes the interpretation of simulation results. The last chapter of the paper handles some examples. They demonstrate methodical aspects of the modelling. (orig.)Available from TIB Hannover: RN 8422(1997,86) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEBundesministerium fuer Umwelt, Naturschutz und Reaktorsicherheit, Bonn (Germany)DEGerman