Geometric and Hydrodynamic Characteristics of Three-dimensional Saturated Prefractal Porous Media Determined with Lattice Boltzmann Modeling

Fractal and prefractal geometric models have substantial potential for contributing to the analysis of flow and transport in porous media such as soils and reservoir rocks. In this study, geometric and hydrodynamic parameters of saturated 3D mass and pore–solid prefractal porous media were characterized using the lattice Boltzmann model (LBM). The percolation thresholds of the 3D prefractal porous media were inversely correlated with the fraction of micro-pore clusters and estimated as 0.36 and 0.30 for mass and pore–solid prefractal porous media, respectively. The intrinsic permeability and the dispersivity of the 3D pore–solid prefractals were larger than those of the 3D mass prefractals, presumably because of the occurrence of larger solid and pore cluster sizes in the former. The intrinsic permeability and dispersivity of both types of structure increased with increasing porosity, indicating a positive relationship between permeability and dispersivity, which is at odds with laboratory data and current theory. This discrepancy may be related to limitations of the convection dispersion equation at the relatively high porosity values employed in the present study.     

Weierstraßscher Approximationssatz und Gleichverteilung

Using uniformly distributed sequences modulo 1 polynomials are formed which approximate continuous functions ofJ, whereJ is at first a compact interval inR ^s . The error of the approximation is estimated using the discrepancy of the sequences. Some cases of unbounded intervals are also studied. Furthermore trigonometric polynomials are considered which approximate periodic continuous functions inR ^s .

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Meinem Freund Prof. L. Schmetterer zum 60. Geburtstag gewidmet     

Percolation Thresholds in 2-Dimensional Prefractal Models of Porous Media*

Considerable effort has been directed towards the application of percolation theory and fractal modeling to porous media. We combine these areas of research to investigate percolation in prefractal porous media. We estimated percolation thresholds in the pore space of homogeneous random 2-dimensional prefractals as a function of the fractal scale invariance ratio b and iteration level i. The percolation thresholds for these simulations were found to increase beyond the 0.5927l... porosity expected in Bernoulli (uncorrelated) percolation networks. Percolation in prefractals occurs through large pores connected by small pores. The thresholds increase with both b (a finite size effect) and i. The results allow the prediction of the onset of percolation in models of prefractal porous media and can be used to bound modeling efforts. More fundamental applications are also possible. Only a limited range of parameters has been explored empirically but extrapolations allow the critical fractal dimension to be estimated for a large combination of b and i values. Extrapolation to infinite iterations suggests that there may be a critical fractal dimension of the solid at which the pore space percolates. The extrapolated value is close to 1.89 – the well-known fractal dimension of percolation clusters in 2-dimensional Bernoulli networks.     

On the reconstruction problem for factorizable homeomorphism groups and foliated manifolds

For a group G of homeomorphisms of a regular topological space X and a subset U⊆X, set . We say that G is a factorizable group of homeomorphisms, if for every open cover U of X, _?U∈UG generates G.

Theorem I. Let G, H be factorizable groups of homeomorphisms of X and Y respectively, and suppose that G, H do not have fixed points. Let φ be an isomorphism between G and H. Then there is a homeomorphism τ between X and Y such thatφ(g)=τ○g○τ−1for everyg∈G.     

A supernodal formulation of vertex colouring with applications in course timetabling

For many problems in scheduling and timetabling, the choice of a mathematical programming formulation is determined by the formulation of the graph colouring component. This paper briefly surveys seven known integer programming formulations of vertex colouring and introduces a new approach using “supernodes”.     

A space-indexed formulation of packing boxes into a larger box

Current integer programming solvers fail to decide whether 12 unit cubes can be packed into a 1×1×11 box within an hour using the natural relaxation of Chen/Padberg. We present an alternative relaxation of the problem of packing boxes into a larger box, which makes it possible to solve much larger instances.     

On the approximability of the Simplified Partial Digest Problem

In this paper, we analyse the computational complexity of an optimization version of the Simplified Partial Digest Problem (SPDP), which is a mathematical model for DNA mapping based on the results of a simplified partial digest experiment. We prove that recognizing 46.16% of the elements of the DNA map in the error-free simplified partial digest experiment is NP-hard in the strong sense. This implies that the problem of maximizing the number of correct elements of the DNA map in the error-free simplified partial digest experiment is pseudopolynomially non-approximable with the approximation ratio .     

Quantum dot materials for terahertz generation applications

Compact and tunable semiconductor terahertz sources providing direct electrical control, efficient operation at room temperatures and device integration opportunities are of great interest at the present time. One of the most well‐established techniques for terahertz generation utilises photoconductive antennas driven by ultrafast pulsed or dual‐wavelength continuous wave laser systems, though some limitations, such as confined optical wavelength pumping range and thermal breakdown, still exist. The use of quantum dot‐based semiconductor materials, having unique carrier dynamics and material properties, can help to overcome limitations and enable efficient optical‐to‐terahertz signal conversion at room temperatures. Here we discuss the construction of novel and versatile terahertz transceiver systems based on quantum dot semiconductor devices. Configurable, energy‐dependent optical and electronic characteristics of quantum‐dot‐based semiconductors are described, and the resonant response to optical pump wavelength is revealed. Terahertz signal generation and detection at energies that resonantly excite only the implanted quantum dots opens the potential for using compact quantum dot‐based semiconductor lasers as pump sources. Proof‐of‐concept experiments are demonstrated here that show quantum dot‐based samples to have higher optical pump damage thresholds and reduced carrier lifetime with increasing pump power.

     

A fast energy‐dispersive multi‐element detector for X‐ray absorption spectroscopy

In this paper results are presented from fluorescence‐yield X‐ray absorption fine‐structure spectroscopy measurements with a new seven‐cell silicon drift detector (SDD) module. The complete module, including an integrated circuit for the detector readout, was developed and realised at DESY utilizing a monolithic seven‐cell SDD. The new detector module is optimized for applications like XAFS which require an energy resolution of ～250–300 eV (FWHM Mn Kα) at high count rates. Measurements during the commissioning phase proved the excellent performance for this type of application.