788 research outputs found

    Entropy of unimodular Lattice Triangulations

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    Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where its entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number of possible triangulations is unknown for large systems. We present a novel algorithm for an approximate enumeration which is based on calculations of the density of states using the Wang-Landau flat histogram sampling. For triangulations on two-dimensional integer lattices we achive excellent agreement with known exact numbers of small triangulations as well as an improvement of analytical calculated asymptotics. The entropy density is C=2.196(3)C=2.196(3) consistent with rigorous upper and lower bounds. The presented numerical scheme can easily be applied to other counting and optimization problems.Comment: 6 pages, 7 figure

    Unimodular lattice triangulations as small-world and scale-free random graphs

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    Real-world networks, e.g. the social relations or world-wide-web graphs, exhibit both small-world and scale-free behaviour. We interpret lattice triangulations as planar graphs by identifying triangulation vertices with graph nodes and one-dimensional simplices with edges. Since these triangulations are ergodic with respect to a certain Pachner flip, applying different Monte-Carlo simulations enables us to calculate average properties of random triangulations, as well as canonical ensemble averages using an energy functional that is approximately the variance of the degree distribution. All considered triangulations have clustering coefficients comparable with real world graphs, for the canonical ensemble there are inverse temperatures with small shortest path length independent of system size. Tuning the inverse temperature to a quasi-critical value leads to an indication of scale-free behaviour for degrees k5k \geq 5. Using triangulations as a random graph model can improve the understanding of real-world networks, especially if the actual distance of the embedded nodes becomes important.Comment: 17 pages, 6 figures, will appear in New J. Phy

    Development of an integrated solar-fossil powered steam generation system for industrial applications

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    Das Poster gibt eine kurze Einführung in das Projekt SolSteam, in dem die Integration solaren Prozessdampfes in einen konventionellen Dampferzeuger untersucht wird

    Evaluation der Hessischen Dorfentwicklung – neue Anforderungsprofile an ein Programm für die nachhaltige Entwicklung des ländlichen Raums im Zeichen des demographischen Wandels

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    Eines der wesentlichen Ergebnisse der Studie ist die Erkenntnis, dass jegliche Art von Flächenmanagement für einen Ort ohne Einbindung in eine kommunale Gesamtstrategie wenig Aussicht auf Erfolg verspricht. Die Studie schließt auf der Grundlage der in der Literatur zurzeit verfügbaren Definitionen über Art und Umfang von Flächenmanagement. Diese Begriffsbestimmung führt dazu, dass Flächenmanagement als ein Instrument verstanden wird, das drei wesentliche Komponenten hat: 1. Ein bau- und planungsrechtliches Umsetzungsszenario 2. Eine bürgerorientierte konzeptionelle Vorleistung der Kommune 3. Ein nicht unerheblich erscheinender Finanzmitteleinsatz durch die Kommun
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