Numerical Simulation of Flows at Low Mach Numbers with Heat Sources

This work is concerned with finite volume methods for flows at low mach numbers which are under buoyancy and heat sources. As a particular application, fires in car tunnels will be considered. To extend the scheme for compressible flow into the low Mach number regime, a preconditioning technique is used and a stability result on this is proven. The source terms for gravity and heat are incorporated using operator splitting and the resulting method is analyzed.

Numerical simulation of tunnel fires using preconditioned finite volume schemes

This article is concerned with the numerical simulation of flows at low Mach numbers which are subject to the gravitational force and strong heat sources. As a specific example for such flows, a fire event in a car tunnel will be considered in detail. The low Mach flow is treated with a preconditioning technique allowing the computation of unsteady flows, while the source terms for gravitation and heat are incorporated via operator splitting. It is shown that a first order discretization in space is not able to compute the buoyancy forces properly on reasonable grids. The feasibility of the method is demonstrated on several test cases.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

On Connection, Linearization and Duplication Coefficients of Classical Orthogonal Polynomials

In this work, we have mainly achieved the following: 1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved; 2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization problem of all orthogonal polynomials of a discrete variable; 3. we propose a method to generate the connection, linearization and duplication coefficients for q-orthogonal polynomials; 4. we propose a unified method to obtain these coefficients in a generic way for orthogonal polynomials on quadratic and q-quadratic lattices. Our algorithmic approach to compute linearization, connection and duplication coefficients is based on the one used by Koepf and Schmersau and on the NaViMa algorithm. Our main technique is to use explicit formulas for structural identities of classical orthogonal polynomial systems. We find our results by an application of computer algebra. The major algorithmic tools for our development are Zeilberger’s algorithm, q-Zeilberger’s algorithm, the Petkovšek-van-Hoeij algorithm, the q-Petkovšek-van-Hoeij algorithm, and Algorithm 2.2, p. 20 of Koepf's book "Hypergeometric Summation" and it q-analogue.

Opportunities and constraints of transhumant small ruminant production in the Chinese Altay Mountains

This PhD thesis focuses on current livelihoods of agro-pastoral livestock keepers, their animal nutrition, herd and rangeland management strategies. It thereby aims to contribute to sustainable rangeland management, livestock production and household income in Qinghe county of the Chinese Altay Mountain region, located in Xinjiang Uyghur Autonomous Region, PR China. In its first part the study characterizes the socio-economic situation and agricultural practices of agro-pastoralists through structured household interviews. The second part provides insights into the grazing behaviour and feed intake of small ruminants on seasonal pastures in this region, and into the quantitative and qualitative biomass offer on natural rangelands. The third part analyses the reproductive performance and annual growth of the local sheep and goat herds, and, by modelling improved feeding and culling strategies, tests herd management options that potentially improve the monetary output per female herd animal without increasing the pressure onto natural rangelands. Taken together, the results of the study suggest that, despite an increase and intensification of cropping and vegetable gardening in the region of Qinghe, livestock rearing is still the major livelihood strategy both in terms of prevalence and relative importance. However, livestock keeping is challenged by low biomass production on rangelands, due to the combined impact of high climate variability and highly localized grazing pressure on the seasonal pastures. Though government regulations try to tackle the latter aspect, their implementation is sometimes difficult. Alternatives to strict regulation of grazing periods and animal numbers on seasonal pastures are, in the case of goats, more rigorous culling strategies and, in the case of sheep and goats, strategic supplementation of the animals in the winter and spring season. However, for the latter strategy to become economically viable, an improvement of live animal and meat marketing options and an investment in local meat processing facilities that add value to the carcasses is needed. As the regional cities grow rapidly, the potential market to absorb diverse and good quality meat products is there, along with the road network connecting Qinghe county to the regional capital. Such governmental measures will not only create new job opportunities in the region but also benefit the cash income of pastoralists in this westernmost region of China.

Free Resolutions from Involutive Bases

We show that the theory of involutive bases can be combined with discrete algebraic Morse Theory. For a graded k[x0 ...,xn]-module M, this yields a free resolution G, which in general is not minimal. We see that G is isomorphic to the resolution induced by an involutive basis. It is possible to identify involutive bases inside the resolution G. The shape of G is given by a concrete description. Regarding the differential dG, several rules are established for its computation, which are based on the fact that in the computation of dG certain patterns appear at several positions. In particular, it is possible to compute the constants independent of the remainder of the differential. This allows us, starting from G, to determine the Betti numbers of M without computing a minimal free resolution: Thus we obtain a new algorithm to compute Betti numbers. This algorithm has been implemented in CoCoALib by Mario Albert. This way, in comparison to some other computer algebra system, Betti numbers can be computed faster in most of the examples we have considered. For Veronese subrings S(d), we have found a Pommaret basis, which yields new proofs for some known properties of these rings. Via the theoretical statements found for G, we can identify some generators of modules in G where no constants appear. As a direct consequence, some non-vanishing Betti numbers of S(d) can be given. Finally, we give a proof of the Hyperplane Restriction Theorem with the help of Pommaret bases. This part is largely independent of the other parts of this work.

Modellbildung in der algebraischen Kryptoanalyse

In der algebraischen Kryptoanalyse werden moderne Kryptosysteme als polynomielle, nichtlineare Gleichungssysteme dargestellt. Das Lösen solcher Gleichungssysteme ist NP-hart. Es gibt also keinen Algorithmus, der in polynomieller Zeit ein beliebiges nichtlineares Gleichungssystem löst. Dennoch kann man aus modernen Kryptosystemen Gleichungssysteme mit viel Struktur generieren. So sind diese Gleichungssysteme bei geeigneter Modellierung quadratisch und dünn besetzt, damit nicht beliebig. Dafür gibt es spezielle Algorithmen, die eine Lösung solcher Gleichungssysteme finden. Ein Beispiel dafür ist der ElimLin-Algorithmus, der mit Hilfe von linearen Gleichungen das Gleichungssystem iterativ vereinfacht. In der Dissertation wird auf Basis dieses Algorithmus ein neuer Solver für quadratische, dünn besetzte Gleichungssysteme vorgestellt und damit zwei symmetrische Kryptosysteme angegriffen. Dabei sind die Techniken zur Modellierung der Chiffren von entscheidender Bedeutung, so das neue Techniken entwickelt werden, um Kryptosysteme darzustellen. Die Idee für das Modell kommt von Cube-Angriffen. Diese Angriffe sind besonders wirksam gegen Stromchiffren. In der Arbeit werden unterschiedliche Varianten klassifiziert und mögliche Erweiterungen vorgestellt. Das entstandene Modell hingegen, lässt sich auch erfolgreich auf Blockchiffren und auch auf andere Szenarien erweitern. Bei diesen Änderungen muss das Modell nur geringfügig geändert werden.