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Now showing items 1-10 of 13
Preprint
Numerical crack path prediction under mixed-mode loading in 1D quasicrystals
(2017-03)
Quasicrystals are being implemented in industry since this new class of materials appears to have some peculiar properties. However, the fracture behavior of quasicrystals is not yet clear, which could be a hindrance to its wide usage. This work adopts the generalized linear elastic framework of fracture theory in quasicrystals and develops numerical tools in a finite element environment to compute the fracture quantities. Crack growth is simulated in diverse specimens undergoing an intrinsic mixed-mode loading and ...
Preprint
Large-scale heat pumps: market potential and barriers, classification and estimation of efficiency
(2019-12-20)
Heat pumps powered by renewable electricity have a significant potential to become a critical technology to disruptively decarbonize an economy. An essential step towards this goal is the development of an accurate understanding and model of how heat pumps in large-scale implementations perform in terms of economics, energy, and the environment. In this study, the influence of system design and operating conditions on the Coefficient of Performance (COP) of large-scale (> 50 kWth) electric driven mechanical compression ...
Preprint
Heapsort for Equal Keys
(2014-09)
Das effiziente Entfernen von Duplikaten in Datenbeständen ist eine algorithmische Herausforderung in theoretischer und praktischer Hinsicht. Tabellen mit Duplikaten entstehen in Datenbanken nach einer Projektion, beim Verfolgen von Seiten im Web, bei Messreihen und in der Stochastik. Ein häufige Methode, diese sog. Multisets in echte Mengen zu wandeln, ist die Sortierung mit folgender Entfernung aller gleichen Sätze bis auf einen. Idealerweise kann dies bereits bei der Sortierung in situ erfolgen, so dass vorne die ...
Preprint
On Solution Sets of Information Inequalities
(2011)
We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.
Preprint
Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach
(2010)
Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the ...
Preprint
On the relationship between the Method of Least Squares and Gram-Schmidt orthogonalization
(2010)
The method of Least Squares is due to Carl Friedrich Gauss. The Gram-Schmidt
orthogonalization method is of much younger date. A method for solving Least Squares Problems is developed which automatically results in the appearance of the Gram-Schmidt orthogonalizers. Given these orthogonalizers an induction-proof is available for solving Least Squares Problems.
Preprint
A free boundary approach to the Rosensweig instability of ferrofluids
(2017-04-18)
We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid which undergoes normal field instability (also known as Rosensweig instability). The starting point consists in the ferro-hydrostatic equations for the magnetic potentials in the ferrofluid and air, and the function describing their interface. The former constitute the strong form for the Euler-Lagrange equations of a convex-concave functional. We extend this functional in order to ...
Preprint
On the existence of symmetric minimizers
(2018-01-23)
In this note we revisit a less known symmetrization method for functions with respect to a topological group, which we call G-averaging. We note that, although quite non-technical in nature, this method yields G-invariant minimizers of functionals satisfying some relaxed convexity properties. We give an abstract theorem and show how it can be applied to the p-Laplace and polyharmonic Poisson problem in order to construct symmetric solutions. We also pose some open problems and explore further possibilities where the ...
Preprint
Convergence analysis of time-discretization schemes for rate-independent systems
(2017-12-21)
It is well known that rate-independent systems involving nonconvex energy functionals in general do not allow for time-continuous solutions even if the given data are smooth. In the last years, several solution concepts were proposed that include discontinuities in the notion of solution, among them the class of global energetic solutions and the class of BV-solutions. In general, these solution concepts are not equivalent and numerical schemes are needed that reliably approximate that type of solutions one is ...