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Preprint
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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
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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
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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
Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads
(2019-09-25)
We study a rate-independent system with non-convex energy and in the case of a time-discontinuous loading. We prove existence of the rate-dependent viscous regularization by time-incremental problems, while the existence of the so called parameterized BV-solutions is obtained via vanishing viscosity in a suitable parameterized setting. In addition, we prove that the solution set is compact.
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
On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices
(2010)
The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation ...
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
Balanced Viscosity solutions to a rate-independent system for damage
(2017-05-02)
This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems. While in the first two papers [KRZ13, KRZ15] the assumptions on the spatial domain $\Omega$ were kept as general as possible (i.e. nonsmooth domain with mixed boundary conditions), we assume here that $\partial\Omega$ is smooth and that the type of boundary conditions does not change. This smoother setting allows us to derive enhanced regularity spatial properties both for the ...