Diploma Thesis
Refine
Year of publication
Document Type
- Diploma Thesis (24) (remove)
Language
- English (24) (remove)
Has Fulltext
- yes (24)
Keywords
Faculty / Organisational entity
In this work a 3-dimensional contact elasticity problem for a thin fiber and a rigid foundation is studied. We describe the contact condition by a linear Robin-condition (by meaning of the penalized and linearized non-penetration and friction conditions).
The dimension of the problem is reduced by an asymptotic approach. Scaling the Robin parameters appropriately we obtain a recurrent chain of Neumann type boundary value problems which are considered only in the microscopic scale. The problem for the leading term is a homogeneous Neumann problem, hence the leading term depends only on the slow variable. This motivates the choice of a multiplicative ansatz in the asymptotic expansion.
The theoretical results are illustrated with numerical examples performed with a commercial finite-element software-tool.
This work is concerned with dynamic flow problems, especially maximal dynamic flows and earliest arrival flows - also called universally maximal flows. First of all, a survey of known results about existence, computation and approximation of earliest arrival flows is given. For the special case of series-parallel graphs a polynomial algorithm for computing maximal dynamic flows is presented and this maximal dynamic flow is proven to be an earliest arrival flow.
* naive examples which show drawbacks of discrete wavelet transform and windowed Fourier transform; * adaptive partition (with a 'best basis' approach) of speech-like signals by means of local trigonometric bases with orthonormal windows. * extraction of formant-like features from the cosine transform; * further proceedingings for classification of vowels or voiced speech are suggested at the end.
Matrices with the consecutive ones property and interval graphs are important notations in the field of applied mathematics. We give a theoretical picture of them in first part. We present the earliest work in interval graphs and matrices with the consecutive ones property pointing out the close relation between them. We pay attention to Tucker's structure theorem on matrices with the consecutive ones property as an essential step that requires a deep considerations. Later on we concentrate on some recent work characterizing the matrices with the consecutive ones property and matrices related to them in the terms of interval digraphs as the latest and most interesting outlook on our topic. Within this framework we introduce a classiffcation of matrices with consecutive ones property and matrices related to them. We describe the applications of matrices with the consecutive ones property and interval graphs in different fields. We make sure to give a general view of application and their close relation to our studying phenomena. Sometimes we mention algorithms that work in certain fields. In the third part we give a polyhedral approach to matrices with the consecutive ones property. We present the weighted consecutive ones problem and its relation to Tucker's matrices. The constraints of the weighted consecutive ones problem are improved by introducing stronger inequalities, based on the latest theorems on polyhedral aspect of consecutive ones property. Finally we implement a separation algorithm of Oswald and Reinhelt on matrices with the consecutive ones property. We would like to mention that we give a complete proof to the theorems when we consider important within our framework. We prove theorems partially when it is worthwhile to have a closer look, and we omit the proof when there are is only an intersection with our studying phenomena.
The understanding of the many fields of control theory can be supported using demonstrators, as
influencing a system to achieve a desired behaviour is the main purpose of control theory. This
thesis covers the setup, implementation and controlling of an inverse multi-pendulum on a cart.
Construction design and brief dimensioning will be described. In addition, a drive to move the
cart and influence the system will be chosen, which will be controlled using industrial automation
technology components. The state feedback controller introduced requires state measurement that
is made available by a radio sensor designed in this thesis. A web user interface is designed and
in addition the data processing structure involving the industrial automation technology and the
custom radio sensor is implemented. The pendulum is then controlled and stabilized by an optimal
controller. Furthermore, an upswing control approach is pointed out using numerical optimal
control.
Hamiltonian daemons allow the transfer of energy from systems with very fast degrees
of freedom to systems with slower ones across several orders of magnitude. They act on
small scales and can be regarded as micro-engines.
Such daemons were previously described in the classical as well as the quantum me-
chanical regime. In this thesis the semi-classical regime is examined, where quantum
phenomena occur as corrections to classical systems. Here, the focus is on numerical
simulations.
First some introductory models are examined. They are concerned with quantum
tunneling, since it occurs as an important quantum correction, as well as with the
capture and decay of bound states, since this represents the transition between the
dynamical phases of a daemon: adiabatic decoupling and downconversion.
The examinations are carried out using wave functions, as solutions to the Schrödinger
equation, and by means of Wigner functions in a quantum mechanical phase-space in
the framework of the Weyl-Wigner-Groenewold-Moyal formalism. For one these Wigner
functions are computed from the wave functions, but they are also obtained from a
numerical method based on the Moyal equation, which will be introduced here.
After developing this methodology, it is employed in the study of a daemon system
with a tilted washboard potential. The daemon behavior is studied with regards to
quantum corrections, especially in phase-space and concerning Kruskal’s theorem, which
describes the capture of phase-space flow via a time-dependent separatrix.
Lastly the semi-classically quantized phase-space will be discussed as a basis for a
combined description of both classical and quantum daemons. The behavior of the
energy spectrum in the deep quantum regime is explained by dynamical tunneling pro-
cesses.
In this thesis we present the implementation of libraries center.lib and perron.lib for the non-commutative extension Plural of the Computer Algebra System Singular. The library center.lib was designed for the computation of elements of the centralizer of a set of elements and the center of a non-commutative polynomial algebra. It also provides solutions to related problems. The library perron.lib contains a procedure for the computation of relations between a set of pairwise commuting polynomials. The thesis comprises the theory behind the libraries, aspects of the implementation and some applications of the developed algorithms. Moreover, we provide extensive benchmarks for the computation of elements of the center. Some of our examples were never computed before.