Interpolatory methods for model reduction of large-scale dynamical systems

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Fabrication and investigation of three-dimensional ferroelectric capacitors for the application of FeRAM

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015

Computational methods for model reduction of large-scale sparse structured descriptor systems

Magdeburg, Univ., Fak. für Mathematik, Diss., 2015

Bilinear H 2-optimal Model Order-Reduction with applications to thermal parametric systems

Magdeburg, Univ., Fak. für Mathematik, Diss., 2015

Line-fitting method of model order reduction for elastic multibody systems

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2015

Prototype based clustering in high-dimensional feature spaces

...In dieser Arbeit untersuche ich den ”Fluch der Dimensionen” mittels dem Begriff der Distanzkonzentration. Ich zeige, dass dieser Effekt im Datenmodell mittels der paarweisen Kovarianzkoeffizienten der Randverteilungen beschrieben werden kann. Zusätzlich vergleiche ich 10 prototypbasierte Clusteralgorithmen mittels 800.000 Clusterergebnissen von künstlich erzeugten Datensätzen. Ich erforsche, wie und warum Clusteralgorithmen von der Anzahl der Merkmale beeinflusst werden. Mit den Clusterergebnissen untersuche ich außerdem, wie gut 5 der populärsten Clusterqualitätsmaße die tatsächliche Clusterqualität schätzen.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Limit Cycles for a class of three dimensional polynomial differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Reduction of periodic difference systems to linear or autonomous ones

We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

Label Space Reduction in All-Optical Label Switchiing Networks

Report for the scientific sojourn at the Department of Information Technology (INTEC) at the Ghent University, Belgium, from january to june 2007. All-Optical Label Swapping (AOLS) forms a key technology towards the implementation of All-Optical Packet Switching nodes (AOPS) for the future optical Internet. The capital expenditures of the deployment of AOLS increases with the size of the label spaces (i.e. the number of used labels), since a special optical device is needed for each recognized label on every node. Label space sizes are affected by the wayin which demands are routed. For instance, while shortest-path routing leads to the usage of fewer labels but high link utilization, minimum interference routing leads to the opposite. This project studies and proposes All-Optical Label Stacking (AOLStack), which is an extension of the AOLS architecture. AOLStack aims at reducing label spaces while easing the compromise with link utilization. In this project, an Integer Lineal Program is proposed with the objective of analyzing the softening of the aforementioned trade-off due to AOLStack. Furthermore, a heuristic aiming at finding good solutions in polynomial-time is proposed as well. Simulation results show that AOLStack either a) reduces the label spaces with a low increase in the link utilization or, similarly, b) uses better the residual bandwidth to decrease the number of labels even more.

Hopf bifurcation in higher dimensional differential systems via the averaging method

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