Symmetry exploiting control of hybrid mechanical systems - Flasskamp, Kathrin; Hage-Packhäuser, Sebastian; Ober-Blöbaum, Sina (Journal of Computational Dynamics)

High order variational integrators in the optimal control of mechanical systems - Campos, Cédric M.; Ober-Blöbaum, Sina; Trélat, Emmanuel (Discrete & Continuous Dynamical Systems - A)

Symmetry exploiting control of hybrid mechanical systems - Flaßkamp, K.; Hage-Packhäuser, S.; Ober-Blöbaum, Sina (Journal of Computational Dynamics)

High order variational integrators in the optimal control of mechanical systems - Campos, C. M.; Ober-Blöbaum, Sina; Trélat, E. (Discrete and Continuous Dynamical Systems)

Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps - ARNOLDI, JEAN FRANCOIS; FAURE, FRÉDÉRIC; Weich, Tobias (Ergodic Theory and Dynamical Systems)
We consider a simple model of an open partially expanding map. Its trapped set ${\mathcal{K}}$ in phase space is a fractal set. We first show that there is a well-defined discrete spectrum of Ruelle resonances which describes the asymptotic of correlation functions for large time and which is parametrized by the Fourier component $\unicode[STIX]{x1D708}$ in the neutral direction of the dynamics. We introduce a specific hypothesis on the dynamics that we call ‘minimal captivity’. This hypothesis is stable under perturbations and means that the dynamics is univalued in a neighborhood of ${\mathcal{K}}$ . Under this hypothesis we show the existence of an asymptotic spectral gap and a fractal Weyl law for the upper bound of density of Ruelle resonances in the semiclassical limit $\unicode[STIX]{x1D708}→ ∞$ . Some numerical computations with the truncated Gauss map and Bowen–Series maps illustrate these results.
Keywords: Applied Mathematics; General Mathematics

Resonance Chains and Geometric Limits on Schottky Surfaces - Weich, Tobias (Communications in Mathematical Physics)
Keywords: Mathematical Physics; Statistical and Nonlinear Physics

Gibbs measures on permutations over one-dimensional discrete point sets - Richthammer, Thomas; Biskup, Marek (Communications in Mathematical Physics)
We consider Gibbs distributions on permutations of a locally finite infinite set X⊂R, where a permutation σ of X is assigned (formal) energy ∑x∈XV(σ(x)−x). This is motivated by Feynman’s path representation of the quantum Bose gas; the choice X:=Z and V(x):=αx2 is of principal interest. Under suitable regularity conditions on the set X and the potential V, we establish existence and a full classification of the infinite-volume Gibbs measures for this problem, including a result on the number of infinite cycles of typical permutations. Unlike earlier results, our conclusions are not limited to small densities and/or high temperatures.

The rate of convergence to stationarity for M/G/1 models with admission controls via coupling - Kolb, Martin; Stadje, Wolfgang; Wübker, Achim (Stochastic Models)
We study the workload processes of two M/G/1 queueing systems with restricted capacity: in Model 1 any service requirement that would exceed a certain capacity threshold is truncated; in Model 2 new arrivals do not enter the system if they have to wait more than a fixed threshold time in line. For Model 1 we obtain several results concerning the rate of convergence to equilibrium. In particular, we derive uniform bounds for geometric ergodicity with respect to certain subclasses. For Model 2 geometric ergodicity follows from the finiteness of the moment-generating function of the service time distribution. We derive bounds for the convergence rates in special cases. The proofs use the coupling method.

Local asymptotics for the area of random walk excursions - Kolb, Martin; Denisov, Denis; Wachtel, Vitali (Journal of the London Mathematical Society)
We prove a local limit theorem for the area of the positive excursion of random walks with zero mean and finite variance. Our main result complements previous work of Caravenna and Chaumont; Sohier, as well as Kim and Pittel.

A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian - Rösler, Margit; Voit, Michael (Symmetry, Integrability and Geometry: Methods and Applications)
Keywords: Geometry and Topology; Mathematical Physics; Analysis

Vector bundles on plane cubic curves and the classical Yang-Baxter equation - Burban, Igor; Henrich, T. (Journal of the European Math. Society)

Mathematikbezogene Kompetenzentwicklung elementarpädagogischer Fachpersonen in Intensiv-Fortbildungen - Bruns, Julia; Eichen, L. (Beiträge zum Mathematikunterricht 2015)

Entwicklung eines videobasierten Instruments zur Erhebung von Handlungsfähigkeiten elementarpädagogischer Fachpersonen im mathematischen Bereich (VimaH) - Bruns, Julia; Eichen, L. (Entwicklung mathematischer Fähigkeiten von Kindern im Grundschulalter – Tagungsband des AK Grundschule in der GDM 2015)

Entwicklung eines videobasierten Instruments zur Erhebung mathematikdidaktischer Handlungskompetenzen elementarpädagogischer Fachpersonen - Bruns, Julia; Eichen, L. (Beiträge zum Mathematikunterricht 2015)

Adaptive Förderung zur Vorbereitung auf den Übergang vom Elementar- in den Primarbereich am Beispiel des Bereichs Mathematik - Bruns, Julia; Eichen, Lars (Frühe Bildung)
Die vorliegende quasi-experimentelle Querschnittsuntersuchung verfolgt das Ziel, adaptive Förderleistungen elementarpädagogischer Fachpersonen zu erfassen und Zusammenhänge mit anderen Komponenten elementarpädagogischer Arbeit aufzudecken. Im Zentrum steht die Frage: Welcher Zusammenhang zeigt sich zwischen der Beobachtungsintensität, den diagnostischen Fähigkeiten und der Qualität der adaptiven Förderpraxis im Elementarbereich? Fokussiert wird die adaptive Förderleistung einer Teilstichprobe mit n = 31 Fachpersonen in Bezug auf die Teilstichprobe von n = 62 Kinder. Dazu werden verschiedene Methoden auf Kinder- und Fachpersonenebene im Sinne eines mixed-methods Designs miteinander verknüpft (Mathematiktest ‚zahlenstark‘, standardisierte Beobachtung, standardisiertes Interview). Die Ergebnisse zeigen, dass keiner Fachperson eine optimale Förderung zweier Kinder gelingt. Im Hinblick auf den Übergang zwischen Elementar- und Primarbereich kann gefolgert werden, dass die Kinder unzureichend in ihren individuellen Bildungsprozessen begleitet werden.
Keywords: General Earth and Planetary Sciences; General Environmental Science

Kann professorale Lehre tutoriell sein? Ein Modellversuch zur Einführung in mathematisches Denken und Arbeiten - Hilgert, Joachim; Hoffmann, Max; Panse, Anja (Tagungsband zum Hansekolloquium zur Hochschuldidaktik der Mathematik.)

Einführung in mathematisches Denken und Arbeiten: tutoriell und transparent - Hilgert, Joachim; Hoffmann, Max; Panse, Anja

Resonances for the Laplacian: the cases BC2 and C2 (except over SOo(p,2), p>0 odd) - Hilgert, Joachim; Pasquale, A.; Przebinda, T.

Contraction of Hamiltonian K-spaces - Hilgert, Joachim; Manon, C.; Martens, J.

Resonances for the Laplacian of products of two rank one Riemannian symmetric spaces - Hilgert, Joachim; Pasquale, A.; Przebinda, T.

Superorbits - Hilgert, Joachim; Alldridge, A.; Wurzbacher, T.

Efficient numerical methods for elliptic and parabolic partial differential equations - Kovács, Balázs

Sprachsensibler Umgang mit Textmustern im Mathematikunterricht am Beispiel von Konstruktionsbeschreibungen - Rezat, Sara; Rezat, Sebastian; Janzen, Sabrina (Beiträge zum Mathematikunterricht 2015. Vorträge auf der 49. Tagung für Didaktik der Mathematik vom 09.02.2015 bis 13.02.2015 in Basel. Band 2)

Online Tests for Evaluating Learning Success - Hesse, Kerstin (Extended Abstract der khdm Conference 2015, 8 Seiten. (Dieser Extended Abstract ist online publiziert als khdm-Report zur khdm Conference 2015.))

Numerical Simulation of the Damping Behavior of Particle-Filled Hollow Spheres - Steinle, Tobias; Vrabec, Jadran; Walther, Andrea (Proc. Modeling, Simulation and Optimization of Complex Processes (HPSC))
In light of an increasing awareness of environmental challenges, extensive research is underway to develop new light-weight materials. A problem arising with these materials is their increased response to vibration. This can be solved using a new composite material that contains embedded hollow spheres that are partially filled with particles. Progress on the adaptation of molecular dynamics towards a particle-based numerical simulation of this material is reported. This includes the treatment of specific boundary conditions and the adaption of the force computation. First results are presented that showcase the damping properties of such particle-filled spheres in a bouncing experiment.

Variational Approach to Molecular Kinetics - Nüske, Feliks; Keller, Bettina G.; Pérez-Hernández, Guillermo; Mey, Antonia S. J. S.; Noé, Frank (Journal of Chemical Theory and Computation)

Mathematik als Werkzeug: Sicht- und Arbeitsweisen von Studierenden am Anfang ihres Mathematikstudiums - Liebendörfer, Michael; Ostsieker, Laura (Mit Werkzeugen Mathematik und Stochastik lernen – Using Tools for Learning Mathematics and Statistics)

The Mathematical Beliefs and Interest Development of Pre-Service Primary Teachers - Liebendörfer, Michael; Hochmuth, Reinhard; Kolter, Jana; Schukajlow, Stanislaw (Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education an the 36th Conference of the North American Chapter of the Psychology of Mathematics Education)

Self-determination and interest development of first-year mathematics students - Liebendörfer, Michael (Oberwolfach Reports)

Vorstellung eines Fragebogens zur Erfassung von Lernstrategien in mathematikhaltigen Studiengängen - Liebendörfer, Michael; Hochmuth, Reinhard; Schreiber, Stephan; Göller, Robin; Kolter, Jana; Biehler, Rolf; Kortemeyer, Jörg; Ostsieker, Laura (Beiträge zum Mathematikunterricht 2014)

The Paradigm of Self-optimization - Dellnitz, Michael; Dumitrescu, Roman; Flaßkamp, Kathrin; Gausemeier, Jürgen; Hartmann, Philip; Iwanek, Peter; Korf, Sebastian; Krüger, Martin; Ober-Blöbaum, Sina; Porrmann, Mario; Priesterjahn, Claudia; Stahl, Katharina; et al. (Lecture Notes in Mechanical Engineering)

Optimal control of a switched reluctance drive by a direct method using a discrete variational principle - Flasskamp, Kathrin; Ober-Blobaum, Sina; Schneider, Tobias; Bocker, Joachim (52nd IEEE Conference on Decision and Control)

Control strategies on stable manifolds for energy-efficient swing-ups of double pendula - Flaßkamp, Kathrin; Timmermann, Julia; Ober-Blöbaum, Sina; Trächtler, Ansgar (International Journal of Control)

Methods for the Design and Development - Anacker, Harald; Dellnitz, Michael; Flaßkamp, Kathrin; Groesbrink, Stefan; Hartmann, Philip; Heinzemann, Christian; Horenkamp, Christian; Kleinjohann, Bernd; Kleinjohann, Lisa; Korf, Sebastian; Krüger, Martin; Müller, Wolfgang; et al. (Lecture Notes in Mechanical Engineering)

The computation of convex invariant sets via Newton's method - Baier, Robert; Dellnitz, Michael; Hessel-von Molo, Mirko; Sertl, Stefan; Kevrekidis, Ioannis G. (Journal of Computational Dynamics)

Variational Lie Group Formulation of Geometrically Exact Beam Dynamics: Synchronous and Asynchronous Integration - Leitz, Thomas; Ober-Blöbaum, Sina; Leyendecker, Sigrid (Multibody Dynamics)

On the role of quadrature rules and system dimensions in variational multirateintegrators - Gail, Tobias; Leyendecker, Sigrid; Ober-Blöbaum, Sina (The 3rdJoint International Conference on Multibody System Dynamics)

Variational formulation and structure-preserving discretization ofnonlinear electric circuits - Ober-Blöbaum, Sina; Lindhorst, Henning (21st International Symposium on Mathematical Theory of Networks and Systems)

Variational formulation and structure-preserving discretization of nonlinear electric circuits - Ober-Blöbaum, Sina; Lindhorst, H. (21st International Symposium on Mathematical Theory of Networks and Systems)

On the role of quadrature rules and system dimensions in variational multirate integrators - Gail, T.; Leyendecker, S.; Ober-Blöbaum, Sina (3rd Joint Interntaional Conference on Multibody System Dynamics)

Case Study - Trächtler, Ansgar; Kleinjohann, Bernd; Heinzemann, Christian; Rasche, Christoph; Priesterjahn, Claudia; Steenken, Dominik; Wehrheim, Heike; Gausemeier, Jürgen; Flaßkamp, Kathrin; Kleinjohann, Lisa; Krüger, Martin; Iwanek, Peter; et al. (Dependability of Self-Optimizing Mechatronic Systems)

Construction and analysis of higher order Galerkin variational integrators - Ober-Blöbaum, Sina; Saake, N. (Advances in Computational Mathematics)

Methods for the Design and Development - Anacker, H.; Dellnitz, M.; Flaßkamp, K.; Grocsbrink, S.; Hartmann, P.; Heinzemann, C.; Horenkamp, C.; Kleinjohann, B.; Korf, S.; Krüger, M.; Müller, W.; Ober-Blöbaum, Sina; et al. (Jürgen Gausemeier, Franz Josef Rammig, and Wilhelm Schäfer, editors, Design Methodology for Intelligent Technical Systems)

Dependability of Self-optimizing Mechatronic Systems - Dangelmeier, W.; Dellnitz, M.; Dorociak, R.; Flaßkamp, K.; Gausemeier, J.; Groesbrink, S.; Hartmann, P.; Heinzemann, C.; Hölscher, C.; Iwanek, P.; Keßler, J.H.; Kleinjohann, B.; et al. (Lecture Notes in Mechanical Engineering)

The paradigm of self-optimization - Dellnitz, M.; Dumitrescu, R.; Flaßkamp, K.; Gausemeier, J.; Hartmann, P.; Iwanek, P.; Korf, S.; Krüger, M.; Ober-Blöbaum, Sina; Porrmann, M.; Priesterjahn, C.; Stahl, K.; et al. (Jürgen Gausemeier, Franz Josef Rammig, and Wilhelm Schäfer, editors, Design Methodology for Intelligent Technical Systems)

Variational Lie group formulation of geometrically exact beam dynamics: Synchronous and asynchronous integration - Leitz, T.; Ober-Blöbaum, Sina; Leyendecker, S. (Zdravko Terze, Multibody Dynamics)

Equivariant spectral asymptotics forh-pseudodifferential operators - Weich, Tobias (Journal of Mathematical Physics)
Keywords: Mathematical Physics; Statistical and Nonlinear Physics

Exponential ergodicity of killed Lévy processes in a finite interval - Kolb, Martin; Savov, Mladen (Electronic Communications in Probability)
Following Bertoin who considered the ergodicity and exponential decay of Lévy processes in a finite domain, we consider general Lévy processes and their ergodicity and exponential decay in a finite interval. More precisely, given Ta=inf{t>0:Xt∉. Under general conditions, e.g. absolute continuity of the transition semigroup of the unkilled Lévy process, we prove that the killed semigroup is a compact operator. Thus, we prove stronger results in view of the exponential ergodicity and estimates of the speed of convergence. Our results are presented in a Lévy processes setting but are well applicable for Markov processes in a finite interval under information about Lebesgue irreducibility of the killed semigroup and that the killed process is a double Feller process. For example, this scheme is applicable to a work of Pistorius.

The Brownian traveller on manifolds - Kolb, Martin; Krejčiřík, David (Journal of Spectral Theory)
We study the influence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemannian manifold. Since we consider killing boundary conditions, there is always an exponential-type decay for the heat semigroup. We show that this exponential-type decay is slower for positively curved manifolds comparing to the flat case. As the main result, we establish a sharp extra polynomial-type decay for the heat semigroup on negatively curved manifolds comparing to the flat case. The proof employs the existence of Hardy-type inequalities for the Dirichlet Laplacian in the tubular neighbourhoods on negatively curved manifolds and the method of self-similar variables and weighted Sobolev spaces for the heat equation.

Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum - Barkhofen, Sonja; Faure, F; Weich, Tobias (Nonlinearity)
Keywords: Applied Mathematics; General Physics and Astronomy; Mathematical Physics; Statistical and Nonlinear Physics