University of Paderborn

About: University of Paderborn is a education organization based out in Paderborn, Nordrhein-Westfalen, Germany. It is known for research contribution in the topics: Control reconfiguration & Software. The organization has 6684 authors who have published 16929 publications receiving 323154 citations.

Piezoelectric ultrasonic motors

Abstract: Piezoelectric ultrasonic motors are a new type of actuator. They are characterized by high torque at low rotational speed, simple mechanical design and good controllability. They also provide a high holding torque even if no power is applied. Compared to electromagnetic actuators the torque per volume ratio of piezoelectric ultrasonic motors can be higher by an order of magnitude. Recently various types of piezoelectric ultrasonic motors have been developed for industrial applications such as cameralens drive or as actuator in the head restraint of automobile seats. This paper describes several types of piezoelectric ultrasonic motors. In the first part the working principle of the travelling wave motor is explained. In the second part other types of piezoelectric ultrasonic motors are described and classified with respect to the vibration modes and contact mechanisms used in their design. Finally some open problems in piezoelectric ultrasonic motor research are addressed.

A generalized solution concept for the Keller–Segel system with logarithmic sensitivity: global solvability for large nonradial data

Abstract: The chemotaxis system $$\begin{aligned} \left\{ \begin{array}{l} u_t = \Delta u - \chi abla \cdot \left( \frac{u}{v} abla v\right) , \\ v_t=\Delta v - v+u, \end{array} \right. \end{aligned}$$ is considered in a bounded domain $$\Omega \subset \mathbb {R}^n$$ with smooth boundary, where $$\chi >0$$ . An apparently novel type of generalized solution framework is introduced within which an extension of previously known ranges for the key parameter $$\chi $$ with regard to global solvability is achieved. In particular, it is shown that under the hypothesis that $$\begin{aligned} \chi <\left\{ \begin{array}{ll} \infty \qquad &{} \text{ if } n=2, \\ \sqrt{8} \qquad &{} \text{ if } n=3, \\ \frac{n}{n-2} \qquad &{} \text{ if } n\ge 4, \end{array} \right. \end{aligned}$$ for all initial data satisfying suitable assumptions on regularity and positivity, an associated no-flux initial-boundary value problem admits a globally defined generalized solution. This solution inter alia has the property that $$\begin{aligned} u\in L^1_{loc}(\overline{\Omega }\times [0,\infty )). \end{aligned}$$

Nashification and the coordination ratio for a selfish routing game

Abstract: We study the problem of n users selfishly routing traffic through a network consisting of m parallel related links. Users route their traffic by choosing private probability distributions over the links with the aim of minimizing their private latency. In such an environment Nash equilibria represent stable states of the system: no user can improve its private latency by unilaterally changing its strategy. Nashification is the problem of converting any given non-equilibrium routing into a Nash equilibrium without increasing the social cost. Our first result is an O(nm2) time algorithm for Nashification. This algorithm can be used in combination with any approximation algorithm for the routing problem to compute a Nash equilibrium of the same quality. In particular, this approach yields a PTAS for the computation of a best Nash equilibrium. Furthermore, we prove a lower bound of Ω(2√n) and an upper bound of O(2n) for the number of greedy selfish steps for identical link capacities in the worst case. In the second part of the paper we introduce a new structural parameter which allows us to slightly improve the upper bound on the coordination ratio for pure Nash equilibria in [3]. The new bound holds for the individual coordination ratio and is asymptotically tight. Additionally, we prove that the known upper bound of 1+√4m-3/2 on the coordination ratio for pure Nash equilibria also holds for the individual coordination ratio in case of mixed Nash equilibria, and we determine the range of m for which this bound is tight.