arXiv subjects

Thomas Jahn

Publications and source records attributed to Thomas Jahn.

24 records · Page 2Linked to original sources

arXiv2015

Successive Radii and Ball Operators in Generalized Minkowski Spaces

We investigate elementary properties of successive radii in generalized Minkowski spaces (that is, with respect to gauges), i.e., we measure the "size" of a given convex set in a finite-dimensional real vector space with respect to another convex set. This is done via formulating some kind of minimal containment problems, where intersections or Minkowski sums of the latter set and affine flats of a certain dimension are incorporated. Since this is strongly related to minimax location problems and to the notions of diametrical completeness and constant width, we also have a look at ball intersections and ball hulls.

math.MG↗

arXiv2014

Minsum Location Extended to Gauges and to Convex Sets

One of the oldest and richest problems from continuous location science is the famous Fermat-Torricelli problem, asking for the unique point in Euclidean space that has minimal distance sum to n given (non-collinear) points. Many natural and interesting generalizations of this problem were investigated, e.g., by extending it to non-Euclidean spaces and modifying the used distance functions, or by generalizing the configuration of participating geometric objects. In the present paper, we extend the Fermat-Torricelli problem in a two-fold way: more general than for normed spaces, the unit balls of our spaces are compact convex sets having the origin as interior point (but without symmetry condition), and the n given objects can be general convex sets (instead of points). We combine these two viewpoints, and the presented sequence of new theorems follows in a comparing sense that of theorems known for normed spaces. Some of these results holding for normed spaces carry over to our more general setting, and others not. In addition, we present analogous results for related questions, like, e.g., for Heron's problem. And finally we derive a collection of results holding particularly for the Euclidean norm.

math.MG↗

arXiv2014

On Bisectors in Normed Spaces

In this note, we completely describe the shape of the bisector of two given points in a two-dimensional normed vector space. More precisely, we show that, depending on the position of two given points with respect to the shape of the unit circle, the following holds: the bisector of a non-strict pair of points consists of two cones and a curve, which has properties similar to those of bisectors of strict pairs of points.

math.MG↗

arXiv2014

Phases of spin- and mass-imbalanced ultracold Fermi gases in harmonic traps

We analyze the phase structure of mass- and spin-imbalanced unitary Fermi gases in harmonic traps. To this end, we employ Density Functional Theory in the local density approximation. Depending on the values of the control parameters measuring mass and spin imbalance, we observe that three regions exist in the trap, namely: a superfluid region at the center, surrounded by a mixed region of resonantly interacting spin-up and spin-down fermions, and finally a fully polarized phase surrounding the previous two regions. We also find regimes in the phase diagram where the existence of a superfluid region at the center of the trap is not energetically favored. We point out the limitations of our approach at the present stage, and call for more detailed (ab initio) studies of the equation of state of uniform, mass-imbalanced unitary Fermi gases.

cond-mat.quant-gas↗

arXiv2012

The ERA2 facility: towards application of a fiber-based astronomical spectrograph for imaging spectroscopy in life sciences

Astronomical instrumentation is most of the time faced with challenging requirements in terms of sensitivity, stability, complexity, etc., and therefore leads to high performance developments that at first sight appear to be suitable only for the specific design application at the telescope. However, their usefulness in other disciplines and for other applications is not excluded. The ERA2 facility is a lab demonstrator, based on a high-performance astronomical spectrograph, which is intended to explore the innovation potential of fiber-coupled multi-channel spectroscopy for spatially resolved spectroscopy in life science, material sciences, and other areas of research.

astro-ph.IM↗

arXiv2011

Stability of Constrained Adaptive Model Predictive Control Algorithms

Recently, suboptimality estimates for model predictive controllers (MPC) have been derived for the case without additional stabilizing endpoint constraints or a Lyapunov function type endpoint weight. The proposed methods yield a posteriori and a priori estimates of the degree of suboptimality with respect to the infinite horizon optimal control and can be evaluated at runtime of the MPC algorithm. Our aim is to design automatic adaptation strategies of the optimization horizon in order to guarantee stability and a predefined degree of suboptimality for the closed loop solution. Here, we present a stability proof for an arbitrary adaptation scheme and state a simple shortening and prolongation strategy which can be used for adapting the optimization horizon.

math.OC↗