Dreidimensionale optische Tarnkappe realisiert

Tarnkappen, die Menschen unsichtbar machen, galten jahrtausendelang als unerreichbarer Mythos. Unlängst konnten wir am Karlsruhe Institute of Technology gemeinsam mit Kollegen aus London jedoch erstmals eine dreidimensionale optische Tarnkappe herstellen und deren Funktion mit Hilfe eines optischen Mikroskops direkt experimentell nachweisen.     

Instability of FIFO in a simple queueing system with arbitrarily low loads

We show, using a simple example, that the First-In-First-Out (FIFO) policy can be unstable in a system with arbitrarily low load. Our proof is based on the observation that the special structure of the example we use allows us to establish stability using a much simpler queueing system.     

The End Results of General Relativity Theory Via Just Energy Conservation and Quantum Mechanics

Herein we present a whole new approach that leads to the end results of the general theory of relativity via just the law of conservation of energy (broadened to embody the mass and energy equivalence of the special theory of relativity) and quantum mechanics. We start with the following postulate. Postulate: The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this, as much as its binding energy vis-á-vis the gravitational field of concern.     

Experimental and analytical investigation of the mechanics of crawl stroke swimming

A three dimensional analytical model for crawl stroke swimming is developed in which the swimmer is modeled as a body and two arms connected to the body at the shoulder joints. Each arm is assumed to consist of three segments. The numerical results obtained from the model are compared with the results of two sets of experiments performed. In the first series of experiments, the tether forces developed in crawl stroke swimming are measured and a linear correlation between the tether force and the stroke rate is obtained. In the second series of experiments, untethered crawl stroke swimming for different arm position angles is recorded. The results are presented in graphical forms and the effect of stroke rate on swimming velocity is discussed.     

Maßgeschneiderter optischer Raum. Transformationsoptik

Die Transformationsoptik erlaubt Verformungen des optischen Raums, die denen der Raumzeit in der Allgemeinen Relativitätstheorie bei Anwesenheit von Materie ähneln. Von Fata Morganas ist der Effekt kontinuierlich veränderlicher Brechzahlprofile vertraut. Doch erst die Theorie der Transformationsoptik erlaubt die systematische Entwicklung völlig neuer optischer Funktionen. Computersimulationen des Karlsruhe Institute of Technology zeigen, wie eine Tarnkappe und eine kugelförmige Strahlumlenkung funktionieren könnten – zwei Beispiele für die ungeahnten prinzipiellen Möglichkeiten der Transformationsoptik. Die experimentelle Umsetzung im optischen Spektralbereich stellt allerdings noch eine große Herausforderung dar.     

Elliptic open books on torus bundles over the circle

As an application of the construction of open books on plumbed 3-manifolds, we construct elliptic open books on torus bundles over the circle. In certain cases these open books are compatible with Stein fillable contact structures and have minimal genus.      

Supramolecular Architecture in the 1:1 Co-Crystallization of 6,7-Dimethoxy-2-methyl-4-phenylisoquinolinium Cation with Perchlorate Anion

Abstract  X-ray crystallographic analysis of the title organic ion–pair complex, C₁₈H₁₈NO₂ ⁺ · ClO₄ ⁻, reveals that 6,7-dimethoxy-2-methyl-4-phenylisoquinolinium cation is co-crystallized with perchlorate counter-anions in 1:1 ratio. The complex crystallizes in space group P 2 ₁ /n, with a = 8.0226(7) ?, b = 12.2552(7) ?, c = 17.9734(16) ?, β = 93.908(7) °, Z = 4, D _x  = 1.431 g/cm³. Aromaticity of isoquinolinium fragment is considerably deformed by the existence of C–H···O type weak H-bonds, leading to chains of topology C ₃ ³(12)[R ₁²(4)] running along b-axis of the unit cell and pseudo-cyclic centrosymmetric R ₄⁴(24)[2R ₁²(4)] synthons. The weak H-bonds serve to stabilize both the extended structure and molecular geometry of the title complex, in particular the disordered perchlorate anion whose components adopt a distorted tetrahedron. Index Abstract  Molecular and the extended structure of 6,7-dimethoxy-2-methyl-4-phenylisoquinolinium perchlorate, C₁₈H₁₈NO₂ ⁺ · ClO₄ ⁻, were determined by single crystal X-ray diffraction study.     

Vibrational energy relaxation of the OH(D) stretch fundamental of methanol in carbon tetrachloride

The lifetimes of the hydroxyl stretch fundamentals of two methanol isotopomers, MeOH and MeOD, in carbon tetrachloride solvent are calculated through the use of the perturbative Landau-Teller and fluctuating Landau-Teller methods. Examination of these systems allows for insight into the nature of the vibrational couplings that lead to intramolecular vibrational energy transfer. While both systems display energy transfer to nearly degenerate modes, MeOD also displays strong coupling to an off-resonant vibration. The relaxation of MeOH and MeOD occurs through transitions involving a total change in the vibrational quanta of 4 and 3, respectively. We calculate vibrational energy relaxation lifetimes of 4-5 ps for MeOH and 2-3 ps for MeOD that agree well with the experimentally determined values.     

A modelling framework for solving restricted planar location problems using phi-objects

This paper presents a general modelling framework for restricted facility location problems with arbitrarily shaped forbidden regions or barriers, where regions are modelled using phi-objects. Phi-objects are an efficient tool in mathematical modelling of 2D and 3D geometric optimization problems, and are widely used in cutting and packing problems and covering problems. The paper shows that the proposed modelling framework can be applied to both median and centre facility location problems, either with barriers or forbidden regions. The resulting models are either mixed-integer linear or non-linear programming formulations, depending on the shape of the restricted region and the considered distance measure. Using the new framework, all instances from the existing literature for this class of problems are solved to optimality. The paper also introduces and optimally solves a realistic multi-facility problem instance derived from an archipelago vulnerable to earthquakes. This problem instance is significantly more complex than any other instance described in the literature.     

Vibrational relaxation of OH and CH fundamentals of polar and nonpolar molecules in the condensed phase

Studies of vibrational energy flow in various polar and nonpolar molecules that follows the ultrafast excitation of the CH and OH stretch fundamentals, modeled using semiclassical methods, are reviewed. Relaxation rates are calculated using Landau-Teller theory and a time-dependent method, both of which consider a quantum mechanical solute molecule coupled to a classical bath of solvent molecules. A wide range of decay rates are observed, ranging from 1 ps for neat methanol to 50 ps for neat bromoform. In order to understand the flow rates, it is argued that an understanding of the subtle mixing between the solute eigenstates is needed and that solute anharmonicities are critical to facilitating condensed phase vibrational relaxation. The solvent-assisted shifts of the solute vibrational energy levels are seen to play a critical role of enhancing or decreasing lifetimes.