Hyperflächen in Finslerschen Räumen als Transversalflächen einer Schar von Extremalen

Ohne ZusammenfassungDiese Arbeit ist meiner am 27. März 1935 der Deutschen Universität in Prag eingereichten Dissertation entnommen. Im folgenden beziehen sich lateinische Indizes stets auf den Raum und laufen von 1 bisn; griechische Indizes beziehen sich auf die Hyperfläche und nehmen die Werte 1, 2, ...,n–1 an.     

Three-dimensional polarization-independent visible-frequency carpet invisibility cloak

We miniaturize all features in a previously introduced polarization-independent three-dimensional carpet invisibility cloak by more than a factor of 2. This leads to operation wavelengths in the visible. The structures are characterized by electron and optical microscopy. In contrast to our previous work at IR wavelengths, we can directly measure two-dimensional images at visible frequencies, perform control experiments from the backside, and compare the images with theory. We find excellent agreement. Furthermore, we study the wavelength dependence in the range from 900 nm down to 500 nm. Cloaking action deteriorates as the woodpile stop band at around 575 nm is approached.     

An adaptive moving mesh approach for hyperbolic conservation laws on time-dependent domains

The general idea of moving mesh approaches is to improve the approximation quality and the numerical performance by redistributing a fixed number of discretization points. This is called rrefinement. The classical approaches are applied to partial differential equations on fixed domains. An extension to time-dependent (expanding) domains is presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the role of reachability and observability in NMR experimentation

It is shown that the system theoretic concepts of reachability and observability are relevant to the analysis of NMR experiments. Moreover, the sets of reachable states are examined and Lie theoretic criteria are given for the reachability of the system. The question is investigated how the set of reachable states depends on the class of input functions that are allowed. Both one‐dimensional and multi‐dimensional NMR experiments are considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Small-dimensional linear programming and convex hulls made easy

We present two randomized algorithms. One solves linear programs involvingm constraints ind variables in expected timeO(m). The other constructs convex hulls ofn points in ℝ ^d ,d>3, in expected timeO(n ^[d/2]). In both boundsd is considered to be a constant. In the linear programming algorithm the dependence of the time bound ond is of the formd!. The main virtue of our results lies in the utter simplicity of the algorithms as well as their analyses. Large portions of the research reported here were conducted while the author visited DIMACS at Princeton University. The author was supported by NSF Presidential Young Investigator Award CCR-9058440.     

Realization of a three-functional-layer negative-index photonic metamaterial

We modify a recently theoretically suggested multilayer negative-index photonic metamaterial design and fabricate corresponding structures with up to three functional layers (seven actual layers) for the first time to our knowledge. Measured transmittance and reflectance spectra agree well with theory.     

Designing Molecular Printboards: A Photolithographic Platform for Recodable Surfaces

A light induced strategy for the design of β‐cyclodextrin (CD) based supramolecular devices is introduced, presenting a novel tool to fabricate multifunctional biointerfaces. Precision photolithography of a modified β‐CD was established on a light sensitive tetrazole surface immobilized on a bioinspired polydopamine (PDA) anchor layer via various shadow masks, as well as via direct laser writing (DLW), in order to craft any desired printboard design. Interfacial molecular recognition provided by light generated cavitate domains was demonstrated via spatially resolved encoding, erasing, and recoding of distinct supramolecular guest patterns. Thus, the light directed shaping of receptor monolayers introduces a powerful path to control supramolecular assemblies on various surfaces.     

Mass transfer enhancement at deformable droplets due to Marangoni convection

One of the key design parameters in liquid/liquid extraction is the mass transfer coefficient. A complex list of parameters including fluid dynamics, drop size distribution, chemical properties of the involved species, local interfacial instabilities (Marangoni convection) is required in order to determine the transient evolution of the mass transfer coefficient. The influence of Marangoni convection on single drop mass transfer cannot yet be described in an analytical manner, and empirical correlations available in literature fail to predict the mass transfer process. In the present study, experimental investigations on deformable single droplets in the toluene/acetone/water system are presented which shows strong interfacial instabilities. Parameters varied are the drop diameter, the initial solute concentration and the mass transfer direction. Experimental results are compared with the well-known models by Kronig and Brink and Handlos and Baron. The Kronig and Brink model cannot describe Marangoni dominated systems, but comparisons reveal the influence of deformation on the mass transfer enhancement. In contrary, with a slight modification to the Handlos and Baron model, the mean droplet concentration of the transferred component was successfully modelled as a function of Fourier number.