Hamiltonian submanifolds of regular polytopes

We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so-called {\it super-neighborly triangulations}) we focus on the case of the cross polytope and the sporadic regular 4-polytopes. By our results the existence of 1-Hamiltonian surfaces is now decided for all regular polytopes. Furthermore we investigate 2-Hamiltonian 4-manifolds in the $d$-dimensional cross polytope. These are the "regular cases" satisfying equality in Sparla's inequality. In particular, we present a new example with 16 vertices which is highly symmetric with an automorphism group of order 128. Topologically it is homeomorphic to a connected sum of 7 copies of $S^2 \times S^2$. By this example all regular cases of $n$ vertices with $n < 20$ or, equivalently, all cases of regular $d$-polytopes with $d\leq 9$ are now decided.Comment: 26 pages, 4 figure

Low Power Measurements on a Finger Drift Tube Linac

The efficiency of RFQs decreases at particle energies higher than a few MeV/u and thus typically DTL structures are used in this energy region. However, the rf field in the gap always has a defocusing influence on the beam. In order to compensate this effect, fingers with quadrupole symmetry were added to the drift tubes, the focusing fingers do not need an additional power source or feed through. Beam dynamics have been studied with the code RFQSIM. Detailed analysis of the field distribution was done and the geometry of the finger array has been optimized with respect to beam dynamics. A prototype cavity with finger drift tubes was built and low power measurements were done. In this contribution, the results of the rf simulation with Microwave Studio are compared to bead perturbation measurements and the focusing effect on the beam is discussed

Perturbative behaviour of a vortex in a trapped Bose-Einstein condensate

We derive a set of equations that describe the shape and behaviour of a single perturbed vortex line in a Bose-Einstein condensate. Through the use of a matched asymptotic expansion and a unique coordinate transform a relation for a vortex's velocity, anywhere along the line, is found in terms of the trapping, rotation, and distortion of the line at that location. This relation is then used to find a set of differential equations that give the line's specific shape and motion. This work corrects a previous similar derivation by Anatoly A. Svidzinsky and Alexander L. Fetter [Phys. Rev. A \textbf{62}, 063617 (2000)], and enables a comparison with recent numerical results.Comment: 12 pages with 3 figure

Asparaginsäure-vermittelte enzymatische Reaktionen

Die vorliegende Arbeit befasst sich mit der Untersuchung der Promiskuität zweier Enzyme aus unterschiedlichen Proteinklassen, die allerdings auf eine gemeinsame, in der Biochemie sehr häufige Reaktion, die Säure-(Base)-Reaktion, zurückgreifen. Beide Enzyme verwenden die Asparaginsäure als katalytisch aktive Aminosäure, wobei Haloalkan Dehalogenasen aus der alpha/beta-Hydrolase-Familie, die deprotonierte Form der Asparaginsäure als nukleophiles Aspartat verwenden, wohingegen die Squalen-Hopen-Zyklasen die protonierte Asparaginsäure als Brønsted-Säure nutzen. Das Substratspektrum der Dehalogenase LinB aus Sphingobium japonicum, das sonst nur halogenierte Alkane umfasst, sollte um alternative Substrate erweitert werden. Es konnte erfolgreich demonstriert werden, dass LinB eine eindeutige Hydrolyseaktivität gegenüber organischen Thiocyanaten und Isothiocyanaten aufweist, was auf erstmals beschriebene promiskuitive Eigenschaften der LinB schließen lässt. Es konnte gezeigt werden, dass Substrate von unterschiedlicher Größe toleriert werden, um dabei Alkohole und Amine zu generieren. Mittels rationalem Design konnten Varianten erzeugt werden, die eine deutliche Verbesserung gegenüber der Bildung von Benzylamin demonstrierten. Zur Untersuchung der Art der Promiskuität, wurden sogenannte knockout-Mutanten der katalytischen Triade der LinB erstellt und für Studien bezüglich des Katalysemechanismus herangezogen. In der Tat konnte über die einfache Substratpromiskuität hinaus, katalytische Promiskuität der LinB in Bezug auf die organischen Isothiocyanate gezeigt werden. Anhand der Squalen-Hopen-Zyklase aus Alicyclobacillus acidocaldarius (AacSHC) wurden Untersuchungen bezüglich intermolekular katalysierter Reaktionen vorgenommen. Diese Fähigkeit der Etherbildung ist zwar bei der nativen AacSHC anhand des Substrates Farnesol bekannt, allerdings nur in geringem Umfang. So konnte mittels Varianten aus einer fokussierten Mutantenbibliothek eine 10-fache Steigerung der Produktbildung erzielt werden. Ferner konnten unter Verwendung nicht-natürlicher Substrate und unterschiedlicher Nukleophile neue, nicht-literaturbekannte intermolekular gebildete Produkte dargestellt werden. Durch die Wahl des Nukleophils und dessen Konzentration gelang es, Produktverhältnisse eindeutig zu Gunsten der intermolekular gebildeten Produkte zu verschieben.The present study deals with the investigation of the promiscuity of two enzymes from different proteinfamilies, which however draw on a common reaction, the acid (-base)-reaction. Both enzymes use an aspartic acid as catalytically active amino acid: haloalkane dehalogenases from the alpha/beta-hydrolase fold family use the deprotonated form for nucleophilic attack, whereas the squalene-hopene-cyclases use the protonated form as Brønsted-acid. The substrate scope of the dehalogenase LinB from Sphingobium japonicum, which includes only halogenated alkanes so far, should be expanded towards alternative substrates. In this work, it was successfully demonstrated, that LinB exhibits unambiguously hydrolysis-activity towards organic thiocyanates and isothiocyanates, which indicates the promiscuous character of LinB for the first time. Different sizes of substrates where tolerated for generating alcohols and amines. Through rational design, variants could be generated, which showed a significant improvement in formation of benzylamine. To study the type of promiscuity, so-called knockout mutants were created for studies concerning the reaction mechanism. In fact, LinB demonstrated not only substrate promiscuity but additional catalytic promiscuity. With the squalene-hopene-cyclase from Alicyclobacillus acidocaldarius (AacSHC), studies concerning intermolecular catalyzed reactions were performed. AacSHC is known to form ethers through intermolecular linkage, when farnesol is used as substrate, but only to a limited extent. In the present study, a 10-fold increase in product formation with variants of a focused AacSHC mutant library was achieved. Using non-natural substrates and an extended set of nucleophiles, new intermolecular formed products could be generated. Furthermore, it was possible to shift the product distribution clearly in favor of intermolecular formed products only with the choice of the nucleophile and its concentration

Topological Modes in Dual Lattice Models

Lattice gauge theory with gauge group $Z_{P}$ is reconsidered in four dimensions on a simplicial complex $K$. One finds that the dual theory, formulated on the dual block complex $\hat{K}$, contains topological modes which are in correspondence with the cohomology group $H^{2}(\hat{K},Z_{P})$, in addition to the usual dynamical link variables. This is a general phenomenon in all models with single plaquette based actions; the action of the dual theory becomes twisted with a field representing the above cohomology class. A similar observation is made about the dual version of the three dimensional Ising model. The importance of distinct topological sectors is confirmed numerically in the two dimensional Ising model where they are parameterized by $H^{1}(\hat{K},Z_{2})$.Comment: 10 pages, DIAS 94-3

Design Studies of an Electrostatic Storage Ring

Electrostatic storage rings combine a number of very interesting characteristics that make them an attractive tool in the low energy range. In contrast to magnetic rings, all of the fields in an electrostatic storage ring are completely mass independent. At the same particle energy and charge state, ions from light protons to heavy biomolecules can in principal be stored with identical field setups. A small ring for ions of energies up to 50 keV is planned to be built up at Goethe University in Frankfurt. Different designs have been calculated and the results are presented in this contribution. Furthermore, prototypes of the necessary optical elements have been manufactured and are described as well

A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in $d$ dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra

Formation of phase lags at the cyclotron energies in the pulse profiles of magnetized, accreting neutron stars

Context: Accretion-powered X-ray pulsars show highly energy-dependent and complex pulse-profile morphologies. Significant deviations from the average pulse profile can appear, in particular close to the cyclotron line energies. These deviations can be described as energy-dependent phase lags, that is, as energy-dependent shifts of main features in the pulse profile. Aims: Using a numerical study we explore the effect of cyclotron resonant scattering on observable, energy-resolved pulse profiles. Methods: We generated the observable emission as a function of spin phase, using Monte Carlo simulations for cyclotron resonant scattering and a numerical ray-tracing routine accounting for general relativistic light-bending effects on the intrinsic emission from the accretion columns. Results: We find strong changes in the pulse profile coincident with the cyclotron line energies. Features in the pulse profile vary strongly with respect to the average pulse profile with the observing geometry and shift and smear out in energy additionally when assuming a non-static plasma. Conclusions: We demonstrate how phase lags at the cyclotron energies arise as a consequence of the effects of angular redistribution of X-rays by cyclotron resonance scattering in a strong magnetic field combined with relativistic effects. We also show that phase lags are strongly dependent on the accretion geometry. These intrinsic effects will in principle allow us to constrain a system's accretion geometry.Comment: 4 pages, 4 figures; updated reference lis

Compact Cryogenic Source of Periodic Hydrogen and Argon Droplet Beams for Relativistic Laser-Plasma Generation

We present a cryogenic source of periodic streams of micrometer-sized hydrogen and argon droplets as ideal mass-limited target systems for fundamental intense laser-driven plasma applications. The highly compact design combined with a high temporal and spatial droplet stability makes our injector ideally suited for experiments using state-of-the-art high-power lasers in which a precise synchronization between the laser pulses and the droplets is mandatory. We show this by irradiating argon droplets with multi-Terawatt pulses.Comment: To be published in Review of Scientific Instrument

Critical Behaviour of Non-Equilibrium Phase Transitions to Magnetically Ordered States

We describe non-equilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spatial coupling we observe transitions to ferromagnetic or antiferromagnetic ordered states. We discuss the phase diagram, the order of the transitions, and the critical behaviour. For global coupling we show analytically that the critical exponent of the magnetization exhibits a transition from the value 1/2 to a non-universal behaviour depending on the ratio of noise strength to the magnitude of the spatial coupling.Comment: 4 pages, 5 figure