Path integrals on manifolds with boundary

We give time-slicing path integral formulas for solutions to the heat equation corresponding to a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold with boundary. More specifically, we show that such a solution can be approximated by integrals over finite-dimensional path spaces of piecewise geodesics subordinated to increasingly fine partitions of the time interval. We consider a subclass of mixed boundary conditions which includes standard Dirichlet and Neumann boundary conditions.Comment: 23 pages, to appear in Comm. Math. Phy

Strong short-time asymptotics and convolution approximation of the heat kernel

We give a short proof of a strong version of the short-time asymptotic expansion of heat kernels associated with Laplace-type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this to show that repeated convolution of the approximate heat kernels can be used to approximate the heat kernel on all of M, which is related to expressing the heat kernel as a path integral. This scheme is then applied to obtain a short-time asymptotic expansion of the heat kernel at the cut locu

Pressure Drop Across Woven Screens Under Uniform and Nonuniform Flow Conditions

Tests were conducted to determine the experimental pressure drop and velocity data for water flowing through woven screens. The types of materials used are dutch twill and square weave fabrics. Pressure drop measures were made at four locations in a rectangular channel. The data are presented as change in pressure compared with the average entry velocity and the numerical relationship is determined by dividing the volumetric flow rate by the screen area open to flow. The equations of continuity and momentum are presented. A computer program listing an extension of a theoretical model and data from that computer program are included

The Chern character of {\theta}-summable Fredholm modules over dg algebras and localization on loop space

We introduce the notion of a {\vartheta}-summable Fredholm module over a locally convex dg algebra {\Omega} and construct its Chern character as a cocycle on the entire cyclic complex of {\Omega}, extending the construction of Jaffe, Lesniewski and Osterwalder to a differential graded setting. Using this Chern character, we prove an index theorem involving an abstract version of a Bismut-Chern character constructed by Getzler, Jones and Petrack in the context of loop spaces. Our theory leads to a rigorous construction of the path integral for N=1/2 supersymmetry which satisfies a Duistermaat-Heckman type localization formula on loop space

Asymptotic eigenfunctions for Schrödinger operators on a vector bundle

In the limit $\hbar\to 0$, we analyze a class of Schr\"odinger operators $H_\hbar = \hbar^2 L + \hbar W + V\cdot \mathrm{id}$ acting on sections of a vector bundle $\mathcal{Eh}$ over a Riemannian manifold $M$ where $L$ is a Laplace type operator, $W$ is an endomorphism field and the potential energy $V$ has a non-degenerate minimum at some point $p\in M$. We construct quasimodes of WKB-type near $p$ for eigenfunctions associated with the low lying eigenvalues of $H_\hbar$. These are obtained from eigenfunctions of the associated harmonic oscillator $H_{p, \hbar}$ at $p$, acting on smooth functions on the tangent space

Warum rauchen Schizophreniepatienten?

Zusammenfassung: Patienten mit schizophrenen Störungen zeigen eine erhöhte Prävalenz der Nikotinabhängigkeit. Diese Arbeit beleuchtet die Zusammenhänge zwischen Schizophrenie und Nikotinkonsum. Es gibt deutliche Hinweise dafür, dass wesentliche Bereiche kognitiver Funktionen bei Patienten mit schizophrenen Erkrankungen durch Nikotin verbessert werden, insbesondere Daueraufmerksamkeit, gerichtete Aufmerksamkeit, Arbeitsgedächtnis, Kurzzeitgedächtnis und Wiedergabe aus dem Gedächtnis. Auch konnten in einigen Studien mittels ereigniskorrelierten Potenzialen (P50-Paradigma) und der Präpulsinhibition des akustisch ausgelösten Schreckreflexes gezeigt werden, dass präattentive Maße der Informationsverarbeitung, die eine zentrale Rolle in der Schizophrenie spielen, durch Gabe von Nikotin verbessert werden können. Weiterhin kann Rauchen die durch antipsychotische Medikamente hervorgerufenen extrapyramidalen Nebenwirkungen verbessern, und es induziert das Zytochrom P4501A2, das auch an der Metabolisierung einiger Neuroleptika beteiligt ist. Zusammenfassend kann festgestellt werden, dass die Nikotinzufuhr bei Patienten mit schizophrenen Störungen eine Form der "Selbstmedikation" darstellen könnte, um Defizite im Bereich Aufmerksamkeit, Kognition und Informationsverarbeitung zu verbessern und um Nebenwirkungen von Antipsychotika zu reduzieren. Mögliche pharmakotherapeutische Ansätze zur Behandlung der gestörten Neurotransmission am nikotinergen Azetylcholinrezeptor werden diskutier

Bouncing trimer: a random self-propelled particle, chaos and periodical motions

A trimer is an object composed of three centimetrical stainless steel beads equally distant and is predestined to show richer behaviours than the bouncing ball or the bouncing dimer. The rigid trimer has been placed on a plate of a electromagnetic shaker and has been vertically vibrated according to a sinusoidal signal. The horizontal translational and rotational motions of the trimer have been recorded for a range of frequencies between 25 and 100 Hz while the amplitude of the forcing vibration was tuned for obtaining maximal acceleration of the plate up to 10 times the gravity. Several modes have been detected like e.g. rotational and pure translational motions. These modes are found at determined accelerations of the plate and do not depend on the frequency. By recording the time delays between two successive contacts when the frequency and the amplitude are fixed, a mapping of the bouncing regime has been constructed and compared to that of the dimer and the bouncing ball. Period-2 and period-3 orbits have been experimentally observed. In these modes, according to observations, the contact between the trimer and the plate is persistent between two successive jumps. This persistence erases the memory of the jump preceding the contact. A model is proposed and allows to explain the values of the particular accelerations for which period-2 and period-3 modes are observed. Finally, numerical simulations allow to reproduce the experimental results. That allows to conclude that the friction between the beads and the plate is the major dissipative process.Comment: 22 pages, 10 figure

Seroprevalence of Toxoplasma gondii in German swine herds

The protozoan parasite Toxoplasma (T) gondii is prevalent worldwide and 1s found in a wide range of warm-blooded hosts mcluding humans. Raw and undercooked pork con taming tissue cysts is an important cause of the T. gondii- infection in humans. The aim of our study was to investigate the occurence of T. gondii-antibodies in German swine herds

Dimensional Crossover in Bragg Scattering from an Optical Lattice

We study Bragg scattering at 1D optical lattices. Cold atoms are confined by the optical dipole force at the antinodes of a standing wave generated inside a laser-driven high-finesse cavity. The atoms arrange themselves into a chain of pancake-shaped layers located at the antinodes of the standing wave. Laser light incident on this chain is partially Bragg-reflected. We observe an angular dependence of this Bragg reflection which is different to what is known from crystalline solids. In solids the scattering layers can be taken to be infinitely spread (3D limit). This is not generally true for an optical lattice consistent of a 1D linear chain of point-like scattering sites. By an explicit structure factor calculation we derive a generalized Bragg condition, which is valid in the intermediate regime. This enables us to determine the aspect ratio of the atomic lattice from the angular dependance of the Bragg scattered light.Comment: 4 pages, 5 figure