1,110 research outputs found
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 , we analyze a class of Schr\"odinger operators acting on sections of a vector bundle over a Riemannian manifold where is a Laplace type operator, is an endomorphism field and the potential energy has a non-degenerate minimum at some point . We construct quasimodes of WKB-type near for eigenfunctions associated with the low lying eigenvalues of . These are obtained from eigenfunctions of the associated harmonic oscillator at , acting on smooth functions on the tangent space
Warum rauchen Schizophreniepatienten?
Zusammenfassung: Patienten mit schizophrenen Störungen zeigen eine erhöhte PrĂ€valenz der NikotinabhĂ€ngigkeit. Diese Arbeit beleuchtet die ZusammenhĂ€nge zwischen Schizophrenie und Nikotinkonsum. Es gibt deutliche Hinweise dafĂŒr, dass wesentliche Bereiche kognitiver Funktionen bei Patienten mit schizophrenen Erkrankungen durch Nikotin verbessert werden, insbesondere Daueraufmerksamkeit, gerichtete Aufmerksamkeit, ArbeitsgedĂ€chtnis, KurzzeitgedĂ€chtnis und Wiedergabe aus dem GedĂ€chtnis. Auch konnten in einigen Studien mittels ereigniskorrelierten Potenzialen (P50-Paradigma) und der PrĂ€pulsinhibition des akustisch ausgelösten Schreckreflexes gezeigt werden, dass prĂ€attentive MaĂe 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 AnsĂ€tze 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
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