Distribution (differential geometry)

About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.

Differential-Geometric Structures On Manifolds

Abstract: In the present chapter we provide most of the prerequisites for reading the rest of the book. In the first two sections we present a review of vector bundles and introduce the main differential operators: Lie derivative, exterior differential, linear connection, general connection. Distributions on manifolds (known as non-holonomic spaces in classical terminology) are then introduced and studied by using both methods of vector fields and of differential 1-forms. We give here the characterization for the existence of a transversal distribution to a foliation, which is found to be very useful in Chapters 4 and 5 for a general study of lightlike submanifolds. In the last two sections we deal with semi-Riemannian manifolds and lightlike manifolds. While the geometry of a semi-Riemannian manifold is fully developed by using the Levi-Civita connection we stress the role of the radical distribution in studying the geometry of a lightlike manifold. The main formulas and results are expressed by using both the invariant form and the index form.

Ricci flat metrics with bidimensional null orbits and non-integrable orthogonal distribution

Abstract: We study Ricci flat 4-metrics of any signature under the assumption that they allow a Lie algebra of Killing fields with 2-dimensional orbits along which the metric degenerates and whose orthogonal distribution is not integrable. It turns out that locally there is a unique (up to a sign) metric which satisfies the conditions. This metric is of signature (++−−) and, moreover, homogeneous possessing a 6-dimensional symmetry algebra.

Representation of complex probabilities and complex Gibbs sampling

Abstract: Complex weights appear in Physics which are beyond a straightforward importance sampling treatment, as required in Monte Carlo calculations This is the wellknown sign problem The complex Langevin approach amounts to effectively construct a positive distribution on the complexified manifold reproducing the expectation values of the observables through their analytical extension Here we discuss the direct construction of such positive distributions paying attention to their localization on the complexified manifold Explicit localized representations are obtained for complex probabilities defined on Abelian and non Abelian groups The viability and performance of a complex version of the heat bath method, based on such representations, is analyzed

A note on -conformally flat contact manifolds.

Abstract: We prove that a contact manifold with the structure vector field ξ belonging to the k-nullity distribution is ξ -conformally flat if and only if it is an η-Einstein manifold and we give some applications. 2000 Mathematics Subject Classification: 53C15, 53C25

Flow Distribution in U- and Z-Type Manifolds: Experimental and Numerical Investigation

Abstract: Heat exchangers are used to transfer energy from one medium to another and increase contact area for higher efficiency In case of fluids, higher flow area would lead to high/low flow zones that severely affect the fluid dynamics and thermal performance Channels are used to distribute the flow uniformly to fully utilize the whole heat exchanger area The flow uniformity in a flow distribution manifold is dependent on several factors such as flow rate, inlet and exit locations, and the manifold and channel geometrical configuration In the current work, flow distribution measurements were performed using a particle image velocimetry (PIV) technique in two types of rectangular manifolds The experimental results are further verified against the results obtained from numerical modeling with similar trends The flow distribution in U- and Z-type arrangements are evaluated and compared with ten channels incorporated in the design It was found that the flow is more in the channels near the inlet for U-type design, while more near the outlet for the Z-type An increase in the inlet flow rate enhances the flow distribution for the U-type while results in more maldistribution for the Z-type For the U-type, the normalized velocity varies from 134 to 052 in a wide manifold, and between 282 and 018 for a narrow manifold A U-type wider manifold is recommended for all conditions examined in this work since at lower flow rates, both have similar mirrored distribution, while at higher flow rates, U-type manifold has better flow distribution