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.

Five dimensional cosmological models in Lyra geometry with time dependent displacement field

Abstract: In this paper exact solutions of the five-dimensional vacuum cosmological field equations based on Lyra geometry are obtained. Further it is shown that neither dust distribution nor perfect fluid distributions survive for the model. Some properties of the vacuum model are also discussed.

Attainment of flowrate uniformity in the channels that link a distribution manifold to a collection manifold

Abstract: A logic-based systematic method of designing manifold systems to achieve flowrate uniformity among the channels that interconnect a distribution manifold and a collection manifold has been developed, implemented, and illustrated by case studies. The method is based on tailoring the flow resistance of the individual channels to achieve equal pressure drops for all the channels. The tailoring of the flow resistance is accomplished by the use of gate-valve-like obstructions. The adjustment of the valve-like obstructions is determined here by means of numerical simulations. Although the method is iterative, it may converge in one cycle of the iterations. Progress toward the goal of per channel uniformity can be accelerated by tuning a multiplicative constant. The only departure of the method from being fully automatic is the selection of the aforementioned multiplicative constant. The method is described in detail in a step-by-step manner. These steps are illustrated both generically and specifically for four case studies. As an example, in one of the case studies, an original flow imbalance of over 100% in an untailored manifold system was reduced to a flow imbalance of less than 10% in one cycle of the method.

Euclidean action and the thermodynamics of manifolds without boundary.

Abstract: I consider general, spherically symmetric spacetimes with cosmological and black-hole horizons. I find that a state of thermal equilibrium may exist in classical manifolds with two horizons as long as a matter distribution is present. The Euclidean action is calculated for general (nonclassical) manifolds without boundary. It is found to equal the grand canonical weighting factor for a spacetime with zero mean thermal energy. I also consider how the Euclidean action is modified by the imposition of fixed-temperature shells in the manifold. I find that the mean thermal energy of the cosmological horizon is negative.

Deforming metrics of foliations

Abstract: Let M be a Riemannian manifold equipped with two complementary orthogonal distributions D and D ⊥. We introduce the conformal flow of the metric restricted to D with the speed proportional to the divergence of the mean curvature vector H, and study the question: When the metrics converge to one for which D enjoys a given geometric property, e.g., is harmonic, or totally geodesic? Our main observation is that this flow is equivalent to the heat flow of the 1-form dual to H, provided the initial 1-form is D ⊥-closed. Assuming that D ⊥ is integrable with compact and orientable leaves, we use known long-time existence results for the heat flow to show that our flow has a solution converging to a metric for which H = 0; actually, under some topological assumptions we can prescribe the mean curvature H.

Manifold system for enabling a distribution of fluids

Abstract: A manifold system for incorporation in a gas panel distribution system for semi-conductor manufacturing includes a plurality of individual manifold blocks with each manifold block having a fluid passageway with an entrance and exit port accessing a common surface. Adjacent manifold blocks are removably interconnected to permit the respective fluid passageways to be in position for interconnection. A plurality of active components can be sealingly fastened to the individual manifold blocks to complete the interconnection of the respective fluid passageways. Each active component can bridge over a pair of adjacent individual manifold blocks and form with the individual manifold blocks an operative gas stick for delivering gas to a semiconductor tool. The individual manifold blocks can be identical in configuration and can include a first upper flange on one side and a second lower flange on an opposite side to enable an interlocking of adjacent manifold blocks.