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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.
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TL;DR: In this paper, the authors provide cohomological description of the structure of these curvature invariants in the cases where the background structure is one of the parabolic geometries.
Abstract: Each sub-Riemannian geometry with bracket generating distribution enjoys a background structure determined by the distribution itself. At the same time, those geometries with constant sub-Riemannian symbols determine a unique Cartan connection leading to their principal invariants. We provide cohomological description of the structure of these curvature invariants in the cases where the background structure is one of the parabolic geometries. As an illustration, constant curvature models are discussed for certain sub-Riemannian geometries.
2 citations
09 Sep 2020
TL;DR: In this article, a three-dimensional solid oxide fuel cell stack numerical model was developed and validated by experimental data, and the stack polarization curve, current density, temperature, and flow distributions were analyzed.
Abstract:
In this study, a three-dimensional solid oxide fuel cell stack numerical model was developed and validated by experimental data. Five-cell SOFC stacks with different inlet and outlet manifold arrangement were investigated employing the numerical model. The stack polarization curve, current density, temperature, and flow distributions were analyzed. The results show that the effect of different manifold arrangement is almost neglected on the polarization curves and flow distribution. However, the current density and temperature distribution in individual unit of the stack can be influenced by the locations of inlets and outlets in the manifolds. Considering current density and temperature distribution uniformity as well as ease manufacturing and installation, the manifold arrangement with inlets at the top and outlets at the bottom for both fuel and air is recommended for SOFC stacks.
2 citations
TL;DR: The Vessiot theory automatically transforms an implicit differential equation into a vector field distribution on a manifold and thus reduces its analysis to standard problems in dynamical systems theory like the integration of a vectors field and the determination of invariant manifolds.
Abstract: We discuss how the geometric theory of differential equations can be used for the numerical integration and visualisation of implicit ordinary differential equations, in particular around singularities of the equation. The Vessiot theory automatically transforms an implicit differential equation into a vector field distribution on a manifold and thus reduces its analysis to standard problems in dynamical systems theory like the integration of a vector field and the determination of invariant manifolds. For the visualisation of low-dimensional situations we adapt the streamlines algorithm of Jobard and Lefer to 2.5 and 3 dimensions. A concrete implementation in Matlab is discussed and some concrete examples are presented.
2 citations
TL;DR: In this article, the authors studied some links between autoparallel distributions and the factorization of a riemannian manifold and proved a splitting theorem for Lie groups with bi-invariant metrics.
Abstract: We study some links between autoparallel distributions and the factorization of a riemannian manifold. Finally, we prove a splitting theorem for Lie groups with biinvariant metrics.
2 citations