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.

Invariance for Single Curved Manifold

Abstract: Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects.

A convexity theorem for torus actions on contact manifolds

Abstract: We show that the cone associated with a moment map for an action of a torus on a contact compact connected manifold is a convex polyhedral cone and that the moment map has connected fibers provided the dimension of the torus is bigger than 2 and that no orbit is tangent to the contact distribution. This may be considered as a version of the Atiyah - Guillemin - Sternberg convexity theorem for torus actions on symplectic cones and as a direct generalization of the convexity theorem of Banyaga and Molino for completely integrable torus actions on contact manifolds.

Chapter 19 – Subsea Manifolds

Abstract: Publisher Summary This chapter discusses the issues and standards related to the design, manufacture, and testing of subsea manifolds. Requirements for individual components such as valves, actuators, and piping will also be detailed. The discussion includes the following contents: manifold components; manifold design and analysis; foundation and suction pile; and installation and maintenance. Subsea manifolds are an integral part of many subsea developments that provides effective gathering and distribution points for subsea systems. The manifolds are designed in various configurations, such as template or cluster manifolds with internal or external pigging loops, horizontal or vertical connectors. Subsea manifolds are installed on the seabed within an array of wells to gather product or to inject water or gas into wells. There are numerous types of manifolds, ranging from a simple pipeline end manifold (PLEM/PLET) to large structures such as an entire subsea process system. A PLEM is one of the most common manifolds in this range. A subsea manifold system is structurally independent from the wells. The wells and pipelines are connected to the manifold by jumpers. The subsea manifold system is mainly comprised of a manifold and a foundation. The manifold support structure is an interface between the manifold and foundation. It provides necessary facilities to guide, level, and orient the manifold relative to the foundation. The connection between the manifold and the manifold supporting structure allows the manifold to retrieve and reinstall with sufficient accuracy so as to allow for the subsequent reuse of the production and well jumpers.

State-Space Models on the Stiefel Manifold with A New Approach to Nonlinear Filtering

Abstract: We develop novel multivariate state-space models wherein the latent states evolve on the Stiefel manifold and follow a conditional matrix Langevin distribution. The latent states correspond to time-varying reduced rank parameter matrices, like the loadings in dynamic factor models and the parameters of cointegrating relations in vector error-correction models. The corresponding nonlinear filtering algorithms are developed and evaluated by means of simulation experiments.

The Computation of Two-Dimensional Manifold for Hindmarsh-Rose Neuron Model

Abstract: The Hind marsh-Rose (HR) Neuron not only contained the features of cell biological physical model, but also included the traits of non-linear dynamical system model. The paper analyzed the HR model by computing manifold. It computed the equilibria, simulated the bifurcation phenomenon of the parameters, estimated the unstable local manifold and computed the global manifold using the angle constraint method. The simulation results showed the trend of the unstable manifold and the distribution of the trajectories. It offered good results to study the chaos phenomenon of the HR mode.