Accessing Earth System Science Data and Applications Through High-Bandwidth Networks

In this paper, we discuss gigabit network applications enabled by Mission to Planet Earth, an international effort to monitor the Earth as a system. We describe the design of a network architecture to support applications developed as part of this program; introduce a new component, public access resource centers (PARC9s); and discuss how PARC\u27s would facilitate access by users outside the traditional research community. We also describe how a particular class of users, agriculture users, might to Planet Earth program and delivered in a value-added form to them by a so-called AgPARC. The suggested architecture requires the deployment of high-bandwidth networks

𝜔-linear vector fields on manifolds

The classical study of a flow near a fixed point is generalized by composing, at each point in the manifold, the flow derivative with a parallel translation back along the flow. Circumstances under which these compositions form a one-parameter group are studied. From the point of view of the linear frame bundle, the condition is that the canonical lift commute with its horizontal part (with respect to some metric connection). The connection form applied to the lift coincides with the infinitesimal generator of the one-parameter group. Analysis of this matrix provides dynamical information about the flow. For example, if such flows are equicontinuous, they have uniformly bounded derivatives and therefore the enveloping semigroup is a Lie transformation group. Subclasses of ergodic, minimal, and weakly mixing flows with integral invariants are determined according to the eigenvalues of the matrices. Such examples as Lie algebra flows, infinitesimal affine transformations, and the geodesic flows on manifolds of constant negative curvature are examined.</p

Extensions of minimal flows on manifolds

Group extensions of vector field flows for which the orbit closure map forms a fiber bundle are constructed for the case of minimal flows on compact manifolds and compact Lie groups. Conditions for which minimal nontoral extensions exist are studied.</p