We present a technique called ow surface probes for interactive visualization of 3D steady vector elds. The user places in the ow eld an arbitrarily-shaped seed surface, which is then deformed over time by the local or global 3D vector eld, producing an animation sequence. This sequence and individual frames are used to probe the behavior of the ow eld.

Geometric methods from dynamical systems are used to study Lagrangian transport in numerically-generated, time-dependent, two-dimensional vector elds. The ows analyzed here are numerical solutions to the barotropic, -plane, potential vorticity equation with viscosity, where the pde parameters have been chosen so that the solution evolves to a meandering jet. Numerical methods for approximating ...

We introduce a systematic approach to the design, implementation and analysis of left-invariant evolution schemes acting on Gabor transform, primarily for applications in signal and image analysis. Within this approach we relate operators on signals to operators on Gabor transforms. In order to obtain a translation and modulation invariant operator on the space of signals, the corresponding ope...

In this paper, we prove that a linear action of a reductive group on a polynomial ring with good ltrations over a eld of characteristic p > 0 yields a strongly F-regular (in particular, Cohen-Macaulay) invariant subring. The strongly F-regular property of some known examples of invariant subrings, such as the coordinate rings of Schubert varieties in Grassmannians, are recovered. A similar resu...

We provide the explicit solutions of linear, left-invariant, diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = R T. These parabolic equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by group convolution with the corresponding Green’s functions...

We provide the explicit solutions of linear, left-invariant, diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = R T. These parabolic equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by group convolution with the corresponding Green’s functions...

We present a technique called ow surface probes for interactive visualization of 3D steady vector elds. The user places in the ow eld an arbitrarily-shaped seed surface, which is then deformed over time by the local or global 3D vector eld, producing an animation sequence. This sequence and individual frames are used to probe the behavior of the ow eld.

Consider a nite n dimensional space with an n dimensional vector S com pletely describes the state in which a nonlinear system resides to know the vector of state changes is a complete representation of the system dynamics provided it is deterministic and of rst order The totality of all state changes form a vector eld that contains the entire system dynamics A trajectory in state space is form...

This study presents cross-sectional vector maps of the magnetic ®eld derived from IMP 8 magnetometer in the magnetosheath at 30 Re behind the Earth. In addition the vector patterns of the magnetosheath ®eld for northward, southward, and east-west interplanetary magnetic ®eld (IMF) directions are qualitatively compared with those obtained from the Spreiter-Stahara gas dynamic (GD) and Fedder-Lyo...