Measurements of solar vector magnetic fields : proceedings of the MSFC workshop /

Includes bibliographies.

Passive vector turbulence

This thesis consists of three articles on passive vector fields in turbulence. The vector fields interact with a turbulent velocity field, which is described by the Kraichnan model. The effect of the Kraichnan model on the passive vectors is studied via an equation for the pair correlation function and its solutions. The first paper is concerned with the passive magnetohydrodynamic equations. Emphasis is placed on the so called "dynamo effect", which in the present context is understood as an unbounded growth of the pair correlation function. The exact analytical conditions for such growth are found in the cases of zero and infinite Prandtl numbers. The second paper contains an extensive study of a number of passive vector models. Emphasis is now on the properties of the (assumed) steady state, namely anomalous scaling, anisotropy and small and large scale behavior with different types of forcing or stirring. The third paper is in many ways a completion to the previous one in its study of the steady state existence problem. Conditions for the existence of the steady state are found in terms of the spatial roughness parameter of the turbulent velocity field.

Bilateral smoothing of gradient vector field and application to image segmentation

Medical image segmentation finds application in computer-aided diagnosis, computer-guided surgery, measuring tissue volumes, locating tumors, and pathologies. One approach to segmentation is to use active contours or snakes. Active contours start from an initialization (often manually specified) and are guided by image-dependent forces to the object boundary. Snakes may also be guided by gradient vector fields associated with an image. The first main result in this direction is that of Xu and Prince, who proposed the notion of gradient vector flow (GVF), which is computed iteratively. We propose a new formalism to compute the vector flow based on the notion of bilateral filtering of the gradient field associated with the edge map - we refer to it as the bilateral vector flow (BVF). The range kernel definition that we employ is different from the one employed in the standard Gaussian bilateral filter. The advantage of the BVF formalism is that smooth gradient vector flow fields with enhanced edge information can be computed noniteratively. The quality of image segmentation turned out to be on par with that obtained using the GVF and in some cases better than the GVF.

Divergence-free vector-field and reduction

By the Lie symmetry group, the reduction for divergence-free vector-fields (DFVs) is studied, and the following results are found. A n-dimensional DFV can be locally reduced to a (n - 1)-dimensional DFV if it admits a one-parameter symmetry group that is spatial and divergenceless. More generally, a n-dimensional DFV admitting a r-parameter, spatial, divergenceless Abelian (commutable) symmetry group can be locally reduced to a (n - r)-dimensional DFV.

2D PIV measurements in the near field of grid turbulence using stitched fields from multiple cameras

We present measurements of grid turbulence using 2D particle image velocimetry taken immediately downstream from the grid at a Reynolds number of Re M = 16500 where M is the rod spacing. A long field of view of 14M x 4M in the down- and cross-stream directions was achieved by stitching multiple cameras together. Two uniform biplanar grids were selected to have the same M and pressure drop but different rod diameter D and crosssection. A large data set (10 4 vector fields) was obtained to ensure good convergence of second-order statistics. Estimations of the dissipation rate ε of turbulent kinetic energy (TKE) were found to be sensitive to the number of meansquared velocity gradient terms included and not whether the turbulence was assumed to adhere to isotropy or axisymmetry. The resolution dependency of different turbulence statistics was assessed with a procedure that does not rely on the dissipation scale η. The streamwise evolution of the TKE components and ε was found to collapse across grids when the rod diameter was included in the normalisation. We argue that this should be the case between all regular grids when the other relevant dimensionless quantities are matched and the flow has become homogeneous across the stream. Two-point space correlation functions at x/M = 1 show evidence of complex wake interactions which exhibit a strong Reynolds number dependence. However, these changes in initial conditions disappear indicating rapid cross-stream homogenisation. On the other hand, isotropy was, as expected, not found to be established by x/M = 12 for any case studied. © Springer-Verlag 2012.

Multi-Scale Vector-Ridge-Detection for Perceptual Organization Without Edges

We present a novel ridge detector that finds ridges on vector fields. It is designed to automatically find the right scale of a ridge even in the presence of noise, multiple steps and narrow valleys. One of the key features of such ridge detector is that it has a zero response at discontinuities. The ridge detector can be applied to scalar and vector quantities such as color. We also present a parallel perceptual organization scheme based on such ridge detector that works without edges; in addition to perceptual groups, the scheme computes potential focus of attention points at which to direct future processing. The relation to human perception and several theoretical findings supporting the scheme are presented. We also show results of a Connection Machine implementation of the scheme for perceptual organization (without edges) using color.

Bond graph models of DC-DC converters operating in both CCM and DCM

In this paper, Bond Graphs are employed to develop a novel mathematical model of conventional switched-mode DC-DC converters valid for both continuous and discontinuous conduction modes. A unique causality bond graph model of hybrid models is suggested with the operation of the switch and the diode to be represented by a Modulated Transformer with a binary input and a resistor with fixed conductance causality. The operation of the diode is controlled using an if-then function within the model. The extracted hybrid model is implemented on a Boost and Buck converter with their operations to change from CCM to DCM and to return to CCM. The vector fields of the models show validity in a wide operation area and comparison with the simulation of the converters using PSPICE reveals high accuracy of the proposed model, with the Normalised Root Means Square Error and the Maximum Absolute Error remaining adequately low. The model is also experimentally tested on a Buck topology.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

Some results on vector bundle monomorphisms

In this paper we use the singularity method of Koschorke [2] to study the question of how many different nonstable homotopy classes of monomorphisms of vector bundles lie in a stable class and the percentage of stable monomorphisms which are not homotopic to stabilized nonstable monomorphisms. Particular attention is paid to tangent vector fields. This work complements some results of Koschorke [3; 4], Libardi-Rossini [7] and Libardi-do Nascimento-Rossini [6].

Periodic orbits for a class of reversible quadratic vector field on R-3

For a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U-2. More specifically, we prove that for all n is an element of N, there exists epsilon(n) > 0 such that the reversible quadratic polynomial differential systemx = a(0) + a(1y) + a(3y)(2) + a(4Y)(2) + epsilon(a(2x)(2) + a(3xz)),y = b(1z) + b(3yz) + epsilon b(2xy),z = c(1y) +c(4az)(2) + epsilon c(2xz)in R-3, with a(0) < 0, b(1)c(1) < 0, a(2) < 0, b(2) < a(2), a(4) > 0, c(2) < a(2) and b(3) is not an element of (c(4), 4c(4)), for epsilon is an element of (0, epsilon(n)) has at least n periodic orbits near the heteroclinic loop. (c) 2007 Elsevier B.V. All rights reserved.

Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

Necessary conditions of optimality for vector-valued impulsive control problems

A vector-valued impulsive control problem is considered whose dynamics, defined by a differential inclusion, are such that the vector fields associated with the singular term do not satisfy the so-called Frobenius condition. A concept of robust solution based on a new reparametrization procedure is adopted in order to derive necessary conditions of optimality. These conditions are obtained by taking a limit of those for an appropriate sequence of auxiliary standard optimal control problems approximating the original one. An example to illustrate the nature of the new optimality conditions is provided. © 2000 Elsevier Science B.V. All rights reserved.

Sobre a estabilidade estrutural e regularizações de campos de vetores descontínuos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Visualization of flow fields in the web platform

Visualization of vector fields plays an important role in research activities nowadays -- Web applications allow a fast, multi-platform and multi-device access to data, which results in the need of optimized applications to be implemented in both high-performance and low-performance devices -- Point trajectory calculation procedures usually perform repeated calculations due to the fact that several points might lie over the same trajectory -- This paper presents a new methodology to calculate point trajectories over highly-dense and uniformly-distributed grid of points in which the trajectories are forced to lie over the points in the grid -- Its advantages rely on a highly parallel computing architecture implementation and in the reduction of the computational effort to calculate the stream paths since unnecessary calculations are avoided, reusing data through iterations -- As case study, the visualization of oceanic currents through in the web platform is presented and analyzed, using WebGL as the parallel computing architecture and the rendering Application Programming Interface

Visualisation of groundwater flow using texture based visualisation techniques

Texture based techniques for visualisation of unsteady vector fields have been applied for the visualisation of a Finite volume model for variably saturated groundwater flow through porous media. This model has been developed by staff in the School of Mathematical Sciences QUT for the study of salt water intrusion into coastal aquifers. This presentation discusses the implementation and effectiveness of the IBFV algorithm in the context of visualisation of the groundwater simulation outputs.