1,733,991 research outputs found
Spectral Processing of Tangential Vector Fields
No full textWe propose a framework for the spectral processing of tangential vector fields on surfaces. The basis is a Fourier‐type representation of tangential vector fields that associates frequencies with tangential vector fields. To implement the representation for piecewise constant tangential vector fields on triangle meshes, we introduce a discrete Hodge–Laplace operator that fits conceptually to the prominent discretization of the Laplace–Beltrami operator. Based on the Fourier representation, we introduce schemes for spectral analysis, filtering and compression of tangential vector fields. Moreover, we introduce a spline‐type editor for modelling of tangential vector fields with interpolation constraints for the field itself and its divergence and curl. Using the spectral representation, we propose a numerical scheme that allows for real‐time modelling of tangential vector fields.We propose a framework for the spectral processing of tangential vector fields on surfaces. The basis is a Fourier‐type representation of tangential vector fields that associates frequencies with tangential vector fields. To implement the representation for piecewise constant tangential vector fields on triangle meshes, we introduce a discrete Hodge–Laplace operator that fits conceptually to the prominent discretization of the Laplace–Beltrami operator. Based on the Fourier representation, we introduce schemes for spectral analysis, filtering and compression of tangential vector fields.Computer Graphics ForumArticles36
Avoiding ergodicity and turbulence in R-3 vector fields
No full textWe show that analytic R-3 vector fields having the property of being transversal to either analytic functions or foliations F-2, or parallel. to a foliation, are free from ergodicity and turbulence. The absence of turbulence and ergodicity via induced vector fields is also proven.Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu
Lagrangian flows for vector fields with gradient given by a singular integral
Full text linkWe prove quantitative estimates on ows of ordinary di�erential equations with vector �field with gradient given by a singular integral of an L1 function. Such estimates allow to prove existence, uniqueness, quantitative stability and compactness for the flow, going beyond the BV theory. We illustrate the related well-posedness theory of Lagrangian solutions to the continuity and transport equations
A uniqueness result for the continuity equation in two dimensions
Full text linkWe characterize the autonomous, divergence-free vector fields on the plane such that the Cauchy problem for the continuity equation admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential associated to .
As a corollary we obtain uniqueness under the assumption that the curl of is a measure. This result can be extended to certain non- autonomous vector fields with bounded divergence
Geometry of conformal vector fields
No full textAbstractIt is well known that the Euclidean space (Rn,〈,〉), the n-sphere Sn(c) of constant curvature c and Euclidean complex space form (Cn,J,〈,〉) are examples of spaces admitting conformal vector fields and therefore conformal vector fields are used in obtaining characterizations of these spaces. In this article, we study the conformal vector fields on a Riemannian manifold and present the existing results as well as some new results on the characterization of these spaces. Taking clue from the analytic vector fields on a complex manifold, we define φ-analytic conformal vector fields on a Riemannian manifold and study their properties as well as obtain characterizations of the Euclidean space (Rn,〈,〉) and the n-sphere Sn(c) of constant curvature c using these vector fields
The natural operators lifting vector fields to (J\sp rT\sp *)\sp *
No full textsummary:For integers and a complete classification of all natural operators lifting vector fields to vector fields on the natural bundle dual to -jet prolongation of the cotangent bundle over -manifolds is given
Nil-Killing vector fields and Kundt structures
Full text linkThis thesis is based on three papers, for which two have been submitted for publication and one is published. A chapter presenting relevant background material is included giving convenient access to preliminary foreknowledge for the papers. The research for which the thesis and papers are based concerns Nil-Killing vector fields, which generalize Killing vector fields in the sense that the Lie derivative of the metric is nilpotent. We study their properties and find that they form infinitesimal automorphisms of certain G-structures. Based on this we are able to express Kundt spacetimes in terms of G-structures, giving new tools for their investigation
Complete algebraic vector fields on Danielewski surfaces
Full text linkWe give the classification of all complete algebraic vector fields on Danielewski surfaces (smooth surfaces given by xy=p(z)). We use the fact that for each such vector field there exists a certain fibration that is preserved under its flow. In order to get the explicit list of vector fields a classification of regular function with general fiber ℂ or ℂ * is required. In this text we present results about such fibrations on Gizatullin surfaces and we give a precise description of these fibrations for Danielewski surfaces
Lifting of projectable vector fields to vertical fiber product preserving vector bundles
Full text linksummary:We classify all natural operators lifting projectable vector fields from fibered manifolds to vector fields on vertical fiber product preserving vector bundles. We explain this result for some more known such bundles
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