منابع مشابه
Computing Beltrami Fields
Abstract. For solving the non-linear equations governing force-free fields, an iterative methodology based on the splitting of the problem is described. On the basis of this splitting, three families of subproblems have to be solved numerically. The first problem consists to find a potential field. A mixed hybrid method is used to solve it. The second problem, which is a curl-div system, is sol...
متن کاملTight Beltrami fields with symmetry.
Tight Beltrami fields with symmetry. Abstract Given a Seifered fibred 3-manifold M equipped with an S 1-invariant contact form α, we provide a bound on the volume Vol(M) and the curvature, in a suitable adapted Riemannian metric to α, which implies universal tightness of the contact structure ξ = ker α.
متن کاملComputing Surface Uniformization Using Discrete Beltrami Flow
In this paper, we propose a novel algorithm for computing surface uniformization for surfaces with arbitrary topology. According to the celebrated uniformization theorem, all Riemann surfaces can be classified as elliptic, parabolic or hyperbolic. Our algorithm is able to work on all these cases by first constructing an initial map onto an appropriate domain, such as sphere, or a polygon in the...
متن کاملOn Beltrami fields with nonconstant proportionality factor on the plane
We consider the equation rot −→ B + α −→ B = 0 (1) in the plane with α being a real-valued function and show that it can be reduced to a Vekua equation of a special form. In the case when α depends on one Cartesian variable a complete system of exact solutions of the Vekua equation and hence of equation (1) is constructed based on L. Bers’ theory of formal powers.
متن کاملAn Index for Closed Orbits in Beltrami Fields
We consider the class of Beltrami fields (eigenfields of the curl operator) on three-dimensional Riemannian solid tori: such vector fields arise as steady incompressible inviscid fluids and plasmas. Using techniques from contact geometry, we construct an integer-valued index for detecting closed orbits in the flow which are topologically inessential (they have winding number zero with respect t...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2009
ISSN: 1064-8275,1095-7197
DOI: 10.1137/070700942