2009/11/01 by L Garcia de Andrade, de Andrade, L Garcia
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Geomagnetism and Paleomagnetism Studies #Geophysics and Gravity Measurements #Solar and Space Plasma Dynamics #math-ph #math.MP #msc:14J32
paper · pdf · doi:10.48550/arxiv.0911.0218
arxiv created 2009/11/01 · arxiv updated 2009/12/01
Earlier, Chicone, Latushkin and Montgomery-Smith [Comm Math Phys (1997)] have proved the existence of a fast dynamo operator, in compact two-dimensional manifold, as long as its Riemannian curvature be constant and negative. More recently Gallet and Petrelis [Phys Rev E, 80 (2009)] have investigated saddle-node bifurcation, in turbulent dynamos as modelling for magnetic field reversals. Since saddle nodes are created in hyperbolic flows, this provides us with physical motivation to investigate these reversals in a simple kinematic dynamo model obtained from a force-free non-geodesic steady flow in Lobachevsky plane. Magnetic vector potential grows in one direction and decays in the other under diffusion. Magnetic field differential 2-form is orthogonal to the plane. A restoring forcing dynamo in hyperbolic space is also given. Magnetic field reversals are obtained from this model. Topological entropies [Klapper and Young, Comm Math Phys (1995)] are also computed.