Examples of conformal dynamo maps have been presented earlier [Phys Plasmas 14(2007)] where fast dynamos in twisted magnetic flux tubes in Riemannian manifolds were obtained. This paper shows that conformal maps, under the Floquet condition, leads to coincidence between exponential stretching or Lyapunov exponent, conformal factor of fast dynamos. Unfolding conformal dynamo maps can be obtained...

the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

We give necessary and suucient conditions for a conformal foliation locally generated by conformal vector elds to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained. Also we obtain reducibility results for harmonic morphisms induced by (innnitesimal) conformal actions on Einstein manifolds.

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss how this may be extended to superconformal maps of N = 1 superspace with links to superconformal field theory and singular vectors of the N = 1 superconformal...

In this note, we nd an explicit relationship between the dimension spectrum for equilibrium measures and the Lyapunov spectrum for conformal repellers. We explicitly compute the Lyapunov spectrum and show that it is a delta function. We observe that while the Lyapunov exponent exists for almost every point with respect to an ergodic measure, the set of points for which the Lyapunov exponent doe...

The conformal model of Geometric Algebra suggests an intimate connection between mathematics and perception, in particular in the handling of the problem of infinity. The observed properties of phenomenal perspective suggest an extension to Hestenes’ conformal mapping by adding a second conformal stage that maps the infinity of external reality to a finite double conformal map. Mathematics Subj...

Abstract. In this paper we investigate theoretically an approximation technique for avoiding the crowding phenomenon in numerical conformal mapping. The method applies to conformal maps from rectangles to "long quadrilaterals," i.e., Jordan domains bounded by two parallel straight lines and two Jordan arcs, where the two arcs are far apart. We require that these maps take the four corners of th...

In this paper, we tackle the problem of generalizing conformal maps to volumetric meshes. Current methods seek for harmonicity but unfortunately, no computational methods optimize conformality in the volumetric context. As it is proven that conformal maps do not exist for general volume transformations, we seek to optimize shape preservation with a generalization of the CauchyRiemann equations....

By exploiting conformal maps to vertically slit regions in the complex plane, a recently developed rational spectral method [27] is able to solve PDEs with interior layer-like behaviour using significantly fewer collocation points than traditional spectral methods. The conformal maps are chosen to ‘enlarge the region of analyticity’ in the solution: an idea which can be extended to other numeri...