Stretch fast dynamo mechanism via conformal mapping in Riemannian manifolds

Garcia de Andrade

Home/Archive/arXiv

arXiv · 0708.0693

Stretch fast dynamo mechanism via conformal mapping in Riemannian manifolds

Garcia de Andrade

View original source ↗Read source document ↗Export metadata ↓

Abstract

Two new analytical solutions of self-induction equation, in Riemannian manifolds are presented. The first represents a twisted magnetic flux tube or flux rope in plasma astrophysics, which shows that the depending on rotation of the flow the poloidal field is amplified from toroidal field which represents a dynamo. The value of the amplification depends on the Frenet torsion of the magnetic axis of the tube. Actually this result illustrates the Zeldovich stretch, twist and fold (STF) method to generate dynamos from straight and untwisted ropes. Motivated by the fact that this problem was treated using a Riemannian geometry of twisted magnetic flux ropes recently developed (Phys Plasmas (2006)), we investigated a second dynamo solution which is conformally related to the Arnold kinematic fast dynamo. In this solution it is shown that the conformal effect on the fast dynamo metric only enhances the Zeldovich stretch, and therefore a new dynamo solution is obtained. When a conformal mapping is performed in Arnold fast dynamo line element a uniform stretch is obtained in the original line element.

Explore related subjects

math-ph math.MP

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Garcia de Andrade. 2007-08-05. Stretch fast dynamo mechanism via conformal mapping in Riemannian manifolds. https://arxiv.org/abs/0708.0693

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Construction of Gross-Neveu model using Polchinski flow equation

We develop a new method for solving the renormalization group flow equation, also known as the Polchinski equation, by formulating it as a well-posed infinite-dimensional partial differential equation on a Banach space. This yields the first direct construction of a solution of this equation via a fixed point argument, circumventing the need for perturbative or expansion-based techniques employed in earlier work. Our approach leverages recent advances in noncommutative probability theory, particularly a scale decomposition of the free fermionic field in a filtered noncommutative probability space equipped with a suitable conditional expectation. As a key application, we construct the Gross-Neveu model, a fermionic, asymptotically free, and scaling-critical quantum field theory. We rigorously establish convergence of the Schwinger functions as the cutoff is removed, and construct a random field on the noncommutative probability space of the free theory whose moments coincide with the Schwinger functions. This provides the first explicit strong coupling between the free and interacting fields for a scaling-critical quantum field theory. The method is expected to apply broadly to other critical or subcritical quantum field theories formulated in terms of bounded fields, including fermionic models such as the symplectic fermion model, as well as certain bosonic theories like the sine-Gordon model.

math-ph↗

arXiv2026

Generalized Dirac Equation in Metric-Affine Spacetimes: Consistency, Effective Mass, and Spinor Curvature

We formulate a generalized Dirac equation in four-dimensional metric-affine spacetimes with curvature, torsion, and non-metricity. The spinor connection is expanded over the complete basis of the Clifford algebra $cl(1,3)$ and contains eight complex coupling constants. Requiring agreement between direct covariantization of the Dirac equation and variation of the corresponding symmetrized Lagrangian imposes eight real consistency conditions, reducing the number of independent real parameters from sixteen to eight. In the static isotropic symmetric teleparallel sector, formal Hermiticity of the Hamiltonian with respect to the curved-space Dirac inner product reproduces the corresponding restrictions on the non-metricity and coframe couplings. The coframe-dependent terms introduce scalar and pseudoscalar mass contributions that persist in Minkowski spacetime. For a single free Dirac field with constant coefficients, they yield one effective mass, $m_{\mathrm{eff}}=\sqrt{(m-4b_3)^2+16b_4^2}$, and a chiral phase removable by a constant chiral field redefinition. A nonzero effective mass is therefore possible even when the original mass parameter vanishes. We also derive the Clifford decomposition of the generalized spinor curvature and show that it can remain nonzero when affine curvature, torsion, and non-metricity all vanish. When $m=0$, the combination $b_3^2+b_4^2$ determines both the effective mass squared and the surviving spinor curvature, establishing an algebraic link between these contributions.

math-ph↗

arXiv2026

A Functorial Theory of Defects in Abelian Chern-Simons Theory

Recent work has constructed Abelian Chern-Simons theories as categorical TQFTs, allowing us to naturally incorporate categorical defects and construct defect extensions of Abelian Chern-Simons TQFTs. We first identify the Turaev-Viro realizations of Abelian Chern-Simons theory in the center and doubled pointed modular cases, clarifying the distinction between single bulk realizations and canonical doubled ones. Then we obtain Turaev-Viro partition functions in terms of Reidemeister-torsion densities. Alternatively, the Alterfold construction supplies the associated topological boundaries, domain walls, and condensation sectors, establishing an explicit Alterfold/Chern-Simons dictionary. We show that the finite quadratic module is the invariant controlling the bulk theory, its topological symmetries, orientation-reversal invariance, and defects. We further show that multicomponent Abelian BF theory arises as the extended TQFT of an off-diagonal Abelian Chern-Simons theory, placing it naturally within the same extended framework. Finally, we demonstrate that recently proposed Abelian Chern-Simons dualities do not define a genuine TQFT duality. These results provide a concrete model for defects in Abelian topological orders and suggest a route toward the non-Abelian case.

math-ph↗