Related papers: The contact property for magnetic flows on surface…
Through a direct comparison between numerical simulations in two and three dimensions, we investigate topological effects in reconnection. A simple estimate on increase in reconnection rate in three dimensions by a factor of $\sqrt{2}$,…
We give a purely contact and symplectic geometric characterization of Anosov flows in dimension 3 and discuss a framework to use tools from contact and symplectic geometry and topology in the study of Anosov dynamics. We also discuss some…
We derive the equations of motion for a planar rigid body of circular shape moving in a 2D perfect fluid with point vortices using symplectic reduction by stages. After formulating the theory as a mechanical system on a configuration space…
We obtain Kupka-Smale theorem and Franks lemma for magnetic flows on manifolds with any dimension. This improves Miranda result on surfaces. However our methods relies on geometric control theory, like in Rifford and Ruggiero articles.
We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta…
As well known, magnetic fields in space are distributed very inhomogeneously. Some-times field distributions have forms of filaments with high magnetic field values. As many ob-servations show, such a filamentation takes place in convective…
This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [Y Eliashberg, A Givental and H Hofer, Introduction to Symplectic Field Theory, Geom. Funct. Anal. Special Volume, Part II (2000) 560--673].…
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
In the first part of these lecture notes, new high-resolution observations of small-scale magnetic flux concentrations are presented and compared to results from new three-dimensional magnetohydrodynamic simulations. Special attention is…
We consider the governing equations for the motion of the viscous fluids in two moving domains and an evolving surface from both energetic and thermodynamic points of view. We make mathematical models for multiphase flow with surface flow…
The paper considers the semiclassical dynamics of electrons on complex Fermi surfaces in the presence of strong magnetic fields. The reconstructions of the general topological structure of such dynamics are accompanied by the appearance of…
We derive basic scaling equations for relativistic magnetic reconnection in the general case of asymmetric inflow conditions and obtain predictions for the outflow Lorentz factor and the reconnection rate. Kinetic Particle-in-Cell…
Solar activity is controlled by the magnetic field, which also causes the variability of the solar irradiance that in turn is thought to influence the climate on Earth. The magnetic field manifests itself in the form of structures of…
Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first…
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity…
We investigate numerically magnetic field generation by thermal convection with square periodicity cells in a rotating horizontal layer of electrically-conducting fluid with stress-free electrically perfectly conducting boundaries for…
We study in detail the dynamics of conformal Hamiltonian flows that are defined on a conformal symplectic manifold (this notion was popularized by Vaisman in 1976). We show that they exhibit some conservative and dissipative behaviours. We…
This review discusses the physics of magnetic reconnection, a process in which the magnetic field topology changes and magnetic energy is converted to kinetic energy, in pair plasmas in the relativistic regime. We focus on recent progress…
Using steady, axisymmetric, ideal magnetohydrodynamics (MHD) we analyze relativistic outflows by means of examining the momentum equation along the flow and in the transfield direction. We argue that the asymptotic Lorentz factor is ~…
An overview of the effect of a magnetic field gradient on fluids with linear magnetic susceptibilities is given. It is shown that two commonly encountered expressions, the magnetic field gradient force and the concentration gradient force…