Coronal mass ejections as expanding force-free structures

We mode Solar coronal mass ejections (CMEs) as expanding force-fee magnetic structures and find the self-similar dynamics of configurations with spatially constant \alpha, where {\bf J} =\alpha {\bf B}, in spherical and cylindrical geometries, expanding spheromaks and expanding Lundquist fields correspondingly. The field structures remain force-free, under the conventional non-relativistic assumption that the dynamical effects of the inductive electric fields can be neglected. While keeping the internal magnetic field structure of the stationary solutions, expansion leads to complicated internal velocities and rotation, induced by inductive electric field. The structures depends only on overall radius R(t) and rate of expansion \dot{R}(t) measured at a given moment, and thus are applicable to arbitrary expansion laws. In case of cylindrical Lundquist fields, the flux conservation requires that both axial and radial expansion proceed with equal rates. In accordance with observations, the model predicts that the maximum magnetic field is reached before the spacecraft reaches the geometric center of a CME.Comment: 19 pages, 9 Figures, accepted by Solar Physic

An extension of the inductive approach to the lace expansion

We extend the inductive approach to the lace expansion, previously developed to study models with critical dimension 4, to be applicable more generally. In particular, the result of this note has recently been used to prove Gaussian asymptotic behaviour for the Fourier transform of the two-point function for sufficiently spread-out lattice trees in dimensions d>8, and it is potentially also applicable to percolation in dimensions d>6

Extension of the generalised inductive approach to the lace expansion: Full proof

This paper extends the inductive approach to the lace expansion of van der Hofstad and Slade in order to prove Gaussian asymptotic behaviour for models with critical dimension other than 4. The results are applied by Holmes to study sufficiently spread-out lattice trees in dimensions d>8 and may also be applicable to percolation in dimensions d>6

On the convergence of cluster expansions for polymer gases

We compare the different convergence criteria available for cluster expansions of polymer gases subjected to hard-core exclusions, with emphasis on polymers defined as finite subsets of a countable set (e.g. contour expansions and more generally high- and low-temperature expansions). In order of increasing strength, these criteria are: (i) Dobrushin criterion, obtained by a simple inductive argument; (ii) Gruber-Kunz criterion obtained through the use of Kirkwood-Salzburg equations, and (iii) a criterion obtained by two of us via a direct combinatorial handling of the terms of the expansion. We show that for subset polymers our sharper criterion can be proven both by a suitable adaptation of Dobrushin inductive argument and by an alternative --in fact, more elementary-- handling of the Kirkwood-Salzburg equations. In addition we show that for general abstract polymers this alternative treatment leads to the same convergence region as the inductive Dobrushin argument and, furthermore, to a systematic way to improve bounds on correlations

A New Matrix Model for Noncommutative Field Theory

We describe a new regularization of quantum field theory on the noncommutative torus by means of one-dimensional matrix models. The construction is based on the Elliott-Evans inductive limit decomposition of the noncommutative torus algebra. The matrix trajectories are obtained via the expansion of fields in a basis of new noncommutative solitons described by projections and partial isometries. The matrix quantum mechanics are compared with the usual zero-dimensional matrix model regularizations and some applications are sketched.Comment: 14 pages, 2 figure

Construction of the dirichlet to neumann boundary operator for triangles and applications in the analysis of polygonal conductors

This paper introduces a fast and accurate method to investigate the broadband inductive and resistive behavior of conductors with a nonrectangular cross section. The presented iterative combined waveguide mode (ICWM) algorithm leads to an expansion of the longitudinal electric field inside a triangle using a combination of parallel-plate waveguide modes in three directions, each perpendicular to one of the triangle sides. This expansion is used to calculate the triangle's Dirichlet to Neumann boundary operator. Subsequently, any polygonal conductor can be modeled as a combination of triangles. The method is especially useful to investigate current crowding effects near sharp conductor corners. In a number of numerical examples, the accuracy of the ICWM algorithm is investigated, and the method is applied to some polygonal conductor configurations

The Instanton Universal Moduli Space of N=2 Supersymmetric Yang-Mills Theory

We use the recursive structure of the compactification of the instanton moduli space of N=2 Super Yang-Mills theory with gauge group SU(2), to construct, by inductive limit, a universal moduli space which includes all the multi-instanton moduli spaces. Furthermore, with the aim of understanding the field theoretic structure of the strong coupling expansion, we perform the Borel sum which acts on the parameter defining such a universal moduli space.Comment: 1+4 pages, LaTeX. Minor changes. To appear in Phys. Lett.