Is magnetic topology important for heating the solar atmosphere?

CEP and JT acknowledge the support of STFC through the St Andrew’s SMTG consolidated grant. JEHS is supported by STFC as a PhD student. SJE is supported STFC through the Durham University Impact Acceleration Account.Magnetic fields permeate the entire solar atmosphere weaving an extremely complex pattern on both local and global scales. In order to understand the nature of this tangled web of magnetic fields, its magnetic skeleton, which forms the boundaries between topologically distinct flux domains, may be determined. The magnetic skeleton consists of null points, separatrix surfaces, spines and separators. The skeleton is often used to clearly visualize key elements of the magnetic configuration, but parts of the skeleton are also locations where currents and waves may collect and dissipate. In this review, the nature of the magnetic skeleton on both global and local scales, over solar cycle time scales, is explained. The behaviour of wave pulses in the vicinity of both nulls and separators is discussed and so too is the formation of current layers and reconnection at the same features. Each of these processes leads to heating of the solar atmosphere, but collectively do they provide enough heat, spread over a wide enough area, to explain the energy losses throughout the solar atmosphere? Here, we consider this question for the three different solar regions: Active regions, open-field regions and the quiet Sun. We find that the heating of active regions and open-field regions is highly unlikely to be due to reconnection or wave dissipation at topological features, but it is possible that these may play a role in the heating of the quiet Sun. In active regions, the absence of a complex topology may play an important role in allowing large energies to build up and then, subsequently, be explosively released in the form of a solar flare. Additionally, knowledge of the intricate boundaries of open-field regions (which the magnetic skeleton provides) could be very important in determining the main acceleration mechanism(s) of the solar wind.PostprintPeer reviewe

Glueball plus Pion Production in Photon-Photon Collisions.

We here compute the reaction $\gamma \; \gamma \rightarrow G \; \pi^{0}$ for various glueball candidates $G$ and their assumed quantum states, using a non-relativistic gluon bound-state model for the glueball.Comment: To appear in Zeit. fur Phys. C; Plain Latex file, 16 pages; 5 figures appended as a uuencoded postscript file

Detection of the Togninia Teleomorph of Phaeoacremonium aleophilum in Australia

Moist incubation of grapevine wood infected with both Phaeoacremonium aleophilum and Phaeomoniella chlamydospora yielded an ascomycete referable to the genus Togninia (Ascomycota, Calosphaeriales). Single ascospore cultures were morphologically identical to Pm. aleophilum. The rDNA ITS sequence of single ascospore isolates was identical to published sequences for the majority of Pm. aleophilum isolates. Comparison with the morphology of other wood staining Togninia species confirms that the teleomorph of Pm. aleophilum is Togninia minima

Phase coexistence of gradient Gibbs states

We consider the (scalar) gradient fields $\eta=(\eta_b)$--with $b$ denoting the nearest-neighbor edges in $\Z^2$--that are distributed according to the Gibbs measure proportional to \texte^{-\beta H(\eta)}\nu(\textd\eta). Here $H=\sum_bV(\eta_b)$ is the Hamiltonian, $V$ is a symmetric potential, $\beta>0$ is the inverse temperature, and $\nu$ is the Lebesgue measure on the linear space defined by imposing the loop condition $\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}$ for each plaquette $(b_1,b_2,b_3,b_4)$ in $\Z^2$. For convex $V$, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex $V$ undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature $\beta$. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., $E \eta_b=0$.Comment: 3 figs, PTRF style files include

The field theoretic derivation of the contact value theorem in planar geometries and its modification by the Casimir effect

The contact value theorem for Coulomb gases in planar or film-like geometries is derived using a Hamiltonian field theoretic representation of the system. The case where the film is enclosed by a material of different dielectric constant to that of the film is shown to contain an additional Casimir-like term which is generated by fluctuations of the electric potential about its mean-field value.Comment: Link between Sine-Gordon and Coulomb gas pressures via subtraction of self interaction terms included. Discussion of results within Debye-Huckel approximation included. Added reference

Finite temperature mobility of a particle coupled to a fermion environment

We study numerically the finite temperature and frequency mobility of a particle coupled by a local interaction to a system of spinless fermions in one dimension. We find that when the model is integrable (particle mass equal to the mass of fermions) the static mobility diverges. Further, an enhanced mobility is observed over a finite parameter range away from the integrable point. We present a novel analysis of the finite temperature static mobility based on a random matrix theory description of the many-body Hamiltonian.Comment: 11 pages (RevTeX), 5 Postscript files, compressed using uufile

Influence of uncorrelated overlayers on the magnetism in thin itinerant-electron films

The influence of uncorrelated (nonmagnetic) overlayers on the magnetic properties of thin itinerant-electron films is investigated within the single-band Hubbard model. The Coulomb correlation between the electrons in the ferromagnetic layers is treated by using the spectral density approach (SDA). It is found that the presence of nonmagnetic layers has a strong effect on the magnetic properties of thin films. The Curie temperatures of very thin films are modified by the uncorrelated overlayers. The quasiparticle density of states is used to analyze the results. In addition, the coupling between the ferromagnetic layers and the nonmagnetic layers is discussed in detail. The coupling depends on the band occupation of the nonmagnetic layers, while it is almost independent of the number of the nonmagnetic layers. The induced polarization in the nonmagnetic layers shows a long-range decreasing oscillatory behavior and it depends on the coupling between ferromagnetic and nonmagnetic layers.Comment: 9 pages, RevTex, 6 figures, for related work see: http://orion.physik.hu-berlin.d

Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio