Collisionless distribution function for the relativistic force-free Harris sheet

A self-consistent collisionless distribution function for the relativistic analogue of the force-free Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the non-relativistic collisionless force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)], as it has the same dependence on the particle energy and canonical momenta. We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters of the distribution function and the macroscopic parameters such as the current sheet thickness is discussed. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3677268]PostprintPeer reviewe

Frequency jumps in the planar vibrations of an elastic beam

The small amplitude transverse vibrations of an elastic beam clamped at both extremities are studied. The beam is modeled as an extensible, shearable planar Kirchhoff elastic rod under large displacements and rotations, and the vibration frequencies are computed both analytically and numerically as a function of the loading. Of particular interest is the variation of mode frequencies as the load is increased through the buckling threshold. While for some modes there is no qualitative changes in the mode frequencies, other modes experience rapid variations after the buckling threshold. For slender beams, these variations become stiffer, eventually resulting in a discontinuous jump of frequency at buckling, in the limit of inextensible, unshearable beams

An approximate self-consistent theory of the magnetic field of fluted penumbrae

A self-consistent mathematical description of the magnetic field of fluted sunspot penumbrae is presented. This description is based on an expansion of the nonlinear force-free magnetohydrostatic equations written in cylindrical coordinates. The lowest order solutions are mathematically equivalent to laminated force-free equilibria in Cartesian geometry. The lowest order solutions have no toroidal component of the magnetic field and the magnetic pressure does not vary with azimuth but the solutions allow arbitrary variations of the magnetic field components with azimuth. Explicit solutions are presented which have a realistic radial profile of the magnetic field strength and reproduce the basic features of the observations.Comment: 8 pages, 4 figures, accepted for publication in Astronomy and Astrophysic

Particle dynamics in a non-flaring solar active region model

The aim of this work is to investigate and characterise particle behaviour in a (observationally-driven) 3D MHD model of the solar atmosphere above a slowly evolving, non-flaring active region. We use a relativistic guiding-centre particle code to investigate particle acceleration in a single snapshot of the 3D MHD simulation. Despite the lack of flare-like behaviour in the active region, direct acceleration of electrons and protons to non-thermal energies (≲ 42 MeV) was found, yielding spectra with high-energy tails which conform to a power law. Examples of particle dynamics, including particle trapping caused by local electric rather than magnetic field effects, are observed and discussed, together with implications for future experiments which simulate non-flaring active region heating and reconnection.Publisher PDFPeer reviewe

Getting DNA twist rigidity from single molecule experiments

We use an elastic rod model with contact to study the extension versus rotation diagrams of single supercoiled DNA molecules. We reproduce quantitatively the supercoiling response of overtwisted DNA and, using experimental data, we get an estimation of the effective supercoiling radius and of the twist rigidity of B-DNA. We find that unlike the bending rigidity, the twist rigidity of DNA seems to vary widely with the nature and concentration of the salt buffer in which it is immerged

Arbitrarily large families of spaces of the same volume

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde

Mechanical response of plectonemic DNA: an analytical solution

We consider an elastic rod model for twisted DNA in the plectonemic regime. The molecule is treated as an impenetrable tube with an effective, adjustable radius. The model is solved analytically and we derive formulas for the contact pressure, twisting moment and geometrical parameters of the supercoiled region. We apply our model to magnetic tweezer experiments of a DNA molecule subjected to a tensile force and a torque, and extract mechanical and geometrical quantities from the linear part of the experimental response curve. These reconstructed values are derived in a self-contained manner, and are found to be consistent with those available in the literature.Comment: 14 pages, 4 figure

Role of electric charge in shaping equilibrium configurations of fluid tori encircling black holes

Astrophysical fluids may acquire non-zero electrical charge because of strong irradiation or charge separation in a magnetic field. In this case, electromagnetic and gravitational forces may act together and produce new equilibrium configurations, which are different from the uncharged ones. Following our previous studies of charged test particles and uncharged perfect fluid tori encircling compact objects, we introduce here a simple test model of a charged perfect fluid torus in strong gravitational and electromagnetic fields. In contrast to ideal magnetohydrodynamic models, we consider here the opposite limit of negligible conductivity, where the charges are tied completely to the moving matter. This is an extreme limiting case which can provide a useful reference against which to compare subsequent more complicated astrophysically-motivated calculations. To clearly demonstrate the features of our model, we construct three-dimensional axisymmetric charged toroidal configurations around Reissner-Nordstr\"om black holes and compare them with equivalent configurations of electrically neutral tori.Comment: 14 pages, 7 figure

Emission heights of coronal bright points on Fe XII radiance map

We study the emission heights of the coronal bright points (BPs) above the photosphere in the bipolar magnetic loops that are apparently associated with them. As BPs are seen in projection against the disk their true emission heights are unknown. The correlation of the BP locations on the Fe XII radiance map from EIT with the magnetic field features (in particular neutral lines) was investigated in detail. The coronal magnetic field was determined by an extrapolation of the photospheric field to different altitudes above the disk. It was found that most BPs sit on or near a photospheric neutral line, but that the emission occurs at a height of about 5 Mm. Some BPs, while being seen in projection, still seem to coincide with neutral lines, although their emission takes place at heights of more than 10 Mm. Such coincidences almost disappear for emissions above 20 Mm. We also projected the upper segments of the 3-D magnetic field lines above different heights, respectively, on to the x-y plane. The shape of each BP was compared with the respective field-line segment nearby. This comparison suggests that most coronal BPs are actually located on the top of their associated magnetic loops. Finally, we calculated for each selected BP region the correlation coefficient between the Fe XII intensity enhancement and the horizontal component of the extrapolated magnetic field vector at the same x-y position in planes of different heights, respectively. We found that for almost all the BP regions we studied the correlation coefficient, with increasing height, increases to a maximal value and then decreases again. The height corresponding to this maximum was defined as the correlation height, which for most bright points was found to range below 20 Mm.Comment: 7 pages, 4 figures, 1 tabl

Fine Selmer Groups and Isogeny Invariance

We investigate fine Selmer groups for elliptic curves and for Galois representations over a number field. More specifically, we discuss Conjecture A, which states that the fine Selmer group of an elliptic curve over the cyclotomic extension is a finitely generated $\mathbb{Z}_p$-module. The relationship between this conjecture and Iwasawa's classical $\mu=0$ conjecture is clarified. We also present some partial results towards the question whether Conjecture A is invariant under isogenies.Comment: 20 page