Magnetic annihilation and reconnection in two dimensions

The problems of incompressible, planar, magnetic annihilation and reconnection are discussed. We first emphasize that steady-state reconnection solutions can be constructed from annihilation models involving harmonic velocity fields. We show, however, that the only harmonic velocity profile capable of supporting inviscid magnetic annihilation is the traditional stagnation point flow φ= −αxy. The implication is that further steady-state planar reconnection models derived from annihilation solutions are impossible. We go on to show that certain classes of nonharmonic stream functions allow reconnection solutions to be developed, once the constraint of time independence is relaxed. In particular, we construct an exact reconnection model based on cellular inflows into a periodic assemblage of magnetic X-points

Exact models for hall current reconnection with axial guide fields

This paper employs an analytic reconnection model to investigate the conditions under which Hall currents can influence reconnection and Ohmic dissipation rates. It is first noted that time dependent magnetohydrodynamic systems can be analyzed by decomposing the magnetic and velocity fields into guide field and reconnecting field components. A formally exact solution shows that Hall currents can speed up or slow down the reconnection rate depending on the strength and orientation of the axial guide field. In particular, merging solutions are developed in which the axial guide field is the dominant driver of the reconnection. The extent to which Hall currents can alleviate the buildup of back pressures in flux pile-up reconnection models is also examined. The analysis shows that, although enhancements of the merging rate can be expected under certain conditions, it is unlikely that Hall currents can completely undo the fundamental pressure limitations associated with flux pile-up reconnection

Dynamic planar magnetic reconnection solutions for incompressible plasmas

The planar magnetic reconnection problem for viscous, resistive plasmas is addressed. We show that solutions can be developed by superposing transient nonlinear disturbances onto quiescent “background” fields. The disturbance fields are unrestricted in form, but the spatial part of the background field must satisfy ∇2K= -λK. This decomposition allows previous analytic reconnection solutions, based on one-dimensional disturbance fields of “plane wave” form, to be recovered as special cases. However, we point out that planar disturbance fields must be fully two-dimensional to avoid the pressure problem associated with analytic merging models, that is, to avoid unbounded current sheet pressures in the limit of small plasma resistivities. The details of the reconnection problem are then illustrated using cellular background field simulations in doubly periodic geometries. The flux pile-up rate is shown to saturate when the pressure of the current sheet exceeds the hydromagnetic pressure of the background field. Although the presaturation regime is well described by one-dimensional current sheet theory, the nonlinear postsaturation regime remains poorly understood. Preliminary evidence suggests that, although after saturation the early evolution of the field can be described by slow Sweet-Parker scalings, the first implosion no longer provides the bulk of the energy release

Fast magnetic reconnection via jets and current microsheets

Numerical simulations of highly nonlinear magnetic reconnection provide evidence of ultrathin current microsheets. These small-scale sheets are formed by strong exhaust jets from a primary large-scale current layer. The overall size of the secondary microsheet is determined by the thickness of the primary sheet. Preliminary scalings show that the thickness of the microsheet varies linearly with the plasma resistivity. This scaling suggests that microsheets may provide fast reconnection sites in magnetically complex plasmas such as the solar corona and planetary magnetospheres

The power output of spine and fan magnetic reconnection solutions

The ability of three-dimensional magnetic “spine” and “fan” reconnection solutions to provide flarelike energy release is discussed. It is pointed out, on the basis of exact analytic solutions, that fast dissipation is possible only if the hydromagnetic pressure in the reconnection region becomes unbounded in the limit of small plasma resistivities. The implication is that some “saturation” of the power output is inevitable for realistic coronal plasmas. Estimates of the saturated power, based on limiting the flux pileup in the field, suggest that the geometry of the spine reconnection mechanism precludes significant flare energy release. However, the current sheet structures involved in fan reconnection seem able to release sufficient magnetic energy fast enough to account for modest flares, even under the conservative assumption of classical plasma resistivities

The impact of small-scale turbulence on laminar magnetic reconnection

Initial states in incompressible two-dimensional magnetohydrodynamics that are known to lead to strong current sheets and (laminar) magnetic reconnection are modified by the addition of small-scale turbulent perturbations of various energies. The evolution of these states is computed with the aim of ascertaining the influence of the turbulence on the underlying laminar solution. Two main questions are addressed here: (1) What effect does small-scale turbulence have on the energy dissipation rate of the underlying solution? (2) What is the threshold turbulent perturbation level above which the original laminar reconnective dynamics is no longer recognizable. The simulations show that while the laminar dynamics persist the dissipation rates are largely unaffected by the turbulence, other than modest increases attributable to the additional small length scales present in the new initial condition. The solutions themselves are also remarkably insensitive to small-scale turbulent perturbations unless the perturbations are large enough to undermine the integrity of the underlying cellular flow pattern. Indeed, even initial states that lead to the evolution of small-scale microscopic sheets can survive the addition of modest turbulence. The role of a large-scale organizing background magnetic field is also addressed

Magnetic reconnection solutions in the presence of multiple nulls

It is known that exact analytic solutions can be constructed for incompressible magnetic reconnection in three space dimensions. In the case of an isolated X-point null, there are two types of reconnection solutions, namely, “spine” and “fan” models, which depend on the form of the X-point disturbance. However, such models cannot describe multiple null “separator” reconnection, for which there is independent observational evidence. Here we show that the spine formalism naturally extends to the case of multiple null fields. Solutions showing the characteristics of fan, spine, and separator are described, and a discussion is given of their energy dissipation properties. We demonstrate a family of multiple null, fast reconnection solutions and point out that the classical Sweet-Parker dissipation rate is the slowest that can be achieved with the present models

Masticatory biomechanics of red and grey squirrels (Sciurus vulgaris and Sciurus carolinensis) modelled with multibody dynamics analysis

The process of feeding in mammals is achieved by moving the mandible relative to the cranium to bring the teeth into and out of occlusion. This process is especially complex in rodents which have a highly specialized configuration of jaw adductor muscles. Here, we used the computational technique of multi-body dynamics analysis (MDA) to model feeding in the red (Sciurus vulgaris) and grey squirrel (Sciurus carolinensis) and determine the relative contribution of each jaw-closing muscle in the generation of bite forces. The MDA model simulated incisor biting at different gapes. A series of ‘virtual ablation experiments' were performed at each gape, whereby the activation of each bilateral pair of muscles was set to zero. The maximum bite force was found to increase at wider gapes. As predicted, the superficial and anterior deep masseter were the largest contributors to bite force, but the temporalis had only a small contribution. Further analysis indicated that the temporalis may play a more important role in jaw stabilization than in the generation of bite force. This study demonstrated the ability of MDA to elucidate details of red and grey squirrel feeding biomechanics providing a complement to data gathered via in vivo experimentation

Fast dynamic reconnection at X-type neutral points

We consider the linear and nonlinear evolution of disturbed magnetic X-type neutral points. The problem is formulated within a unified analytic and computational framework which highlights the essence of the magnetic annihilation process, namely, the coupling of a global convection region to a localized diffusion region surrounding the neutral point. An analytic treatment is given for the case of small disturbances of the equilibrium field in the absence of gas pressure. This problem admits well-defined azimuthal modes which allow a formally exact determination of the magnetic annihilation rate. It is shown that reconnection can only occur in the case of purely radial (m = 0) disturbances: the reconnection process is oscillatory and "fast," depending only logarithmically on the plasma resistivity (η). We show that the linear theory supports the notion of an initial implosive stage which rapidly releases the bulk of the energy associated with reconnective field disturbances. This phase is initiated by the advective focusing of the perturbation energy into the neutral point and culminates in the formation of a cylindrical diffusion region of area A ∼ η and current density J ∼ η-1. This scaling provides a signature for fast linear reconnection. Next we consider the breakdown of the linear theory. Although fast reconnection is maintained for low-amplitude disturbances in noncylindrical geometries, it is shown that finite gas pressure can stall the reconnection if sufficiently large. This effect, however, may not be critical in more complex X-point geometries. More seriously, for finite-amplitude displacements the cylindrical current structure close to the neutral point is distorted into a quasi-one-dimensional current sheet whose thickness is limited by resistive diffusion. In this case fast reconnection is consistent with a flux pileup solution in which the bulk of the energy is released as heat rather than as the kinetic energy of mass motion

HONEYDEW SUGARS ELIMINATED BY STIGMACOCCUS SP. NR. ASPER HEMPEL (HEMIPTERA: MARGARODIDAE) FEEDING ON LEGUMINOUS TREES IN BRAZIL.

HONEYDEW SUGARS ELIMINATED BY STIGMACOCCUS SP. NR ASPER HEMPEL (HEMIPTERA: MARGARODIDAE) FEEDING ON LEGUMINOUS TREES IN BRAZIL. The sooty mould coating the trunks of mature trees of Schizolobium excelsum in Brazil was found to be associated with honeydew being eliminated by an undescribed species of margarodid near Stigmacoccus asper Hempel. Analysis of the honeydew sugars by paper chromatography revealed a complex composition. The principal sugar was sucrose, but there were significant amounts of fructose, glucose and three components identified as di-, tri- and tetrasaccharides. The disaccharides were maltose, trehalose, trehalulose and a hexose-hexitol. The other, apparently novel, pair of oligosaccharides were composed of glucose(s) 1,4 linked to the glucose of sucrose. The sugar composition of the tree sap was also determined and found to be glucose and sucrose only. The findings, therefore, imply significant and novel metabolic transformations of sugars by the scale insect and/or its microbial symbionts. Key words: Xylococcinae, sexual reproduction, stigmatriose, stigmatetraose, Amazonia