Dynamic magnetic reconnection in three space dimensions: Fan current solutions

The problem of incompressible, nonlinear magnetic reconnection in three-dimensional "open" geometries is considered. An analytic treatment shows that dynamic "fan current" reconnection may be driven by superposing long wavelength, finite amplitude, plane wave disturbances onto three-dimensional magnetic X-points. The nonlinear reconnection of the field is preceded by an advection phase in which magnetic shear waves drive large currents as they localize in the vicinity of the magnetic null. Analytic arguments, reinforced by detailed simulations, show that the ohmic dissipation rate can be independent of the plasma resistivity if the merging is suitably driven

On the dimension of Z-sets

We offer a short and elementary proof that, for a Z-set A in a finite-dimensional ANR Y, dimA<dimY. This result is relevant to the study of group boundaries. The original proof by Bestvina and Mess relied on cohomological dimension theory.Comment: 4 pages, no figure

Hall current effects in dynamic magnetic reconnection solutions

The impact of Hall current contributions on flow driven planar magnetic merging solutions is discussed. The Hall current is important if the dimensionless Hall parameter (or normalized ion skin depth) satisfies cH>η where η is the inverse Lundquist number for the plasma. A dynamic analysis of the problem shows, however, that the Hall current initially manifests itself, not by modifying the planar reconnection field, but by inducing a non-reconnecting perpendicular "separator" component in the magnetic field. Only if the stronger condition c2/H > η is satisfied can Hall currents be expected to affect the planar merging. These analytic predictions are then tested by performing a series of numerical experiments in periodic geometry, using the full system of planar magnetohydrodynamic (MHD) equations. The numerical results confirm that the nature of the merging changes dramatically when the Hall coupling satisfies c2/H > η. In line with the analytic treatment of sheared reconnection, the coupling provided by the Hall term leads to the emergence of multiple current layers that can enhance the global Ohmic dissipation at the expense of the reconnection rate. However, the details of the dissipation depend critically on the symmetries of the simulation, and when the merging is "head-on" (i.e., comprises fourfold symmetry) the reconnection rate can be enhanced

Substructure coupling for dynamic analysis and testing

Fixed interface and free interface methods of substructure coupling for dynamic analysis are discussed. Three methods for reducing the number of coordinates required by fixed interface methods are introduced. Matrix ordinary differential equations are employed to improve accuracy in free interface substructure coupling methods

A review of substructure coupling methods for dynamic analysis

The state of the art is assessed in substructure coupling for dynamic analysis. A general formulation, which permits all previously described methods to be characterized by a few constituent matrices, is developed. Limited results comparing the accuracy of various methods are presented

A modal parameter extraction procedure applicable to linear time-invariant dynamic systems

Modal analysis has emerged as a valuable tool in many phases of the engineering design process. Complex vibration and acoustic problems in new designs can often be remedied through use of the method. Moreover, the technique has been used to enhance the conceptual understanding of structures by serving to verify analytical models. A new modal parameter estimation procedure is presented. The technique is applicable to linear, time-invariant systems and accommodates multiple input excitations. In order to provide a background for the derivation of the method, some modal parameter extraction procedures currently in use are described. Key features implemented in the new technique are elaborated upon

Dual-currency economies as multiple-payment systems

Monetary search models are valuable for studying how a second currency's acceptability arises endogenously in an economy that lacks a stable domestic currency and other more sophisticated payment systems. Search models' basic assumptions (absence of credit, lack of smoothly functioning banking systems, reliance on currency as the sole medium of exchange, and primitive trading environments) are not necessarily consistent with modern financial systems. They do, however, provide good descriptions of transitional and developing economies, particularly in the countries of the former Soviet Union, and may yield helpful policy prescriptions.Money ; Monetary theory

Supernova Asymmetries

All core collapse supernovae are strongly aspherical. The "Bochum event," with velocity components displaced symmetrically about the principal H$\alpha$ line, strongly suggests that SN 1987A was a bi-polar rather than a uni-polar explosion. While there is a general tendency to display a single prominant axis in images and spectropolarimetry, there is also growing evidence for frequent departures from axisymmetry. There are various mechanisms that might contribute to large scale departures from spherical symmetry: jet-induced processes, the spherical shock accretion instability (SASI) and associated phenomena, and non-axisymmetric instabilities (NAXI). The MRI gives inevitable production of large toroidal magnetic fields. In sum: no $\Omega$ without B. The role of magnetic fields, non-axisymmetric instabilities, and of the de-leptonization phase are discussed.Comment: 8 pages, 3 figures, to be published in the proceedings of the conference "Supernova 1987A: 20 Years After" Aspen, 200