The strongly regular (45,12,3,3) graphs

Using two backtrack algorithms based on dierent techniques, designed and implemented independently, we were able to determine up to isomorphism all strongly regular graphs with parameters v = 45, k = 12, λ = μ = 3. It turns out that there are 78 such graphs, having automorphism groups with sizes ranging from 1 to 51840

Contributions of the low-latitude boundary layer to the finite width magnetotail convection model

Convection of plasma within the terrestrial nightside plasma sheet contributes to the structure and, possibly, the dynamical evolution of the magnetotail. In order to characterize the steady state convection process, we have extended the finite tail width model of magnetotail plasma sheet convection. The model assumes uniform plasma sources and accounts for both the duskward gradient/curvature drift and the earthward E × B drift of ions in a two-dimensional magnetic geometry. During periods of slow convection (i.e., when the cross-tail electric potential energy is small relative to the source plasma\u27s thermal energy), there is a significant net duskward displacement of the pressure-bearing ions. The electrons are assumed to be cold, and we argue that this assumption is appropriate for plasma sheet parameters. We generalize solutions previously obtained along the midnight meridian to describe the variation of the plasma pressure and number density across the width of the tail. For a uniform deep-tail source of particles, the plasma pressure and number density are unrealistically low along the near-tail dawn flank. We therefore add a secondary source of plasma originating from the dawnside low-latitude boundary layer (LLBL). The dual plasma sources contribute to the plasma pressure and number density throughout the magnetic equatorial plane. Model results indicate that the LLBL may be a significant source of near-tail central plasma sheet plasma during periods of weak convection. The model predicts a cross-tail pressure gradient from dawn to dusk in the near magnetotail. We suggest that the plasma pressure gradient is balanced in part by an oppositely directed magnetic pressure gradient for which there is observational evidence. Finally, the pressure to number density ratio is used to define the plasma “temperature.” We stress that such quantities as temperature and polytropic index must be interpreted with care as they lose their nominal physical significance in regions where the two-source plasmas intermix appreciably and the distributions become non-Maxwellian

On the possibility of quasi-static convection in the quiet magnetotail

Abstract The magnetotail is known to serve as a reservoir of energy transferred into the terrestrial magnetosphere from the solar wind. In principle, the stored energy can be dissipated impulsively, as in a substorm, or steadily through the process of steady adiabatic plasma convection. However, some theoretical arguments have suggested that quasi-static adiabatic convection cannot occur throughout the magnetotail because of the structure of the magnetic field. Here we reexamine the question. We show that in a magnetotail of finite width, downtail pressure gradients depend strongly on the ratio of the potential across half the tail to the ion temperature in the far tail (60 RE). For pertinent quiet time ratios (∼3), a Tsyganenko quiet-time magnetic field model is consistent with steady convection

DMSP F7 observations of a substorm field‐aligned current

In this paper we present observations of a substorm field-aligned current (FAC) system that DMSP F7 traversed just after 0300 UT on April 25, 1985. Ground magnetometer data show that a major substorm was in progress at that time and that DMSP F7 flew through a region of predominantly upward FAC. The DMSP F7 magnetic field data are consistent with this interpretation. The precipitating particle data suggest that there were three distinct large-scale FAC systems. In ascending latitude these were a downward current, an upward current, and a paired upward/downward current system. We identify the first current, which was coincident with the diffuse aurora, as region 2. The next (upward) FAC was coincident with a spatially unstructured region of energetic (∼12 keV) electron precipitation. This was the substorm-associated FAC that made up part of the current wedge. The upward/downward current pair was coincident with a region of highly structured precipitation. We suggest that these currents may have been the duskside region 1 and, poleward of that, the extension of the dawnside region 1. The particle data show that the upward substorm current lay well equatorward of the boundary between open and closed field lines. In fact, using a model field, the equatorward boundary of the substorm FAC maps to the neutral sheet at 6.9 RE. While one should be cautious in stressing results obtained by mapping model field lines, our result is consistent with scenarios for substorms which postulate a disruption and diversion of the near-Earth cross-tail current

Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs

In this and a sequel paper [10] we study combinatorial designs whose incidence matrix has two distinct singular values.These generalize 2-(v, k, É) designs, and include partial geometric designs and uniform multiplicative designs.Here we study the latter, which are precisely the nonsingular designs.We classify all such designs with smallest singular value at most, generalize the Bruck-Ryser-Chowla conditions, and enumerate, partly by computer, all uniform multiplicative designs on at most 30 points.combinatorics;matrices;singularities

Combinatorial Designs with Two Singular Values II. Partial Geometric Designs

In this and an earlier paper [17] we study combinatorial designs whose incidence matrix has two distinct singular values.These generalize (v, k, ë) designs, and include uniform multiplicative designs and partial geometric designs.Here we study the latter, which are precisely the designs with constant replication and block size.We collect most known results, give new characterization results, and we enumerate, partly by computer, all small ones.matrices;singularities;geometry;combinatorics