Minimal connected enclosures on an embedded planar graph

We study five problems of finding minimal enclosures comprised of elements of a connected, planar graph with a plane embedding. The first three problems consider the identification of a shortest enclosing walk, cycle or trail surrounding a polygonal, simply connected obstacle on the plane. We propose polynomial algorithms that improve on existing algorithms. The last two problems consider the formation of minimal zones (sets of adjacent regions such that any pair of points in a zone can be connected by a non-zero width curve that lies entirely in the zone). Specifically, we assume that the regions of the graph have nonnegative weights and seek the formation of minimum weight zones containing a set of points or a set of regions. We prove that the last two problems are NP-hard and transform them to Steiner arboresccnce/fixed-charge flow problems

First simultaneous observations of flux transfer events at the high-latitude magnetopause by the cluster spacecraft and pulsed radar signatures in the conjugate ionosphere by the CUTLASS and EISCAT radars

Cluster magnetic field data are studied during an outbound pass through the post-noon high-latitude magnetopause region on 14 February 2001. The onset of several minute perturbations in the magnetospheric field was observed in conjunction with a southward turn of the interplanetary magnetic field observed upstream by the ACE spacecraft and lagged to the subsolar magnetopause. These perturbations culminated in the observation of four clear magnetospheric flux transfer events (FTEs) adjacent to the magnetopause, together with a highly-structured magnetopause boundary layer containing related field features. Furthermore, clear FTEs were observed later in the magnetosheath. The magnetospheric FTEs were of essentially the same form as the original “flux erosion events” observed in HEOS-2 data at a similar location and under similar interplanetary conditions by Haerendel et al. (1978). We show that the nature of the magnetic perturbations in these events is consistent with the formation of open flux tubes connected to the northern polar ionosphere via pulsed reconnection in the dusk sector magnetopause. The magnetic footprint of the Cluster spacecraft during the boundary passage is shown to map centrally within the fields-of-view of the CUTLASS SuperDARN radars, and to pass across the field-aligned beam of the EISCAT Svalbard radar (ESR) system. It is shown that both the ionospheric flow and the backscatter power in the CUTLASS data pulse are in synchrony with the magnetospheric FTEs and boundary layer structures at the latitude of the Cluster footprint. These flow and power features are subsequently found to propagate poleward, forming classic “pulsed ionospheric flow” and “poleward-moving radar auroral form” structures at higher latitudes. The combined Cluster-CUTLASS observations thus represent a direct demonstration of the coupling of momentum and energy into the magnetosphere-ionosphere system via pulsed magnetopause reconnection. The ESR observations also reveal the nature of the structured and variable polar ionosphere produced by the structured and time-varying precipitation and flow

Currents associated with Saturn's intra-D ring azimuthal field perturbations

During the final 22 full revolutions of the Cassini mission in 2017, the spacecraft passed at periapsis near the noon meridian through the gap between the inner edge of Saturn’s D ring and the denser layers of the planet’s atmosphere, revealing the presence of an unanticipated low-latitude current system via the associated azimuthal perturbation field peaking typically at ~10-30 nT. Assuming approximate axisymmetry, here we use the field data to calculate the associated horizontal meridional currents flowing in the ionosphere at the feet of the field lines traversed, together with the exterior field-aligned currents required by current continuity. We show that the ionospheric currents are typically~0.5–1.5 MA per radian of azimuth, similar to auroral region currents, while the field-aligned current densities above the ionosphere are typically ~5-10 nA m-2 , more than an order less than auroral values. The principal factor involved in this difference is the ionospheric areas into which the currents map. While around a third of passes exhibit unidirectional currents flowing northward in the ionosphere closing southward along exterior field lines, many passes also display layers of reversed northward field-aligned current of comparable or larger magnitude in the region interior to the D ring, which may reverse sign again on the innermost field lines traversed. Overall, however, the currents generally show a high degree of north-south conjugacy indicative of an interhemispheric system, certainly on the larger overall spatial scales involved, if less so for the smaller-scale structures, possibly due to rapid temporal or local time variations

Chloroplast microsatellites: measures of genetic diversity and the effect of homoplasy

Chloroplast microsatellites have been widely used in population genetic studies of conifers in recent years. However, their haplotype configurations suggest that they could have high levels of homoplasy, thus limiting the power of these molecular markers. A coalescent-based computer simulation was used to explore the influence of homoplasy on measures of genetic diversity based on chloroplast microsatellites. The conditions of the simulation were defined to fit isolated populations originating from the colonization of one single haplotype into an area left available after a glacial retreat. Simulated data were compared with empirical data available from the literature for a species of Pinus that has expanded north after the Last Glacial Maximum. In the evaluation of genetic diversity, homoplasy was found to have little influence on Nei's unbiased haplotype diversity (H(E)) while Goldstein's genetic distance estimates (D2sh) were much more affected. The effect of the number of chloroplast microsatellite loci for evaluation of genetic diversity is also discussed

Magnetic Field Observations on Cassini's Proximal Periapsis Passes: Planetary Period Oscillations and Mean Residual Fields

We analyze periapsis pass magnetic field data from the final 23 orbits of the Cassini spacecraft at Saturn, uniquely encompassing auroral, subauroral, ring region, and intra‐ring field lines, to determine the planetary period oscillations (PPOs) and mean residual fields in these regions. Dual modulation by northern and southern PPO systems is found almost continuously, demonstrating for the first time the presence of PPOs on and inside ring region field lines. The azimuthal component displays the largest ~10–15nT PPO amplitudes on auroral field lines, falling across the subauroral region to ~3–5 nT on main ring field lines in the northern hemisphere, less in the southern hemisphere, while increasing to ~5–8 nT on D ring and intra‐D ring field lines. Auroral and subauroral amplitudes mapped along field lines are in good agreement with previous analyses in regions of overlap. Colatitudinal and radial field oscillations generally have a half and a quarter the amplitude of the azimuthal component, respectively. Inner region oscillation phases are typically several tens of degrees “earlier” than those of outer subauroral and auroral regions. Mean residual poloidal fields (internal and ring current fields subtracted) show quasi‐sinusoidal latitude variations of ~2.5nT amplitude, with radial and colatitudinal fields approximately in quadrature. Mean azimuthal fields peaking at ~15 nT are approximately symmetrical about the equator on and inside D ring field lines as previously reported, but are unexpectedly superposed on ~3–5nT “lagging” fields which extend continuously through the ring region onto subauroral field lines north and south

Saturn's Auroral Field-Aligned Currents: Observations from the Northern Hemisphere Dawn Sector During Cassini's Proximal Orbits

We examine the azimuthal magnetic field signatures associated with Saturn's northern hemisphere auroral field‐aligned currents observed in the dawn sector during Cassini's Proximal orbits (April 2017 and September 2017). We compare these currents with observations of the auroral currents from near noon taken during the F‐ring orbits prior to the Proximal orbits. First, we show that the position of the main auroral upward current is displaced poleward between the two local times (LTs). This is consistent with the statistical position of the ultraviolet auroral oval for the same time interval. Second, we show the overall average ionospheric meridional current profile differs significantly on the equatorward boundary of the upward current with a swept‐forward configuration with respect to planetary rotation present at dawn. We separate the planetary period oscillation (PPO) currents from the PPO‐independent currents and show their positional relationship is maintained as the latitude of the current shifts in LT implying an intrinsic link between the two systems. Focusing on the individual upward current sheets pass‐by‐pass, we find that the main upward current at dawn is stronger compared to near noon. This results in the current density being ~1.4 times higher in the dawn sector. We determine a proxy for the precipitating electron power and show that the dawn PPO‐independent upward current electron power is ~1.9 times higher than at noon. These new observations of the dawn auroral region from the Proximal orbits may show evidence of an additional upward current at dawn likely associated with strong flows in the outer magnetosphere

Degeneracy Algorithm for Random Magnets

It has been known for a long time that the ground state problem of random magnets, e.g. random field Ising model (RFIM), can be mapped onto the max-flow/min-cut problem of transportation networks. I build on this approach, relying on the concept of residual graph, and design an algorithm that I prove to be exact for finding all the minimum cuts, i.e. the ground state degeneracy of these systems. I demonstrate that this algorithm is also relevant for the study of the ground state properties of the dilute Ising antiferromagnet in a constant field (DAFF) and interfaces in random bond magnets.Comment: 17 pages(Revtex), 8 Postscript figures(5color) to appear in Phys. Rev. E 58, December 1st (1998

Saturn's Nightside Ring Current During Cassini's Grand Finale

During Cassini's Grand Finale proximal orbits, the spacecraft traversed the nightside magnetotail to ∼21 Saturn radii. Clear signatures of Saturn's equatorial current sheet are observed in the magnetic field data. An axisymmetric model of the ring current is fitted to these data, amended to take into account the tilt of the current layer by solar wind forcing, its teardrop‐shaped nature and the magnetotail and magnetopause fringing fields. Variations in ring current parameters are examined in relation to external driving of the magnetosphere by the solar wind and internal driving by the two planetary period oscillations (PPOs), and compared with previous dawn and dayside observations. We find that the relative phasing of the PPOs determines the ring current's response to solar wind conditions. During solar wind compressions when the PPOs are in antiphase, a thick partial ring current is formed on the nightside, dominated by hot plasma injected by tail reconnection. This partial ring current should close partly via magnetopause currents and possibly via field‐aligned currents into the ionosphere. However, during solar wind compressions when the PPOs are in phase, this partial ring current is not detected. During solar wind rarefactions an equatorial “magnetodisc” configuration is observed in the dayside/dawn/nightside regions, with similar total currents flowing at these local times. During very quiet intervals of prolonged solar wind rarefaction, a thin current sheet with an enhanced current density is formed, indicative of a ring current dominated by cool, dense, Enceladus water group ions