[1] The open-closed magnetic field line boundary (OCB) is an important indicator of magnetospheric dynamics and can be used to identify locations of particle precipitation at the edge of the magnetosphere. The OCB can fluctuate during geomagnetic events, and the extent of this variability is a vital component of space weather research and modeling. There was a unique opportunity to identify and study the synoptic variability of the OCB during the extended 2007-2009 solar quiet period through use of the Polar Experiment Network for Geophysical Upper-atmosphere Investigations-Automatic Geophysical Observatory (PENGUIn-AGO) network of ground-based fluxgate magnetometers on the Antarctic continent. The fluxgates, which measured the occurrence of standing Pc5 modes on closed field magnetic field lines, allowed for identification of the OCB structure and study of the synoptic behavior of the OCB before and during a corotating interaction region (CIR)-driven magnetic storm. Observations were compared with results from the BATSRUS space weather model and show 83% agreement for over ∼2 days before the CIR event. It is shown that such synoptic magnetometer data sets of the OCB during these storms allow for a careful test of current space weather models. The current study investigates the pre-storm time period, while a future paper will address the storm time evolution of the OCB.

Blackmore-Samulyak-Rosato (BSR) fields, originally developed as a means of obtaining reliable continuum approximations for granular flow dynamics in terms of relatively simple integro-differential equations, can be used to model a wide range of physical phenomena. Owing to results obtained for one-dimensional granular flow configurations, it has been conjectured that BSR models of fields with perfectly elastic interactions are completely integrable infinite-dimensional Hamiltonian systems. This conjecture is proved for BSR models in one space dimension, and analogues of BSR fields involving fractional time derivatives are briefly investigated.

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The dynamics of a vertical stack of particles subject to gravity and a sequence of small, periodically applied taps is considered. First, the motion of the particles, assumed to be identical, is modeled as a system of ordinary differential equations, which is analyzed with an eye to observing connections with finite-dimensional Hamiltonian systems. Then, two approaches to obtaining approximate continuum models for large numbers of particles are described: the long-wave approximation that yields partial differential equations and the BSR method that employs integro-partial differential models. These approximate continuum models, which comprise infinite-dimensional dynamical systems, are studied with a focus on nonlinear wave type behavior, which naturally leads to investigating links to infinitedimensional Hamiltonian systems. Several examples are solved numerically to show similarities among the solution properties of the finite-dimensional (lattice-dynamics), and the approximate long-wave and BSR continuum models. Extensions to higher dimensions and more general dynamically driven particle configurations are also sketched.

The day‐to‐day evolution and statistical features of Pc3‐Pc7 band ultralow frequency (ULF) power throughout the southern polar cap suggest that the corrected geomagnetic (CGM) coordinates do not adequately organize the observed hydromagnetic spatial structure. It is shown that that the local‐time distribution of ULF power at sites along CGM latitudinal parallels exhibit fundamental differences and that the CGM latitude of a site in general is not indicative of the site's projection into the magnetosphere. Thus, ULF characteristics observed at a single site in the polar cap cannot be freely generalized to other sites of similar CGM latitude but separated in magnetic local time, and the inadequacy of CGM coordinates in the polar cap has implications for conjugacy/mapping studies in general. In seeking alternative, observationally motivated systems of “polar cap latitudes,” it is found that eccentric dipole (ED) coordinates have several strengths in organizing the hydromagnetic spatial structure in the polar cap region. ED latitudes appear to better classify the local‐time ULF power in both magnitude and morphology and better differentiate the “deep polar cap” (where the ULF power is largely UT dependent and nearly free of local‐time structure) from the “peripheral polar cap” (where near‐magnetic noon pulsations dominate at lower and lower frequencies as one increases in ED latitude). Eccentric local time is shown to better align the local‐time profiles in the magnetic east component over several PcX bands but worsen in the magnetic north component. It is suggested that a hybrid ED‐CGM coordinate system might capture the strengths of both CGM and ED coordinates. It is shown that the local‐time morphology of median ULF power at high‐latitude sites is dominantly driven by where they project into the magnetosphere, which is best quantified by their proximity to the low‐altitude cusp on the dayside (which is not necessarily quantified by a site's CGM latitude), and that variations in the local‐time morphology at sites similar in ED latitude are due to both geographic local‐time control (relative amplification or dampening by the diurnal variation in the local ionospheric conductivity) and geomagnetic coastal effects (enhanced power in a coastally mediated direction). Regardless of cause, it is emphasized that the application of CGM latitudes in the polar cap region is not entirely meaningful and likely should be dispensed with in favor of a scheme that is in better accord with the observed hydromagnetic spatial structure.