Modulation of radio frequency signals by ULF waves

The ionospheric plasma is continually perturbed by ultra-low frequency (ULF; 1–100 mHz) plasma waves that are incident from the magnetosphere. In this paper we present a combined experimental and modeling study of the variation in radio frequency of signals propagating in the ionosphere due to the interaction of ULF wave energy with the ionospheric plasma. Modeling the interaction shows that the magnitude of the ULF wave electric field, <B>e</B>, and the geomagnetic field, <B>B</B><sub>0</sub>, giving an <B>e</B>×<B>B</B><sub>0</sub> drift, is the dominant mechanism for changing the radio frequency. We also show how data from high frequency (HF) Doppler sounders can be combined with HF radar data to provide details of the spatial structure of ULF wave energy in the ionosphere. Due to spatial averaging effects, the spatial structure of ULF waves measured in the ionosphere may be quite different to that obtained using ground based magnetometer arrays. The ULF wave spatial structure is shown to be a critical parameter that determines how ULF wave effects alter the frequency of HF signals propagating through the ionosphere

Remote sensing the plasmasphere, plasmapause, plumes and other features using ground-based magnetometers

The plasmapause is a highly dynamic boundary between different magnetospheric particle populations and convection regimes. Some of the most important space weather processes involve wave-particle interactions in this region, but wave properties may also be used to remote sense the plasmasphere and plasmapause, contributing to plasmasphere models. This paper discusses the use of existing ground magnetometer arrays for such remote sensing. Using case studies we illustrate measurement of plasmapause location, shape and movement during storms; refilling of flux tubes within and outside the plasmasphere; storm-time increase in heavy ion concentration near the plasmapause; and detection and mapping of density irregularities near the plasmapause, including drainage plumes, biteouts and bulges. We also use a 2D MHD model of wave propagation through the magnetosphere, incorporating a realistic ionosphere boundary and Alfvén speed profile, to simulate ground array observations of power and cross-phase spectra, hence confirming the signatures of plumes and other density structures

Generalizing Generic Differentiability Properties from Convex to Locally Lipschitz Functions

AbstractDavid Preiss proved that every locally Lipschitz function on an open subset of a Banach space which has an equivalent norm Gâteaux (Fréchet) differentiable away from the origin is Gâteaux (Fréchet) differentiable on a dense subset of its domain. It is known that every continuous convex function on an open convex subset of such a space is Gâteaux (Fréchet) differentiable on a residual subset of its domain. We show that for a locally Lipschitz function on a separable Banach space (with separable dual) there are residual subsets which if the function were convex would coincide with its set of points of differentiability. These are the sets where the function is fully intermediately differentiable (fully and uniformly intermediately differentiable) and sets where the subdifferential mapping is weak* (norm) lower semi-continuous. We discuss the role of these sets in generating the subdifferential and present a refinement of Preiss′ result

Fréchet directional differentiability and Fréchet differentiability

summary:Zaj'\i ček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any real-valued function on a normed linear space, the set of points where the function is Fréchet directionally differentiable but not Fréchet differentiable is first category

Relationship between ULF wave mode mix, equatorial electric fields, and ground magnetometer data

The magnetized plasma of near‐Earth space supports the shear and fast Alfvén, ultralow‐frequency (ULF; 1–100 mHz), magnetohydrodynamic wave modes. The fast mode may propagate across the magnetic field, spreading ULF wave energy throughout the magnetosphere, and couple with the shear Alfvén mode to form field line resonances (FLRs). The FLR electric field in the magnetosphere may have sufficiently large amplitudes to energize electrons and enhance radiation belt particle diffusion rates. Ozeke et al. (2009) recently described a technique that related the observed north‐south ULF magnetic component at the ground, b_v^g, with the radial electric field component in the equatorial plane of the magnetosphere, e_v^eq, via the fields in the ionosphere. In this paper we use a fully coupled ULF wave model to determine the ratio e_v^eq/b_v^g for a 5 mHz FLR formed at high latitudes. We find that Ozeke et al. (2009) underestimated the ULF wave magnetic field on the ground which varies with ionosphere Hall conductance. This difference is found to be caused by assuming a decoupled wave mode model for the ionosphere fields. Any relationship that involves ULF wavefields in the ionosphere must include the effects of ULF wave mode mixing

Appropriate modelling of school compositional effects: A response to Malatinszky and Armor, and Marks

We respond to Malatinszky and Armor’s, and Marks’ comments on our article recently published in this journal. We agree with Marks in the use of prior achievement to control for spurious effects in school effects research. Marks makes an incorrect statement about our article, refers to dated critiques, and presents an empirical demonstration with some problems. We agree with Malatinszky and Armor that school composition may have sufficient within-student variation to detect a potential effect on achievement growth in fixed-effects models. We argue that fixed-effects models exclude most of the variation in socioeconomic composition, are incapable of measuring the commonly defined conceptualisation of school composition and can mischaracterise the relative importance of socioeconomic composition

Does school socioeconomic composition matter more in some countries than others, and if so, why?

International research has consistently found that the socioeconomic segregation of schools may worsen inequalities in schooling outcomes through the socioeconomic compositional effect. This study examines whether the socioeconomic compositional effect varies between developed countries and potential mechanisms by which national schooling systems moderate its effect. The results suggest that the socioeconomic compositional effect does vary between developed countries and that national differences in its size were partially explained by policies of tracking age and the proportion of students that attend public schools. We conclude schooling systems in developed countries would require substantial reform to reduce the detrimental effects of school composition on disadvantaged students