Suprathermal electron evolution in a Parker spiral magnetic field

Suprathermal electrons (>70 eV) form a small fraction of the total solar wind electron density but serve as valuable tracers of heliospheric magnetic field topology. Their usefulness as tracers of magnetic loops with both feet rooted on the Sun, however, most likely fades as the loops expand beyond some distance owing to scattering. As a first step toward quantifying that distance, we construct an observationally constrained model for the evolution of the suprathermal electron pitch-angle distributions on open field lines. We begin with a near-Sun isotropic distribution moving antisunward along a Parker spiral magnetic field while conserving magnetic moment, resulting in a field-aligned strahl within a few solar radii. Past this point, the distribution undergoes little evolution with heliocentric distance. We then add constant (with heliocentric distance, energy, and pitch angle) ad-hoc pitch-angle scattering. Close to the Sun, pitch-angle focusing still dominates, again resulting in a narrow strahl. Farther from the Sun, however, pitch-angle scattering dominates because focusing is effectively weakened by the increasing angle between the magnetic field direction and intensity gradient, a result of the spiral field. We determine the amount of scattering required to match Ulysses observations of strahl width in the fast solar wind, providing an important tool for inferring the large-scale properties and topologies of field lines in the interplanetary medium. Although the pitch-angle scattering term is independent of energy, time-of-flight effects in the spiral geometry result in an energy dependence of the strahl width that is in the observed sense although weaker in magnitude.

Forecasting models of retail rents

The authors model retail rents in the United Kingdom with use of vector-autoregressive and time-series models. Two retail rent series are used, compiled by LaSalle Investment Management and CB Hillier Parker, and the emphasis is on forecasting. The results suggest that the use of the vector-autoregression and time-series models in this paper can pick up important features of the data that are useful for forecasting purposes. The relative forecasting performance of the models appears to be subject to the length of the forecast time-horizon. The results also show that the variables which were appropriate for inclusion in the vector-autoregression systems differ between the two rent series, suggesting that the structure of optimal models for predicting retail rents could be specific to the rent index used. Ex ante forecasts from our time-series suggest that both LaSalle Investment Management and CB Hillier Parker real retail rents will exhibit an annual growth rate above their long-term mean.

Parliamentary sovereignty, popular sovereignty, and Henry Parker's adjudicative standpoint

Discussions of popular sovereignty in early modern England have usually been premised upon a sharp distinction between ‘legal/constitutional’ forms of discourse (which merely interpret the law) and ‘political’ ones (which focus upon the right to make it). In such readings of the period, Henry Parker has a pivotal position as a writer who abandoned merely legalistic thinking. This chapter takes a different view. It argues that Parker’s major intellectual achievement was not so much to abandon legal/constitutional discourse as to offer a theorisation of its most distinctive features: he offered an account of a new kind of politics in which concern for ‘interests’ in property and in self-preservation replaced humanist concern with promotion of virtue. Parker drew upon ideas about representation best expressed by Sir Thomas Smith and ideas about law best expressed by Oliver St John. The theory he developed was not intended as a justification of legislative sovereignty, but of adjudicative supremacy. His picture of the two Houses as supreme adjudicators was meant to block the path to direct democracy. But the adjudicative standpoint they came to occupy presupposed that freeborn adults had ‘interests’ in life, liberty, and possessions. This had democratising implications.