Electron Population Aging Models for Wide-Angle Tails

Color-color diagrams have been useful in studying the spectral shapes in radio galaxies. At the workshop we presented color-color diagrams for two wide-angle tails, 1231+674 and 1433+553, and found that the standard aging models do not adequately represent the observed data. Although the JP and KP models can explain some of the observed points in the color-color diagram, they do not account for those found near the power-law line. This difficulty may be attributable to several causes. Spectral tomography has been previously used to discern two separate electron populations in these sources. The combination spectra from two such overlying components can easily resemble a range of power-laws. In addition, any non-uniformity in the magnetic field strength can also create a power-law-like spectrum. We will also discuss the effects that angular resolution has on the shape of the spectrum.Comment: 4 pages, 1 figure, proceedings from 1999 'Life Cycles of Radio Galaxies' workshop at STScI in Baltimore, M

Generalised Cesaro Convergence, Root Identities and the Riemann Hypothesis

We extend the notion of generalised Cesaro summation/convergence developed previously to the more natural setting of what we call "remainder" Cesaro summation/convergence and, after illustrating the utility of this approach in deriving certain classical results, use it to develop a notion of generalised root identities. These extend elementary root identities for polynomials both to more general functions and to a family of identities parametrised by a complex parameter \mu. In so doing they equate one expression (the derivative side) which is defined via Fourier theory, with another (the root side) which is defined via remainder Cesaro summation. For \mu a non-positive integer these identities are naturally adapted to investigating the asymptotic behaviour of the given function and the geometric distribution of its roots. For the Gamma function we show that it satisfies the generalised root identities and use them to constructively deduce Stirling's theorem. For the Riemann zeta function the implications of the generalised root identities for \mu=0,-1 and -2 are explored in detail; in the case of \mu=-2 a symmetry of the non-trivial roots is broken and allows us to conclude, after detailed computation, that the Riemann hypothesis must be false. In light of this, some final direct discussion is given of areas where the arguments used throughout the paper are deficient in rigour and require more detailed justification. The conclusion of section 1 gives guidance on the most direct route through the paper to the claim regarding the Riemann hypothesis

An analogue of Hawking radiation in the quantum Hall effect

We use the identification of the edge mode of the filling fraction $\nu=1$ quantum Hall phase with a 1+1 dimensional chiral Dirac fermion to construct an analogue model for a chiral fermion in a space-time geometry possessing an event horizon. By solving the model in the lowest Landau level, we show that the event horizon emits particles and holes with a thermal spectrum. Each emitted quasiparticle is correlated with an opposite-energy partner on the other side of the event horizon. Once we trace out these "unobservable" partners, we are left with a thermal density matrix.Comment: 16 pages, five figure

Library impact data: investigating library use and student attainment

Analytics are increasingly being used to uncover new narratives and demonstrate new types of value and impact for libraries and their institutions. This section will explore some of the current opportunities that institutions are exploiting with the use of analytics and the innovative services and tools they are developing