Graduating live and on line: the multimedia webcast of the Open Universitys worldwide virtual degree ceremony

As the foremost international open learning institution, the UK Open University has now webcast two live and on-line degree ceremonies. Most higher education establishments routinely videotape degree presentations and many now broadcast these videos as ways of including remote family and friends who could not attend the physical event. In contrast, the UKOU has presented live ceremonies at which the graduands themselves, plus guests, family and friends were all remote and online! The first worldwide virtual degree ceremony took place at 15:00 GMT/UT on March 31st 2000. This ceremony was the first in the Open University’s calendar for 2000, and therefore the first formal ceremony of this leading open learning institution in the new millennium. The second online ceremony took place on 18th April 2001, and further ceremonies are planned as part of the routine of open learning

Rotation of a Bose-Einstein Condensate held under a toroidal trap

The aim of this paper is to perform a numerical and analytical study of a rotating Bose Einstein condensate placed in a harmonic plus Gaussian trap, following the experiments of \cite{bssd}. The rotational frequency $\Omega$ has to stay below the trapping frequency of the harmonic potential and we find that the condensate has an annular shape containing a triangular vortex lattice. As $\Omega$ approaches $\omega$, the width of the condensate and the circulation inside the central hole get large. We are able to provide analytical estimates of the size of the condensate and the circulation both in the lowest Landau level limit and the Thomas-Fermi limit, providing an analysis that is consistent with experiment

Cryogenic systems for the large deployable reflector

There are five technologies which may have application for Large Deployable Reflector (LDR), one passive and four active. In order of maturity, they are passive stored cryogen systems, and mechanical, sorption, magnetic, and pulse-tube refrigerators. In addition, deep space radiators will be required to reject the heat of the active systems, and may be useful as auxiliary coolers for the stored cryogen systems. Hybrid combinations of these technologies may well be more efficient than any one alone, and extensive system studies will be required to determine the best trade-offs. Stored cryogen systems were flown on a number of missions. The systems are capable of meeting the temperature requirements of LDR. The size and weight of stored cryogen systems are proportional to heat load and, as a result, are applicable only if the low-temperature heat load can be kept small. Systems using chemisorption and physical adsorption for compressors and pumps have received considerable attention in the past few years. Systems based on adiabatic demagnetization of paramagnetic salts were used for refrigeration for many years. Pulse-tube refrigerators were recently proposed which show relatively high efficiency for temperatures in the 60 to 80 K range. The instrument heat loads and operating temperatures are critical to the selection and design of the cryogenic system. Every effort should be made to minimize heat loads, raise operating temperatures, and to define these precisely. No one technology is now ready for application to LDR. Substantial development efforts are underway in all of the technologies and should be monitored and advocated. Magnetic and pulse-tube refrigerators have high potential

Randomly Weighted Self-normalized L\'evy Processes

Let $(U_t,V_t)$ be a bivariate L\'evy process, where $V_t$ is a subordinator and $U_t$ is a L\'evy process formed by randomly weighting each jump of $V_t$ by an independent random variable $X_t$ having cdf $F$. We investigate the asymptotic distribution of the self-normalized L\'evy process $U_t/V_t$ at 0 and at $\infty$. We show that all subsequential limits of this ratio at 0 ($\infty$) are continuous for any nondegenerate $F$ with finite expectation if and only if $V_t$ belongs to the centered Feller class at 0 ($\infty$). We also characterize when $U_t/V_t$ has a non-degenerate limit distribution at 0 and $\infty$.Comment: 32 page

On the Breiman conjecture

Let $Y_{1},Y_{2},\ldots$ be positive, nondegenerate, i.i.d. $G$ random variables, and independently let $X_{1},X_{2},\ldots$ be i.i.d. $F$ random variables. In this note we show that whenever $\sum X_{i}Y_{i}/\sum Y_{i}$ converges in distribution to nondegenerate limit for some $F\in \mathcal{F}$, in a specified class of distributions $\mathcal{F}$, then $G$ necessarily belongs to the domain of attraction of a stable law with index less than 1. The class $\mathcal{F}$ contains those nondegenerate $X$ with a finite second moment and those $X$ in the domain of attraction of a stable law with index $1<\alpha <2$

A classification of the ground states and topological defects in a rotating two-component Bose-Einstein condensate

We classify the ground states and topological defects of a rotating two-component condensate when varying several parameters: the intracomponent coupling strengths, the intercomponent coupling strength and the particle numbers.No restriction is placed on the masses or trapping frequencies of the individual components. We present numerical phase diagrams which show the boundaries between the regions of coexistence, spatial separation and symmetry breaking. Defects such as triangular coreless vortex lattices, square coreless vortex lattices and giant skyrmions are classified. Various aspects of the phase diagrams are analytically justified thanks to a non-linear $\sigma$ model that describes the condensate in terms of the total density and a pseudo-spin representation

Time-dependent Real-space Renormalization-Group Approach: application to an adiabatic random quantum Ising model

We develop a time-dependent real-space renormalization-group approach which can be applied to Hamiltonians with time-dependent random terms. To illustrate the renormalization-group analysis, we focus on the quantum Ising Hamiltonian with random site- and time-dependent (adiabatic) transverse-field and nearest-neighbour exchange couplings. We demonstrate how the method works in detail, by calculating the off-critical flows and recovering the ground state properties of the Hamiltonian such as magnetization and correlation functions. The adiabatic time allows us to traverse the parameter space, remaining near-to the ground state which is broadened if the rate of change of the Hamiltonian is finite. The quantum critical point, or points, depend on time through the time-dependence of the parameters of the Hamiltonian. We, furthermore, make connections with Kibble-Zurek dynamics and provide a scaling argument for the density of defects as we adiabatically pass through the critical point of the system

Communities in Networks

We survey some of the concepts, methods, and applications of community detection, which has become an increasingly important area of network science. To help ease newcomers into the field, we provide a guide to available methodology and open problems, and discuss why scientists from diverse backgrounds are interested in these problems. As a running theme, we emphasize the connections of community detection to problems in statistical physics and computational optimization.Comment: survey/review article on community structure in networks; published version is available at http://people.maths.ox.ac.uk/~porterm/papers/comnotices.pd

Observations of Early Optical Afterglows

The Swift Ultra-Violet/Optical Telescope (UVOT) has performed extensive follow-up on 71 Swift Burst Alert Telescope triggered gamma-ray bursts (GRBs) in its first ten months of operations. In this paper, we discuss some of the UV and optical properties of UVOT detected afterglows such as XRF 050406, the bright GRB 050525A, the high redshift GRB 050730, the early flaring GRB 050801, and others. We also discuss some of the implications of why 75% of GRB afterglows observed by UVOT in less than one hour are "dark."Comment: 10 pages, 6 figures, to appear in the Proceedings of the 16th Annual Astrophysics Conference in Maryland "Gamma Ray Bursts in the Swift Era," Washington, DC, November 29 - December 2, 200

The Bowl Championship Series: A Mathematical Review

We discuss individual components of the college football Bowl Championship Series, compare with a simple algorithm defined by random walks on a biased graph, attempt to predict whether the proposed changes will truly lead to increased BCS bowl access for non-BCS schools, and conclude by arguing that the true problem with the BCS Standings lies not in the computer algorithms, but rather in misguided addition.Comment: 12 pages, 2 figures, submitted to Notices of the AM