Focussing effects in laser-electron Thomson scattering

We study the effects of laser pulse focussing on the spectral properties of Thomson scattered radiation. Modelling the laser as a paraxial beam we find that, in all but the most extreme cases of focussing, the temporal envelope has a much bigger effect on the spectrum than the focussing itself. For the case of ultra-short pulses, where the paraxial model is no longer valid, we adopt a sub-cycle vector beam description of the field. It is found that the emission harmonics are blue shifted and broaden out in frequency space as the pulse becomes shorter. Additionally the carrier envelope phase becomes important, resulting in an angular asymmetry in the spectrum. We then use the same model to study the effects of focussing beyond the limit where the paraxial expansion is valid. It is found that fields focussed to sub-wavelength spot sizes produce spectra that are qualitatively similar to those from sub-cycle pulses due to the shortening of the pulse with focussing. Finally, we study high-intensity fields and find that, in general, the focussing makes negligible difference to the spectra in the regime of radiation reaction.Comment: 14 pages, 17 figure

Insensitive control technology development

THe investigation of two insensitive controller synthesis techniques was reported. The finite dimensional inverse approach produces a time varying insensitive controller and/or parameter identifier by constructing inverse functions derived from a finite number of input output pair relationships. The MD/IM concept relies on the information matrix theory that was developed in the estimation and identification field. The MD/IM synthesis technique is based on the hypothesis that minimizing the information matrix will reduce system identifiability and consequently system sensitivity to uncertain parameters. The controllers designed with both techniques were evaluated on a realistic C-5A aircraft flight control problem. Results indicate that the FDI controller is more suited to trajectory type problems because of its time varying nature. The MD/IM controller performed as well as the top-rated controllers of the initial effort and has direct application to aircraft flight control problems

High-Precision Thermodynamics and Hagedorn Density of States

We compute the entropy density of the confined phase of QCD without quarks on the lattice to very high accuracy. The results are compared to the entropy density of free glueballs, where we include all the known glueball states below the two-particle threshold. We find that an excellent, parameter-free description of the entropy density between 0.7Tc and Tc is obtained by extending the spectrum with the exponential spectrum of the closed bosonic string.Comment: 4 pages, 3 figure

Umbral Moonshine and the Niemeier Lattices

In this paper we relate umbral moonshine to the Niemeier lattices: the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier lattice we attach a finite group by considering a naturally defined quotient of the lattice automorphism group, and for each conjugacy class of each of these groups we identify a vector-valued mock modular form whose components coincide with mock theta functions of Ramanujan in many cases. This leads to the umbral moonshine conjecture, stating that an infinite-dimensional module is assigned to each of the Niemeier lattices in such a way that the associated graded trace functions are mock modular forms of a distinguished nature. These constructions and conjectures extend those of our earlier paper, and in particular include the Mathieu moonshine observed by Eguchi-Ooguri-Tachikawa as a special case. Our analysis also highlights a correspondence between genus zero groups and Niemeier lattices. As a part of this relation we recognise the Coxeter numbers of Niemeier root systems with a type A component as exactly those levels for which the corresponding classical modular curve has genus zero.Comment: 181 pages including 95 pages of Appendices; journal version, minor typos corrected, Research in the Mathematical Sciences, 2014, vol.

Wind tunnel testing of low-drag airfoils

Results are presented for the measured performance recently obtained on several airfoil concepts designed to achieve low drag by maintaining extensive regions of laminar flow without compromising high-lift performance. The wind tunnel results extend from subsonic to transonic speeds and include boundary-layer control through shaping and suction. The research was conducted in the NASA Langley 8-Ft Transonic Pressure Tunnel (TPT) and Low Turbulence Pressure Tunnel (LTPT) which have been developed for testing such low-drag airfoils. Emphasis is placed on identifying some of the major factors influencing the anticipated performance of low-drag airfoils

Hand pollination to increase seed-set of red helleborine Cephalanthera rubra in the Chiltern Hills, Buckinghamshire, England

In 2007 and in previous years, as part of ongoing attempts to improve red helleborine Cephalanthera rubra seed-set, hand pollination of florets has been undertaken at a small colony of this species in Buckinghamshire, southern England. Natural pollination rarely occurs (one mature pod recorded in 10 years) at this site. In 2007, hand pollination resulted in the production of four seed pods, of which one withered and died. Upon ripening, the three remaining pods were removed for attempted micropropagation of the seeds. Ongoing conservation management has probably benefited the solitary bee Chelostoma campanularum which now appears fairly plentiful at the site, but despite the presence of this red helleborine flower visitor, natural pollination remains virtually unrecorded at this locality; field observations suggest that C.campanularum is in fact probably not large enough to act as an effective red helleborine pollinator as it can slip in and out of the flowers without removing the pollinia, unlike it larger relative C.fuliginosum, absent from the UK but which is a known pollinator of red helleborine in continental Europe

Final evaluation of the saving gateway 2 pilot: main report

The Saving Gateway is a government initiative aimed at encouraging savings behaviour among people who do not usually save. Each pound placed into a Saving Gateway account is matched by the government at a certain rate and up to a monthly contribution limit. Matching provides a transparent and understandable incentive for eligible individuals to place funds in an account