Block diagonalisation of four-dimensional metrics

It is shown that, in 4-dimensions, it is possible to introduce coordinates so that an analytic metric locally takes block diagonal form. i.e. one can find coordinates such that g = 0 for (, ) 2 S where S = {(1, 3), (1, 4), (2, 3), (2, 4)}. We call a coordinate system in which the metric takes this form a ‘doubly biorthogonal coordinate system’. We show that all such coordinate systems are determined by a pair of coupled second-order partial differential equation

Digital micromirror devices for laser-based manufacturing

Digital Micromirror Devices (DMDs), containing arrays of around one million individually-controllable ~10µm square mirrors, provide an extremely cost-effective and practical method to modulate the spatial beam profile of a pulsed laser source for both additive and subtractive laser processing and printing. When demagnified by a factor of ~100 in one dimension (hence ~10,000 in area) a ~1mJ/cm2 laser pulse reflected from the mirrors on the DMD surface that are switched to the 'on' position, attains a fluence of ~10J/cm2 at the workpiece, which is more than sufficient to ablate most materials of interest to the laser-manufacturing community. More familiar in the context of high values of magnification by the laser projection industry, reversing the role to use them for equally high values of demagnification opens up a wealth of possibilities for ablation, multiphoton polymerization, security marking and fabrication of features that perhaps surprisingly can be well below the wavelength of the laser used. Of key relevance is that very high-resolution patterning can be achieved by a single laser pulse, and step-and-repeat processes, when combined with the refresh rates of the DMD pattern that are currently at the 30kHz level, open up the possibility of processing areas of up to 1cm2 per second with micron-scale resolution where each ~100µm x 100µm area patterned per pulse can display arbitrary pixelated content. We will discuss the application of DMD-baser laser processing to the following areas of interest to the laser-manufacturing community

Southward expansion: The myth of the West in the promotion of Florida, 1876–1900

This article examines the ways in which promoters and developers of Florida, in the decades after Reconstruction, engaged with a popular myth of the West as a means of recasting and selling their state to prospective settlers in the North and Midwest. The myth envisaged a cherished region to the west where worthy Americans could migrate and achieve social and economic independence away from the crowded confines of the East, or Europe. According to state immigration agents, land-promoters and other booster writers, Florida, although a Southern ex-Confederate state, offered precisely these 'western' opportunities for those hard-working Northerners seeking land and an opening for agrarian prosperity. However, the myth, which posited that, in the west, an individual's labour and thrift were rewarded with social and economic improvement, meshed awkwardly with the contemporary emergence of Florida as a popular winter destination for wealthy tourists and invalids seeking leisure and healthfulness away from the North. Yet it also reflected and reinforced promotional notions of racial improvement which would occur with an influx of enterprising Anglo-Americans, who would effectively displace the state's large African American population. In Florida, the myth of the West supported the linked post-Reconstruction processes of state development and racial subjugation

Femtosecond laser-induced patterned transfer of intact semiconductor and polymer thin films via a digital micromirror device

The laser-induced forward transfer (LIFT) of thin films is an attractive technique to deposit materials on a size scale that can span nanometres to millimeters. During LIFT, the energy of a laser pulse is absorbed in a small volume of a thin film (donor) causing an explosive expansion which is used to propel a portion of the donor away from the carrier substrate and transfer it onto a receiver substrate as shown in Fig.1(a). Ultrashort laser systems can limit laser damage to remaining areas of the donor usually present using laser systems with longer (nanosecond) pulse widths

Yb:YAG planar waveguide lasers grown by pulsed laser deposition: 70% slope efficiencies at 16 W of output power

We present our recent advances in the use of pulsed laser deposition (PLD) to fabricate active gain elements for use as amplifiers and laser oscillators. Record output powers exceeding 16 W and slope efficiencies of 70% are reported for optimized epitaxial growth of Yb(7.5%):YAG on to YAG substrates. We show for the first time that the performance of PLD material can meet or even exceed that of materials grown by more established methods such as the Czochralski technique. Details of fabrication, characterization and laser performance are presented in addition to outlining expected future improvements

Comparative study of rare-earth doped sesquioxides grown by pulsed laser deposition and their performance as planar waveguide lasers

The sesquioxides yttria, scandia and lutetia have been identified as promising host materials for high power lasers due to their excellent thermal properties, their ability to incorporate RE-ions and their resulting spectroscopic properties [1]. However, the melting points of these materials exceed 2400°C and are therefore problematic to grow from the melt. Pulsed laser deposition (PLD) is an alternative method of growing thin crystalline films of these materials, avoiding the requirement for such high temperature growth

The wave equation on singular space-times

We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.Comment: Latex, 19 pages, 1 figure. Discussion of class of metrics covered by our results and some examples added. Conclusion more detailed. Version to appear in Communications in Mathematical Physic

Comparison of Three CIDR Based Fixed-time AI Protocols for Beef Heifers

Several effective fixed-time AI (FTAI) protocols have been developed to facilitate AI while eliminating the need for estrus detection. Among these are the 5-d CO-Synch+CIDR (5d), PG 6-d CIDR (PG-CIDR), and 14-d CIDR-PG (CIDR-PG) protocols. While each of these protocols varies in duration and approach to synchronizing estrus and ovulation, each has been reported as an effective method to facilitate FTAI in beef heifers. Therefore, the objective of this study was to compare FTAI pregnancy rates in beef heifers synchronized with these three CIDR based protocols. Virgin beef heifers (n = 801) at four locations were synchronized with one of three protocols: 1) (5-day CO-Synch + CIDR) an injection of GnRH (100 μg; i.m.) and insertion of a CIDR on d -5, PG (25 mg; i.m.) and CIDR removal on d 0 with a second injection of PG (\u3e4 h after CIDR removal) on d 0 and FTAI at 72 h after CIDR removal, 2) (PG 6-day CIDR) PG (25 mg; i.m.) on d -9, GnRH (100 μg; i.m.) and insertion of a CIDR on d -6, PG and CIDR removal on d 0, and FTAI at 66 h after CIDR removal, or 3) (14-day CIDR-PG) a 14-day CIDR insert from d -30 to -16, PG (25 mg; i.m.) on d 0, and FTAI at 66 h after PG. All heifers received an injection of GnRH (100 μg; i.m.) concurrent with FTAI. Timing of treatment initiation was offset to allow all heifers to receive FTAI concomitantly and at random. Pregnancy success was determined between 35 and 40 d after FTAI by transrectal ultrasonography. Blood samples were collected approximately 12 d before the beginning of each protocol and at the initiation of each protocol to determine estrous cycling status (77%). Data were analyzed using the GLIMMIX procedures of SAS. Fixed-time AI pregnancy success did not differ between treatments (P = 0.13; 62.5%, 56.9%, and 53.3%, for 5-day CO-Synch + CIDR, PG 6-day CIDR, and 14-day CIDR-PG; respectively) or location (P = 0.16; 51.5%, 62.7%, 56.1%, and 58.6% for location 1, 2, 3, and 4; respectively). However, heifers that had reached puberty by initiation of synchronization had greater (P \u3c 0.01) pregnancy success compared to heifers that were prepubertal (60.7% and 47.3%; respectively). In summary, all three protocols had similar FTAI pregnancy success, and puberty status had the greatest impact on pregnancy success

Bubbling Orientifolds

We investigate a class of 1/2-BPS bubbling geometries associated to orientifolds of type IIB string theory and thereby to excited states of the SO(N)/Sp(N) N=4 supersymmetric Yang-Mills theory. The geometries are in correspondence with free fermions moving in a harmonic oscillator potential on the half-line. Branes wrapped on torsion cycles of these geometries are identified in the fermi fluid description. Besides being of intrinsic interest, these solutions may also occur as local geometries in flux compactifications where orientifold planes are present to ensure global charge cancellation. We comment on the extension of this procedure to M-theory orientifolds.Comment: 25 pages, 11 figures. v2: few references adde

The tan(beta) - M_H^\pm bound from inclusive semi-tauonic B-decays in the MSSM

We compute the O(alpha_s) SUSY-QCD corrections to the W and charged Higgs mediated inclusive semi-tauonic B-decay, B->tau antineutrino_tau X. Combining the SUSY contribution with the SM result obtained from the heavy quark effective field theory, plus ordinary QCD corrections, we find that the allowed region in the (tan(beta),M_H^\pm)-plane could be significantly modified by the short-distance supersymmetric effects. Since the sensitivity to the SUSY parameters other than mu (the higgsino mixing mass) is rather low, the following effective bound emerges for mu<0 at the 2 sigma level: tan(beta)~< 0.43 (M_H^\pm/GeV). Remarkably, for mu>0 there could be no bound at all. Finally, we provide a combined (tan(beta,M_H^\pm) exclusion plot using our B-meson results together with the recent data from top quark decays.Comment: 15 pages, LaTeX, 1 table and 3 figs included as a separate file, full postscript version avaliable at ftp://ftp.ifae.es/preprint/ft/uabft407.ps . New comments and references added. Accepted version in Phys. Lett.