Survival of near-critical branching Brownian motion

Consider a system of particles performing branching Brownian motion with negative drift $\mu = \sqrt{2 - \epsilon}$ and killed upon hitting zero. Initially there is one particle at $x>0$. Kesten showed that the process survives with positive probability if and only if $\epsilon>0$. Here we are interested in the asymptotics as \eps\to 0 of the survival probability $Q_\mu(x)$. It is proved that if $L= \pi/\sqrt{\epsilon}$ then for all $x \in \R$, $\lim_{\epsilon \to 0} Q_\mu(L+x) = \theta(x) \in (0,1)$ exists and is a travelling wave solution of the Fisher-KPP equation. Furthermore, we obtain sharp asymptotics of the survival probability when $x<L$ and $L-x \to \infty$. The proofs rely on probabilistic methods developed by the authors in a previous work. This completes earlier work by Harris, Harris and Kyprianou and confirms predictions made by Derrida and Simon, which were obtained using nonrigorous PDE methods

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate $n^{-1/2}$, $n$ being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.Comment: To appear in the Annals of the Institute of Statistical Mathematics, this http://www.ism.ac.jp/editsec/aism-e.htm

3D printed fluidics with embedded analytic functionality for automated reaction optimisation

Additive manufacturing or ‘3D printing’ is being developed as a novel manufacturing process for the production of bespoke micro- and milliscale fluidic devices. When coupled with online monitoring and optimisation software, this offers an advanced, customised method for performing automated chemical synthesis. This paper reports the use of two additive manufacturing processes, stereolithography and selective laser melting, to create multifunctional fluidic devices with embedded reaction monitoring capability. The selectively laser melted parts are the first published examples of multifunctional 3D printed metal fluidic devices. These devices allow high temperature and pressure chemistry to be performed in solvent systems destructive to the majority of devices manufactured via stereolithography, polymer jetting and fused deposition modelling processes previously utilised for this application. These devices were integrated with commercially available flow chemistry, chromatographic and spectroscopic analysis equipment, allowing automated online and inline optimisation of the reaction medium. This set-up allowed the optimisation of two reactions, a ketone functional group interconversion and a fused polycyclic heterocycle formation, via spectroscopic and chromatographic analysis

Quantifying the frequency and volume of urine deposition by grazing sheep using tri-axial accelerometers

Urine patches deposited in pasture by grazing animals are sites of reactive nitrogen (N) loss to the environment due to high concentrations of N exceeding pasture uptake requirements. In order to upscale N losses from the urine patch, several urination parameters are required, including where, when and how often urination events occur as well as the volume and chemical composition. There are limited data available in this respect, especially for sheep. Here, we seek to address this knowledge gap by using non-invasive sensor-based technology (accelerometers) on ewes grazing in situ, using a Boolean algorithm to detect urination events in the accelerometer signal. We conducted an initial study with penned Welsh Mountain ewes (n = 5), with accelerometers attached to the hind, to derive urine flow rate and to determine whether urine volume could be estimated from ewe squat time. Then accelerometers attached to the hind of Welsh Mountain ewes (n = 30 at each site) were used to investigate the frequency of sheep urination events (n = 35 946) whilst grazing two extensively managed upland pastures (semi-improved and unimproved) across two seasons (spring and autumn) at each site (35–40 days each). Sheep urinated at a frequency of 10.2 ± 0.2 and 8.1 ± 0.3 times per day in the spring and autumn, respectively, while grazing the semi-improved pasture. Urination frequency was greater (19.0 ± 0.4 and 15.3 ± 0.3 times per day in the spring and autumn, respectively) in the unimproved pasture. Ewe squat duration could be reliably used to predict the volume of urine deposited per event and was thus used to estimate mean daily urine production volumes. Sheep urinated at a rate of 16.6 mL/s and, across the entire dataset, sheep squatted for an average of 9.62 ± 0.03 s per squatting event, producing an estimated average individual urine event volume of 159 ± 1 mL (n = 35 946 events), ranging between 17 and 745 mL (for squat durations of 1 to 45 s). The estimated mean daily urine volume was 2.15 ± 0.04 L (n = 2 669 days) across the entire dataset. The data will be useful for modelling studies estimating N losses (e.g. ammonia (NH3) volatilisation, nitrous oxide (N2O) emission via nitrification and denitrification and nitrate (NO3−) leaching) from urine patches

Monitoring Cross-Linking, the Evolution of Refractive Index and the Glass Transition Temperature of an Epoxy Resin Using an Optical Fiber Sensor

Hyphenated analytical techniques enable the simultaneous measurement of relevant processing and materials parameters under identical environmental conditions. In the current study, a power-compensated differential scanning calorimeter (DSC) was custom-modified to enable the integration of an optical fibre sensor to monitor in situ the progression of the cross-linking reactions by inferring the evolution of the refractive index. A cleaved optical fibre was used and it served as a Fresnel reflection sensor (FRS). The DSC was calibrated with and without the integrated FRS and it was demonstrated that it did not influence the performance of the DSC. The FRS was calibrated using reference refractive index oils within the DSC. An epoxy/amine resin system was cross-linked at 70 ^oC and the enthalpy of cross-linking and the evolution of the refractive index were monitored simultaneously using the DSC and FRS respectively. After the cross-linking was completed, the DSC was programmed to perform a ramped heating schedule from ambient temperature to 150 ^oC. The FRS was capable of detecting glass transition temperature (Tg) of the cross-linked resin. An excellent correlation was observed for the Tg obtained by the FRS and DSC. The contribution of factors affecting the resolution of the data from the FRS are discussed.</p

Transverse Fresnel-Fizeau drag effects in strongly dispersive media

A light beam normally incident upon an uniformly moving dielectric medium is in general subject to bendings due to a transverse Fresnel-Fizeau light drag effect. In conventional dielectrics, the magnitude of this bending effect is very small and hard to detect. Yet, it can be dramatically enhanced in strongly dispersive media where slow group velocities in the m/s range have been recently observed taking advantage of the electromagnetically induced transparency (EIT) effect. In addition to the usual downstream drag that takes place for positive group velocities, we predict a significant anomalous upstream drag to occur for small and negative group velocities. Furthermore, for sufficiently fast speeds of the medium, higher order dispersion terms are found to play an important role and to be responsible for peculiar effects such as light propagation along curved paths and the restoration of the spatial coherence of an incident noisy beam. The physics underlying this new class of slow-light effects is thoroughly discussed

Pulsed Magnetic Field Measurements of the Composite Fermion Effective Mass

Magnetotransport measurements of Composite Fermions (CF) are reported in 50 T pulsed magnetic fields. The CF effective mass is found to increase approximately linearly with the effective field $B^*$, in agreement with our earlier work at lower fields. For a $B^*$ of 14 T it reaches $1.6m_e$, over 20 times the band edge electron mass. Data from all fractions are unified by the single parameter $B^*$ for all the samples studied over a wide range of electron densities. The energy gap is found to increase like $\sqrt{B^*}$ at high fields.Comment: Has final table, will LaTeX without error

Notes on a paper of Mess

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.Comment: 26 page