Characterising small solutions in delay differential equations through numerical approximations

This paper discusses how the existence of small solutions for delay differential equations can be predicted from the behaviour of the spectrum of the finite dimensional approximations.Manchester Centre for Computational Mathematic

Neutrinoless Double Beta Decay with SNO+

SNO+ will search for neutrinoless double beta decay by loading 780 tonnes of linear alkylbenzene liquid scintillator with O(tonne) of neodymium. Using natural Nd at 0.1% loading will provide 43.7 kg of 150Nd given its 5.6% abundance and allow the experiment to reach a sensitivity to the effective neutrino mass of 100-200 meV at 90% C.L in a 3 year run. The SNO+ detector has ultra low backgrounds with 7000 tonnes of water shielding and self-shielding of the scintillator. Distillation and several other purification techniques will be used with the aim of achieving Borexino levels of backgrounds. The experiment is fully funded and data taking with light-water will commence in 2012 with scintillator data following in 2013.Comment: 4 pages, 2 figures, prepared for TAUP 201

Free energy of formation of clusters of sulphuric acid and water molecules determined by guided disassembly

We evaluate the grand potential of a cluster of two molecular species, equivalent to its free energy of formation from a binary vapour phase, using a nonequilibrium molecular dynamics technique where guide particles, each tethered to a molecule by a harmonic force, move apart to disassemble a cluster into its components. The mechanical work performed in an ensemble of trajectories is analysed using the Jarzynski equality to obtain a free energy of disassembly, a contribution to the cluster grand potential. We study clusters of sulphuric acid and water at 300 K, using a classical interaction scheme, and contrast two modes of guided disassembly. In one, the cluster is broken apart through simple pulling by the guide particles, but we find the trajectories tend to be mechanically irreversible. In the second approach, the guide motion and strength of tethering are modified in a way that prises the cluster apart, a procedure that seems more reversible. We construct a surface representing the cluster grand potential, and identify a critical cluster for droplet nucleation under given vapour conditions. We compare the equilibrium populations of clusters with calculations reported by Henschel et al. [J. Phys. Chem. A 118, 2599 (2014)] based on optimised quantum chemical structures

Gravitons and Lightcone Fluctuations II: Correlation Functions

A model of a fluctuating lightcone due to a bath of gravitons is further investigated. The flight times of photons between a source and a detector may be either longer or shorter than the light propagation time in the background classical spacetime, and will form a Gaussian distribution centered around the classical flight time. However, a pair of photons emitted in rapid succession will tend to have correlated flight times. We derive and discuss a correlation function which describes this effect. This enables us to understand more fully the operational significance of a fluctuating lightcone. Our results may be combined with observational data on pulsar timing to place some constraints on the quantum state of cosmological gravitons.Comment: 16 pages and two figures, uses eps

A quantum weak energy inequality for the Dirac field in two-dimensional flat spacetime

Fewster and Mistry have given an explicit, non-optimal quantum weak energy inequality that constrains the smeared energy density of Dirac fields in Minkowski spacetime. Here, their argument is adapted to the case of flat, two-dimensional spacetime. The non-optimal bound thereby obtained has the same order of magnitude, in the limit of zero mass, as the optimal bound of Vollick. In contrast with Vollick's bound, the bound presented here holds for all (non-negative) values of the field mass.Comment: Version published in Classical and Quantum Gravity. 7 pages, 1 figur

The unphysical nature of "Warp Drive"

We will apply the quantum inequality type restrictions to Alcubierre's warp drive metric on a scale in which a local region of spacetime can be considered ``flat''. These are inequalities that restrict the magnitude and extent of the negative energy which is needed to form the warp drive metric. From this we are able to place limits on the parameters of the ``Warp Bubble''. It will be shown that the bubble wall thickness is on the order of only a few hundred Planck lengths. Then we will show that the total integrated energy density needed to maintain the warp metric with such thin walls is physically unattainable.Comment: 11 pages, 3 figures, latex. This revision corrects a typographical sign error in Eq. (3

Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics

Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly. The quantum dynamics near the classical limit displays both exponential separation of adjacent distributions and long time relaxation, two characteristic features of classical chaotic motion.Comment: 10 pages, ReVTeX, to appear in Phys. Rev. Lett. 13 figures NOT included. Available either as LARGE (uuencoded gzipped) postscript files or hard-copies from [email protected]

Whole-blood thiopurine S-methyltransferase activity with genotype concordance: a new, simplified phenotyping assay.

BackgroundWe have developed a new thiopurine S-methyltransferase (TPMT) phenotyping method that measures TPMT activity in whole blood. To evaluate this assay, we compared it with conventional TPMT phenotyping, which uses a red blood cell (RBC) lysate and genotyping for analysis of common TPMT mutations.MethodsWhole-blood and RBC lysates were prepared from 402 patients' samples received for routine analysis. The TPMT activity of lysates was determined using 6-thioguanine as substrate with high-performance liquid chromatographic (HPLC) analysis and fluorimetric detection. DNA was extracted from buffy coats using phenol-chloroform extraction. A multiplex amplification refractory mutation system (ARMS) strategy was used to screen for the common TPMT mutations TPMT*2 and TPMT*3 (TPMT*3A, TPMT*3C and TPMT*3D).ResultsTPMT activities were higher in the whole-blood (mean TPMT activity 51 nmol 6-MTG/gHb/h) compared with the RBC lysate (37 nmol 6-MTG/gHb/h). Overall, concordance with TPMT genotypic analysis was 97% for both the new whole-blood and standard RBC lysate methods. Between low TPMT activity and heterozygotes, both phenotypic methods gave a concordance of 79%.ConclusionUsing multiplex ARMS testing for TPMT*2 and 3*C mutations to define the cut-off between low and normal TPMT activity, we have demonstrated that the new whole-blood TPMT phenotyping method performs as well as the conventional RBC lysate assay. This new method overcomes the need to prepare a RBC lysate, a process which is time consuming and increases analytical variation. The resulting assay is better suited to a regional or national TPMT phenotyping service

Classical Scalar Fields and the Generalized Second Law

It has been shown that classical non-minimally coupled scalar fields can violate all of the standard energy conditions in general relativity. Violations of the null and averaged null energy conditions obtainable with such fields have been suggested as possible exotic matter candidates required for the maintenance of traversable wormholes. In this paper, we explore the possibility that if such fields exist, they might be used to produce large negative energy fluxes and macroscopic violations of the generalized second law (GSL) of thermodynamics. We find that it appears to be very easy to produce large magnitude negative energy fluxes in flat spacetime. However we also find, somewhat surprisingly, that these same types of fluxes injected into a black hole do {\it not} produce violations of the GSL. This is true even in cases where the flux results in a decrease in the area of the horizon. We demonstrate that two effects are responsible for the rescue of the GSL: the acausal behavior of the horizon and the modification of the usual black hole entropy formula by an additional term which depends on the scalar field.Comment: 25 pages, 2 figures; paper substantially rewritten, major changes in the conclusion

Quantum Inequalities for the Electromagnetic Field

A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential, and the sampling function used to weight the energy integrals is left arbitrary up to the constraints that it be a positive, continuous function of unit area and that it decays at infinity. Examples of the quantum inequality are developed for Minkowski spacetime, Rindler spacetime and the Einstein closed universe.Comment: 19 pages, 1 table and 1 figure. RevTex styl