Note on the derivative of the hyperbolic cotangent

In a letter to Nature (Ford G W and O'Connell R F 1996 Nature 380 113) we presented a formula for the derivative of the hyperbolic cotangent that differs from the standard one in the literature by an additional term proportional to the Dirac delta function. Since our letter was necessarily brief, shortly after its appearance we prepared a more extensive unpublished note giving a detailed explanation of our argument. Since this note has been referenced in a recent article (Estrada R and Fulling S A 2002 J. Phys. A: Math. Gen. 35 3079) we think it appropriate that it now appear in print. We have made no alteration to the original note

What Brown saw and you can too

A discussion is given of Robert Brown's original observations of particles ejected by pollen of the plant \textit{Clarkia pulchella} undergoing what is now called Brownian motion. We consider the nature of those particles, and how he misinterpreted the Airy disc of the smallest particles to be universal organic building blocks. Relevant qualitative and quantitative investigations with a modern microscope and with a "homemade" single lens microscope similar to Brown's, are presented.Comment: 14.1 pages, 11 figures, to be published in the American Journal of Physics. This differs from the previous version only in the web site referred to in reference 3. Today, this Brownian motion web site was launched, and http://physerver.hamilton.edu/Research/Brownian/index.html, is now correc

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

The Effects of Stress Tensor Fluctuations upon Focusing

We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources. We give explicit results for the case of a scalar field on a flat background in a thermal state.Comment: 26 pages, 1 figure, new material added in Sect. III and in Appendices B and

Inelastic scattering calculations with projected Hartree-Fock wave functions: Coupled channel treatment

Microscopic coupled-channel analysis of proton inelastic scattering from neon and magnesium ion

How accessible and acceptable are current GP referral mechanisms for IAPT for low-income patients? Lay and primary care perspectives

Background: Improving Access to Psychological Therapies (IAPT) constitutes a key element of England’s national mental health strategy. Accessing IAPT usually requires patients to self-refer on the advice of their GP. Little is known about how GPs perceive and communicate IAPT services with patients from low-income communities, nor how the notion of self-referral is understood and responded to by such patients. Aims: This paper examines how IAPT referrals are made by GPs and how these referrals are perceived and acted on by patients from low-income backgrounds Method: Findings are drawn from in-depth interviews with low-income patients experiencing mental distress (n = 80); interviews with GPs (n = 10); secondary analysis of video-recorded GP-patient consultations for mental health (n = 26). Results: GPs generally supported self-referral, perceiving it an important initial step towards patient recovery. Most patients however, perceived self-referral as an obstacle to accessing IAPT, and felt their mental health needs were being undermined. The way that IAPT was discussed and the pathway for referral appears to affect uptake of these services. Conclusions: A number of factors deter low-income patients from self-referring for IAPT. Understanding these issues is necessary in enabling the development of more effective referral and support mechanisms within primary care

Multi-scale Renormalisation Group Improvement of the Effective Potential

Using the renormalisation group and a conjecture concerning the perturbation series for the effective potential, the leading logarithms in the effective potential are exactly summed for $O(N)$ scalar and Yukawa theories.Comment: 19 pages, DIAS STP 94-09. Expanded to check large N limit, typo's corrected, to appear in Phys Rev

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