Rotational Structure of Extremely Floppy van der Waals Complexes: Adiabatic Separation of Angular and Radial Motion

The adiabatic or Born-Oppenheimer approximation is often used in molecular calculations to simplify the solution to the Schrodinger equation. The basis of the approximation is the large difference in the relative motions of the nuclei and electrons in the molecule-the electrons are able to respond almost instantly to the movements of the nuclei. Thus, the nuclei may be regarded as being fixed in a certain position and the Schrodinger equation can then be solved using the potential obtained by solving the electronic problem at fixed nuclear configuration. A similar argument can be used to decouple the angular and radial motions of many van der Waals complexes because, like nuclei in molecules, the radial motions in many van der Waals complexes are strongly localized. Fixing the radial separation between the atoms and molecules in the complex to a particular value results in a Schrodinger equation that is much simpler to solve because it is only dependent on angles. van der Waals complexes containing helium atoms, however, present a dilemma because the extremely weak interactions present also lead to large amplitude radial as well as angular motions. Because the basis of the adiabatic approximation is a large difference in time scale between the angular and radial motions, the validity of the adiabatic approximation for helium complexes is uncertain. In this thesis, the adiabatic separation of angular and radial motion is shown to be accurate for extremely floppy complexes of helium by demonstrating its use on the van der Waals molecule He-HCN. A major application of this method is expected to be the quick calculation of approximate wave functions for Diffusion Monte Carlo studies of the rotation of impurity molecules inside ultra-cold droplets of helium. The method presented here is significantly faster than other methods (e.g., Variational Monte Carlo) that have been used to calculate approximate wave functions for Diffusion Monte Carlo

How to find discrete contact symmetries

This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that the adjoint action of any contact symmetry is an automorphism of the Lie algebra of generators of Lie contact symmetries. Consequently, all contact symmetries satisfy various compatibility conditions. These conditions enable the discrete symmetries to be found systematically, with little effort

Sleep characteristics modify the association between genetic predisposition to obesity and anthropometric measurements in 119,679 UK Biobank participants

Background - Obesity is a multifactorial condition influenced by genetics, lifestyle and environment. Objective - To investigate whether the association between a validated genetic profile risk score for obesity (GPRS-obesity) with body mass index (BMI) and waist circumference (WC) was modified by sleep characteristics. Design - This study included cross-sectional data from 119,859 white European adults, aged 37-73 years, participating on the UK Biobank. Interactions between GPRS-obesity, and sleep characteristics (sleep duration, chronotype, day napping, and shift work) in their effects on BMI and WC were investigated. Results - The GPRS-obesity was associated with BMI (β:0.57 kg.m-2 per standard deviation (SD) increase in GPRS, [95%CI:0.55, 0.60]; P=6.3x10-207) and WC (β:1.21 cm, [1.15, 1.28]; P=4.2x10-289). There were significant interactions between GPRS-obesity and a variety of sleep characteristics in their relationship with BMI (P-interaction <0.05). In participants who slept <7 hrs or >9 hrs daily, the effect of GPRS-obesity on BMI was stronger (β:0.60 [0.54, 0.65] and 0.73 [0.49, 0.97] kg.m-2 per SD increase in GPRS, respectively) than in normal length sleepers (7-9 hours; β:0.52 [0.49, 0.55] kg.m-2 per SD). A similar pattern was observed for shiftworkers (β:0.68 [0.59, 0.77] versus 0.54 [0.51, 0.58] kg.m-2 for non-shiftworkers) and for night-shiftworkers (β:0.69 [0.56, 0.82] versus 0.55 [0.51, 0.58] kg.m-2 for non-night- shiftworkers), for those taking naps during the day (β:0.65 [0.52, 0.78] versus 0.51 [0.48, 0.55] kg.m-2 for those who never/rarely had naps) and for those with a self-reported evening chronotype (β:0.72 [0.61, 0.82] versus β:0.52 [0.47, 0.57] kg.m-2 for morning chronotype). Similar findings were obtained using WC as the outcome. Conclusions – This study shows that the association between genetic risk for obesity and phenotypic adiposity measures is exacerbated by adverse sleeping characteristics

Alzheimer disease genetic risk factor APOE e4, and cognitive abilities in 111,739 UK Biobank participants

Background: the apolipoprotein (APOE) e4 locus is a genetic risk factor for dementia. Carriers of the e4 allele may be more vulnerable to conditions that are independent risk factors for cognitive decline, such as cardiometabolic diseases. Objective: we tested whether any association with APOE e4 status on cognitive ability was larger in older ages or in those with cardiometabolic diseases. Subjects: UK Biobank includes over 500,000 middle- and older aged adults who have undergone detailed medical and cognitive phenotypic assessment. Around 150,000 currently have genetic data. We examined 111,739 participants with complete genetic and cognitive data. Methods: baseline cognitive data relating to information processing speed, memory and reasoning were used. We tested for interactions with age and with the presence versus absence of type 2 diabetes (T2D), coronary artery disease (CAD) and hypertension. Results: in several instances, APOE e4 dosage interacted with older age and disease presence to affect cognitive scores. When adjusted for potentially confounding variables, there was no APOE e4 effect on the outcome variables. Conclusions: future research in large independent cohorts should continue to investigate this important question, which has potential implications for aetiology related to dementia and cognitive impairment

Limits on Radio Continuum Emission from a Sample of Candidate Contracting Starless Cores

We used the NRAO Very Large Array to search for 3.6 cm continuum emission from embedded protostars in a sample of 8 nearby ``starless'' cores that show spectroscopic evidence for infalling motions in molecular emission lines. We detect a total of 13 compact sources in the eight observed fields to 5 sigma limiting flux levels of typically 0.09 mJy. None of these sources lie within 1' of the central positions of the cores, and they are all likely background objects. Based on an extrapolation of the empirical correlation between the bolometric luminosity and 3.6 cm luminosity for the youngest protostars, these null-detections place upper limits of ~0.1 L_sun (d/140pc)^2 on the luminosities of protostellar sources embedded within these cores. These limits, together with the extended nature of the inward motions inferred from molecular line mapping (Lee et al. 2001), are inconsistent with the inside-out collapse model of singular isothermal spheres and suggest a less centrally condensed phase of core evolution during the earliest stages of star formation.Comment: Accepted to the Astronomical Journal; 12 pages, 1 figur