Dual kinetic balance approach to basis set expansions for the Dirac equation

A new approach to finite basis sets for the Dirac equation is developed. It solves the problem of spurious states and, as a result, improves the convergence properties of basis set calculations. The efficiency of the method is demonstrated for finite basis sets constructed from B splines by calculating the one-loop self-energy correction for a hydrogenlike ion.Comment: 14 pages, 1 tabl

Experimental and theoretical lifetimes and transition probabilities in Sb I

We present experimental atomic lifetimes for 12 levels in Sb I, out of which seven are reported for the first time. The levels belong to the 5p$^2$($^3$P)6s $^{2}$P, $^{4}$P and 5p$^2$($^3$P)5d $^{4}$P, $^{4}$F and $^{2}$F terms. The lifetimes were measured using time-resolved laser-induced fluorescence. In addition, we report new calculations of transition probabilities in Sb I using a Multiconfigurational Dirac-Hartree-Fock method. The physical model being tested through comparisons between theoretical and experimental lifetimes for 5d and 6s levels. The lifetimes of the 5d $^4$F$_{3/2, 5/2, 7/2}$ levels (19.5, 7.8 and 54 ns, respectively) depend strongly on the $J$-value. This is explained by different degrees of level mixing for the different levels in the $^4$F term.Comment: 10 page

Ignoring species availability biases occupancy estimates in single-scale occupancy models

Most applications of single-scale occupancy models do not differentiate between availability and detectability, even though species availability is rarely equal to one. Species availability can be estimated using multi-scale occupancy models; however, for the practical application of multi-scale occupancy models, it can be unclear what a robust sampling design looks like and what the statistical properties of the multi-scale and single-scale occupancy models are when availability is less than one. Using simulations, we explore the following common questions asked by ecologists during the design phase of a field study: (Q1) what is a robust sampling design for the multi-scale occupancy model when there are a priori expectations of parameter estimates? (Q2) what is a robust sampling design when we have no expectations of parameter estimates? and (Q3) can a single-scale occupancy model with a random effects term adequately absorb the extra heterogeneity produced when availability is less than one and provide reliable estimates of occupancy probability? Our results show that there is a tradeoff between the number of sites and surveys needed to achieve a specified level of acceptable error for occupancy estimates using the multi-scale occupancy model. We also document that when species availability is low (\u3c0.40 on the probability scale), then single-scale occupancy models underestimate occupancy by as much as 0.40 on the probability scale, produce overly precise estimates, and provide poor parameter coverage. This pattern was observed when a random effects term was and was not included in the single-scale occupancy model, suggesting that adding a random-effects term does not adequately absorb the extra heterogeneity produced by the availability process. In contrast, when species availability was high (\u3e0.60), single-scale occupancy models performed similarly to the multi-scale occupancy model. Users can further explore our results and sampling designs across a number of different scenarios using the RShiny app https://gdire nzo.shiny apps.io/multiscale -occ/. Our results suggest that unaccounted for availability can lead to underestimating species distributions when using single-scale occupancy models

Models for Chronology Selection

In this paper, we derive an expression for the grand canonical partition function for a fluid of hot, rotating massless scalar field particles in the Einstein universe. We consider the number of states with a given energy as one increases the angular momentum so that the fluid rotates with an increasing angular velocity. We find that at the critical value when the velocity of the particles furthest from the origin reaches the speed of light, the number of states tends to zero. We illustrate how one can also interpret this partition function as the effective action for a boosted scalar field configuration in the product of three dimensional de Sitter space and $S^1$. In this case, we consider the number of states with a fixed linear momentum around the $S^1$ as the particles are given more and more boost momentum. At the critical point when the spacetime is about to develop closed timelike curves, the number of states again tends to zero. Thus it seems that quantum mechanics naturally enforces the chronology protection conjecture by superselecting the causality violating field configurations from the quantum mechanical phase space.Comment: 20 pages, Late

Effect of suspension systems on the physiological and psychological responses to sub-maximal biking on simulated smooth and bumpy tracks

The aim of this study was to compare the physiological and psychological responses of cyclists riding on a hard tail bicycle and on a full suspension bicycle. Twenty males participated in two series of tests. A test rig held the front axle of the bicycle steady while the rear wheel rotated against a heavy roller with bumps (or no bumps) on its surface. In the first series of tests, eight participants (age 19 – 27 years, body mass 65 – 82 kg) were tested on both the full suspension and hard tail bicycles with and without bumps fitted to the roller. The second series of test repeated the bump tests with a further six participants (age 22 – 31 years, body mass 74 – 94 kg) and also involved an investigation of familiarization effects with the final six participants (age 21 – 30 years, body mass 64 – 80 kg). Heart rate, oxygen consumption (VO<sub>2</sub>), rating of perceived exertion (RPE) and comfort were recorded during 10 min sub-maximal tests. Combined data for the bumps tests show that the full suspension bicycle was significantly different (P < 0.001) from the hard tail bicycle on all four measures. Oxygen consumption, heart rate and RPE were lower on average by 8.7 (s = 3.6) ml · kg<sup>-1</sup> · min<sup>-1</sup>, 32.1 (s = 12.1) beats · min<sup>-1</sup> and 2.6 (s = 2.0) units, respectively. Comfort scores were higher (better) on average by 1.9 (s = 0.8) units. For the no bumps tests, the only statistically significant difference (P = 0.008) was in VO<sub>2</sub>, which was lower for the hard tail bicycle by 2.2 (s = 1.7) ml · kg-1 · min<sup>-1</sup>. The results indicate that the full suspension bicycle provides a physiological and psychological advantage over the hard tail bicycle during simulated sub-maximal exercise on bumps

Hydrodynamic bubble coarsening in off-critical vapour-liquid phase separation

Late-stage coarsening in off-critical vapour-liquid phase separation is re-examined. In the limit of bubbles of vapour distributed throughout a continuous liquid phase, it is argued that coarsening proceeds via inertial hydrodynamic bubble collapse. This replaces the Lifshitz-Slyozov-Wagner mechanism seen in binary liquid mixtures. The arguments are strongly supported by simulations in two dimensions using a novel single-component soft sphere fluid.Comment: 5 pages, 3 figures, revtex3.