Distributional fixed point equations for island nucleation in one dimension: a retrospective approach for capture zone scaling

The distributions of inter-island gaps and captures zones for islands nucleated on a one-dimensional substrate during submonolayer deposition are considered using a novel retrospective view. This provides an alternative perspective on why scaling occurs in this continuously evolving system. Distributional fixed point equations for the gaps are derived both with and without a mean field approximation for nearest neighbour gap size correlation. Solutions to the equations show that correct consideration of fragmentation bias justifies the mean field approach which can be extended to provide closed-from equations for the capture zones. Our results compare favourably to Monte Carlo data for both point and extended islands using a range of critical island size $i=0,1,2,3$. We also find satisfactory agreement with theoretical models based on more traditional fragmentation theory approaches.Comment: 9 pages, 7 figures and 1 tabl

The random phase approximation applied to ice

Standard density functionals without van der Waals interactions yield an unsatisfactory description of ice phases, specifically, high density phases occurring under pressure are too unstable compared to the common low density phase I$_h$ observed at ambient conditions. Although the description is improved by using functionals that include van der Waals interactions, the errors in relative volumes remain sizable. Here we assess the random phase approximation (RPA) for the correlation energy and compare our results to experimental data as well as diffusion Monte Carlo data for ice. The RPA yields a very balanced description for all considered phases, approaching the accuracy of diffusion Monte Carlo in relative energies and volumes. This opens a route towards a concise description of molecular water phases on surfaces and in cavities

Limit curve theorems in Lorentzian geometry

The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the beginning are one, two or at most denumerable. Some applications are considered. It is proved that in chronological spacetimes, strong causality is either everywhere verified or everywhere violated on maximizing lightlike segments with open domain. As a consequence, if in a chronological spacetime two distinct lightlike lines intersect each other then strong causality holds at their points. Finally, it is proved that two distinct components of the chronology violating set have disjoint closures or there is a lightlike line passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio

Wave-number Selection by Target Patterns and Side Walls in Rayleigh-Benard Convection

We present experimental results for Rayleigh-Benard convection patterns in a cylindrical container with static side-wall forcing induced by a heater. This forcing stabilized a pattern of concentric rolls (a target pattern) with the central roll (the umbilicus) at the center of the cell after a jump from the conduction to the convection state. A quasi-static increase of the control parameter (epsilon) beyond 0.8 caused the umbilicus of the pattern to move off center. As observed by others, a further quasi-static increase of epsilon up to 15.6 caused a sequence of transitions. Each transition began with the displacement of the umbilicus and then proceeded with the loss of one convection roll at the umbilicus and the return of the umbilicus to a location near the center of the cell. Alternatively, with decreasing epsilon new rolls formed at the umbilicus but large umbilicus displacements did not occur. In addition to quantitative measurements of the umbilicus displacement, we determined and analyzed the entire wave-director field of each image. The wave numbers varied in the axial direction, with minima at the umbilicus and at the cell wall and a maximum at a radial position close to 2/3 Gamma. The wave numbers at the maximum showed hysteretic jumps at the transitions, but on average agreed well with the theoretical predictions for the wave numbers selected in the far field of an infinitely extended target pattern.Comment: ReVTeX, 11 pages, 16 eps figures include

Deriving genetic programming fitness properties by static analysis

Deriving Genetic Programming Fitness Properties by Static Analysis Colin G. Johnson The aim of this paper is to introduce the idea of using static analysis of computer programs as a way of measuring fitness in genetic programming. Such techniques extract information about the programs without explicitly running them, and in particular they infer properties which hold across the whole of the input space of a program. This can be applied to measure fitness, and has a number of advantages over measuring fitness by running members of the population on test cases. The most important advantage is that if a solution is found then it is possible to formally trust that solution to be correct across all inputs. This paper introduces these ideas, discusses various ways in which they could be applied, discusses the type of problems for which they are appropriate, and ends by giving a simple test example and some questions for future research

Integration of the Friedmann equation for universes of arbitrary complexity

An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models consisting of an arbitrary number of non-interacting species. The inheritance of constants of the motion from simpler models as more species are added is stressed. It is then argued that all FLRW models admit what amounts to a unique candidate for a gravitational epoch function (a dimensionless scalar invariant derivable from the Riemann tensor without differentiation which is monotone throughout the evolution of the universe). The same relations that lead to the construction of constants of the motion allow an explicit evaluation of this function. In the simplest of all models, the $\Lambda$CDM model, it is shown that the epoch function exists for all models with $\Lambda > 0$, but for almost no models with $\Lambda \leq 0$.Comment: Final form to appear in Physical Review D1

Synchrotron radiation study of the relation between structure and strain in polyurethane elastomers

This paper describes a system for the study of the relation between structure and applied strain in thermoplastic polyurethane elastomers using the Australian National Beamline Facility at the Photon Factory, KEK, Tsukuba, Japan. The system uses the sagittal focusing monochromator at beamline 20B to provide a high-intensity focused beam which then falls on the specimen mounted in a miniature tensometer mounted in the unique vacuum diffractometer (BIGDIFF). Imaging plates were used to record simultaneously SAXS and WAXS patterns from the specimen at a particular strain. The change in SAXS and WAXS patterns with loading and unloading was recorded using a ten-plate imaging-plate changer

Painleve-Gullstrand Coordinates for the Kerr Solution

We construct a coordinate system for the Kerr solution, based on the zero angular momentum observers dropped from infinity, which generalizes the Painleve-Gullstrand coordinate system for the Schwarzschild solution. The Kerr metric can then be interpreted as describing space flowing on a (curved) Riemannian 3-manifold. The stationary limit arises as the set of points on this manifold where the speed of the flow equals the speed of light, and the horizons as the set of points where the radial speed equals the speed of light. A deeper analysis of what is meant by the flow of space reveals that the acceleration of free-falling objects is generally not in the direction of this flow. Finally, we compare the new coordinate system with the closely related Doran coordinate system.Comment: 6 pages; v2: new section, matches final published version; v3: sign error in the expression of the function delta correcte

Solution-Phase Synthesis of Heteroatom-Substituted Carbon Scaffolds for Hydrogen Storage

This paper reports a bottom-up solution-phase process for the preparation of pristine and heteroatom (boron, phosphorus, or nitrogen)-substituted carbon scaffolds that show good surface areas and enhanced hydrogen adsorption capacities and binding energies. The synthesis method involves heating chlorine-containing small organic molecules with metallic sodium at reflux in high-boiling solvents. For heteroatom incorporation, heteroatomic electrophiles are added to the reaction mixture. Under the reaction conditions, micrometer-sized graphitic sheets assembled by 3−5 nm-sized domains of graphene nanoflakes are formed, and when they are heteroatom-substituted, the heteroatoms are uniformly distributed. The substituted carbon scaffolds enriched with heteroatoms (boron ~7.3%, phosphorus ~8.1%, and nitrogen ~28.1%) had surface areas as high as 900 m^2 g^(−1) and enhanced reversible hydrogen physisorption capacities relative to pristine carbon scaffolds or common carbonaceous materials. In addition, the binding energies of the substituted carbon scaffolds, as measured by adsorption isotherms, were 8.6, 8.3, and 5.6 kJ mol^(−1) for the boron-, phosphorus-, and nitrogen-enriched carbon scaffolds, respectively

Demography and disorders of the French Bulldog population under primary veterinary care in the UK in 2013

Abstract Background Despite its Gallic name, the French Bulldog is a breed of both British and French origin that was first recognised by The Kennel Club in 1906. The French Bulldog has demonstrated recent rapid rises in Kennel Club registrations and is now (2017) the second most commonly registered pedigree breed in the UK. However, the breed has been reported to be predisposed to several disorders including ocular, respiratory, neurological and dermatological problems. The VetCompass™ Programme collates de-identified clinical data from primary-care veterinary practices in the UK for epidemiological research. Using VetCompass™ clinical data, this study aimed to characterise the demography and common disorders of the general population of French Bulldogs under veterinary care in the UK. Results French Bulldogs comprised 2228 (0.49%) of 445,557 study dogs under veterinary care during 2013. Annual proportional birth rates showed that the proportional ownership of French Bulldog puppies rose steeply from 0.02% of the annual birth cohort attending VetCompass™ practices in 2003 to 1.46% in 2013. The median age of the French Bulldogs overall was 1.3 years (IQR 0.6–2.5, range 0.0–13.0). The most common colours of French Bulldogs were brindle (solid or main) (32.36%) and fawn (solid or main) (29.9%). Of the 2228 French Bulldogs under veterinary care during 2013, 1612 (72.4%) had at least one disorder recorded. The most prevalent fine-level precision disorders recorded were otitis externa (14.0%, 95% CI: 12.6–15.5), diarrhoea (7.5%, 95% CI: 6.4–8.7), conjunctivitis (3.2%, 95% CI: 2.5–4.0), nails overlong (3.1%, 95% CI% 2.4–3.9) and skin fold dermatitis (3.0%, 95% CI% 2.3–3.8). The most prevalent disorder groups were cutaneous (17.9%, 95% CI: 16.3–19.6), enteropathy (16.7%, 95% CI: 15.2–18.3), aural (16.3%, 95% CI: 14.8–17.9), upper respiratory tract (12.7%, 95% CI: 11.3–14.1) and ophthalmological (10.5%, 95% CI: 9.3–11.9). Conclusions Ownership of French Bulldogs in the UK is rising steeply. This means that the disorder profiles reported in this study reflect a current young UK population and are likely to shift as this cohort ages. Otitis externa, diarrhoea and conjunctivitis were the most common disorders in French Bulldogs. Identification of health priorities based on VetCompass™ data can support evidence–based reforms to improve health and welfare within the breed