Factorization of correlations in two-dimensional percolation on the plane and torus

Recently, Delfino and Viti have examined the factorization of the three-point density correlation function P_3 at the percolation point in terms of the two-point density correlation functions P_2. According to conformal invariance, this factorization is exact on the infinite plane, such that the ratio R(z_1, z_2, z_3) = P_3(z_1, z_2, z_3) [P_2(z_1, z_2) P_2(z_1, z_3) P_2(z_2, z_3)]^{1/2} is not only universal but also a constant, independent of the z_i, and in fact an operator product expansion (OPE) coefficient. Delfino and Viti analytically calculate its value (1.022013...) for percolation, in agreement with the numerical value 1.022 found previously in a study of R on the conformally equivalent cylinder. In this paper we confirm the factorization on the plane numerically using periodic lattices (tori) of very large size, which locally approximate a plane. We also investigate the general behavior of R on the torus, and find a minimum value of R approx. 1.0132 when the three points are maximally separated. In addition, we present a simplified expression for R on the plane as a function of the SLE parameter kappa.Comment: Small corrections (final version). In press, J. Phys.

Three Dimensional Mapping of Texture in Dental Enamel

We have used synchrotron x-ray diffraction to study the crystal orientation in human dental enamel as a function of position within intact tooth sections. Keeping tooth sections intact has allowed us to construct 2D and 3D spatial distribution maps of the magnitude and orientation of texture in dental enamel. We have found that the enamel crystallites are most highly aligned at the expected occlusal points for a maxillary first premolar, and that the texture direction varies spatially in a three dimensional curling arrangement. Our results provide a model for texture in enamel which can aid researchers in developing dental composite materials for fillings and crowns with optimal characteristics for longevity, and will guide clinicians to the best method for drilling into enamel, in order to minimize weakening of remaining tooth structure, during dental restoration procedure

Central Corneal Thickness: A Retrospective Comparison of Handheld Ultrasound Pachymetry and Optical Biometric Analysis Measurements

Purpose To determine if the measure of central cornea thickness among suspected and confirmed glaucomatous patients is significantly influenced by instrument device. Methods We retrospectively examined the charts of all patients having a central corneal thickness (CCT) measured with both ultrasound pachymetry and IOL Master 700 at the Kresge Eye Institute within the past year. Intraocular pressure and demographic data including age and race, were also collected. Significant corneal disease such as Fuchs corneal dystrophy, other corneal dystrophies, corneal transplant, and corneal edema were excluded. Statistical analysis of the paired CCT measurements were performed with a paired t-test and regression analysis. Results The total number of patients having a CCT measured with both ultrasound pachymetry and IOLMaster700 was 59. Mean CCT measured with ultrasound pachymetry was 539.38 ± 49.56 µm (n=118). Mean CCT measured with IOLMaster700 was 536.83 ± 42.52 µm (n=112). The intraparticipant mean of differences between the ultrasound pachymetry and the IOLMaster700 was 3.16 ± 25 µm. Analysis with a paired t-test did not find a significant difference between the two groups (p=0.19). A regression analysis of the paired CCTs yielded an R2 value of 0.74. Conclusion There is no significant difference between CCT measurements taken with handheld ultrasound pachymetry compared to the IOL Master 700. More data is warranted to confirm, but the IOL Master 700 may yield lower variability and a lower mean CCT, possibly due to greater instrument precision and increased likelihood of a central measurement. In practice, the IOL Master 700 may provide a more reliable measure of central cornea thickness when compared with ultrasound pachymetry

Scattering polarization due to light source anisotropy

We consider the polarization arising from scattering in an envelope illuminated by a central anisotropic source. Spherical harmonics are used to describe both the light source anisotropy and the envelope density distribution functions of the scattering particles. This framework demonstrates how the net resultant polarization arises from a superposition of three basic "shape" functions: the distribution of source illumination, the distribution of envelope scatterers, and the phase function for dipole scattering. Specific expressions for the Stokes parameters and scattered flux are derived for the case of an ellipsoidal light source inside an ellipsoidal envelope, with principal axes that are generally not aligned. Two illustrative examples are considered: (a) axisymmetric mass loss from a rapidly rotating star, such as may apply to some Luminous Blue Variables, and (b) a Roche-lobe filling star in a binary system with a circumstellar envelope. As a general conclusion, the combination of source anisotropy with distorted scattering envelopes leads to more complex polarimetric behavior such that the source characteristics should be carefully considered when interpreting polarimetric data.Comment: to appear in A&

Peramorphosis, an evolutionary developmental mechanism in neotropical bat skull diversity

Background The neotropical leaf‐nosed bats (Chiroptera, Phyllostomidae) are an ecologically diverse group of mammals with distinctive morphological adaptations associated with specialized modes of feeding. The dramatic skull shape changes between related species result from changes in the craniofacial development process, which brings into focus the nature of the underlying evolutionary developmental processes. Results In this study, we use three‐dimensional geometric morphometrics to describe, quantify, and compare morphological modifications unfolding during evolution and development of phyllostomid bats. We examine how changes in development of the cranium may contribute to the evolution of the bat craniofacial skeleton. Comparisons of ontogenetic trajectories to evolutionary trajectories reveal two separate evolutionary developmental growth processes contributing to modifications in skull morphogenesis: acceleration and hypermorphosis. Conclusion These findings are consistent with a role for peramorphosis, a form of heterochrony, in the evolution of bat dietary specialists

Computational investigation of flows and pressure fields associated with spur gear meshing

The efficiency of power transmission systems is increasingly targeted with a view to reducing parasitic losses and improving specific fuel consumption (SFC). One of the effects associated with such parasitic losses is the successive compression and expansion of fluid within the cavities between teeth of a meshing gear pair as they rotate. This process is cyclic and there are multiple cavities compressed and expanded at the same time. During the meshing process the volume of the cavity between the teeth suddenly contracts and as a result pressure rises. The fluid is therefore expelled primarily in the axial direction (for spur gears) since this area is considerably larger compared to the backlash area. Once the cavity starts to expand fluid is drawn into the cavity between the teeth by the negative pressure. Besides the air flow in the gear box, the meshing point is of particular interest to the oil flow, since oil is typically injected at or upstream of the meshing point. Good understanding of such flows can be used to balance lubrication needs with the need to minimise the required oil volumes and parasitic losses. This paper proposes the use of Computational Fluid Dynamics (CFD) as a means to investigate the phenomenon. A simplified two-dimensional CFD approach has been developed to study flows and pressure fields associated with spur gear meshing. The influence of the rotational speed has been investigated. Good validation is shown for the transient pressure variation within the tooth space. The limitations and potential applications of the modelling strategy are then discussed

On three-point connectivity in two-dimensional percolation

We argue the exact universal result for the three-point connectivity of critical percolation in two dimensions. Predictions for Potts clusters and for the scaling limit below p_c are also given.Comment: 10 pages, 1 figur

The vertical structure of ocean heat transport

One of the most important contributions the ocean makes to Earth's climate is through its poleward heat transport: about 1.5 PW or more than 30% of that accomplished by the ocean-atmosphere system (Trenberth and Caron, 2001). Recently, concern has arisen over whether global warming could affect this heat transport (Watson et al., 2001), for example, reducing high latitude convection and triggering a collapse of the deep overturning circulation (Rahmstorf, 1995). While the consequences of abrupt changes in oceanic circulation should be of concern, we argue that the attention devoted to deep circulations is disproportionate to their role in heat transport. For this purpose, we introduce a heat function which identifies the contribution to the heat transport by different components of the oceanic circulation. A new view of the ocean emerges in which a shallow surface intensified circulation dominates the poleward heat transport

Predictors of failed attendances in a multi-specialty outpatient centre using electronic databases.

BACKGROUND: Failure to keep outpatient medical appointments results in inefficiencies and costs. The objective of this study is to show the factors in an existing electronic database that affect failed appointments and to develop a predictive probability model to increase the effectiveness of interventions. METHODS: A retrospective study was conducted on outpatient clinic attendances at Tan Tock Seng Hospital, Singapore from 2000 to 2004. 22864 patients were randomly sampled for analysis. The outcome measure was failed outpatient appointments according to each patient's latest appointment. RESULTS: Failures comprised of 21% of all appointments and 39% when using the patients' latest appointment. Using odds ratios from the mutliple logistic regression analysis, age group (0.75 to 0.84 for groups above 40 years compared to below 20 years), race (1.48 for Malays, 1.61 for Indians compared to Chinese), days from scheduling to appointment (2.38 for more than 21 days compared to less than 7 days), previous failed appointments (1.79 for more than 60% failures and 4.38 for no previous appointments, compared with less than 20% failures), provision of cell phone number (0.10 for providing numbers compared to otherwise) and distance from hospital (1.14 for more than 14 km compared to less than 6 km) were significantly associated with failed appointments. The predicted probability model's diagnostic accuracy to predict failures is more than 80%. CONCLUSION: A few key variables have shown to adequately account for and predict failed appointments using existing electronic databases. These can be used to develop integrative technological solutions in the outpatient clinic