Scaling of the surface vasculature on the human placenta.

The networks of veins and arteries on the chorionic plate of the human placenta are analyzed in terms of Voronoi cells derived from these networks. Two groups of placentas from the United States are studied: a population cohort with no prescreening, and a cohort from newborns with an elevated risk of developing autistic spectrum disorder. Scaled distributions of the Voronoi cell areas in the two cohorts collapse onto a single distribution, indicating common mechanisms for the formation of the complete vasculatures, but which have different levels of activity in the two cohorts.

Free-energy coarse-grained potential for C60.

We propose a new deformable free energy method for generating a free-energy coarse-graining potential for C60. Potentials generated from this approach exhibit a strong temperature dependence and produce excellent agreement with benchmark fully atomistic molecular dynamics simulations. Parameter sets for analytical fits to this potential are provided at four different temperatures.

Optimization algorithm for rate equations with an application to epitaxial graphene.

We describe an algorithm that searches the parameter space of rate theories to optimize the associated rate coefficients based on a fit to experimental (or any other) data. Beginning with an initial set of parameters, which may be estimated, partially calculated, or indeed random, the algorithm follows a path, calculating the error at each point, until a minimum error is reached. We illustrate our method by correcting a previously proposed rate theory for the nucleation and growth of graphene on Ru(0 0 0 1) and Ir(1 1 1) to account for the temperature dependence of the graphene island density. This quantity shows an exponential decrease as the temperature is raised, in contrast to the power law decrease predicted by conventional nucleation theory, which indicates that a qualitatively different mechanism is operative for graphene island formation. Other applications of our method are also discussed.

Probability distributions for measures of placental shape and morphology.

Birthweight at delivery is a standard cumulative measure of placental growth, but is a crude summary of other placental characteristics, such as, e.g., the chorionic plate size, and the shape and position of the umbilical cord insertion. Distributions of such measures across a cohort reveal information about the developmental history of the chorionic plate which is unavailable from an analysis based solely on the mean and standard deviation. Various measures were determined from digitized images of chorionic plates obtained from the pregnancy, infection, and nutrition study, a prospective cohort study of preterm birth in central North Carolina between 2002 and 2004. Centroids (geometric centers) and umbilical cord insertions were taken directly from the images. Chorionic plate outlines were obtained from an interpolation based on a Fourier series, while eccentricity (of the best-fit ellipse), skewness, and kurtosis were determined from the method of moments. Histograms of each variable were compared against the normal, lognormal, and Lévy distributions. Only a single measure (eccentricity) followed a normal distribution. All others followed lognormal or 'heavy-tailed' distributions for moderate to extreme deviations from the mean, where the relative likelihood far exceeded those of a normal distribution.

Self-limiting evolution of seeded quantum wires and dots on patterned substrates.

Extensive experimental data and an accompanying theoretical model are presented for the self-limiting profiles and Ga segregation on patterned GaAs(111)B substrates during metalorganic vapor-phase epitaxy of Al(x)Ga(1-x)As. Self-limiting widths and segregation of Ga produce quantum dots along the base of pyramidal recesses bounded by (111)A planes and quantum wires along the vertical axis of the template, respectively. Coupled reaction-diffusion equations for precursor and adatom kinetics reproduce the measured concentration and temperature dependence of the self-limiting width and segregation. Our model can be extended to other patterned systems, providing a new paradigm for predicting the morphology of surface nanostructures and inferring their quantum optical properties.

Modeling oxygen transport in human placental terminal villi.

Oxygen transport from maternal blood to fetal blood is a primary function of the placenta. Quantifying the effectiveness of this exchange remains key in identifying healthy placentas because of the great variability in capillary number, caliber and position within the villus-even in placentas deemed clinically "normal". By considering villous membrane to capillary membrane transport, stationary oxygen diffusion can be numerically solved in terminal villi represented by digital photomicrographs. We aim to provide a method to determine whether and if so to what extent diffusional screening may operate in placental villi. Segmented digital photomicrographs of terminal villi from the Pregnancy, Infection and Nutrition study in North Carolina 2002 are used as a geometric basis for solving the stationary diffusion equation. Constant maternal villous oxygen concentration and perfect fetal capillary membrane absorption are assumed. System efficiency is defined as the ratio of oxygen flux into a villus and the sum of the capillary areas contained within. Diffusion screening is quantified by comparing numerical and theoretical maximum oxygen fluxes. A strong link between various measures of villous oxygen transport efficiency and the number of capillaries within a villus is established. The strength of diffusional screening is also related to the number of capillaries within a villus. Our measures of diffusional efficiency are shown to decrease as a function of the number of capillaries per villus. This low efficiency, high capillary number relationship supports our hypothesis that diffusional screening is present in this system. Oxygen transport per capillary is reduced when multiple capillaries compete for diffusing oxygen. A complete picture of oxygen fluxes, capillary and villus areas is obtainable and presents an opportunity for future work.

Fokker-Planck equation for lattice deposition models.

An asymptotically exact Fokker-Planck equation for the height fluctuations of lattice deposition models is derived from a Van Kampen expansion of the master equation. Using an Edwards-Wilkinson-type model as an example, the solution of the equivalent Langevin equation reproduces the surface roughness and lateral height correlations obtained with kinetic Monte Carlo (KMC) simulations. Our discrete equations of motion thereby provide an exact analytic and computational alternative to KMC simulations of these models.