Photon Channelling in Foams

Experiments by Gittings, Bandyopadhyay, and Durian [Europhys. Lett.\ \textbf{65}, 414 (2004)] demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first derive a central relation in the work of Gitting {\em et al.} without any free parameters. It links the photon's path-length fraction $f$ in the liquid phase to the liquid fraction $\epsilon$. We then construct two-dimensional Voronoi foams, replace the cell edges by channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling only occurs in a finite range of $\epsilon$.Comment: 9 pages, minor change

Developmental Trajectories of Body Mass Index Among Japanese Children and Impact of Maternal Factors during Pregnancy

Background The aims of this study were to 1) determine the distinct patterns of body mass index (BMI) trajectories in Japanese children, and 2) elucidate the maternal factors during pregnancy, which contribute to the determination of those patterns. Methodology/Principal Findings All of the children (1,644 individuals) born in Koshu City, Japan, between 1991 and 1998 were followed in a longitudinal study exploring the subjects’ BMI. The BMI was calculated 11 times for each child between birth and 12 years of age. Exploratory latent class growth analyses were conducted to identify trajectory patterns of the BMI z-scores. The distribution of BMI trajectories were best characterized by a five-group model for boys and a six-group model for girls. The groups were named “stable thin,” “stable average,” “stable high average,” “progressive overweight,” and “progressive obesity” in both sexes; girls were allocated to an additional group called “progressive average.” Multinomial logistic regression found that maternal weight, smoking, and skipping breakfast during pregnancy were associated with children included in the progressive obesity pattern rather than the stable average pattern. These associations were stronger for boys than for girls. Conclusions/Significance Multiple developmental patterns in Japanese boys and girls were identified, some of which have not been identified in Western countries. Maternal BMI and some unfavorable behaviors during early pregnancy may impact a child’s pattern of body mass development. Further studies to explain the gender and regional differences that were identified are warranted, as these may be important for early life prevention of weight-associated health problems

The role of liquid films for light transport in dry foams

We study the role of liquid films for light transport in dry foams based on ray optics. The foams are modelled by two-dimensional Voronoi tessellations with varying degree of disorder. We perform extensive simulations to determine the diffusive limit of light for two models. In model I, we choose a constant intensity reflectance r to explore the effect of disorder. We show that the honeycomb structure sets the right order of magnitude for the diffusion constant D by providing a master curve for $D(r)$, whereas disorder reveals itself in a fine structure. In model II, the reflectance for thin films as determined by Fresnel's formulae is chosen as well as some disorder in the film thickness. We argue that this model reproduces experimental features and the right order of magnitude for the diffusion constant. This suggests that the liquids films in combination with ray optics are relevant for explaining photon diffusion in foams