Variational Methods and Planar Elliptic Growth

A nested family of growing or shrinking planar domains is called a Laplacian growth process if the normal velocity of each domain's boundary is proportional to the gradient of the domain's Green function with a fixed singularity on the interior. In this paper we review the Laplacian growth model and its key underlying assumptions, so that we may consider a generalization to so-called elliptic growth, wherein the Green function is replaced with that of a more general elliptic operator--this models, for example, inhomogeneities in the underlying plane. In this paper we continue the development of the underlying mathematics for elliptic growth, considering perturbations of the Green function due to those of the driving operator, deriving characterizations and examples of growth, developing a weak formulation of growth via balayage, and discussing of a couple of inverse problems in the spirit of Calder\'on. We conclude with a derivation of a more delicate, reregularized model for Hele-Shaw flow

Predicting date of birth: the best time to date a pregnancy?

Objective: To compare the estimated date of birth calculations from last menstrual period (LMP) and ultrasounds at varying gestations (<70, 70-106, 110-140, 141-196 and 200-276) against the actual date of birth (DOB). Methods: This cohort study in a single local health district, Australia included 18,708 women with spontaneous labor who gave birth to a single live born infant without major anomalies between 2007 and 2011. Data were sourced from a computerized population birth database. The outcome of interest was duration of pregnancy expressed as total days, and the difference between actual DOB and estimated date of birth by dating method. Results: Only 5% of births occurred on the estimated date of birth regardless of the timing of the estimate. Approximately 66% of births occurred +/-7 days of the estimated date of birth, and there was little difference between ultrasound gestational week bands. The 110-140 weeks of gestation ultrasound performed as well if not better than ultrasounds conducted at other gestations. Maternal factors such as ethnicity and smoking status during pregnancy influenced duration of pregnancy; however, their explanatory power was too low to support incorporating these characteristics in dating estimations. Conclusion: An early dating scan (10 weeks or earlier) is unnecessary if LMP is reliable.Australian National Health and Medical Research Council (NHMRC) Centre for Research Excellence Grant (#APP1001066), Sydney Medical School Summer Research Scholarship, NHMRC Senior Research Fellowship (#APP1021025)

Field dependence of the electronic phase separation in Pr0.67Ca0.33MnO3 by small angle magnetic neutron scattering

We have studied by small angle neutron scattering the evolution induced by the application of magnetic field of the coexistence of ferromagnetism (F) and antiferromagnetism (AF) in a crystal of Pr$_{0.67}$Ca$_{0.33}$MnO$_3$. The results are compared to magnetic measurements which provide the evolution of the ferromagnetic fraction. These results show that the growth of the ferromagnetic phase corresponds to an increase of the thickness of the ferromagnetic ''cabbage'' sheets

NF539 Yield Suppressions of Glyphosate-Resistant (Roundup Ready) Soybeans

Research description and results of testing for effect of glyphosate herbicide application and the effect of the glyphosate-resistant gene in soybean production. Glyphosate is a popular postemergence herbicide. Glyphosate-resistant soybean technology is gaining acceptance in Nebraska and in U.S. cropping systems; however, potential yield suppression from either genetic differences among varieties, the glyphosate-resistant gene/gene insertion process, or glyphosate is a concern. The first of these could contribute to a yield lag; the latter two could contribute to a yield drag. Research Goals We designed experiments to test for both elements of yield drag: the effect of glyphosate herbicide application and the effect of the glyphosate-resistant gene. Since we could not distinguish between yield drag associated with the glyphosate-resistant gene or effects of its insertion, reference to this gene in the following could mean either or both of these possibilities. Two experiments were conducted at each of four Nebraska locations for two years with the intent to: 1) investigate the glyphosate herbicide effect on 12-13 varieties; and 2) look at the effect of the glyphosate-resistant (glyphosate-resistant) gene on five pairs of glyphosate- resistant, nonglyphosate-resistant sister cultivars (eight other cultivars were included as checks). Summary: Yield suppressions were observed. Yield drag from glyphosate application was not observed. Yield drag from glyphosate-resistant gene = 5 percent. Yield lag from variety genetic differences =

Pairing, Charge, and Spin Correlations in the Three-Band Hubbard Model

Using the Constrained Path Monte Carlo (CPMC) method, we simulated the two-dimensional, three-band Hubbard model to study pairing, charge, and spin correlations as a function of electron and hole doping and the Coulomb repulsion $V_{pd}$ between charges on neighboring Cu and O lattice sites. As a function of distance, both the $d_{x^2 - y^2}$-wave and extended s-wave pairing correlations decayed quickly. In the charge-transfer regime, increasing $V_{pd}$ decreased the long-range part of the correlation functions in both channels, while in the mixed-valent regime, it increased the long-range part of the s-wave behavior but decreased that of the d-wave behavior. Still the d-wave behavior dominated. At a given doping, increasing $V_{pd}$ increased the spin-spin correlations in the charge-transfer regime but decreased them in the mixed-valent regime. Also increasing $V_{pd}$ suppressed the charge-charge correlations between neighboring Cu and O sites. Electron and hole doping away from half-filling was accompanied by a rapid suppression of anti-ferromagnetic correlations.Comment: Revtex, 8 pages with 15 figure