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In this paper we are interested in the finite-time stability of transition solutions of the Cahn-Hilliard equation and its connection to the Willmore functional. We show that the Willmore functional locally decreases or increases in time in the linearly stable or unstable case respectively. This linear analysis explains the behavior near stationary solutions of the Cahn-Hilliard equation. We perform numerical examples in one and two dimensions and show that in the neighbourhood of transition solutions local instabilities occur in finite time. We also show convergence of solutions of the Cahn-Hilliard equation for arbitrary dimension to a stationary state by proving asymptotic decay of the Willmore functional in time.

Despite numerous studies reporting an increased risk of cesarean delivery among overweight or obese compared with normal weight women, the magnitude of the association remains uncertain. Therefore, we conducted a meta‐analysis of the current literature to provide a quantitative estimate of this association. We identified studies from three sources: (i) a PubMed search of relevant articles published between January 1980 and September 2005; (ii) reference lists of publications selected from the search; and (iii) reference lists of review articles published between 2000 and 2005. We included cohort designed studies that reported obesity measures reflecting pregnancy body mass, had a normal weight comparison group, and presented data allowing a quantitative measurement of risk. We used a Bayesian random effects model to perform the meta‐analysis and meta‐regression. Thirty‐three studies were included. The unadjusted odd ratios of a cesarean delivery were 1.46 [95% confidence interval (CI): 1.34–1.60], 2.05 (95% CI: 1.86–2.27) and 2.89 (95% CI: 2.28–3.79) among overweight, obese and severely obese women, respectively, compared with normal weight pregnant women. The meta‐regression found no evidence that these estimates were affected by selected study characteristics. Our findings provide a quantitative estimate of the risk of cesarean delivery associated with high maternal body mass.

We report on the preparation and characterization of single crystal gamma phase NaxCoO2 with 0.25 < x < 0.84 using a non-aqueous electrochemical chronoamperemetry technique. By carefully mapping the overpotential versus x (for x < 0.84), we find six distinct stable phases with Na levels corresponding to x ~ 0.75, 0.71, 0.50, 0.43, 0.33 and 0.25. The composition with x ~0.55 appears to have a critical Na concentration which separates samples with different magnetic behavior as well as different Na ion diffusion mechanisms. Chemical analysis of an aged crystal reveals different Na ion diffusion mechanisms above and below x_c ~ 0.53, where the diffusion process above x_c has a diffusion coefficient about five times larger than that below x_c. The series of crystals were studied with X-ray diffraction, susceptibility, and transport measurements. The crystal with x = 0.5 shows a weak ferromagnetic transition below T=27 K in addition to the usual transitions at T = 51 K and 88 K. The resistivity of the Curie-Weiss metallic Na0.71CoO2 composition has a very low residual resistivity, which attests to the high homogeneity of the crystals prepared by this improved electrochemical method. Our results on the various stable crystal compositions point to the importance of Na ion ordering across the phase diagram., 9 pages, 9 figures

We present a new type of flow analysis, based on a particle-pair correlation function, in which there is no need for an event-by-event determination of the reaction plane. Consequently, the need to correct for dispersion in an estimated reaction plane does not arise. Our method also offers the option to avoid any influence from particle misidentification. Using this method, streamer chamber data for collisions of Ar+KCl and Ar+BaI2 at 1.2 GeV/nucleon are compared with predictions of a nuclear transport model.