Transition from rotating waves to modulated rotating waves on the sphere

We study non-resonant and resonant Hopf bifurcation of a rotating wave in SO(3)-equivariant reaction-diffusion systems on a sphere. We obtained reduced differential equations on so(3), the characterization of modulated rotating waves obtained by Hopf bifurcation of a rotating wave, as well as results regarding the resonant case. Our main tools are the equivariant center manifold reduction and the theory of Lie groups and Lie algebras, especially for the group SO(3) of all rigid rotations on a sphere

Risk of miscarriage following amniocentesis or chorionic villus sampling: systematic review of literature and updated meta-analysis

Objectives: To estimate the procedure-related risks of miscarriage after amniocentesis and trans-abdominal chorionic villus sampling (CVS) based on a systematic review of the literature and an updated meta-analysis. Methods: A search of MEDLINE, EMBASE, and The Cochrane Library was carried out to identify studies reporting complications following CVS or amniocentesis. The inclusion criteria for the systematic review were studies reporting results from large controlled studies and those reporting data for pregnancy loss prior to 24 weeks’ gestation. Study authors were contacted when required to identify additional necessary data. Data for cases that had invasive procedure and controls groups were inputted in contingency tables and risk of miscarriage was estimated for each study. Summary statistics based on a fixed and random effects model were calculated after taking into account the weighting for each study included in the systematic review. Procedure-related risk of miscarriage was estimated as a weighted risk difference from the summary statistics for cases and controls. A subgroup analyses according to the similarity risk levels in the invasive testing and control groups was performed. Heterogeneity was assessed using Cochrane’s Q and I2 statistic. Egger Bias was estimated to assess reporting bias in published studies. Summary statistics for procedure-related risk of miscarriage were graphically represented in Forest plots. Results: The electronic search from the databases yielded 2,943 potential citations, from which, we selected 20 controlled studies for inclusion in the systematic review to estimate the procedure-related risk of miscarriage from invasive procedures. There were a total of 580 miscarriages from 63,273 amniocentesis procedures with a weighted risk of pregnancy loss of 0.91% (95%CI: 0.73 to 1.09). In the control group, there were 1,726 miscarriages in 330,469 pregnancies with a loss rate of 0.58% (95CI%: 0.47 to 0.70). The weighted procedure-related risk of miscarriage was 0.30% (95%CI: 0.11 to 0.49, I2=70.1%). There were a total of 163 miscarriages from 13,011 CVS procedures with a risk of pregnancy loss of 1.39% (95%CI: 0.76 to 2.02). In the control group, there were 1,946 miscarriages in 232,680 pregnancies with a loss rate of 1.23% (95CI%: 0.86 to 1.59). The weighted procedure-related risk of miscarriage following CVS was 0.20% (95%CI: -0.12 to 0.52, I2=51.9%). However, when only studies with similar risk profiles between the intervention and control groups were considered, the procedure related risk for amniocentesis became 0.03% (95%CI -0.08 to 0.14, I2=0%) and for CVS -0.38 (95% CI -1.12 to 0.36, I2=0%). Conclusion: The procedure-related risks of miscarriage following amniocentesis and CVS are lower than currently quoted to women. The risk appears to be negligible when these interventions are compared to control groups of the same risk profile

Forced Symmetry Breaking from SO(3) to SO(2) for Rotating Waves on the Sphere

We consider a small SO(2)-equivariant perturbation of a reaction-diffusion system on the sphere, which is equivariant with respect to the group SO(3) of all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a rotating wave on the sphere that persists to a normally hyperbolic SO(2)-invariant manifold $M(\epsilon)$. We investigate the effects of this forced symmetry breaking by studying the perturbed dynamics induced on $M(\epsilon)$ by the above reaction-diffusion system. We prove that depending on the frequency vectors of the rotating waves that form the relative equilibrium SO(3)u_{0}, these rotating waves will give SO(2)-orbits of rotating waves or SO(2)-orbits of modulated rotating waves (if some transversality conditions hold). The orbital stability of these solutions is established as well. Our main tools are the orbit space reduction, Poincare map and implicit function theorem

Simulation of fluid-solid coexistence in finite volumes: A method to study the properties of wall-attached crystalline nuclei

The Asakura-Oosawa model for colloid-polymer mixtures is studied by Monte Carlo simulations at densities inside the two-phase coexistence region of fluid and solid. Choosing a geometry where the system is confined between two flat walls, and a wall-colloid potential that leads to incomplete wetting of the crystal at the wall, conditions can be created where a single nanoscopic wall-attached crystalline cluster coexists with fluid in the remainder of the simulation box. Following related ideas that have been useful to study heterogeneous nucleation of liquid droplets at the vapor-liquid coexistence, we estimate the contact angles from observations of the crystalline clusters in thermal equilibrium. We find fair agreement with a prediction based on Young's equation, using estimates of interface and wall tension from the study of flat surfaces. It is shown that the pressure versus density curve of the finite system exhibits a loop, but the pressure maximum signifies the "droplet evaporation-condensation" transition and thus has nothing in common with a van der Waals-like loop. Preparing systems where the packing fraction is deep inside the two-phase coexistence region, the system spontaneously forms a "slab state", with two wall-attached crystalline domains separated by (flat) interfaces from liquid in full equilibrium with the crystal in between; analysis of such states allows a precise estimation of the bulk equilibrium properties at phase coexistence

Anisotropic Coarsening: Grain Shapes and Nonuniversal Persistence

We solve a coarsening system with small but arbitrary anisotropic surface tension and interface mobility. The resulting size-dependent growth shapes are significantly different from equilibrium microcrystallites, and have a distribution of grain sizes different from isotropic theories. As an application of our results, we show that the persistence decay exponent depends on anisotropy and hence is nonuniversal.Comment: 4 pages (revtex), 2 eps figure

First-trimester prediction of preterm prelabour rupture of membranes incorporating cervical length measurement

Objectives: To examine early pregnancy risk factors for preterm prelabour rupture of membranes (PPROM) and develop a predictive model. Study design: Retrospective analysis of a cohort of mixed-risk singleton pregnancies screened in the first and second trimesters in three Danish tertiary fetal medicine centres, including a cervical length measurement at 11–14 weeks, at 19–21 weeks and at 23–24 weeks of gestation. Univariable and multivariable logistic regression analyses were employed to identify predictive maternal characteristics, biochemical and sonographic factors. Receiver operating characteristic (ROC) curve analysis was used to determine predictors for the most accurate model. Results: Of 3477 screened women, 77 (2.2%) had PPROM. Maternal factors predictive of PPROM in univariable analysis were nulliparity (OR 2.0 (95% CI 1.2–3.3)), PAPP-A < 0.5 MoM (OR 2.6 (1.1–6.2)), previous preterm birth (OR 4.2 (1.9–8.9)), previous cervical conization (OR 3.6 (2.0–6.4)) and cervical length ≤ 25 mm on transvaginal imaging (first-trimester OR 15.9 (4.3–59.3)). These factors all remained statistically significant in a multivariable adjusted model with an AUC of 0.72 in the most discriminatory first-trimester model. The detection rate using this model would be approximately 30% at a false-positive rate of 10%. Potential predictors such as bleeding in early pregnancy and pre-existing diabetes mellitus affected very few cases and could not be formally assessed. Conclusions: Several maternal characteristics, placental biochemical and sonographic features are predictive of PPROM with moderate discrimination. Larger numbers are required to validate this algorithm and additional biomarkers, not currently used for first-trimester screening, may improve model performance

The radiosensitizing effect of platinum nanoparticles in proton irradiations is not caused by an enhanced proton energy deposition at the macroscopic scale

Objective. Due to the radiosensitizing effect of biocompatible noble metal nanoparticles (NPs), their administration is considered to potentially increase tumor control in radiotherapy. The underlying physical, chemical and biological mechanisms of the NPs' radiosensitivity especially when interacting with proton radiation is not conclusive. In the following work, the energy deposition of protons in matter containing platinum nanoparticles (PtNPs) is experimentally investigated. Approach. Surfactant-free monomodal PtNPs with a mean diameter of (40 ± 10) nm and a concentration of 300 μg ml−1, demonstrably leading to a substantial production of reactive oxygen species (ROS), were homogeneously dispersed into cubic gelatin samples serving as tissue-like phantoms. Gelatin samples without PtNPs were used as control. The samples' dimensions and contrast of the PtNPs were verified in a clinical computed tomography scanner. Fields from a clinical proton machine were used for depth dose and stopping power measurements downstream of both samples types. These experiments were performed with a variety of detectors at a pencil beam scanning beam line as well as a passive beam line with proton energies from about 56–200 MeV. Main results. The samples' water equivalent ratios in terms of proton stopping as well as the mean proton energy deposition downstream of the samples with ROS-producing PtNPs compared to the samples without PtNPs showed no differences within the experimental uncertainties of about 2%. Significance. This study serves as experimental proof that the radiosensitizing effect of biocompatible PtNPs is not due to a macroscopically increased proton energy deposition, but is more likely caused by a catalytic effect of the PtNPs. Thus, these experiments provide a contribution to the highly discussed radiobiological question of the proton therapy efficiency with noble metal NPs and facilitate initial evidence that the dose calculation in treatment planning is straightforward and not affected by the presence of sensitizing PtNPs

Front Stability in Mean Field Models of Diffusion Limited Growth

We present calculations of the stability of planar fronts in two mean field models of diffusion limited growth. The steady state solution for the front can exist for a continuous family of velocities, we show that the selected velocity is given by marginal stability theory. We find that naive mean field theory has no instability to transverse perturbations, while a threshold mean field theory has such a Mullins-Sekerka instability. These results place on firm theoretical ground the observed lack of the dendritic morphology in naive mean field theory and its presence in threshold models. The existence of a Mullins-Sekerka instability is related to the behavior of the mean field theories in the zero-undercooling limit.Comment: 26 pp. revtex, 7 uuencoded ps figures. submitted to PR

Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground

By making an appropriate choice for gauge fixing kappa-symmetry we obtain a relatively simple form of the actions for a D=11 superparticle in AdS(4) x S(7)/Z_k, and for a D0-brane, fundamental string and D2-branes in the AdS(4) x CP(3) superbackground. They can be used to study various problems of string theory and the AdS4/CFT3 correspondence, especially in regions of the theory which are not reachable by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In particular, we present a simple form of the gauge-fixed superstring action in AdS(4) x CP(3) and briefly discuss issues of its T-dualization.Comment: 1+36 pages, v2,v3 clarifications and references adde