3-Body Dynamics in a (1+1) Dimensional Relativistic Self-Gravitating System

The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of the system and discuss the numerical solution of the resulting equations of motion. This solution is compared to the corresponding non-relativistic and post-Newtonian approximation solutions so that the dynamics of the fully relativistic system can be interpretted as a correction to the one-dimensional Newtonian self-gravitating system. We find that the structure of the phase space of each of these systems yields a large variety of interesting dynamics that can be divided into three distinct regions: annulus, pretzel, and chaotic; the first two being regions of quasi-periodicity while the latter is a region of chaos. By changing the relative masses of the three particles we find that the relative sizes of these three phase space regions changes and that this deformation can be interpreted physically in terms of the gravitational interactions of the particles. Furthermore, we find that many of the interesting characteristics found in the case where all of the particles share the same mass also appears in our more general study. We find that there are additional regions of chaos in the unequal mass system which are not present in the equal mass case. We compare these results to those found in similar systems.Comment: latex, 26 pages, 17 figures, high quality figures available upon request; typos and grammar correcte

1,5-Anhydroglucitol as a marker of maternal glycaemic control and predictor of neonatal birthweight in pregnancies complicated by type 1 diabetes mellitus

AIMS/HYPOTHESIS: Most pregnant women with type 1 diabetes mellitus achieve HbA(1c) targets; however, macrosomia remains prevalent and better pregnancy glycaemic markers are therefore needed. 1,5-Anhydroglucitol (1,5-AG) is a short-term marker of glycaemia, reflecting a period of 1 to 2 weeks. Its excretion rate depends on the renal glucose threshold and thus it is unclear whether it may be used in pregnant type 1 diabetes women. We evaluated 1,5-AG as a glycaemic marker and birthweight predictor in pregnant women with type 1 diabetes, and compared its performance with HbA(1c). METHODS: 1,5-AG and HbA(1c) were measured in 82 pregnant women with type 1 diabetes. In addition, 58 continuous glucose monitoring system (CGMS) records were available. Macrosomia was defined as birthweight >90th centile. The data were analysed with Pearson’s correlations, and linear and logistic regression models. Receiver operating characteristic (ROC) analysis was used to evaluate third trimester 1,5-AG as a predictor of macrosomia. RESULTS: Unlike HbA(1c), 1,5-AG strongly correlated with CGMS indices: the AUC above 7.8 mmol/l (r = −0.66; p < 0.001), average maximum glucose (r = −0.58; p < 0.001) and mean glucose (r = −0.54; p < 0.001). In the third trimester, 1,5-AG was the strongest predictor of macrosomia, with ROC AUC 0.81 (95% CI 0.70, 0.89). In contrast, HbA(1c) in the third trimester had a ROC AUC of 0.69 (95% CI 0.58, 0.81). The best discrimination was achieved when both markers were used jointly, yielding a ROC AUC of 0.84 (95% CI 0.76, 0.93). CONCLUSIONS/INTERPRETATION: In pregnant women with type 1 diabetes, 1,5-AG is a better glycaemic marker than HbA(1c), as assessed by CGMS. A decreased third trimester 1,5-AG level, either singly or with HbA(1c), is a strong predictor of macrosomia

Chaos in an Exact Relativistic 3-body Self-Gravitating System

We consider the problem of three body motion for a relativistic one-dimensional self-gravitating system. After describing the canonical decomposition of the action, we find an exact expression for the 3-body Hamiltonian, implicitly determined in terms of the four coordinate and momentum degrees of freedom in the system. Non-relativistically these degrees of freedom can be rewritten in terms of a single particle moving in a two-dimensional hexagonal well. We find the exact relativistic generalization of this potential, along with its post-Newtonian approximation. We then specialize to the equal mass case and numerically solve the equations of motion that follow from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining orbits in both the hexagonal and 3-body representations of the system, and plot the Poincare sections as a function of the relativistic energy parameter $\eta$. We find two broad categories of periodic and quasi-periodic motions that we refer to as the annulus and pretzel patterns, as well as a set of chaotic motions that appear in the region of phase-space between these two types. Despite the high degree of non-linearity in the relativistic system, we find that the the global structure of its phase space remains qualitatively the same as its non-relativisitic counterpart for all values of $\eta$ that we could study. However the relativistic system has a weaker symmetry and so its Poincare section develops an asymmetric distortion that increases with increasing $\eta$. For the post-Newtonian system we find that it experiences a KAM breakdown for $\eta \simeq 0.26$: above which the near integrable regions degenerate into chaos.Comment: latex, 65 pages, 36 figures, high-resolution figures available upon reques

Scanning Electron Microscopy of High-Pressure-Frozen Sea Urchin Embryos

High-pressure-freezing permits direct cryo-fixation of sea urchin embryos having a defined developmental state without the formation of large ice crystals. We have investigated preparation protocols for observing high-pressure-frozen and freeze-fractured samples in the scanning electron microscope. High-pressure-freezing was superior to other freezing protocols, because the whole bulk sample was reasonably well frozen and the overall three-dimensional shape of the embryos was well preserved. The samples were either dehydrated by freeze-substitution and critical-point-drying, or imaged in the partially hydrated state, using a cold stage in the SEM. During freeze-substitution the samples were stabilized by fixatives. The disadvantage of this method was that shrinking and extraction effects, caused by the removal of the water, could not be avoided. These disadvantages were avoided when. the sample was imaged in the frozen-hydrated state using a cold-stage in the SEM. This would be the method of choice for morphometric studies. Frozen-hydrated samples, however, were very beam sensitive and many structures remained covered by the ice and were not visible. Frozen-hydrated samples were partially freeze-dried to make visible additional structures that had been covered by ice. However, this method also caused drying artifacts when too much water was removed

Environmental exposures during windows of susceptibility for breast cancer: a framework for prevention research.

BackgroundThe long time from exposure to potentially harmful chemicals until breast cancer occurrence poses challenges for designing etiologic studies and for implementing successful prevention programs. Growing evidence from animal and human studies indicates that distinct time periods of heightened susceptibility to endocrine disruptors exist throughout the life course. The influence of environmental chemicals on breast cancer risk may be greater during several windows of susceptibility (WOS) in a woman's life, including prenatal development, puberty, pregnancy, and the menopausal transition. These time windows are considered as specific periods of susceptibility for breast cancer because significant structural and functional changes occur in the mammary gland, as well as alterations in the mammary micro-environment and hormone signaling that may influence risk. Breast cancer research focused on these breast cancer WOS will accelerate understanding of disease etiology and prevention.Main textDespite the plausible heightened mechanistic influences of environmental chemicals on breast cancer risk during time periods of change in the mammary gland's structure and function, most human studies of environmental chemicals are not focused on specific WOS. This article reviews studies conducted over the past few decades that have specifically addressed the effect of environmental chemicals and metals on breast cancer risk during at least one of these WOS. In addition to summarizing the broader evidence-base specific to WOS, we include discussion of the NIH-funded Breast Cancer and the Environment Research Program (BCERP) which included population-based and basic science research focused on specific WOS to evaluate associations between breast cancer risk and particular classes of endocrine-disrupting chemicals-including polycyclic aromatic hydrocarbons, perfluorinated compounds, polybrominated diphenyl ethers, and phenols-and metals. We outline ways in which ongoing transdisciplinary BCERP projects incorporate animal research and human epidemiologic studies in close partnership with community organizations and communication scientists to identify research priorities and effectively translate evidence-based findings to the public and policy makers.ConclusionsAn integrative model of breast cancer research is needed to determine the impact and mechanisms of action of endocrine disruptors at different WOS. By focusing on environmental chemical exposure during specific WOS, scientists and their community partners may identify when prevention efforts are likely to be most effective

The Two Dimensional Kondo Model with Rashba Spin-Orbit Coupling

We investigate the effect that Rashba spin-orbit coupling has on the low energy behaviour of a two dimensional magnetic impurity system. It is shown that the Kondo effect, the screening of the magnetic impurity at temperatures T < T_K, is robust against such spin-orbit coupling, despite the fact that the spin of the conduction electrons is no longer a conserved quantity. A proposal is made for how the spin-orbit coupling may change the value of the Kondo temperature T_K in such systems and the prospects of measuring this change are discussed. We conclude that many of the assumptions made in our analysis invalidate our results as applied to recent experiments in semi-conductor quantum dots but may apply to measurements made with magnetic atoms placed on metallic surfaces.Comment: 22 pages, 1 figure; reference update

Quantum Gravity and Inflation

Using the Ashtekar-Sen variables of loop quantum gravity, a new class of exact solutions to the equations of quantum cosmology is found for gravity coupled to a scalar field, that corresponds to inflating universes. The scalar field, which has an arbitrary potential, is treated as a time variable, reducing the hamiltonian constraint to a time-dependent Schroedinger equation. When reduced to the homogeneous and isotropic case, this is solved exactly by a set of solutions that extend the Kodama state, taking into account the time dependence of the vacuum energy. Each quantum state corresponds to a classical solution of the Hamiltonian-Jacobi equation. The study of the latter shows evidence for an attractor, suggesting a universality in the phenomena of inflation. Finally, wavepackets can be constructed by superposing solutions with different ratios of kinetic to potential scalar field energy, resolving, at least in this case, the issue of normalizability of the Kodama state.Comment: 18 Pages, 2 Figures; major corrections to equations but prior results still hold, updated reference

Molecular self-organization: Predicting the pattern diversity and lowest energy state of competing ordering motifs

Self-organized monolayers of highly flexible \Frechet dendrons were deposited on graphite surfaces by solution casting. Scanning tunneling microscopy (STM) reveals an unprecedented variety of patterns with up to seven stable hierarchical ordering motifs serving as a versatile model system. The essential molecular properties determined by molecular mechanics simulations are condensed to a coarse grained interaction site model of various chain configurations. In a Monte Carlo approach with random starting configurations the experimental pattern diversity can be reproduced in all facets of the local and global ordering. Based on an energy analysis of the Monte Carlo and molecular mechanics modeling the thermodynamically most stable pattern is predicted coinciding with the pattern, which dominates in the STM images after several hours or upon moderate heating.Comment: 6 pages, 7 figure

Improved performance of the LHCb Outer Tracker in LHC Run 2

The LHCb Outer Tracker is a gaseous detector covering an area of $5\times 6 m^2$ with 12 double layers of straw tubes. The performance of the detector is presented based on data of the LHC Run 2 running period from 2015 and 2016. Occupancies and operational experience for data collected in $p p$, pPb and PbPb collisions are described. An updated study of the ageing effects is presented showing no signs of gain deterioration or other radiation damage effects. In addition several improvements with respect to LHC Run 1 data taking are introduced. A novel real-time calibration of the time-alignment of the detector and the alignment of the single monolayers composing detector modules are presented, improving the drift-time and position resolution of the detector by 20\%. Finally, a potential use of the improved resolution for the timing of charged tracks is described, showing the possibility to identify low-momentum hadrons with their time-of-flight.Comment: 29 pages, 20 figures, minor changes to match the published versio