Approximating multi-dimensional Hamiltonian flows by billiards

Consider a family of smooth potentials $V_{\epsilon}$, which, in the limit $\epsilon\to0$, become a singular hard-wall potential of a multi-dimensional billiard. We define auxiliary billiard domains that asymptote, as $\epsilon\to0$ to the original billiard, and provide asymptotic expansion of the smooth Hamiltonian solution in terms of these billiard approximations. The asymptotic expansion includes error estimates in the $C^{r}$ norm and an iteration scheme for improving this approximation. Applying this theory to smooth potentials which limit to the multi-dimensional close to ellipsoidal billiards, we predict when the separatrix splitting persists for various types of potentials

A maximum density rule for surfaces of quasicrystals

A rule due to Bravais of wide validity for crystals is that their surfaces correspond to the densest planes of atoms in the bulk of the material. Comparing a theoretical model of i-AlPdMn with experimental results, we find that this correspondence breaks down and that surfaces parallel to the densest planes in the bulk are not the most stable, i.e. they are not so-called bulk terminations. The correspondence can be restored by recognizing that there is a contribution to the surface not just from one geometrical plane but from a layer of stacked atoms, possibly containing more than one plane. We find that not only does the stability of high-symmetry surfaces match the density of the corresponding layer-like bulk terminations but the exact spacings between surface terraces and their degree of pittedness may be determined by a simple analysis of the density of layers predicted by the bulk geometric model.Comment: 8 pages of ps-file, 3 Figs (jpg

Convergence of invariant densities in the small-noise limit

This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in the small-noise limit is frequently governed by power laws. In addition, a simple heuristic is proposed and found to correctly predict the power law exponent in exponentially mixing systems. In systems which are not exponentially mixing, the heuristic provides only an upper bound on the power law exponent. As this numerical study requires the computation of invariant densities across more than 2 decades of noise amplitudes, it also provides an opportunity to discuss and compare standard numerical methods for computing invariant probability densities.Comment: 27 pages, 19 figures, revised with minor correction

On stochastic sea of the standard map

Consider a generic one-parameter unfolding of a homoclinic tangency of an area preserving surface diffeomorphism. We show that for many parameters (residual subset in an open set approaching the critical value) the corresponding diffeomorphism has a transitive invariant set $\Omega$ of full Hausdorff dimension. The set $\Omega$ is a topological limit of hyperbolic sets and is accumulated by elliptic islands. As an application we prove that stochastic sea of the standard map has full Hausdorff dimension for sufficiently large topologically generic parameters.Comment: 36 pages, 5 figure

Oxidation and magnetic states of chalcopyrite CuFeS2: a first principles calculation

The ground state band structure, magnetic moments, charges and population numbers of electronic shells of Cu and Fe atoms have been calculated for chalcopyrite CuFeS2 using density functional theory. The comparison between our calculation results and experimental data (X ray photoemission, X ray absorption and neutron diffraction spectroscopy) has been made. Our calculations predict a formal oxidation state for chalcopyrite as Cu1+Fe3+S. However, the assignment of formal valence state to transition metal atoms appears to be oversimplified. It is anticipated that the valence state can be confirmed experimentally by nuclear magnetic and nuclear quadrupole resonance and Mössbauer spectroscopy methods

Highly efficient separation of actinides from lanthanides by a phenanthroline-derived bis-triazine ligand

The synthesis, lanthanide complexation, and solvent ex- traction of actinide(III) and lanthanide(III) radiotracers from nitric acid solutions by a phenanthroline-derived quadridentate bis-triazine ligand are described. The ligand separates Am(III) and Cm(III) from the lanthanides with remarkably high efficiency, high selectivity, and fast extraction kinetics compared to its 2,2'-bipyridine counterpart. Structures of the 1:2 bis-complexes of the ligand with Eu(III) and Yb(III) were elucidated by X-ray crystallography and force field calculations, respec-tively. The Eu(III) bis-complex is the first 1:2 bis-complex of a quadridentate bis-triazine ligand to be characterized by crystallography. The faster rates of extraction were verified by kinetics measurements using the rotating membrane cell technique in several diluents. The improved kinetics of metal ion extraction are related to the higher surface activity of the ligand at the phase interface. The improvement in the ligand's properties on replacing the bipyridine unit with a phenanthroline unit far exceeds what was anticipated based on ligand design alone

Track billiards

We study a class of planar billiards having the remarkable property that their phase space consists up to a set of zero measure of two invariant sets formed by orbits moving in opposite directions. The tables of these billiards are tubular neighborhoods of differentiable Jordan curves that are unions of finitely many segments and arcs of circles. We prove that under proper conditions on the segments and the arcs, the billiards considered have non-zero Lyapunov exponents almost everywhere. These results are then extended to a similar class of of 3-dimensional billiards. Finally, we find that for some subclasses of track billiards, the mechanism generating hyperbolicity is not the defocusing one that requires every infinitesimal beam of parallel rays to defocus after every reflection off of the focusing boundary.Comment: 7 figure

Measuring What Works: An Impact Evaluation of Women's Groups on Maternal Health Uptake in Rural Nepal.

BACKGROUND: There is a need for studies evaluating maternal health interventions in low-income countries. This paper evaluates one such intervention designed to promote maternal health among rural women in Nepal. METHODS AND RESULTS: This was a five-year controlled, non-randomised, repeated cross-sectional study (2007, 2010, 2012) of a participatory community-based maternal health promotion intervention focusing on women's groups to improve maternal health services uptake. In total 1,236 women of childbearing age, who had their last child ≤ two years ago, were interviewed. Difference-in-Difference estimation assessed the effects of the intervention on selected outcome variables while controlling for a constructed wealth index and women's characteristics. In the first three years (from 2007 to the 2010), the intervention increased women's likelihood of attending for antenatal care at least once during pregnancy by seven times [OR = 7.0, 95%CI (2.3; 21.4)], of taking iron and folic acid by three times [OR = 3.0, 95%CI (1.2; 7.8)], and of seeking four or more antenatal care visits of two times, although not significantly [OR = 2.2, 95%CI (1.0; 4.7)]. Over five years, women were more likely to seek antenatal care at least once [OR = 3.0, 95%CI (1.5; 5.2)], to take iron/folic acid [OR = 1.9, [95% CI (1.1; 3.2)], and to attend postnatal care [OR = 1.5, [95% CI (1.1; 2.2)]. No improvement was found on attending antenatal care in the first trimester, birthing at an institution or with a skilled birth attendant. CONCLUSION: Community-based health promotion has a much stronger effect on the uptake of antenatal care and less on delivery care. Other factors not easily resolved through health promotion interventions may influence these outcomes, such as costs or geographical constraints. The evaluation has implications for policy and practice in public health, especially maternal health promotion

Taking two to tango:fMRI analysis of improvised joint action with physical contact

<div><p>Many forms of joint action involve physical coupling between the participants, such as when moving a sofa together or dancing a tango. We report the results of a novel two-person functional MRI study in which trained couple dancers engaged in bimanual contact with an experimenter standing next to the bore of the magnet, and in which the two alternated between being the leader and the follower of joint improvised movements. Leading showed a general pattern of self-orientation, being associated with brain areas involved in motor planning, navigation, sequencing, action monitoring, and error correction. In contrast, following showed a far more sensory, externally-oriented pattern, revealing areas involved in somatosensation, proprioception, motion tracking, social cognition, and outcome monitoring. We also had participants perform a “mutual” condition in which the movement patterns were pre-learned and the roles were symmetric, thereby minimizing any tendency toward either leading or following. The mutual condition showed greater activity in brain areas involved in mentalizing and social reward than did leading or following. Finally, the analysis of improvisation revealed the dual importance of motor-planning and working-memory areas. We discuss these results in terms of theories of both joint action and improvisation.</p></div