Fractional Hamiltonian Monodromy from a Gauss-Manin Monodromy

Fractional Hamiltonian Monodromy is a generalization of the notion of Hamiltonian Monodromy, recently introduced by N. N. Nekhoroshev, D. A. Sadovskii and B. I. Zhilinskii for energy-momentum maps whose image has a particular type of non-isolated singularities. In this paper, we analyze the notion of Fractional Hamiltonian Monodromy in terms of the Gauss-Manin Monodromy of a Riemann surface constructed from the energy-momentum map and associated to a loop in complex space which bypasses the line of singularities. We also prove some propositions on Fractional Hamiltonian Monodromy for 1:-n and m:-n resonant systems.Comment: 39 pages, 24 figures. submitted to J. Math. Phy

Transport of Cosmic Rays in Chaotic Magnetic Fields

The transport of charged particles in disorganised magnetic fields is an important issue which concerns the propagation of cosmic rays of all energies in a variety of astrophysical environments, such as the interplanetary, interstellar and even extra-galactic media, as well as the efficiency of Fermi acceleration processes. We have performed detailed numerical experiments using Monte-Carlo simulations of particle propagation in stochastic magnetic fields in order to measure the parallel and transverse spatial diffusion coefficients and the pitch angle scattering time as a function of rigidity and strength of the turbulent magnetic component. We confirm the extrapolation to high turbulence levels of the scaling predicted by the quasi-linear approximation for the scattering frequency and parallel diffusion coefficient at low rigidity. We show that the widely used Bohm diffusion coefficient does not provide a satisfactory approximation to diffusion even in the extreme case where the mean field vanishes. We find that diffusion also takes place for particles with Larmor radii larger than the coherence length of the turbulence. We argue that transverse diffusion is much more effective than predicted by the quasi-linear approximation, and appears compatible with chaotic magnetic diffusion of the field lines. We provide numerical estimates of the Kolmogorov length and magnetic line diffusion coefficient as a function of the level of turbulence. Finally we comment on applications of our results to astrophysical turbulence and the acceleration of high energy cosmic rays in supernovae remnants, in super-bubbles, and in jets and hot spots of powerful radio-galaxies.Comment: To be published in Physical Review D, 20 pages 9 figure

Simulating the Multi-Epoch Direct Detection Technique to Isolate the Thermal Emission of the Non-Transiting Hot Jupiter HD187123B

We report the 6.5$\sigma$ detection of water from the hot Jupiter HD187123b with a Keplerian orbital velocity $K_p$ of 53 $\pm$ 13 km/s. This high confidence detection is made using a multi-epoch, high resolution, cross correlation technique, and corresponds to a planetary mass of 1.4$^{+0.5}_{-0.3}$ $M_J$ and an orbital inclination of 21 $\pm$ 5$^{\circ}$. The technique works by treating the planet/star system as a spectroscopic binary and obtaining high signal-to-noise, high resolution observations at multiple points across the planet's orbit to constrain the system's binary dynamical motion. All together, seven epochs of Keck/NIRSPEC $L$-band observations were obtained, with five before the instrument upgrade and two after. Using high resolution SCARLET planetary and PHOENIX stellar spectral models, along with a line-by-line telluric absorption model, we were able to drastically increase the confidence of the detection by running simulations that could reproduce, and thus remove, the non-random structured noise in the final likelihood space well. The ability to predict multi-epoch results will be extremely useful for furthering the technique. Here, we use these simulations to compare three different approaches to combining the cross correlations of high resolution spectra and find that the Zucker 2003 log(L) approach is least affected by unwanted planet/star correlation for our HD187123 data set. Furthermore, we find that the same total S/N spread across an orbit in many, lower S/N epochs rather than fewer, higher S/N epochs could provide a more efficient detection. This work provides a necessary validation of multi-epoch simulations which can be used to guide future observations and will be key to studying the atmospheres of further separated, non-transiting exoplanets.Comment: Accepted to AJ, 14 pages, 10 figure

Pair Plasma Dominance in the Parsec-Scale Relativistic Jet of 3C345

We investigate whether a pc-scale jet of 3C345 is dominated by a normal plasma or an electron-positron plasma. We present a general condition that a jet component becomes optically thick for synchrotron self-absorption, by extending the method originally developed by Reynolds et al. The general condition gives a lower limit of the electron number density, with the aid of the surface brightness condition, which enables us to compute the magnetic field density. Comparing the lower limit with another independent constraint for the electron density that is deduced from the kinetic luminosity, we can distinguish the matter content. We apply the procedure to the five components of 3C345 (C2, C3, C4, C5, and C7) of which angular diameters and radio fluxes at the peak frequencies were obtainable from literature. Evaluating the representative values of Doppler beaming factors by their equipartition values, we find that all the five components are likely dominated by an electron-positron plasma. The conclusion does not depend on the lower cutoff energy of the power-law distribution of radiating particles.Comment: 17 page

Geo-additive models of Childhood Undernutrition in three Sub-Saharan African Countries

We investigate the geographical and socioeconomic determinants of childhood undernutrition in Malawi, Tanzania and Zambia, three neighboring countries in Southern Africa using the 1992 Demographic and Health Surveys. We estimate models of undernutrition jointly for the three countries to explore regional patterns of undernutrition that transcend boundaries, while allowing for country-specific interactions. We use semiparametric models to flexibly model the effects of selected so-cioeconomic covariates and spatial effects. Our spatial analysis is based on a flexible geo-additive model using the district as the geographic unit of anal-ysis, which allows to separate smooth structured spatial effects from random effect. Inference is fully Bayesian and uses recent Markov chain Monte Carlo techniques. While the socioeconomic determinants generally confirm what is known in the literature, we find distinct residual spatial patterns that are not explained by the socioeconomic determinants. In particular, there appears to be a belt run-ning from Southern Tanzania to Northeastern Zambia which exhibits much worse undernutrition, even after controlling for socioeconomic effects. These effects do transcend borders between the countries, but to a varying degree. These findings have important implications for targeting policy as well as the search for left-out variables that might account for these residual spatial patterns

Stochastic Assembly of Bacteria in Microwell Arrays Reveals the Importance of Confinement in Community Development

Citation: Hansen, R. H., Timm, A. C., Timm, C. M., Bible, A. N., Morrell-Falvey, J. L., Pelletier, D. A., . . . Retterer, S. T. (2016). Stochastic Assembly of Bacteria in Microwell Arrays Reveals the Importance of Confinement in Community Development. Plos One, 11(5), 18. doi:10.1371/journal.pone.0155080The structure and function of microbial communities is deeply influenced by the physical and chemical architecture of the local microenvironment and the abundance of its community members. The complexity of this natural parameter space has made characterization of the key drivers of community development difficult. In order to facilitate these characterizations, we have developed a microwell platform designed to screen microbial growth and interactions across a wide variety of physical and initial conditions. Assembly of microbial communities into microwells was achieved using a novel biofabrication method that exploits well feature sizes for control of innoculum levels. Wells with incrementally smaller size features created populations with increasingly larger variations in inoculum levels. This allowed for reproducible growth measurement in large (20 mu m diameter) wells, and screening for favorable growth conditions in small (5, 10 mu m diameter) wells. We demonstrate the utility of this approach for screening and discovery using 5 mu m wells to assemble P. aeruginosa colonies across a broad distribution of innoculum levels, and identify those conditions that promote the highest probability of survivial and growth under spatial confinement. Multi-member community assembly was also characterized to demonstrate the broad potential of this platform for studying the role of member abundance on microbial competition, mutualism and community succession

Analysis of Coaxial Soil Cell in Reflection and Transmission

Accurate measurement of moisture content is a prime requirement in hydrological, geophysical and biogeochemical research as well as for material characterization and process control. Within these areas, accurate measurements of the surface area and bound water content is becoming increasingly important for providing answers to many fundamental questions ranging from characterization of cotton fiber maturity, to accurate characterization of soil water content in soil water conservation research to bio-plant water utilization to chemical reactions and diffusions of ionic species across membranes in cells as well as in the dense suspensions that occur in surface films. In these bound water materials, the errors in the traditional time-domain-reflectometer, “TDR”, exceed the range of the full span of the material’s permittivity that is being measured. Thus, there is a critical need to re-examine the TDR system and identify where the errors are to direct future research. One promising technique to address the increasing demands for higher accuracy water content measurements is utilization of electrical permittivity characterization of materials. This technique has enjoyed a strong following in the soil-science and geological community through measurements of apparent permittivity via time-domain-reflectometery as well in many process control applications. Recent research however, is indicating a need to increase the accuracy beyond that available from traditional TDR. The most logical pathway then becomes a transition from TDR based measurements to network analyzer measurements of absolute permittivity that will remove the adverse effects that high surface area soils and conductivity impart onto the measurements of apparent permittivity in traditional TDR applications. This research examines the theoretical basis behind the coaxial probe, from which the modern TDR probe originated from, to provide a basis on which to perform absolute permittivity measurements. The research reveals currently utilized formulations in accepted techniques for permittivity measurements which violate the underlying assumptions inherent in the basic models due to the TDR acting as an antenna by radiating energy off the end of the probe, rather than returning it back to the source as is the current assumption. To remove the effects of radiation from the experimental results obtain herein, this research utilized custom designed coaxial probes of various diameters and probe lengths by which to test the coaxial cell measurement technique for accuracy in determination of absolute permittivity. In doing so, the research reveals that the basic models available in the literature all omitted a key correction factor that is hypothesized by this research as being most likely due to fringe capacitance. To test this theory, a Poisson model of a coaxial cell was formulated to calculate the effective extra length provided by the fringe capacitance which is then used to correct the experimental results such that experimental measurements utilizing differing coaxial cell diameters and probe lengths, upon correction with the Poisson model derived correction factor, all produce the same results thereby lending support for the use of an augmented measurement technique, described herein, for measurement of absolute permittivity, as opposed to the traditional TDR measurement of apparent permittivity