Surpassing the Ratios Conjecture in the 1-level density of Dirichlet LL-functions

We study the $1$-level density of low-lying zeros of Dirichlet $L$-functions in the family of all characters modulo $q$, with $Q/2 < q\leq Q$. For test functions whose Fourier transform is supported in $(-3/2, 3/2)$, we calculate this quantity beyond the square-root cancellation expansion arising from the $L$-function Ratios Conjecture of Conrey, Farmer and Zirnbauer. We discover the existence of a new lower-order term which is not predicted by this powerful conjecture. This is the first family where the 1-level density is determined well enough to see a term which is not predicted by the Ratios Conjecture, and proves that the exponent of the error term $Q^{-\frac 12 +\epsilon}$ in the Ratios Conjecture is best possible. We also give more precise results when the support of the Fourier Transform of the test function is restricted to the interval $[-1,1]$. Finally we show how natural conjectures on the distribution of primes in arithmetic progressions allow one to extend the support. The most powerful conjecture is Montgomery's, which implies that the Ratios Conjecture's prediction holds for any finite support up to an error $Q^{-\frac 12 +\epsilon}$.Comment: Version 1.2, 30 page

The jumping champion conjecture

An integer $d$ is called a jumping champion for a given $x$ if $d$ is the most common gap between consecutive primes up to $x$. Occasionally several gaps are equally common. Hence, there can be more than one jumping champion for the same $x$. For the $n$th prime $p_{n}$, the $n$th primorial $p_{n}^{\sharp}$ is defined as the product of the first $n$ primes. In 1999, Odlyzko, Rubinstein and Wolf provided convincing heuristics and empirical evidence for the truth of the hypothesis that the jumping champions greater than 1 are 4 and the primorials $p_{1}^{\sharp}, p_{2}^{\sharp}, p_{3}^{\sharp}, p_{4}^{\sharp}, p_{5}^{\sharp}, ...$, that is, $2, 6, 30, 210, 2310, ....$ In this paper, we prove that an appropriate form of the Hardy-Littlewood prime $k$-tuple conjecture for prime pairs and prime triples implies that all sufficiently large jumping champions are primorials and that all sufficiently large primorials are jumping champions over a long range of $x$.Comment: 19 pages, 1 tabl

Measuring magnetic fields in galaxies

The magnetic (B) field in the disk of a galaxy may play an important role in the dynamics and evolution of the interstellar medium (ISM). The process by which the interstellar B-field is generated and maintained is not well understood, but the general expectation is that the generated B-field will be toroidal (parallel to the disk of the galaxy). The large-scale B-field threading the cold ISM of external galaxies can be probed via optical and near-infrared (NIR) polarimetric observations. However, scattered light can introduce false-positive B-field detections into these observations and is a source of contamination. This dissertation sets a context for observations of the Milky Way B-field by assessing the degree to which scattered light affects NIR polarimetry and reporting measurements of the B-fields in the disks of several external galaxies. The polarization properties of scattered light were investigated in order to better understand the degree to which scattered light may be a source of contamination in studies of the cold ISM B-field of external galaxies. The optical and NIR polarization of three, nearby, reflection nebulae was observed, and the wavelength dependence of the polarization percentage was measured. This wavelength dependence was found to be related to the characteristics of the scattering dust grain population with the general conclusion that the total amount of polarized, scattered light decreases with increasing wavelength. This analysis was repeated for the scattering-dominated galaxy M82 to test if similar results obtained for galaxies outside the Milky Way. Observations of this object indicate that the total amount of contamination from scattered light in this object is also less at NIR wavelengths than at optical wavelengths, and they confirm that B-field generated polarization can be detected in external galaxies. A sample of edge-on galaxies was observed for NIR polarization to measure the cold ISM B-field there. These observations indicate the likely presence of non-toroidal B-fields, localized, coherent B-field structures, and spiral disk structure detectable via NIR polarimetry. A comparison of the B-fields threading the cold and hot components of the ISM suggests that these B-fields may be dynamically distinct under certain conditions

Characteristics and likelihood of ongoing homelessness among unsheltered veterans

INTRODUCTION: Unsheltered homelessness is an important phenomenon yet difficult to study due to lack of data. The Veterans Health Administration administers a universal homelessness screener, which identifies housing status for Veterans screening positive for homelessness. METHODS: This study compared unsheltered and sheltered Veterans, assessed differences in rates of ongoing homelessness, and estimated a mixed-effect logistic regression model to examine the relationship between housing status and ongoing homelessness. RESULTS: Eleven percent of Veterans who screened positive for homelessness were unsheltered; 40% of those who rescreened were homeless six months later, compared with less than 20% of sheltered Veterans. Unsheltered Veterans were 2.7 times as likely to experience ongoing homelessness. DISCUSSION: Unsheltered Veterans differ from their sheltered counterparts-they are older, more likely to be male, less likely to have income-and may be good candidates for an intensive housing intervention. Future research will assess clinical characteristics and services utilization among this population

Selective decay and coherent vortices in two-dimensional incompressible turbulence

Numerical solution of two-dimensional incompressible hydrodynamics shows that states of a near-minimal ratio of enstrophy to energy can be attained in times short compared with the flow decay time, confirming the simplest turbulent selective decay conjecture, and suggesting that coherent vortex structures do not terminate nonlinear processes. After all possible vortex mergers occur, the vorticity attains a particlelike character, suggested by the late-time similarity of the streamlines to Ewald potential contours

Lattice Boltzmann Magnetohydrodynamics

Lattice gas and lattice Boltzmann methods are recently developed numerical schemes for simulating a variety of physical systems. In this paper a new lattice Boltzmann model for modeling two-dimensional incompressible magnetohydrodynamics (MHD) is presented. The current model fully utilizes the flexibility of the lattice Boltzmann method in comparison with previous lattice gas and lattice Boltzmann MHD models, reducing the number of moving directions from $36$ in other models to $12$ only. To increase computational efficiency, a simple single time relaxation rule is used for collisions, which directly controls the transport coefficients. The bi-directional streaming process of the particle distribution function in this paper is similar to the original model [ H. Chen and W. H. Matthaeus, Phys. Rev. Lett., {\bf 58}, 1845(1987), S.Chen, H.Chen, D.Mart\'{\i}nez and W.H.Matthaeus, Phys. Rev. Lett. {\bf 67},3776 (1991)], but has been greatly simplified, affording simpler implementation of boundary conditions and increasing the feasibility of extension into a workable three-dimensional model. Analytical expressions for the transport coefficients are presented. Also, as example cases, numerical calculation for the Hartmann flow is performed, showing a good agreement between the theoreticalComment: 45 pages, to appear in Physics of Plasma

Modifying memory for a museum tour in older adults: reactivation-related updating that enhances and distorts memory is reduced in ageing

Memory reactivation, the activation of a latent memory trace when we are reminded of a past experience, strengthens memory but can also contribute to distortions if new information present during reactivation is integrated with existing memory. In a previous study in young adults (St. Jacques & Schacter, 2013; Psychological Science) we found that the quality of memory reactivation, manipulated using the principle of encoding specificity and indexed by recollection ratings, modulated subsequent true and false memories for events experienced during a museum tour. Here, we examined age-related changes in the quality of memory reactivation on subsequent memory. Young and older adults reactivated memories for museum stops immediately followed by the presentation of a novel lure photo from an alternate tour version (i.e., reactivation plus new information). There was an increase in subsequent true memories for reactivated targets and for subsequent false memories for lures that followed reactivated targets, when compared to baseline target and lure photos. However, the influence of reactivation on subsequent memories was reduced in older adults. These data reveal that aging alters reactivation-related updating processes that allow memories to be strengthened and updated with new information- consequently reducing memory distortions in older compared to young adults