Gaps between zeros of the Riemann zeta-function

We prove that there exist infinitely many consecutive zeros of the Riemann zeta-function on the critical line whose gaps are greater than $3.18$ times the average spacing. Using a modification of our method, we also show that there are even larger gaps between the multiple zeros of the zeta function on the critical line (if such zeros exist)

Central values of derivatives of Dirichlet L-functions

Let C(q,+) be the set of even, primitive Dirichlet characters (mod q). Using the mollifier method we show that L^{(k)}(1/2,chi) is not equal to zero for almost all the characters chi in C(q,+) when k and q are large. Here, L^{(k)}(s,chi) is the k-th derivative of of the Dirichlet L-function L(s,chi).Comment: submitted for publicatio

A note on the gaps between consecutive zeros of the Riemann zeta-function

Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and infinitely often they differ by at least 2.69 times the average spacing.Comment: 7 pages. Submitted for publicatio

On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t) in the theory of the Riemann zeta-function.Comment: 11 page

High Reynolds number tests of a Douglas DLBA 032 airfoil in the Langley 0.3-meter transonic cryogenic tunnel

A wind-tunnel investigation of a Douglas advanced-technology airfoil was conducted in the Langley 0.3-Meter Transonic Cryogenic Tunnel (0.3-m TCT). The temperature was varied from 227 K (409 R) to 100 K (180 R) at pressures ranging from about 159 kPa (1.57 atm) to about 514 kPa (5.07 atm). Mach number was varied from 0.50 to 0.78. These variables provided a Reynolds number range (based on airfoil chord) from 6.0 to 30.0 x 10 to the 6th power. This investigation was specifically designed to: (1) test a Douglas airfoil from moderately low to flight-equivalent Reynolds numbers, and (2) evaluate sidewall-boundary-layer effects on transonic airfoil performance characteristics by a systematic variation of Mach number, Reynolds number, and sidewall-boundary-layer removal. Data are included which demonstrate the effects of fixing transition, Mach number, Reynolds number, and sidewall-boundary-layer removal on the aerodynamic characteristics of the airfoil. Also included are remarks on model design and model structural integrity

The Proteus Navier-Stokes code

An effort is currently underway at NASA Lewis to develop two- and three-dimensional Navier-Stokes codes, called Proteus, for aerospace propulsion applications. The emphasis in the development of Proteus is not algorithm development or research on numerical methods, but rather the development of the code itself. The objective is to develop codes that are user-oriented, easily-modified, and well-documented. Well-proven, state-of-the-art solution algorithms are being used. Code readability, documentation (both internal and external), and validation are being emphasized. This paper is a status report on the Proteus development effort. The analysis and solution procedure are described briefly, and the various features in the code are summarized. The results from some of the validation cases that have been run are presented for both the two- and three-dimensional codes

Modèle élasto-plastique constitutif pour les sols fins dans les zones de saturation partielle à totale

International audienceNear saturation, air bubbles and pockets can be trapped in the porous network of soils. The aim of this paper was to present a coupled model that takes into account the effect of this entrapped air on the poro-elasto-plastic behavior of the soil. The model takes into account the physical-mechanical interactions between different phases as well as the kinematics of each constituent (liquid water, dissolved air, gaseous air and solid grains). This new model was implemented in a FEM code. Some numerical simulations were performed to demonstrate its ability to reproduce a continuous transition of unsaturated to saturated states.Près de saturation, les bulles d'air et les poches d'air peuvent être emprisonnées dans le réseau poreux des sols. Le but de cet article est de présenter un modèle couplé qui tient compte de l'effet de cet air emprisonné sur le comportement poro-élasto-plastique du sol. Le modèle prend en compte les interactions physico-mécaniques entre les différentes phases ainsi que la cinématique de chaque constituant (eau liquide, air dissous, air gazeux et grains solides). Ce nouveau modèle a été implémenté dans un code d'éléments finis. Des simulations numériques ont été effectuées pour démontrer sa capacité à reproduire une transition continue d'un état non-saturé vers un état totalement saturé

Electrical conductivity beyond linear response in layered superconductors under magnetic field

The time-dependent Ginzburg-Landau approach is used to investigate nonlinear response of a strongly type-II superconductor. The dissipation takes a form of the flux flow which is quantitatively studied beyond linear response. Thermal fluctuations, represented by the Langevin white noise, are assumed to be strong enough to melt the Abrikosov vortex lattice created by the magnetic field into a moving vortex liquid and marginalize the effects of the vortex pinning by inhomogeneities. The layered structure of the superconductor is accounted for by means of the Lawrence-Doniach model. The nonlinear interaction term in dynamics is treated within Gaussian approximation and we go beyond the often used lowest Landau level approximation to treat arbitrary magnetic fields. The I-V curve is calculated for arbitrary temperature and the results are compared to experimental data on high-$T_{c}$ superconductor YBa$_{2}$Cu$_{3}$O$$.Comment: 8 pages, 3 figure

Analysis of a jet stream induced gravity wave associated with an observed ice cloud over Greenland

International audienceA polar stratospheric ice cloud (PSC type II) was observed by airborne lidar above Greenland on 14 January 2000. It was the unique observation of an ice cloud over Greenland during the SOLVE/THESEO 2000 campaign. Mesoscale simulations with the hydrostatic HRM model are presented which, in contrast to global analyses, are capable to produce a vertically propagating gravity wave that induces the low temperatures at the level of the PSC afforded for the ice formation. The simulated minimum temperature is ~8 K below the driving analyses and ~4.5 K below the frost point, exactly coinciding with the location of the observed ice cloud. Despite the high elevations of the Greenland orography the simulated gravity wave is not a mountain wave. Analyses of the horizontal wind divergence, of the background wind profiles, of backward gravity wave ray-tracing trajectories, of HRM experiments with reduced Greenland topography and of several diagnostics near the tropopause level provide evidence that the wave is emitted from an intense, rapidly evolving, anticyclonically curved jet stream. The precise physical process responsible for the wave emission could not be identified definitely, but geostrophic adjustment and shear instability are likely candidates. In order to evaluate the potential frequency of such non-orographic polar stratospheric cloud events, the non-linear balance equation diagnostic is performed for the winter 1999/2000. It indicates that ice-PSCs are only occasionally generated by gravity waves emanating from spontaneous adjustment