On the ratio of consecutive gaps between primes

In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60 years old problem of Erd\"os, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively

Primes in short intervals

Contrary to what would be predicted on the basis of Cram\'er's model concerning the distribution of prime numbers, we develop evidence that the distribution of $\psi(x+H)- \psi(x)$, for $0\le x\le N$, is approximately normal with mean $\sim H$ and variance $\sim H\log N/H$, when $N^\delta \le H \le N^{1-\delta}$.Comment: 29 page

A Benign Synthesis of Alane by the Composition-Controlled Mechanochemical Reaction of Sodium Hydride and Aluminum Chloride

Solid-state mechanochemical synthesis of alane (AlH3) starting from sodium hydride (NaH) and aluminum chloride (AlCl3) has been achieved at room temperature. The transformation pathway of this solid-state reaction was controlled by a step-wise addition of AlCl3 to the initial reaction mixture that contained sodium hydride in excess of stoichiometric amount. As in the case of previously investigated LiH-AlCl3 system, complete selectivity was achieved whereby formation of unwanted elemental aluminum was fully suppressed, and AlH3 was obtained in quantitative yield. Reaction progress during each step was investigated by means of solid-state NMR and powder X-ray diffraction, which revealed that the overall reaction proceeds through a series of intermediate alanates that may be partially chlorinated. The NaH-AlCl3 system present some subtle differences compared to LiH-AlCl3 system particularly with respect to optimal concentrations needed during one of the reaction stages. Based on the results we postulate that high local concentrations of NaH may stabilize chlorine-containing derivatives and prevent decomposition into elemental aluminum with hydrogen evolution. Complete conversion with quantitative yield of alane was confirmed both by SSNMR and hydrogen desorption analysis

Comparison between resistive and collisionless double tearing modes for nearby resonant surfaces

The linear instability and nonlinear dynamics of collisional (resistive) and collisionless (due to electron inertia) double tearing modes (DTMs) are compared with the use of a reduced cylindrical model of a tokamak plasma. We focus on cases where two q = 2 resonant surfaces are located a small distance apart. It is found that regardless of the magnetic reconnection mechanism, resistivity or electron inertia, the fastest growing linear eigenmodes may have high poloidal mode numbers m ~ 10. The spectrum of unstable modes tends to be broader in the collisionless case. In the nonlinear regime, it is shown that in both cases fast growing high-m DTMs lead to an annular collapse involving small magnetic island structures. In addition, collisionless DTMs exhibit multiple reconnection cycles due to reversibility of collisionless reconnection and strong ExB flows. Collisionless reconnection leads to a saturated stable state, while in the collisional case resistive decay keeps the system weakly dynamic by driving it back towards the unstable equilibrium maintained by a source term.Comment: 15 pages, 9 figure

Low angular momentum flow model of Sgr A* activity

Sgr A* is the closest massive black hole and can be observed with the highest angular resolution. Nevertheless, our current understanding of the accretion process in this source is very poor. The inflow is almost certainly of low radiative efficiency and it is accompanied by a strong outflow and the flow is strongly variable but the details of the dynamics are unknown. Even the amount of angular momentum in the flow is an open question. Here we argue that low angular momentum scenario is better suited to explain the flow variability. We present a new hybrid model which describes such a flow and consists of an outer spherically symmetric Bondi flow and an inner axially symmetric flow described through MHD simulations. The assumed angular momentum of the matter is low, i.e. the corresponding circularization radius in the equatorial plane of the flow is just above the innermost stable circular orbit in pseudo-Newtonian potential. We compare the radiation spectrum from such a flow to the broad band observational data for Sgr A*.Comment: Proceedings of the AHAR 2008 Conference: The Universe under the Microscope; Astrophysics at High Angular Resolution, Bad Honef

The two states of Sgr A* in the near-infrared: bright episodic flares on top of low-level continuous variability

In this paper we examine properties of the variable source Sgr A* in the near-infrared (NIR) using a very extensive Ks-band data set from NACO/VLT observations taken 2004 to 2009. We investigate the variability of Sgr A* with two different photometric methods and analyze its flux distribution. We find Sgr A* is continuously emitting and continuously variable in the near-infrared, with some variability occurring on timescales as long as weeks. The flux distribution can be described by a lognormal distribution at low intrinsic fluxes (<~5 mJy, dereddened with A_{Ks}=2.5). The lognormal distribution has a median flux of approximately 1.1 mJy, but above 5 mJy the flux distribution is significantly flatter (high flux events are more common) than expected for the extrapolation of the lognormal distribution to high fluxes. We make a general identification of the low level emission above 5 mJy as flaring emission and of the low level emission as the quiescent state. We also report here the brightest Ks-band flare ever observed (from August 5th, 2008) which reached an intrinsic Ks-band flux of 27.5 mJy (m_{Ks}=13.5). This flare was a factor 27 increase over the median flux of Sgr A*, close to double the brightness of the star S2, and 40% brighter than the next brightest flare ever observed from Sgr~A*.Comment: 14 pages, 6 figures, accepted for publication in Ap

Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring

We construct a zero-curvature Lax connection in a sub-sector of the superstring theory on AdS(4) x CP(3) which is not described by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet fermions associated to eight broken supersymmetries of the type IIA background are physical fields. As such, the prescription for the construction of the Lax connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4) does not do the job. So, to construct the Lax connection we have used an alternative method which nevertheless relies on the isometry of the target superspace and kappa-symmetry of the Green-Schwarz superstring.Comment: 1+26 pages; v2: minor typos corrected, acknowledgements adde

Bandlimited approximations to the truncated Gaussian and applications

In this paper we extend the theory of optimal approximations of functions $f: \R \to \R$ in the $L^1(\R)$-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd Gaussians using explicit integral representations and fine properties of truncated theta functions obtained via the maximum principle for the heat operator. As applications, we recover most of the previously known examples in the literature and further extend the class of truncated and odd functions for which this extremal problem can be solved, by integration on the free parameter and the use of tempered distribution arguments. This is the counterpart of the work \cite{CLV}, where the case of even functions is treated.Comment: to appear in Const. Appro

The Mikheyev-Smirnov-Wolfenstein Effect as a Probe of the Solar Interior

We relate the MSW effect to the efective absorption of the electronic collective motion energy by retaining the imaginary part of the index of refraction associated with the charged-current scattering and show that the small angle MSW solution to the solar neutrino anomaly can be used as a probe of the physical conditions of the solar interior if it is correct. We find that the constraint on the absorption imposed by the small angle MSW solution and the theoretical estimate of the absorption by the Boltzmann kinetic theory are consistent, which shows that a consistent theoretical picture can be developed when plasma absorption processes are taken into account.Comment: 4 pages, no figure, REVTeX, to appear in Phys. Rev.