On the density of the odd values of the partition function, II: An infinite conjectural framework

We continue our study of a basic but seemingly intractable problem in integer partition theory, namely the conjecture that $p(n)$ is odd exactly $50\%$ of the time. Here, we greatly extend on our previous paper by providing a doubly-indexed, infinite framework of conjectural identities modulo 2, and show how to, in principle, prove each such identity. However, our conjecture remains open in full generality. A striking consequence is that, under suitable existence conditions, if any $t$-multipartition function is odd with positive density and $t\not \equiv 0$ (mod 3), then $p(n)$ is also odd with positive density. These are all facts that appear virtually impossible to show unconditionally today. Our arguments employ a combination of algebraic and analytic methods, including certain technical tools recently developed by Radu in his study of the parity of the Fourier coefficients of modular forms.Comment: 14 pages. To appear in the J. of Number Theor

On the density of the odd values of the partition function

The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo 2. Our main result will relate the densities, say $\delta_t$, of the odd values of the $t$-multipartition functions $p_t(n)$, for several integers $t$. In particular, we will show that if $\delta_t>0$ for some $t\in \{5,7,11,13,17,19,23,25\}$, then (assuming it exists) $\delta_1>0$; that is, $p(n)$ itself is odd with positive density. Notice that, currently, the best unconditional result does not even imply that $p(n)$ is odd for $\sqrt{x}$ values of $n\le x$. In general, we conjecture that $\delta_t=1/2$ for all $t$ odd, i.e., that similarly to the case of $p(n)$, all multipartition functions are in fact equidistributed modulo 2. Our arguments will employ a number of algebraic and analytic methods, ranging from an investigation modulo 2 of some classical Ramanujan identities and several other eta product results, to a unified approach that studies the parity of the Fourier coefficients of a broad class of modular form identities recently introduced by Radu.Comment: Several changes with respect to the 2015 version. 18 pages. To appear in the Annals of Combinatoric

Irradiation of carbon nanotubes with carbon projectiles: A molecular dynamics study

The irradiation of carbon based nanostructures with ions and electrons has been shown to be an appropriate tool to tailor their properties. The defects induced in the nanostructures during irradiation are able to modify their mechanical and electronic properties. Here we simulate the irradiation of carbon nanotubes with carbon ions using a molecular dynamics code. We use the Tersoff potential joined smoothly to the Universal Ziegler-Biersack-Littmark potential at short distances. We study the number of defects produced after irradiation with a single carbon ion finding a saturation with its energy at ∼ 3 keV. We observe, after continuum irradiation with low energy ions, the formation of bumps in the irradiated region. For larger energy ions we find that the diameter of the nanotube shrinks as shown in previous works.This work has been financially supported by Project FIS2010-17225 by the Spanish Ministerio de Ciencia e Innovación

Simulation of swift boron clusters traversing amorphous carbon foils

We use a simulation code to study the interaction of swift boron clusters (Bn+, n=2–6, 14) with amorphous carbon foils. We analyze different aspects of this interaction, such as the evolution of the cluster structure inside the target, the energy and angle distributions at the detector or the stopping power ratio. Our simulation code follows in detail the motion of the cluster fragments through the target and in the vacuum until reaching a detector, taking into account the following interactions: (i) wake force, (ii) Coulomb repulsion among cluster fragments, (iii) stopping force, and (iv) elastic scattering with the target nuclei. Electron capture and loss by each fragment is also included in the code, affecting the above-mentioned interactions. The clusters size grows inside the foil due mainly to the Coulomb explosion but this increase is less pronounced in the plane transversal to the beam direction because of the alignment effect of the wake forces. We obtain an enhancement of the stopping power ratio that increases with the projectile energy and with the number of molecular constituents. Our results agree very well with the available experimental data for the thicker foils (≳10 μg∕cm2) and are compatible (within the experimental error bars) for the thinner foils.This work has been financially supported by the Spanish Ministerio de Educación y Ciencia (Contract Nos. BFM2003-04457-C02-01 and BFM2003-04457-C02-02). S.H.A. thanks the Fundación CajaMurcia for financial support and C.D.D. thanks the Spanish Ministerio de Educación y Ciencia for support under the Ramón y Cajal Program

A novel experimental approach for the detection of the dynamic Casimir effect

The Casimir effect is a well-known macroscopic consequence of quantum vacuum fluctuations, but whereas the static effect (Casimir force) has long been observed experimentally, the dynamic Casimir effect is up to now undetected. From an experimental viewpoint a possible detection would imply the vibration of a mirror at gigahertz frequencies. Mechanical motions at such frequencies turn out to be technically unfeasible. Here we present a different experimental scheme where mechanical motions are avoided, and the results of laboratory tests showing that the scheme is practically feasible. We think that at present this approach gives the only possibility of detecting this phenomenon.Comment: Submitted to the Physical Review Letters. RevTeX. 4 pages, 2 figure

Effects of Mild Hypercapnia During Head-Down Bed Rest on Ocular Structures, Cerebral Blood Flow, aud Visual Acuity in Healthy Human Subjects

The cephalad fluid shift induced by microgravity has been hypothesized to cause an elevation in intracranial pressure (ICP) and contribute to the development of the Visual Impairment/Intracranial Pressure (VIIP) syndrome, as experienced by some astronauts during long-duration space flight. Elevated ambient partial pressure of carbon dioxide (PCO2) on ISS may also raise ICP and contribute to VIIP development. We seek to determine if the combination of mild CO2 exposure, similar to that occurring on the International Space Station, with the cephalad fluid shift induced by head-down tilt, will induce ophthalmic and cerebral blood flow changes similar to those described in the VIIP syndrome. We hypothesize that mild hypercapnia in the head-down tilt position will increase choroidal blood volume and cerebral blood flow, raise intraocular pressure (IOP), and transiently reduce visual acuity as compared to the seated or the head-down tilt position without elevated CO2, respectively

AGILE detection of delayed gamma-ray emission from GRB 080514B

GRB 080514B is the first gamma ray burst (GRB), since the time of EGRET, for which individual photons of energy above several tens of MeV have been detected with a pair-conversion tracker telescope. This burst was discovered with the Italian AGILE gamma-ray satellite. The GRB was localized with a cooperation by AGILE and the interplanetary network (IPN). The gamma-ray imager (GRID) estimate of the position, obtained before the SuperAGILE-IPN localization, is found to be consistent with the burst position. The hard X-ray emission observed by SuperAGILE lasted about 7 s, while there is evidence that the emission above 30 MeV extends for a longer duration (at least ~13 s). Similar behavior was seen in the past from a few other GRBs observed with EGRET. However, the latter measurements were affected, during the brightest phases, by instrumental dead time effects, resulting in only lower limits to the burst intensity. Thanks to the small dead time of the AGILE/GRID we could assess that in the case of GRB 080514B the gamma-ray to X-ray flux ratio changes significantly between the prompt and extended emission phase.Comment: A&A letters, in pres

AGILE observation of a gamma-ray flare from the blazar 3C 279

Context. We report the detection by the AGILE satellite of an intense gamma-ray flare from the gamma-ray source 3EG J1255-0549, associated to the Flat Spectrum Radio Quasar 3C 279, during the AGILE pointings towards the Virgo Region on 2007 July 9-13. Aims. The simultaneous optical, X-ray and gamma-ray covering allows us to study the spectral energy distribution (SED) and the theoretical models relative to the flaring episode of mid-July. Methods. AGILE observed the source during its Science Performance Verification Phase with its two co-aligned imagers: the Gamma- Ray Imaging Detector (GRID) and the hard X-ray imager (Super-AGILE) sensitive in the 30 MeV - 50 GeV and 18 - 60 keV respectively. During the AGILE observation the source was monitored simultaneously in optical band by the REM telescope and in the X-ray band by the Swift satellite through 4 ToO observations. Results. During 2007 July 9-13 July 2007, AGILE-GRID detected gamma-ray emission from 3C 279, with the source at ~2 deg from the center of the Field of View, with an average flux of (210+-38) 10^-8 ph cm^-2 s^-1 for energy above 100 MeV. No emission was detected by Super-AGILE, with a 3-sigma upper limit of 10 mCrab. During the observation lasted about 4 days no significative gamma-ray flux variation was observed. Conclusions. The Spectral Energy Distribution is modelled with a homogeneous one-zone Synchrotron Self Compton emission plus the contributions by external Compton scattering of direct disk radiation and, to a lesser extent, by external Compton scattering of photons from the Broad Line Region.Comment: Accepted for publication in Astronomy and Astrophysic

Direct Evidence for Hadronic Cosmic-Ray Acceleration in the Supernova Renmant IC 443

The Supernova Remnant (SNR) IC 443 is an intermediate-age remnant well known for its radio, optical, X-ray and gamma-ray energy emissions. In this Letter we study the gamma-ray emission above 100 MeV from IC 443 as obtained by the AGILE satellite. A distinct pattern of diffuse emission in the energy range 100 MeV-3 GeV is detected across the SNR with its prominent maximum (source "A") localized in the Northeastern shell with a flux F = (47 \pm 10) 10^{-8} photons cm^{-2} s^{-1} above 100 MeV. This location is the site of the strongest shock interaction between the SNR blast wave and the dense circumstellar medium. Source "A" is not coincident with the TeV source located 0.4 degree away and associated with a dense molecular cloud complex in the SNR central region. From our observations, and from the lack of detectable diffuse TeV emission from its Northeastern rim, we demonstrate that electrons cannot be the main emitters of gamma-rays in the range 0.1-10 GeV at the site of the strongest SNR shock. The intensity, spectral characteristics, and location of the most prominent gamma-ray emission together with the absence of co-spatial detectable TeV emission are consistent only with a hadronic model of cosmic-ray acceleration in the SNR. A high-density molecular cloud (cloud "E") provides a remarkable "target" for nucleonic interactions of accelerated hadrons: our results show enhanced gamma-ray production near the molecular cloud/shocked shell interaction site. IC 443 provides the first unambiguous evidence of cosmic-ray acceleration by SNRs.Comment: 5 pages, 2 figures; accepted by ApJLetters on Jan 21, 201

Search for Second-Generation Scalar Leptoquarks in ppˉ\bm{p \bar{p}} Collisions at s\sqrt{s}=1.96 TeV

Results on a search for pair production of second generation scalar leptoquark in $p \bar{p}$ collisions at $\sqrt{s}$=1.96 TeV are reported. The data analyzed were collected by the CDF detector during the 2002-2003 Tevatron Run II and correspond to an integrated luminosity of 198 pb$^{-1}$. Leptoquarks (LQ) are sought through their decay into (charged) leptons and quarks, with final state signatures represented by two muons and jets and one muon, large transverse missing energy and jets. We observe no evidence for $LQ$ production and derive 95% C.L. upper limits on the $LQ$ production cross sections as well as lower limits on their mass as a function of $\beta$, where $\beta$ is the branching fraction for $LQ \to \mu q$.Comment: 9 pages (3 author list) 5 figure