Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case

In this article, we show that the double scaling limit correlation functions of a random matrix model when two cuts merge with degeneracy $2m$ (i.e. when $y\sim x^{2m}$ for arbitrary values of the integer $m$) are the same as the determinantal formulae defined by conformal $(2m,1)$ models. Our approach follows the one developed by Berg\`{e}re and Eynard in \cite{BergereEynard} and uses a Lax pair representation of the conformal $(2m,1)$ models (giving Painlev\'e II integrable hierarchy) as suggested by Bleher and Eynard in \cite{BleherEynard}. In particular we define Baker-Akhiezer functions associated to the Lax pair to construct a kernel which is then used to compute determinantal formulae giving the correlation functions of the double scaling limit of a matrix model near the merging of two cuts.Comment: 37 pages, 4 figures. Presentation improved, typos corrected. Published in Journal Of Statistical Mechanic

Methanesulfonic acid (MSA) migration in polar ice : data synthesis and theory

© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Cryosphere 11 (2017): 2439-2462, doi:10.5194/tc-11-2439-2017.Methanesulfonic acid (MSA; CH3SO3H) in polar ice is a unique proxy of marine primary productivity, synoptic atmospheric transport, and regional sea-ice behavior. However, MSA can be mobile within the firn and ice matrix, a post-depositional process that is well known but poorly understood and documented, leading to uncertainties in the integrity of the MSA paleoclimatic signal. Here, we use a compilation of 22 ice core MSA records from Greenland and Antarctica and a model of soluble impurity transport in order to comprehensively investigate the vertical migration of MSA from summer layers, where MSA is originally deposited, to adjacent winter layers in polar ice. We find that the shallowest depth of MSA migration in our compilation varies over a wide range (∼ 2 to 400 m) and is positively correlated with snow accumulation rate and negatively correlated with ice concentration of Na+ (typically the most abundant marine cation). Although the considered soluble impurity transport model provides a useful mechanistic framework for studying MSA migration, it remains limited by inadequate constraints on key physico-chemical parameters – most notably, the diffusion coefficient of MSA in cold ice (DMS). We derive a simplified version of the model, which includes DMS as the sole parameter, in order to illuminate aspects of the migration process. Using this model, we show that the progressive phase alignment of MSA and Na+ concentration peaks observed along a high-resolution West Antarctic core is most consistent with 10−12 m2 s−1 < DMS < 10−11 m2 s−1, which is 1 order of magnitude greater than the DMS values previously estimated from laboratory studies. More generally, our data synthesis and model results suggest that (i) MSA migration may be fairly ubiquitous, particularly at coastal and (or) high-accumulation regions across Greenland and Antarctica; and (ii) can significantly change annual and multiyear MSA concentration averages. Thus, in most cases, caution should be exercised when interpreting polar ice core MSA records, although records that have undergone severe migration could still be useful for inferring decadal and lower-frequency climate variability.Matthew Osman acknowledges government support awarded by DoD, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a. This work was supported by the US NSF (ANT-0632031 and PLR-1205196 to Sarah B. Das, and NSF-MRI-1126217 to Matthew J. Evans) and a Woods Hole Oceanographic Institution Interdisciplinary Research award to Sarah B. Das and Olivier Marchal

Cell-Associated HIV-1 RNA in Blood as Indicator of Virus Load in Lymph Nodes

We have developed sensitive assays for viremia and cell-associated human immunodeficiency virus type 1 (HIV-1) RNA and DNA to assess the predictive value of virological parameters determined in blood for virus load in lymph nodes (LNs). Eighteen patients were included; 13 received stavudine/didanosine/hydroxyurea and 5 stavudine/didanosine, and all had viremia 3 months. At the time of LN biopsy (median, 10 months), the median viremia was 2.09 log copies/mL (range, <0.70-3.34). Cell-associated HIV-1 RNA and DNA were detectable in blood and LNs of all patients. The median cell-associated RNA and DNA were 2.16 log copies/106 cells and 2.60 log copies/106 cells in blood versus 4.31 log RNA copies/106 cells and 3.26 log DNA copies/106 cells in LNs. Regression analysis shows that, in treated patients with sustained low viremia, cell-associated RNA and DNA in blood are better predictors of virus load in LNs than viremi

Depth of interaction and bias voltage depenence of the spectral response in a pixellated CdTe detector operating in time-over-threshold mode subjected to monochromatic X-rays

High stopping power is one of the most important figures of merit for X-ray detectors. CdTe is a promising material but suffers from: material defects, non-ideal charge transport and long range X-ray fluorescence. Those factors reduce the image quality and deteriorate spectral information. In this project we used a monochromatic pencil beam collimated through a 20μm pinhole to measure the detector spectral response in dependance on the depth of interaction. The sensor was a 1mm thick CdTe detector with a pixel pitch of 110μm, bump bonded to a Timepix readout chip operating in Time-Over-Threshold mode. The measurements were carried out at the Extreme Conditions beamline I15 of the Diamond Light Source. The beam was entering the sensor at an angle of \texttildelow20 degrees to the surface and then passed through \texttildelow25 pixels before leaving through the bottom of the sensor. The photon energy was tuned to 77keV giving a variation in the beam intensity of about three orders of magnitude along the beam path. Spectra in Time-over-Threshold (ToT) mode were recorded showing each individual interaction. The bias voltage was varied between -30V and -300V to investigate how the electric field affected the spectral information. For this setup it is worth noticing the large impact of fluorescence. At -300V the photo peak and escape peak are of similar height. For high bias voltages the spectra remains clear throughout the whole depth but for lower voltages as -50V, only the bottom part of the sensor carries spectral information. This is an effect of the low hole mobility and the longer range the electrons have to travel in a low field

Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach

We solve the loop equations of the $\beta$-ensemble model analogously to the solution found for the Hermitian matrices $\beta=1$. For \beta=1$, the solution was expressed using the algebraic spectral curve of equation$y^2=U(x)$. For arbitrary$\beta$, the spectral curve converts into a Schr\"odinger equation$((\hbar\partial)^2-U(x))\psi(x)=0$with$\hbar\propto (\sqrt\beta-1/\sqrt\beta)/N$. This paper is similar to the sister paper~I, in particular, all the main ingredients specific for the algebraic solution of the problem remain the same, but here we present the second approach to finding a solution of loop equations using sectorwise definition of resolvents. Being technically more involved, it allows defining consistently the B-cycle structure of the obtained quantum algebraic curve (a D-module of the form$y^2-U(x)$, where$[y,x]=\hbar$) and to construct explicitly the correlation functions and the corresponding symplectic invariants$F_h$, or the terms of the free energy, in 1/N^2$-expansion at arbitrary $\hbar$. The set of "flat" coordinates comprises the potential times $t_k$ and the occupation numbers \widetilde{\epsilon}_\alpha$. We define and investigate the properties of the A- and B-cycles, forms of 1st, 2nd and 3rd kind, and the Riemann bilinear identities. We use these identities to find explicitly the singular part of$\mathcal F_0$that depends exclusively on$\widetilde{\epsilon}_\alpha$.Comment: 58 pages, 7 figure

The SFXC software correlator for Very Long Baseline Interferometry: Algorithms and Implementation

In this paper a description is given of the SFXC software correlator, developed and maintained at the Joint Institute for VLBI in Europe (JIVE). The software is designed to run on generic Linux-based computing clusters. The correlation algorithm is explained in detail, as are some of the novel modes that software correlation has enabled, such as wide-field VLBI imaging through the use of multiple phase centres and pulsar gating and binning. This is followed by an overview of the software architecture. Finally, the performance of the correlator as a function of number of CPU cores, telescopes and spectral channels is shown.Comment: Accepted by Experimental Astronom

Large deviations of the maximal eigenvalue of random matrices

We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not restricted to the standard values beta = 1 (hermitian matrices), beta = 1/2 (symmetric matrices), beta = 2 (quaternionic self-dual matrices). This model allows to study the statistic of the maximum eigenvalue of random matrices. We compute the large deviation function to the left of the expected maximum. We specialize our results to the gaussian beta-ensembles and check them numerically. Our method is based on general results and procedures already developed in the literature to solve the Pastur equations (also called "loop equations"). It allows to compute the left tail of the analog of Tracy-Widom laws for any beta, including the constant term.Comment: 62 pages, 4 figures, pdflatex ; v2 bibliography corrected ; v3 typos corrected and preprint added ; v4 few more numbers adde

Collinear solution to the general relativistic three-body problem

The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and always line up. The solution is unstable. Hence it is unlikely that such a simple configuration would exist owing to general relativistic forces dependent not only on the masses but also on the velocity of each body. However, we show that the collinear solution remains true with a correction to the spatial separation between masses. Relativistic corrections to the Sun-Jupiter Lagrange points L1, L2 and L3 are also evaluated.Comment: 12 pages, 2 figures, accepted for publication in PR

Uniqueness of collinear solutions for the relativistic three-body problem

Continuing work initiated in an earlier publication [Yamada, Asada, Phys. Rev. D 82, 104019 (2010)], we investigate collinear solutions to the general relativistic three-body problem. We prove the uniqueness of the configuration for given system parameters (the masses and the end-to-end length). First, we show that the equation determining the distance ratio among the three masses, which has been obtained as a seventh-order polynomial in the previous paper, has at most three positive roots, which apparently provide three cases of the distance ratio. It is found, however, that, even for such cases, there exists one physically reasonable root and only one, because the remaining two positive roots do not satisfy the slow motion assumption in the post-Newtonian approximation and are thus discarded. This means that, especially for the restricted three-body problem, exactly three positions of a third body are true even at the post-Newtonian order. They are relativistic counterparts of the Newtonian Lagrange points L1, L2 and L3. We show also that, for the same masses and full length, the angular velocity of the post-Newtonian collinear configuration is smaller than that for the Newtonian case. Provided that the masses and angular rate are fixed, the relativistic end-to-end length is shorter than the Newtonian one.Comment: 18 pages, 1 figure; typos corrected, text improved; accepted by PR