Non-hermitean delocalization in an array of wells with variable-range widths

Nonhermitean hamiltonians of convection-diffusion type occur in the description of vortex motion in the presence of a tilted magnetic field as well as in models of driven population dynamics. We study such hamiltonians in the case of rectangular barriers of variable size. We determine Lyapunov exponent and wavenumber of the eigenfunctions within an adiabatic approach, allowing to reduce the original d=2 phase space to a d=1 attractor. PACS numbers:05.70.Ln,72.15Rn,74.60.GeComment: 20 pages,10 figure

Combinatorial Alexander Duality -- a Short and Elementary Proof

Let X be a simplicial complex with the ground set V. Define its Alexander dual as a simplicial complex X* = {A \subset V: V \setminus A \notin X}. The combinatorial Alexander duality states that the i-th reduced homology group of X is isomorphic to the (|V|-i-3)-th reduced cohomology group of X* (over a given commutative ring R). We give a self-contained proof.Comment: 7 pages, 2 figure; v3: the sign function was simplifie

Biocompatible silk fibroin scaffold prepared by reactive inkjet printing

It has recently been shown that regenerated silk fibroin (RSF) aqueous solution can be printed using an inkjet printer. In this communication, we demonstrate an alternative reactive inkjet printing method that provides control over RSF crystallinity through β-sheet concentration. A biocompatible film has successfully been produced through the alternate printing of RSF aqueous solution and methanol using reactive inkjet printing. Control over the formation of the β-sheet structure was achieved by printing different ratios of RSF to methanol and was confirmed using Fourier Transform Infra Red spectroscopy. The biocompatibility of the printed silk scaffold was demonstrated by the growth of fibroblast cells upon its surface

Quantum Probabilistic Subroutines and Problems in Number Theory

We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for extracting the periodicity of a function, and their combined use in the counting algorithm originally introduced by Brassard et al. One of the main features of our quantum probabilistic algorithm is its full unitarity and reversibility, which would make its use possible as part of larger and more complicated networks in quantum computers. As an example of this we describe polynomial time algorithms for studying some important problems in number theory, such as the test of the primality of an integer, the so called 'prime number theorem' and Hardy and Littlewood's conjecture about the asymptotic number of representations of an even integer as a sum of two primes.Comment: 9 pages, RevTex, revised version, accepted for publication on PRA: improvement in use of memory space for quantum primality test algorithm further clarified and typos in the notation correcte

Measuring Black Hole Spin using X-ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on "best practices" that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GROJ1655-40 and 4U1543-475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.Comment: 19 pages. To appear in proceedings of the ISSI-Bern workshop on "The Physics of Accretion onto Black Holes" (8-12 Oct 2012). Revised version adds a missing source to Table 1 and Fig.6 (IRAS13224-3809) and corrects the referencing of the discovery of soft lags in 1H0707-495 (which were in fact first reported in Fabian et al. 2009

Renormalization of the mass gap

The full gluon propagator relevant for the description of the truly non-perturbative QCD dynamics, the so-called intrinsically non-perturbative gluon propagator has been derived in our previous work. It explicitly depends on the regularized mass gap, which dominates its structure at small gluon momentum. It is automatically transversal in a gauge invariant way. It is characterized by the presence of severe infrared singularities at small gluon momentum, so the gluons remain massless, and this does not depend on the gauge choice. In this paper we have shown how precisely the renormalization program for the regularized mass gap should be performed. We have also shown how precisely severe infrared singularities should be correctly treated. This allowed to analytically formulate the exact and gauge-invariant criteria of gluon and quark confinement. After the renormalization program is completed, one can derive the gluon propagator applicable for the calculation of physical observables processes, etc., in low-energy QCD from first principles.Comment: 16 pages, no figures, no tables, some minor changes are introduce

Bridging the gap between stellar-mass black holes and ultraluminous X-ray sources

The X-ray spectral and timing properties of ultraluminous X-ray sources (ULXs) have many similarities with the very high state of stellar-mass black holes (power-law dominated, at accretion rates greater than the Eddington rate). On the other hand, their cool disk components, large characteristic inner-disk radii and low characteristic timescales have been interpreted as evidence of black hole masses ~ 1000 Msun (intermediate-mass black holes). Here we re-examine the physical interpretation of the cool disk model, in the context of accretion states of stellar-mass black holes. In particular, XTE J1550-564 can be considered the missing link between ULXs and stellar-mass black holes, because it exhibits a high-accretion-rate, low-disk-temperature state (ultraluminous branch). On the ultraluminous branch, the accretion rate is positively correlated with the disk truncation radius and the bolometric disk luminosity, while it is anti-correlated with the peak temperature and the frequency of quasi-periodic-oscillations. Two prototypical ULXs (NGC1313 X-1 and X-2) also seem to move along that branch. We use a phenomenological model to show how the different range of spectral and timing parameters found in the two classes of accreting black holes depends on both their masses and accretion rates. We suggest that ULXs are consistent with black hole masses ~ 50-100 Msun, moderately inefficiently accreting at ~20 times Eddington.Comment: 11 pages, accepted for publication in Astrophysics and Space Science. Based on work presented at the Fifth Stromlo Symposium, Australian National University, Dec 200

States and transitions in black-hole binaries

With the availability of the large database of black-hole transients from the Rossi X-Ray Timing Explorer, the observed phenomenology has become very complex. The original classification of the properties of these systems in a series of static states sorted by mass accretion rate proved not to be able to encompass the new picture. I outline here a summary of the current situation and show that a coherent picture emerges when simple properties such as X-ray spectral hardness and fractional variability are considered. In particular, fast transition in the properties of the fast time variability appear to be crucial to describe the evolution of black-hole transients. Based on this picture, I present a state-classification which takes into account the observed transitions. I show that, in addition to transients systems, other black-hole binaries and Active Galactic Nuclei can be interpreted within this framework. The association between these states and the physics of the accretion flow around black holes will be possible only through modeling of the full time evolution of galactic transient systems.Comment: 30 pages, 11 figures, To appear in Belloni, T. (ed.): The Jet Paradigm - From Microquasars to Quasars, Lect. Notes Phys. 794 (2009

Solution of generalized fractional reaction-diffusion equations

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.Comment: LaTeX, 18 pages, corrected typo

Topological mirror symmetry with fluxes

Motivated by SU(3) structure compactifications, we show explicitly how to construct half--flat topological mirrors to Calabi--Yau manifolds with NS fluxes. Units of flux are exchanged with torsion factors in the cohomology of the mirror; this is the topological complement of previous differential--geometric mirror rules. The construction modifies explicit SYZ fibrations for compact Calabi--Yaus. The results are of independent interest for SU(3) compactifications. For example one can exhibit explicitly which massive forms should be used for Kaluza--Klein reduction, proving previous conjectures. Formality shows that these forms carry no topological information; this is also confirmed by infrared limits and old classification theorems.Comment: 35 pages, 5 figure