Directed abelian algebras and their applications to stochastic models

To each directed acyclic graph (this includes some D-dimensional lattices) one can associate some abelian algebras that we call directed abelian algebras (DAA). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground state wavefunctions (stationary states probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and choose Hamiltonians linear in the generators, in the finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent $z = D$. One possible application of the DAA is to sandpile models. In the paper we present this application considering one and two dimensional lattices. In the one dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent $\sigma_{\tau} = 3/2$). We study the local densityof particles inside large avalanches showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found $\sigma_{\tau} = 1.782 \pm 0.005$.Comment: 14 pages, 9 figure

Lensing of ultra-high energy cosmic rays in turbulent magnetic fields

We consider the propagation of ultra high energy cosmic rays through turbulent magnetic fields and study the transition between the regimes of single and multiple images of point-like sources. The transition occurs at energies around $E_c\simeq Z~41 {\rm EeV}(B_{rms}/5 \mu{\rm G}) (L/ 2 {\rm kpc})^{3/2}\sqrt{50 {\rm pc}/L_c}$, where $L$ is the distance traversed by the CR's with electric charge $Ze$ in the turbulent magnetic field of root mean square strength $B_{rms}$ and coherence length $L_c$. We find that above $2 E_c$ only sources located in a fraction of a few % of the sky can reach large amplifications of its principal image or start developing multiple images. New images appear in pairs with huge magnifications, and they remain amplified over a significant range of energies. At decreasing energies the fraction of the sky in which sources can develop multiple images increases, reaching about 50% for $E>E_c/2$. The magnification peaks become however increasingly narrower and for $E<E_c/3$ their integrated effect becomes less noticeable. If a uniform magnetic field component is also present it would further narrow down the peaks, shrinking the energy range in which they can be relevant. Below $E\simeq E_c/10$ some kind of scintillation regime is reached, where many demagnified images of a source are present but with overall total magnification of order unity. We also search for lensing signatures in the AGASA data studying two-dimensional correlations in angle and energy and find some interesting hints.Comment: 30 pages, 16 figures, final version with minor change

Tidal Analysis of Long Series

It is shown how M (≥5) sets of Fourier coefficients obtained from M successive Fast Fourier Transforms (FFT) of 214 tapered hourly heights can be combined to obtain the harmonic constants of the clusters of the main astronomical and shallow-water constituents and their respective satellites. It is also shown how the clusters of the shallow-water constituents are formed

On the Stability of Long Series Tidal Analyses

Fourteen analyses with a nodal cycle resolution of filtered daily values of the 'mean' sea level at Cananéia (Brazil) were worked out, with a one-year shift. The results were examined for the stability of the harmonic constants of constituents Sa, Ssa, Mm, MSf, Mf and Mtm. Simultaneous barometric pressure data were available to correct the filtered tidal heights and the analyses were worked out with and without these corrections.The general conclusion is that the harmonic constants of Sa and Ssa were not stable and that their phase lags increased in the successive analyses. The harmonic constants of the remaining long period constituents were absolutely unstable and completely unreliable. Other fourteen harmonic analyses of 10*214 hourly tidal heights were worked out, for determining the harmonic constants of constituents with higher frequencies, in the same port. The results of these analyses, with a one-year shift,were very stable and gave an excellent insight of the micro-structure of the phenomenon

Lymphangioleiomyomatosis: What do we know and what are we looking for?

Lymphangioleiomyomatosis (LAM) is a rare disease characterised by proliferation of abnormal smooth muscle-like cells (LAM cells) leading to progressive cystic destruction of the lung, lymphatic abnormalities and abdominal tumours. It affects predominantly females and can occur sporadically or in patients with tuberous sclerosis complex. This review describes the recent progress in our understanding of the molecular pathogenesis of the disease and LAM cell biology. It also summarises current therapeutic approaches and the most promising areas of research for future therapeutic strategies

FSI Rescattering in B±B^\pm Decays via States with η,η′,ω\eta, \eta', \omega and ϕ\phi

New results going beyond those obtained from isospin and flavor symmetry and subject to clear experimental tests are obtained for effects of FSI in $B^\pm$ decays to charmless strange final states containing neutral flavor-mixed mesons like $\omega$, $\phi$, $\eta$ and $\eta'$. The most general strong-interaction diagrams containing arbitrary numbers of quarks and gluons are included with the assumptions that any $q \bar q$ pair created by gluons must be a flavor singlet, and that there are no hairpin diagrams in which a final meson contains a $q \bar q$ pair from the same gluon vertex. The smallness of $K^- \eta$ suggests that it might have a large CP violation. A sum rule is derived to test whether the large $K^- \eta'$ requires the addition of an additional glueball or charm admixture. Further analysis from $D_s$ decay systematics supports this picture of FSI and raises questions about charm admixture in the $\eta'$

Preon Prophecies by the Standard Model

The Standard Model of quarks and leptons is, at first sight, nothing but a set of {\it ad hoc} rules, with no connections, and no clues to their true background. At a closer look, however, there are many inherent prophecies that point in the same direction: {\it Compositeness} in terms of three stable preons.Comment: 13 pages, 8 eps-figures, invited talk at Beyond the Desert '03, Schloss Ringberg, Bavaria, June 2003; to be published in the Proceeding

Thermal annealing study of swift heavy-ion irradiated zirconia

Sintered samples of monoclinic zirconia (alpha-ZrO2) have been irradiated at room temperature with 6.0-GeV Pb ions in the electronic slowing down regime. X-ray diffraction (XRD) and micro-Raman spectroscopy measurements showed unambiguously that a transition to the 'metastable' tetragonal phase (beta-ZrO2) occurred at a fluence of 6.5x10^12 cm-2 for a large electronic stopping power value (approx 32.5 MeV $\mu$m-1). At a lower fluence of 1.0x10^12 cm-2, no such phase transformation was detected. The back-transformation from beta- to alpha-ZrO2 induced by isothermal or isochronal thermal annealing was followed by XRD analysis. The back-transformation started at an onset temperature around 500 K and was completed by 973 K. Plots of the residual tetragonal phase fraction deduced from XRD measurements versus annealing temperature or time are analyzed with first- or second-order kinetic models. An activation energy close to 1 eV for the back-transformation process is derived either from isothermal annealing curves, using the so-called "cross-cut" method, or from the isochronal annealing curve, using a second-order kinetic law. Correlation with the thermal recovery of ion-induced paramagnetic centers monitored by EPR spectroscopy is discussed. Effects of crystallite size evolution and oxygen migration upon annealing are also addressed

B polarization of the CMB from Faraday rotation

We study the effect of Faraday rotation due to a homogeneous magnetic field on the polarization of the cosmic microwave background (CMB). Scalar fluctuations give rise only to parity-even E-type polarization of the CMB. However in the presence of a magnetic field, a non-vanishing parity-odd B-type polarization component is produced through Faraday rotation. We derive the exact solution for the E and B modes generated by scalar perturbations including the Faraday rotation effect of a uniform magnetic field, and evaluate their cross-correlations with temperature anisotropies. We compute the angular autocorrelation function of the B-modes in the limit that the Faraday rotation is small. We find that primordial magnetic fields of present strength around $B_0=10^{-9}$G rotate E-modes into B-modes with amplitude comparable to those due to the weak gravitational lensing effect at frequencies around $\nu=30$ GHz. The strength of B-modes produced by Faraday rotation scales as $B_0/\nu^2$. We evaluate also the depolarizing effect of Faraday rotation upon the cross correlation between temperature anisotropy and E-type polarization.Comment: 11 pages, 4 figures. Minor changes to match the published versio

UHECR observations and lensing in the magnetic field of the Virgo cluster

We discuss how lensing by magnetic fields in galaxy clusters affects ultrahigh energy cosmic ray (UHECR) observations. As specific example, we use Virgo together with the cluster magnetic fields obtained earlier in a constrained simulation of structure formation including MHD processes. We find that, if M87 is the single source of UHECRs from Virgo, the emitted flux is strongly anisotropic in the most interesting energy range, (50-100)EeV, and differs from the average value by a factor five or more for a significant fraction of observers. Since magnetic lensing is energy dependent, the external energy spectrum as seen by different observers varies strongly too. These anisotropies are averaged out in the case that all active galactic nuclei in Virgo emit UHECRs. In both cases, the anisotropies of the emitted UHECR flux may introduce an important bias in the interpretation of UHECR data like, e.g., the determination of the source density n_s and the source energy spectrum of UHECRs.Comment: 12 pages, 15 eps figures; v2: extended discussion of modifications in external energy spectrum, matches version to be publishe