Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

We find a Hermite-type basis for which the eigenvalue problem associated to the operator $H_{A,B}:=B(-\partial_x^2)+Ax^2$ acting on $L^2({\bf R};{\bf C}^2)$ becomes a three-terms recurrence. Here $A$ and $B$ are two constant positive definite matrices with no other restriction. Our main result provides an explicit characterization of the eigenvectors of $H_{A,B}$ that lie in the span of the first four elements of this basis when $AB\not= BA$.Comment: 11 pages, 1 figure. Some typos where corrected in this new versio

Markov Process of Muscle Motors

We study a Markov random process describing a muscle molecular motor behavior. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spend an exponential time depending on the state. The thin filament moves at its velocity proportional to average of all displacements of all motors. We assume that the time which a motor stays at the bound state does not depend on its displacement. Then one can find an exact solution of a non-linear equation appearing in the limit of infinite number of the motors.Comment: 10 page

The extended structure of the remote cluster B514 in M31. Detection of extra-tidal stars

We present a study of the density profile of the remote M31 globular cluster B514, obtained from HST/ACS observations. Coupling the analysis of the distribution of the integrated light with star counts we can reliably follow the profile of the cluster out to r~35", corresponding to ~130pc. The profile is well fitted, out to ~15 core radii, by a King Model having C=1.65. With an estimated core radius r_c=0.38", this corresponds to a tidal radius of r_t~17" (~65pc). We find that both the light and the star counts profiles show a departure from the best fit King model for r>~8" - as a surface brightness excess at large radii, and the star counts profile shows a clear break in correspondence of the estimated tidal radius. Both features are interpreted as the signature of the presence of extratidal stars around the cluster. We also show that B514 has a half-light radius significantly larger than ordinary globular clusters of the same luminosity. In the M_V vs. log r_h plane, B514 lies in a region inhabited by peculiar clusters, like Omega Cen, G1, NGC2419 and others, as well as by the nuclei of dwarf elliptical galaxies.Comment: 9 pages, 6 figures. Accepted for publication in Astronomy & Astrophysic

Correlations of Globular Cluster Properties: Their Interpretations and Uses

Correlations among the independently measured physical properties of globular clusters (GCs) can provide powerful tests for theoretical models and new insights into their dynamics, formation, and evolution. We review briefly some of the previous work, and present preliminary results from a comparative study of GC correlations in the Local Group galaxies. The results so far indicate that these diverse GC systems follow the same fundamental correlations, suggesting a commonality of formative and evolutionary processes which produce them.Comment: An invited review, to appear in "New Horizons in Globular Cluster Astronomy", eds. G. Piotto, G. Meylan, S.G. Djorgovski, and M. Riello, ASPCS, in press (2003). Latex file, 8 pages, 5 eps figures, style files include

Dynamic correlation functions and Boltzmann Langevin approach for driven one dimensional lattice gas

We study the dynamics of the totally asymmetric exclusion process with open boundaries by phenomenological theories complemented by extensive Monte-Carlo simulations. Upon combining domain wall theory with a kinetic approach known as Boltzmann-Langevin theory we are able to give a complete qualitative picture of the dynamics in the low and high density regime and at the corresponding phase boundary. At the coexistence line between high and low density phases we observe a time scale separation between local density fluctuations and collective domain wall motion, which are well accounted for by the Boltzmann-Langevin and domain wall theory, respectively. We present Monte-Carlo data for the correlation functions and power spectra in the full parameter range of the model.Comment: 10 pages, 9 figure

The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics

We discuss a new class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting non-conserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high an low density phases, two and three phase coexistence regions and a boundary independent ``Meissner'' phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert $W$-functions. It allows to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.Comment: 22 pages, 23 figures. Accepted for publication on Phys. Rev.

Instabilities and shape variation phase transitions in tubular lipid membranes

Changes of external parameters in proximity of critical point can increase thermal fluctuations of tubular lipid membrane (TLM) and result in variation of the membrane shape. The phase transitions in the system are shown to be controlled by a single effective parameter, which depends on the pressure difference between inner and outer regions of membrane and the applied stretching force. We determine an interval of the parameter values corresponding to the stability region of the cylindrical shape of TLM and investigate the behavior of the system in the vicinity of critical instabilities, where the cylindrical shape of membrane becomes unstable with respect to thermal fluctuations. The applied boundary conditions strongly influence the behavior of TLM. For example, small negative effective parameter corresponds to chiral shape of TLM only in the case of periodic boundary conditions. We also discuss other three types of phase transitions emerging in the system.Comment: 15 pages, 6 figures, in Russia

The red stellar population in NGC 1569

We present HST NICMOS photometry of the resolved stellar population in NGC 1569. The CMD in the F110W and F160W photometric bands contains ~2400 stars with a formal photometric error < 0.1 mag down to J~23.5 and H~22.5. We describe the data processing which is required to calibrate the instrumental peculiarities of NICMOS. Two different packages for PSF-fitting photometry are used to strengthen the photometric results in the crowded stellar field of NGC 1569. The resulting CMD is discussed in terms of the major evolutionary properties of the resolved stellar populations. For a distance modulus of 26.71 and a reddening E(B-V)=0.56, our CMD samples stars down to ~0.8 Mo, corresponding to look-back times > 15 Gyr. This is clear indication of SF activity spanning an entire Hubble time. The metallicity of the reddest RGB stars is in better agreement with Z=0.004 as measured in HII regions, than with Z=0.0004 as expected from the stellar ages. The presence of - yet undetected - very metal-poor stars embedded in the stellar distribution around J=22.75 and J-H=1.15 is, however, not ruled out. The youngest stars (< 50 Myr) are preferentially found around the two central super star clusters, whereas the oldest population has a more uniform spatial distribution. A SFR per unit area of 1 Mo yr*(-1) kpc*(-2) and a mass formed in stars of ~ 1.4x10*6 Mo in the last 50 Myr are derived from the CMD. The NIR CMD places strong constraints on the lower limit of the onset of SF in NGC 1569. The exceptionally high crowding in the NICMOS images of NGC 1569 is a challenge for the photometric analysis. As a result, optical and NIR images of NGC 1569 sample different populations and cannot be cross-correlated. Nevertheless, we demonstrate the consistency of the SF histories derived from the optical and NIR CMDs.Comment: 41 pages including 1 table (Latex) and 14 figures (postscript). Accepted for publication in the Astronomical Journal, March 2001 issu

Increased expression of interleukin-22 in patients with giant cell arteritis

GCA is characterized by arterial remodelling driven by inflammation. IL-22 is an attractive cytokine which acts at the crosstalk between immune and stromal cells. We hypothesized that IL-22 might be induced in GCA and might be involved in disease pathogenesis