Breaking of ergodicity and long relaxation times in systems with long-range interactions

The thermodynamic and dynamical properties of an Ising model with both short range and long range, mean field like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long range interactions and are expected to be valid even when the interaction is slowly decaying with distance.Comment: 4 pages, 5 figure

Socio-economic status over the life-course and depressive symptoms in men and women in Eastern Europe

Objective: Research into social inequalities in depression has studied western populations but data from non-western countries are sparse. In this paper, we investigate the extent of social inequalities in depression in Eastern Europe, the relative importance of social position at different points of the life-course, and whether social patterning of depression differs between men and women.Method: A cross-sectional study examined 12,053 men and 13,582 women in Russia, Poland and the Czech Republic. Depressive symptoms (16 or above on the CESD-20) were examined in relation to socio-economic circumstances at three phases of the life-course: childhood (household amenities and father's education); own education; current circumstances (financial difficulties and possession of household items).Results: Pronounced social differences in depression exist in men and women throughout Eastern Europe. Depression was largely influenced by current circumstances rather than by early life or education, with effects stronger in Poland and Russia. Odds ratios in men for current disadvantage were 3.16 [95% CI: 2.57-3.89], 3.16 [2.74-3.64] and 2.17 [1.80-2.63] in Russia, Poland and the Czech Republic respectively. Social variables did not explain the female excess in depression, which varied from 2.91 [2.58-3.27] in Russia to 1.90 [1.74-2.08] in Poland. Men were more affected by adult disadvantage than women, leading to narrower sex differentials in the presence of disadvantage.Limitations: Cross-sectional data with recall of childhood conditions were used.Conclusion: Current social circumstances are the strongest influence on increased depressive symptoms in countries which have recently experienced social changes. (C) 2007 Elsevier B.V. All rights reserved

Longitudinal Momentum Fraction X_L for Two High P_t Protons in pp->ppX Reaction

We present an analysis of new data from Experiment E850 at BNL. We have characterized the inclusive cross section near the endpoint for pp exclusive scattering in Hydrogen and in Carbon with incident beam energy of 6 GeV. We select events with a pair of back-to-back hadrons at large transverse momentum. These cross sections are parameterized with a form $\frac{d \sigma}{d X_{L}}$ $\sim(1-X_{L})^{p}$, where ${X_{L}}$ is the ratio of the longitudinal momentum of the observed pair to the total incident beam momentum. Small value of $p$ may suggest that the number of partons participating in the reaction is large and reaction has a strong dependence on the center-of-mass energy. We also discuss nuclear effects observed in our kinematic region.Comment: 4 pages, 2 figures, to be published in Proceedings of CIPANP2000, Quebec, May 22-28, 2000, requires aipproc.sty(included

Models of the SL9 Impacts II. Radiative-hydrodynamic Modeling of the Plume Splashback

We model the plume "splashback" phase of the SL9 collisions with Jupiter using the ZEUS-3D hydrodynamic code. We modified the Zeus code to include gray radiative transport, and we present validation tests. We couple the infalling mass and momentum fluxes of SL9 plume material (from paper I) to a jovian atmospheric model. A strong and complex shock structure results. The modeled shock temperatures agree well with observations, and the structure and evolution of the modeled shocks account for the appearance of high excitation molecular line emission after the peak of the continuum light curve. The splashback region cools by radial expansion as well as by radiation. The morphology of our synthetic continuum light curves agree with observations over a broad wavelength range (0.9 to 12 microns). A feature of our ballistic plume is a shell of mass at the highest velocities, which we term the "vanguard". Portions of the vanguard ejected on shallow trajectories produce a lateral shock front, whose initial expansion accounts for the "third precursors" seen in the 2-micron light curves of the larger impacts, and for hot methane emission at early times. Continued propagation of this lateral shock approximately reproduces the radii, propagation speed, and centroid positions of the large rings observed at 3-4 microns by McGregor et al. The portion of the vanguard ejected closer to the vertical falls back with high z-component velocities just after maximum light, producing CO emission and the "flare" seen at 0.9 microns. The model also produces secondary maxima ("bounces") whose amplitudes and periods are in agreement with observations.Comment: 13 pages, 9 figures (figs 3 and 4 in color), accepted for Ap.J. latex, version including full figures at: http://oobleck.tn.cornell.edu/jh/ast/papers/slplume2-20.ps.g

Phase transitions in self-gravitating systems and bacterial populations with a screened attractive potential

We consider a system of particles interacting via a screened Newtonian potential and study phase transitions between homogeneous and inhomogeneous states in the microcanonical and canonical ensembles. Like for other systems with long-range interactions, we obtain a great diversity of microcanonical and canonical phase transitions depending on the dimension of space and on the importance of the screening length. We also consider a system of particles in Newtonian interaction in the presence of a ``neutralizing background''. By a proper interpretation of the parameters, our study describes (i) self-gravitating systems in a cosmological setting, and (ii) chemotaxis of bacterial populations in the original Keller-Segel model

Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems

We derive a necessary and sufficient condition of linear dynamical stability for inhomogeneous Vlasov stationary states of the Hamiltonian Mean Field (HMF) model. The condition is expressed by an explicit disequality that has to be satisfied by the stationary state, and it generalizes the known disequality for homogeneous stationary states. In addition, we derive analogous disequalities that express necessary and sufficient conditions of formal stability for the stationary states. Their usefulness, from the point of view of linear dynamical stability, is that they are simpler, although they provide only sufficient criteria of linear stability. We show that for homogeneous stationary states the relations become equal, and therefore linear dynamical stability and formal stability become equivalent.Comment: Submitted to Journal of Statistical Mechanics: Theory and Experimen