Equilibrium and dynamical properties of two dimensional self-gravitating systems

A system of N classical particles in a 2D periodic cell interacting via long-range attractive potential is studied. For low energy density $U$ a collapsed phase is identified, while in the high energy limit the particles are homogeneously distributed. A phase transition from the collapsed to the homogeneous state occurs at critical energy U_c. A theoretical analysis within the canonical ensemble identifies such a transition as first order. But microcanonical simulations reveal a negative specific heat regime near $U_c$. The dynamical behaviour of the system is affected by this transition : below U_c anomalous diffusion is observed, while for U > U_c the motion of the particles is almost ballistic. In the collapsed phase, finite $N$-effects act like a noise source of variance O(1/N), that restores normal diffusion on a time scale diverging with N. As a consequence, the asymptotic diffusion coefficient will also diverge algebraically with N and superdiffusion will be observable at any time in the limit N \to \infty. A Lyapunov analysis reveals that for U > U_c the maximal exponent \lambda decreases proportionally to N^{-1/3} and vanishes in the mean-field limit. For sufficiently small energy, in spite of a clear non ergodicity of the system, a common scaling law \lambda \propto U^{1/2} is observed for any initial conditions.Comment: 17 pages, Revtex - 15 PS Figs - Subimitted to Physical Review E - Two column version with included figures : less paper waste

Virologic, immunologic, and clinical response to highly active antiretroviral therapy: the gender issue revisited

Not the final published versionBACKGROUND: Highly active antiretroviral therapy (HAART) has dramatically improved the prognosis for patients with HIV. There is ongoing debate over a potential gender effect on patient outcome after HAART. METHODS: Individuals were from the EuroSIDA cohort, naive to protease inhibitors and nonnucleoside reverse transcriptase inhibitors, and had at least one viral load and CD4 measurement prior to starting HAART. Endpoints were virologic (time to 500 copies/mL]), immunologic (time to a 100/mm cell rise in CD4 count) and clinical (time to new AIDS and death). Hazard ratios (HR), derived using Cox regression models, compared female to male rates of achieving endpoints. RESULTS: Of 2547 patients, 20% (511) were female. Significantly more females than males were nonwhite (24% vs. 10%, p <.001). Males were older (median age 39 vs. 35 years, p <.0001), had lower CD4 counts (211 vs. 240/mm, p =.03), higher viral loads (4.6 vs. 4.4 log copies/mL, p <.0001), were more likely to have a history of AIDS (26% vs. 18%, p <.001) and were more likely to be treatment-naive (34% vs. 29%, p =.03). Adjusted HR for association between gender (comparing females with males) and the outcomes studied were as follows: for reaching <500 copies/mL 0.91 (0.81-1.03, p =.17), rebound 1.17 (0.95-1.44, p =.15), for 100 cell CD4 count rise 1.02 (0.88-1.14, p =.99), for progression to new AIDS 1.12 (0.73-1.71, p =.59) and for time to death 1.15 (0.69-1.92, p =.57). CONCLUSIONS: We found no significant evidence of a gender difference in virologic, immunologic, or clinical outcomes after starting HAART