Statistical Mechanics of the Self-gravitating gas with two or more kinds of Particles

We study the statistical mechanics of the self-gravitating gas at thermal equilibrium with two kinds of particles. We start from the partition function in the canonical ensemble which we express as a functional integral over the densities of the two kinds of particles for a large number of particles. The system is shown to possess an infinite volume limit when (N_1,N_2,V)->infty, keeping N_1/V^{1/3} and N_2/V^{1/3} fixed. The saddle point approximation becomes here exact for (N_1,N_2,V)->infty.It provides a nonlinear differential equation on the particle densities. For the spherically symmetric case, we compute the densities as functions of two dimensionless physical parameters: eta_1=G m_1^2 N_1/[V^{1/3} T] and eta_2=G m_2^2 N_2/[V^{1/3} T] (where G is Newton's constant, m_1 and m_2 the masses of the two kinds of particles and T the temperature). According to the values of eta_1 and eta_2 the system can be either in a gaseous phase or in a highly condensed phase.The gaseous phase is stable for eta_1 and eta_2 between the origin and their collapse values. The gas is inhomogeneous and the mass M(R) inside a sphere of radius R scales with R as M(R) propto R^d suggesting a fractal structure. The value of d depends in general on eta_1 and eta_2 except on the critical line for the canonical ensem- ble where it takes the universal value d simeq 1.6 for all values of N_1/N_2. The equation of state is computed.It is found to be locally a perfect gas equation of state. Thermodynamic functions are computed as functions of eta_1 and eta_2. They exhibit a square root Riemann sheet with the branch points on the critical canonical line. This treatment is further generalized to the self-gravitating gas with n-types of particles.Comment: LaTex, 29 pages, 11 .ps figures, expanded version to appear in Phys. Rev.

Prova tuberculínica, BCG oral e infecção tuberculosa em crianças menores de 5 anos Tuberculin test, oral BCG vaccine, and tuberculosis infection among children under five years of age

São relatados os resultados das provas tuberculínicas com PPD Rt23, 2 UT, em crianças menores de um ano e de um a 4 anos, matriculadas na Clínica Pediátrica do Hospital das Clínicas da Faculdade de Medicina da USP, São Paulo, Brasil, no período de 1971 a 1975. Em 665 crianças menores de um ano encontrou-se 3,15% de reatores fracos e 6,62% de reatores fortes e em 1.298 crianças de um a 4 anos, 0,69% de reatores fracos e 5,5% de reatores fortes. Nas mesmas crianças, foram estudadas as relações entre vacinação BCG oral prévia e positividade à prova tuberculínica nos 2 grupos etários considerados e nos quais se obteve a informação de vacinação anterior com BCG oral. Em 575 crianças menores de um ano e 1.113 de um a 4 anos encontrou-se associação positiva entre vacinação BCG oral prévia e positividade à prova tuberculínica. Analisando a relação entre o número de doses de BCG oral prévio e o resultado das provas tuberculínicas pelo método de Goodman, verificou-se que a proporção de crianças que tinham tomado 3 doses e mais de BCG oral e que apresentaram reação forte à prova tuberculínica é significantemente maior que a observada para os não reatores, fato esse não verificado para o grupo de um a 4 anos. Nas crianças que tomaram uma ou duas doses não foram encontradas diferenças estatisticamente significantes.<br>Results of tuberculin reaction from PPD Rt 23, 2UT are reported on children under one year of age and children from one to four years of age who were registered in the Pediatric Clinics of the Hospital das Clinicas of the College of Medicine of the State University of São Paulo. The study was carried out from 1971 through 1975. In a group of 665 children under one year of age, 3.15% were weak reactors while 6.62% were strong reactors, and, in a group of 1298 children between one to four years of age, 0.69% were weak reactors while 5.5% were strong reactors. The relationship between prior BCG oral vaccination and positivation to the tuberculin test in the two age groups was studied, thus obtaining information about the previous oral BCG vaccination. Likewise, in 575 children under one year of age and 1113 children one to four years of age, a positive relationship between the previous oral administration of BCG and the positivation to the tuberculin test was found. In analyzing the relationship between the number of doses of previous oral BCG administration and the results of the tuberculin test by the Goodman method, it was found that the proportion of children who had taken three or more doses of BCG by oral administration and showed strong reaction to the tuberculin test is significantly greater than that observed for the non-reactors, a fact which does not hold true for the one to four age group. For the children who had taken one or two doses there was no significant statistical difference

Advances in Plasmaspheric Wave Research with CLUSTER and IMAGE Observations

International audienceThis paper highlights significant advances in plasmaspheric wave research with Cluster and Image observations. This leap forward was made possible thanks to the new observational capabilities of these space missions. On one hand, the multipoint view of the four Cluster satellites, a unique capability, has enabled the estimation of wave characteristics impossible to derive from single spacecraft measurements. On the other hand, the Image experiments have enabled to relate large-scale plasmaspheric density structures with wave observations and provide radio soundings of the plasmasphere with unprecedented details. After a brief introduction on Cluster and Image wave instrumentation, a series of sections, each dedicated to a specific type of plasmaspheric wave, put into context the recent advances obtained by these two revolutionary missions