Analysis of Jeans instability from the Boltzmann equation

The dynamics of self-gravitating fluids is analyzed within the framework of a collisionless Boltzmann equation in the presence of gravitational fields and Poisson equation. Two cases are analyzed: a system with baryonic and dark matter in a static universe and a single system in an expanding universe. The amplitudes of the perturbed distribution functions are considered as a linear combination of the collision invariants of the Boltzmann equation. For the system of baryonic and dark matter, the Jeans mass of the combined system is smaller than the one of the single system indicating that a smaller mass is needed to initiate the collapse. For the single system in an expanding universe it is not necessary to make use of Jeans "swindle"and it shown that for small wavelengths the density contrast oscillates while for large wavelengths it grows with time and the Jeans instability emerges.Comment: 10 pages, 1 figure, new analysi

Brane cosmology with a van der Waals equation of state

The evolution of a Universe confined onto a 3-brane embedded in a five-dimensional space-time is investigated where the cosmological fluid on the brane is modeled by the van der Waals equation of state. It is shown that the Universe on the brane evolves in such a manner that three distinct periods concerning its acceleration field are attained: (a) an initial accelerated epoch where the van der Waals fluid behaves like a scalar field with a negative pressure; (b) a past decelerated period which has two contributions, one of them is related to the van der Waals fluid which behaves like a matter field with a positive pressure, whereas the other contribution comes from a term of the Friedmann equation on the brane which is inversely proportional to the scale factor to the fourth power and can be interpreted as a radiation field, and (c) a present accelerated phase due to a cosmological constant on the brane.Comment: 9 pages, 2 figures, to be published in General Relativity and Gravitatio

The Boltzmann equation in special and general relativity

Relativistic field equations for a gas in special and general relativity are determined from the Boltzmann equation. The constitutive equations are obtained from the Chapman-Enskog methodology applied to a relativistic model equation proposed by Anderson and Witting. Two applications in general relativity are considered: one refers to a gas in a homogeneous and isotropic Universe where irreversible processes are present during its evolution; in the other it is analyzed a gas under the influence of a spherically symmetrical non-rotating and uncharged source of the gravitational field.Comment: 8 pages, contributed paper at the 28th International Symposium on Rarefied Gas Dynamics (Zaragoza, Spain, July 9-13, 2012) correction: eqs. (40), (42) and (43

Fiscal rules and monetary policy in a dynamic stochastic general equilibrium model

In this paper an anti-cyclical fiscal policy rule is introduced into a dynamic stochastic general equilibrium model with New-Keynesian features. The rule allows the deficit to deviate from target in proportion to the impact of automatic stabilisers while any additional impact on the deficit, for example on interest expenditure, has to be offset through adjustments of government consumption or taxes. The size of the automatic stabilisers is endogenously determined as the change in the primary deficit that is induced by economic fluctuations for a given tax system. The model is calibrated, and it is shown how the conditions for monetary policy to secure stability and determinacy of the model's equilibrium depend on the fiscal policy rule and, in particular, on the means used to fulfil the rule. It is demonstrated that the Taylor principle holds for reasonable values of the fiscal policy parameter if fiscal policy relies on changes in lump-sum taxes. This runs counter to the benchmark result of Leeper (1991). The same goes for the cases that consumption taxes, profit taxes or government consumption are adjusted to fulfil the fiscal rule. However, if the fiscal rule is met through adjustments of wage or interest tax rates, the range of values of the monetary policy parameter that ensures stability and determinacy change significantly. --dynamic stochastic general equilibrium model,monetary policy rules,fiscal policy rules,stability

Can Having Fewer Partners Increase Prevalence of Aids?

Under asymmetric information about sexual history, sexual activity creates externalities. Abstinence by those with few partners perversely increases the average probability of HIV infection in the pool of available partners. Since this increases prevalence among the high activity people who disproportionately influence the disease's future spread, it may increase long-run prevalence. Preliminary calculations using standard epidemiological models and survey data on sexual activity suggest that most people have few enough partners that further reductions would increase steady-state prevalence. To the extent the results prove robust, they suggest that public health messages will be more likely to reduce steady-state prevalence and create positive externalities if they stress condom use rather than abstinence.