Error estimation for the MAP experiment

We report here the first full sky component separation and CMB power spectrum estimation using a Wiener filtering technique on simulated data from the upcoming MAP experiment, set to launch in early 2001. The simulations included contributions from the three dominant astrophysical components expected in the five MAP spectral bands, namely CMB radiation, Galactic dust, and synchrotron emission. We assumed a simple homogeneous and isotropic white noise model and performed our analysis up to a spherical harmonic multipole lmax=512 on the fraction of the sky defined by b>20 degrees. We find that the reconstruction errors are reasonably well fitted by a Gaussian with an rms of 24 $\mu$K, but with significant deviations in the tails. Our results further support the predictions on the resulting CMB power spectrum of a previous estimate by Bouchet and Gispert (1999), which entailed a number of assumptions this work removes.Comment: 5 pages, 3 color figures, version accepted in A&A Letter

Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model

We perform a detailed study of the relaxation towards equilibrium in the Hamiltonian Mean-Field (HMF) model, a prototype for long-range interactions in $N$-particle dynamics. In particular, we point out the role played by the infinity of stationary states of the associated $N ~$ Vlasov dynamics. In this context, we derive a new general criterion for the stability of any spatially homogeneous distribution, and compare its analytical predictions with numerical simulations of the Hamiltonian, finite $N$, dynamics. We then propose and verify numerically a scenario for the relaxation process, relying on the Vlasov equation. When starting from a non stationary or a Vlasov unstable stationary initial state, the system shows initially a rapid convergence towards a stable stationary state of the Vlasov equation via non stationary states: we characterize numerically this dynamical instability in the finite $N$ system by introducing appropriate indicators. This first step of the evolution towards Boltzmann-Gibbs equilibrium is followed by a slow quasi-stationary process, that proceeds through different stable stationary states of the Vlasov equation. If the finite $N$ system is initialized in a Vlasov stable homogenous state, it remains trapped in a quasi-stationary state for times that increase with the nontrivial power law $N^{1.7}$. Single particle momentum distributions in such a quasi-stationary regime do not have power-law tails, and hence cannot be fitted by the $q$-exponential distributions derived from Tsallis statistics.Comment: To appear in Physica

Ensemble inequivalence, bicritical points and azeotropy for generalized Fofonoff flows

We present a theoretical description for the equilibrium states of a large class of models of two-dimensional and geophysical flows, in arbitrary domains. We account for the existence of ensemble inequivalence and negative specific heat in those models, for the first time using explicit computations. We give exact theoretical computation of a criteria to determine phase transition location and type. Strikingly, this criteria does not depend on the model, but only on the domain geometry. We report the first example of bicritical points and second order azeotropy in the context of systems with long range interactions.Comment: 4 pages, submitted to Phys. Rev. Let

Kinetic theory for non-equilibrium stationary states in long-range interacting systems

We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic fields. The system reaches stationary states where external forces balance dissipation on average. These states do not respect detailed balance and support non-vanishing fluxes of conserved quantities. We generalize the kinetic theory of isolated long-range systems to describe the dynamics of this non-equilibrium problem. The kinetic equation that we obtain applies to plasmas, self-gravitating systems, and to a broad class of other systems. Our theoretical results hold for homogeneous states, but may also be generalized to apply to inhomogeneous states. We obtain an excellent agreement between our theoretical predictions and numerical simulations. We discuss possible applications to describe non-equilibrium phase transitions.Comment: 11 pages, 2 figures; v2: small changes, close to the published versio

Algebraic Correlation Function and Anomalous Diffusion in the HMF model

In the quasi-stationary states of the Hamiltonian Mean-Field model, we numerically compute correlation functions of momenta and diffusion of angles with homogeneous initial conditions. This is an example, in a N-body Hamiltonian system, of anomalous transport properties characterized by non exponential relaxations and long-range temporal correlations. Kinetic theory predicts a striking transition between weak anomalous diffusion and strong anomalous diffusion. The numerical results are in excellent agreement with the quantitative predictions of the anomalous transport exponents. Noteworthy, also at statistical equilibrium, the system exhibits long-range temporal correlations: the correlation function is inversely proportional to time with a logarithmic correction instead of the usually expected exponential decay, leading to weak anomalous transport properties

Breathing mode for systems of interacting particles

We study the breathing mode in systems of trapped interacting particles. Our approach, based on a dynamical ansatz in the first equation of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy allows us to tackle at once a wide range of power law interactions and interaction strengths, at linear and non linear levels. This both puts in a common framework various results scattered in the literature, and by widely generalizing these, emphasizes universal characters of this breathing mode. Our findings are supported by direct numerical simulations.Comment: 4 pages, 4 figure

Beyond Zel'dovich-Type Approximations in Gravitational Instability Theory --- Pad\'e Prescription in Spheroidal Collapse ---

Among several analytic approximations for the growth of density fluctuations in the expanding Universe, Zel'dovich approximation in Lagrangian coordinate scheme is known to be unusually accurate even in mildly non-linear regime. This approximation is very similar to the Pad\'e approximation in appearance. We first establish, however, that these two are actually different and independent approximations with each other by using a model of spheroidal mass collapse. Then we propose Pad\'e-prescribed Zel'dovich-type approximations and demonstrate, within this model, that they are much accurate than any other known nonlinear approximations.Comment: 4 pages, latex, 3 figures include