Kinematic deprojection and mass inversion of spherical systems of known velocity anisotropy

Traditionally, the mass / velocity anisotropy degeneracy (MAD) inherent in the spherical, stationary, non-streaming Jeans equation has been handled by assuming a mass profile and fitting models to the observed kinematical data. Here, the opposite approach is considered: the equation of anisotropic kinematic projection is inverted for known arbitrary anisotropy to yield the space radial velocity dispersion profile in terms of an integral involving the radial profiles of anisotropy and isotropic dynamical pressure. Then, through the Jeans equation, the mass profile is derived in terms of double integrals of observable quantities. Single integral formulas for both deprojection and mass inversion are provided for several simple anisotropy models (isotropic, radial, circular, general constant, Osipkov-Merritt, Mamon-Lokas and Diemand-Moore-Stadel). Tests of the mass inversion on NFW models with these anisotropy models yield accurate results in the case of perfect observational data, and typically better than 70% (in 4 cases out of 5) accurate mass profiles for the sampling errors expected from current observational data on clusters of galaxies. For the NFW model with mildly increasing radial anisotropy, the mass is found to be insensitive to the adopted anisotropy profile at 7 scale radii and to the adopted anisotropy radius at 3 scale radii. This anisotropic mass inversion method is a useful complementary tool to analyze the mass and anisotropy profiles of spherical systems. It provides the practical means to lift the MAD in quasi-spherical systems such as globular clusters, round dwarf spheroidal and elliptical galaxies, as well as groups and clusters of galaxies, when the anisotropy of the tracer is expected to be linearly related to the slope of its density.Comment: Accepted in MNRAS. 19 pages. Minor changes from previous version: Table 1 of nomenclature, some math simplifications, paragraph in Discussion on alternative deprojection method by deconvolution. 19 pages. 6 figure

Random matrix theory and symmetric spaces

In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero--Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.Comment: 161 pages, LaTeX, no figures. Revised version with major additions in the second part of the review. Version accepted for publication on Physics Report

Cone spherical metrics and stable vector bundles

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have monodromy lying in ${\rm U(1)}$. We establish on compact Riemann surfaces of positive genera a correspondence between irreducible cone spherical metrics with cone angles being integral multiples of $2\pi$ and line subbundles of rank two stable vector bundles. Then we are motivated by it to prove a theorem of Lange-type that there always exists a stable extension of $L^*$ by $L$, for $L$ being a line bundle of negative degree on each compact Riemann surface of genus greater than one. At last, as an application of these two results, we obtain a new class of irreducible spherical metrics with cone angles being integral multiples of $2\pi$ on each compact Riemann surface of genus greater than oneComment: 22 pages, Submitte

On the free volume in nuclear multifragmentation

In many statistical multifragmentation models the volume available to the $N$ nonoverlapping fragments forming a given partition is a basic ingredient serving to the simplification of the density of states formula. One therefore needs accurate techniques for calculating this quantity. While the direct Monte-Carlo procedure consisting of randomly generating the fragments into the freeze-out volume and counting the events with no overlapped fragments is numerically affordable only for partitions with small $N$, the present paper proposes a Metropolis - type simulation which allows accurate evaluations of the free volume even for cases with large $N$. This procedure is used for calculating the available volume for various situations. Though globally this quantity has an exponential dependence on $N$, variations of orders of magnitude for partitions with the same $N$ may be identified. A parametrization based on the virial approximation adjusted with a calibration function, describing very well the variations of the free volume for different partitions having the same $N$ is proposed. This parametrization was successfully tested within the microcanonical multifragmentation model from [Al. H. Raduta and Ad. R. Raduta, Phys. Rev. C {\bf 55}, 1344 (1997); {\it ibid.}, {\bf 56}, 2059 (1997)]. Finally, it is proven that parametrizations of the free volume solely dependent on $N$ are rather inadequate for multifragmentation studies producing important deviations from the exact results.Comment: 20 pages, 9 figures, Nucl. Phys. A (in press

Time and position distributions in large volume spherical scintillation detectors

Large spherical scintillation detectors are playing an increasingly important role in experimental neutrino physics studies. From the instrumental point of view the primary signal response of these set-ups is constituted by the time and amplitude of the anode pulses delivered by each individual phototube following a particle interaction in the scintillator. In this work, under some approximate assumptions, we derive a number of analytical formulas able to give a fairly accurate description of the most important timing features of these detectors, intended to complement the more complete Monte Carlo studies normally used for a full modelling approach. The paper is completed with a mathematical description of the event position distributions which can be inferred, through some inference algorithm, starting from the primary time measures of the photomultiplier tubes.Comment: 29 pages, 20 figures, accepted for publication on Nucl. Instr. and Meth.

Reconstruction of primordial density fields

The Monge-Ampere-Kantorovich (MAK) reconstruction is tested against cosmological N-body simulations. Using only the present mass distribution sampled with particles, and the assumption of homogeneity of the primordial distribution, MAK recovers for each particle the non-linear displacement field between its present position and its Lagrangian position on a primordial uniform grid. To test the method, we examine a standard LCDM N-body simulation with Gaussian initial conditions and 6 models with non-Gaussian initial conditions: a chi-squared model, a model with primordial voids and four weakly non-Gaussian models. Our extensive analyses of the Gaussian simulation show that the level of accuracy of the reconstruction of the nonlinear displacement field achieved by MAK is unprecedented, at scales as small as about 3 Mpc. In particular, it captures in a nontrivial way the nonlinear contribution from gravitational instability, well beyond the Zel'dovich approximation. This is also confirmed by our analyses of the non-Gaussian samples. Applying the spherical collapse model to the probability distribution function of the divergence of the displacement field, we also show that from a well-reconstructed displacement field, such as that given by MAK, it is possible to accurately disentangle dynamical contributions induced by gravitational clustering from possible initial non-Gaussianities, allowing one to efficiently test the non-Gaussian nature of the primordial fluctuations. In addition, a simple application of MAK using the Zel'dovich approximation allows one to also recover accurately the present-day peculiar velocity field on scales of about 8 Mpc.Comment: Version to appear in MNRAS, 24 pages, 21 figures appearing (uses 35 figure files), 1 tabl

Elastic electron scattering by fullerene, C60

We report cross sections for elastic scattering of low-energy electrons by fullerene, C60, calculated within the static-exchange approximation. The calculations are carried out via the Schwinger multichannel (SMC) method, equivalent in this case to the standard Schwinger variational principle. Combining the high parallel efficiency of the SMC method with a quadrature specially adapted to the high symmetry of C60 facilitates the most demanding step of the calculation and so permits the use of a large basis set. We analyze the structure of the cross section with reference to a simple spherical-shell model, and we compare our results to prior measurements and calculations