Bimodality Phenomenon in Finite and Infinite Systems Within an Exactly Solvable Statistical Model

We present a few explicit counterexamples to the widely spread belief about an exclusive role of the bimodal nuclear fragment size distributions as the first order phase transition signal. In thermodynamic limit the bimodality may appear at the supercritical temperatures due to the negative values of the surface tension coefficient. Such a result is found within a novel exactly solvable formulation of the simplified statistical multifragmentation model based on the virial expansion for a system of the nuclear fragments of all sizes. The developed statistical model corresponds to the compressible nuclear liquid with the tricritical endpoint located at one third of the normal nuclear density. Its exact solution for finite volumes demonstrates the bimodal fragment size distribution right inside the finite volume analog of a gaseous phase. These counterexamples clearly demonstrate the pitfalls of Hill approach to phase transitions in finite systems.Comment: Talk given at the Helmholtz International Summer School "Physics of Heavy Quarks and Hadrons", held in Dubna, Russia, July 15-28, 201

Coarse Graining of Nonbonded Inter-particle Potentials Using Automatic Simplex Optimization to Fit Structural Properties

We implemented a coarse-graining procedure to construct mesoscopic models of complex molecules. The final aim is to obtain better results on properties depending on slow modes of the molecules. Therefore the number of particles considered in molecular dynamics simulations is reduced while conserving as many properties of the original substance as possible. We address the problem of finding nonbonded interaction parameters which reproduce structural properties from experiment or atomistic simulations. The approach consists of optimizing automatically nonbonded parameters using the simplex algorithm to fit structural properties like the radial distribution function as target functions. Moreover, any mix of structural and thermodynamic properties can be included in the target function. Different spherically symmetric inter-particle potentials are discussed. Besides demonstrating the method for Lennard--Jones liquids, it is applied to several more complex molecular liquids such as diphenyl carbonate, tetrahydrofurane, and monomers of poly(isoprene).Comment: 24 pages, 3 tables, 14 figures submitted to the Journal of Chemical Physics (JCP

Prospects in Constraining the Dark Energy Potential

We generalize to non-flat geometries the formalism of Simon et al. (2005) to reconstruct the dark energy potential. This formalism makes use of quantities similar to the Horizon-flow parameters in inflation, can, in principle, be made non-parametric and is general enough to be applied outside the simple, single scalar field quintessence. Since presently available and forthcoming data do not allow a non-parametric and exact reconstruction of the potential, we consider a general parametric description in term of Chebyshev polynomials. We then consider present and future measurements of H(z), Baryon Acoustic Oscillations surveys and Supernovae type 1A surveys, and investigate their constraints on the dark energy potential. We find that, relaxing the flatness assumption increases the errors on the reconstructed dark energy evolution but does not open up significant degeneracies, provided that a modest prior on geometry is imposed. Direct measurements of H(z), such as those provided by BAO surveys, are crucially important to constrain the evolution of the dark energy potential and the dark energy equation of state, especially for non-trivial deviations from the standard LambdaCDM model.Comment: 22 pages, 7 figures. 2 references correcte

An Axisymmetric Distribution Function for the Galactic Bulge

We describe a method for parameterizing two-integral distribution functions, based on triangular tesselations of the integral plane. We apply the method to the axisymmetric isotropic rotator model for the Galactic bulge of Kent~(1992), and compare the results with observations of proper motions in Baade's Window, and with radial velocity surveys. In spite of mounting evidence from surface photometry and from study of the gas kinematics that the Galactic bulge is not axisymmetric, the stellar kinematics in Baade's Window are very similar to those of an isotropic oblate rotator. Another field at large radius does not fit this model, though. In any case, the edge-on kinematics of a hot stellar population are a poor handle on the existence or otherwise of a bar.Comment: 19 pages, 700 kb uu-encoded compressed postscript file, CfA preprin

Tracking Dark Energy with the ISW effect: short and long-term predictions

We present an analysis of the constraining power of future measurements of the Integrated Sachs-Wolfe (ISW) effect on models of the equation of state of dark energy as a function of redshift, w(z). To achieve this, we employ a new parameterization of w, which utilizes the mean value of w(z) () as an explicit parameter. This helps to separate the information contained in the estimation of the distance to the last scattering surface (from the CMB) from the information contained in the ISW effect. We then use Fisher analysis to forecast the expected uncertainties in the measured parameters from future ISW observations for two models of dark energy with very different time evolution properties. For example, we demonstrate that the cross-correlation of Planck CMB data and LSST galaxy catalogs will provide competitive constraints on w(z), compared to a SNAP-like SNe project, for models of dark energy with a rapidly changing equation of state (e.g. 'Kink' models). Our work confirms that, while SNe measurements are more suitable for constraining variations in w(z) at low redshift, the ISW effect can provide important independent constraints on w(z) at high z.Comment: 15 pages, 17 figures. Added discussion, references, 2 new figures. Minor errors fixed in the calculation. The predicted ISW constraints on w(z) are slightly tighter. Matches the version accepted to PR