Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model

We show how the expectation values of geometrical quantities in 3d quantum gravity can be explicitly computed using grasping rules. We compute the volume of a labelled tetrahedron using the triple grasping. We show that the large spin expansion of this value is dominated by the classical expression, and we study the next to leading order quantum corrections.Comment: 18 pages, 1 figur

Leading slow roll corrections to the volume of the universe and the entropy bound

We make an extension to recent calculations of the probability density \rho(V) for the volume of the universe after inflation. Previous results have been accurate to leading order in the slow roll parameters \epsilon=\dot{H}/H^2 and \eta=\ddot{\phi}/(\dot{\phi} H), and 1/N_c, where H is the Hubble parameter and N_c is the classical number of e-foldings. Here, we present a modification which captures effects of order \epsilon N_c, which amounts to letting the parameters of inflation H and \dot{\phi} depend on the value of the inflaton \phi. The phase of slow roll eternal inflation can be defined as when the probability to have an infinite volume is greater than zero. Using this definition, we study the Laplace transform of \rho(V) numerically to determine the condition that triggers the transition to eternal inflation. We also study the average volume analytically and show that it satisfies the universal volume bound. This bound states that, in any realization of inflation which ends with a finite volume, an initial volume must grow by less than a factor of exp(S_{dS}/2), where S_{dS} is the de Sitter (dS) entropy.Comment: 18 pages, 3 figure

Surface Incompressibility from Semiclassical Relativistic Mean Field Calculations

By using the scaling method and the Thomas-Fermi and Extended Thomas-Fermi approaches to Relativistic Mean Field Theory the surface contribution to the leptodermous expansion of the finite nuclei incompressibility has been self-consistently computed. The validity of the simplest expansion, which contains volume, volume-symmetry, surface and Coulomb terms, is examined by comparing it with self-consistent results of the finite nuclei incompressibility for some currently used non-linear sigma-omega parameter sets. A numerical estimate of higher-order contributions to the leptodermous expansion, namely the curvature and surface-symmetry terms, is made.Comment: 18 pages, REVTeX, 3 eps figures, changed conten

Computation of volume potentials over bounded domains via approximate approximations

We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced to the quadrature of one dimensional integrals over the halfline. We conclude the paper providing numerical tests which show that these formulas give very accurate approximations and confirm the predicted order of convergence.Comment: 18 page

Volume 4, Chapter 1-18: Aquatic and Wet Marchantiophyta, Order Lunulariales

https://digitalcommons.mtu.edu/bryo-ecol-subchapters/1249/thumbnail.jp

Bimodalities : a survey of experimental data and models

Bimodal distributions of some chosen variables measured in nuclear collisions were recently proposed as a non ambiguous signature of a first order phase transition in nuclei. This section presents a compilation of both theoretical and experimental studies on bimodalities performed so far, in relation with the liquid-gas phase transition in nuclear matter.Comment: 12 pages, 18 figures, 1 table Appeared in European Physics Journal A as part of the Topical Volume "Dynamics and Thermodynamics with Nuclear Degrees of Freedom

Fitting two nucleons inside a box: exponentially suppressed corrections to the Luscher's formula

Scattering observables can be computed in lattice field theory by measuring the volume dependence of energy levels of two particle states. The dominant volume dependence, proportional to inverse powers of the volume, is determined by the phase shifts. This universal relation (\Lu's formula) between energy levels and phase shifts is distorted by corrections which, in the large volume limit, are exponentially suppressed. They may be sizable, however, for the volumes used in practice and they set a limit on how small the lattice can be in these studies. We estimate these corrections, mostly in the case of two nucleons. Qualitatively, we find that the exponentially suppressed corrections are proportional to the {\it square} of the potential (or to terms suppressed in the chiral expansion) and the effect due to pions going ``around the world'' vanishes. Quantitatively, the size of the lattice should be greater than $\approx(5 {fm})^3$ in order to keep finite volume corrections to the phase less than $1^\circ$ for realistic pion mass.Comment: 18 pages, 5 figures, 6 figure