State-dependent diffusion coefficients and free energies for nucleation processes from Bayesian trajectory analysis.

The rate of nucleation processes such as the freezing of a supercooled liquid or the condensation of supersaturated vapour is mainly determined by the height of the nucleation barrier and the diffusion coefficient for the motion across it. Here, we use a Bayesian inference algorithm for Markovian dynamics to extract simultaneously the free energy profile and the diffusion coefficient in the nucleation barrier region from short molecular dynamics trajectories. The specific example we study is the nucleation of vapour bubbles in liquid water under strongly negative pressures, for which we use the volume of the largest bubble as a reaction coordinate. Particular attention is paid to the effects of discretisation, the implementation of appropriate boundary conditions and the optimal selection of parameters. We find that the diffusivity is a linear function of the bubble volume over wide ranges of volumes and pressures, and is mainly determined by the viscosity of the liquid, as expected from the Rayleigh-Plesset theory for macroscopic bubble dynamics. The method is generally applicable to nucleation processes and yields important quantities for the estimation of nucleation rates in classical nucleation theory

Effects of quarks on the formation and evolution of Z(3) walls and strings in relativistic heavy-ion collisions

We investigate the effects of explicit breaking of Z(3) symmetry due to the presence of dynamical quarks on the formation and evolution of Z(3) walls and associated QGP strings within Polyakov loop model. We carry out numerical simulations of the first order quark-hadron phase transition via bubble nucleation (which may be appropriate, for example, at finite baryon chemical potential) in the context of relativistic heavy-ion collision experiments. Using appropriate shifting of the order parameter in the Polyakov loop effective potential, we calculate the bubble profiles using bounce technique, for the true vacuum as well as for the metastable Z(3) vacua, and estimate the associated nucleation probabilities. These different bubbles are then nucleated and evolved and resulting formation and dynamics of Z(3) walls and QGP strings is studied. We discuss various implications of the existence of these Z(3) interfaces and the QGP strings, especially in view of the effects of the explicit breaking of the Z(3) symmetry on the formation and dynamical evolution of these objects.Comment: 17 pages, 9 figures, PDFLate

Stabilization arising from PGEM : a review and further developments

The aim of this paper is twofold. First, we review the recent Petrov-Galerkin enriched method (PGEM) to stabilize numerical solutions of BVP's in primal and mixed forms. Then, we extend such enrichment technique to a mixed singularly perturbed problem, namely, the generalized Stokes problem, and focus on a stabilized finite element method arising in a natural way after performing static condensation. The resulting stabilized method is shown to lead to optimal convergences, and afterward, it is numerically validated

Dynamical Viscosity of Nucleating Bubbles

We study the viscosity corrections to the growth rate of nucleating bubbles in a first order phase transition in scalar field theory. We obtain the non-equilibrium equation of motion of the coordinate that describes small departures from the critical bubble and extract the growth rate consistently in weak coupling and in the thin wall limit. Viscosity effects arise from the interaction of this coordinate with the stable quantum and thermal fluctuations around a critical bubble. In the case of 1+1 dimensions we provide an estimate for the growth rate that depends on the details of the free energy functional. In 3+1 dimensions we recognize robust features that are a direct consequence of the thin wall approximation and give the leading viscosity corrections.These are long-wavelength hydrodynamic fluctuations that describe surface waves, quasi-Goldstone modes which are related to ripples on interfaces in phase ordered Ising-like systems. We discuss the applicability of our results to describe the growth rate of hadron bubbles in a quark-hadron first order transition.Comment: 40 pages, 4 figures, revtex, minor changes, to be published in Phys. Rev.

Incompressible fluid inside an astrophysical black hole?

It is argued that under natural hypothesis the Fermions inside a black hole formed after the collapse of a neutron star could form a non compressible fluid (well before reaching the Planck scale) leading to some features of integer Quantum Hall Effect. The relations with black hole entropy are analyzed. Insights coming from Quantum Hall Effect are used to analyze the coupling with Einstein equations. Connections with some cosmological scenarios and with higher dimensional Quantum Hall Effect are shortly pointed out.Comment: 30 pages, 2 figures. Accepted for publication on Physical Review D: references added, typos corrected, test polishe