806 research outputs found
Relativistic Kinetic Equations for Finite Domains and Freeze-out Problem
The relativistic kinetic equations for the two domains separated by the
hypersurface with both space- and time-like parts are derived. The particle
exchange between the domains separated by the time-like boundaries generates
source terms and modifies the collision term of the kinetic equation. The
correct hydrodynamic equations for the ``hydro+cascade'' models are obtained
and their differences from existing freeze-out models of the hadronic matter
are discussed
Particle Freeze-out and Discontinuities in Relativistic Hydrodynamics
Freeze-out of particles in relativistic hydrodynamics is considered across a
3-dimensional space-time hypersurface. The conservation laws for time-like
parts of the freeze-out hypersurface require different values of temperature,
baryonic chemical potential and flow velocity in the fluid and in the final
particle spectra. We analyze this freeze-out discontinuity and its connection
to the shock-wave phenomena in relativistic hydrodynamics.Comment: 6 figure
Exactly Solvable Model for the QCD Tricritcal Endpoint
An inclusion of temperature and chemical potential dependent surface tension
into the gas of quark-gluon bags model resolves a long standing problem of a
unified description of the first and second order phase transition with the
cross-over. The suggested model has an exact analytical solution and allows one
to rigorously study the vicinity of the critical endpoint of the deconfinement
phase transition. It is found that at the curve of a zero surface tension
coefficient there must exist the surface induced phase tranition of the 2-nd or
higher order. The present model predicts that the critical endpoint (CEP) of
quantum chromodynamics is the tricritical endpoint.Comment: 14 pages, 3 figures, invited talk given at the International Workshop
``Relativistic Nuclear Physics: from Nuclotron to LHC Energies'', Kiev,
Ukraine, June 18-22, 200
Surface Partition of Large Fragments
The surface partition of large fragments is derived analytically within a
simple statistical model by the Laplace-Fourier transformation method. In the
limit of small amplitude deformations, a suggested Hills and Dales Model
reproduces the leading term of the famous Fisher result for the surface entropy
with an accuracy of a few percent. The surface partition of finite fragments is
discussed as well.Comment: 4 pages, 1 figur
Exactly Solvable Models: The Road Towards a Rigorous Treatment of Phase Transitions in Finite Systems
We discuss exact analytical solutions of a variety of statistical models
recently obtained for finite systems by a novel powerful mathematical method,
the Laplace-Fourier transform. Among them are a constrained version of the
statistical multifragmentation model, the Gas of Bags Model and the Hills and
Dales Model of surface partition. Thus, the Laplace-Fourier transform allows
one to study the nuclear matter equation of state, the equation of state of
hadronic and quark gluon matter and surface partitions on the same footing. A
complete analysis of the isobaric partition singularities of these models is
done for finite systems. The developed formalism allows us, for the first time,
to exactly define the finite volume analogs of gaseous, liquid and mixed phases
of these models from the first principles of statistical mechanics and
demonstrate the pitfalls of earlier works. The found solutions may be used for
building up a new theoretical apparatus to rigorously study phase transitions
in finite systems. The strategic directions of future research opened by these
exact results are also discussed.Comment: Contribution to the ``World Consensus Initiative III, Texas A & M
University, College Station, Texas, USA, February 11-17, 2005, 21
Modified Boltzmann Transport Equation and Freeze Out
We study Freeze Out process in high energy heavy ion reaction. The
description of the process is based on the Boltzmann Transport Equation (BTE).
We point out the basic limitations of the BTE approach and introduce Modified
BTE. The Freeze Out dynamics is presented in the 4-dimensional space-time in a
layer of finite thickness, and we employ Modified BTE for the realistic Freeze
Out description.Comment: 9 pages, 2 figure
The complement: a solution to liquid drop finite size effects in phase transitions
The effects of the finite size of a liquid drop undergoing a phase transition
are described in terms of the complement, the largest (but still mesoscopic)
drop representing the liquid in equilibrium with the vapor. Vapor cluster
concentrations, pressure and density from fixed mean density lattice gas
(Ising) model calculations are explained in terms of the complement. Accounting
for this finite size effect is key to determining the infinite nuclear matter
phase diagram from experimental data.Comment: Four two column pages, four figures, two tables; accepted for
publication in PR
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