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##
One dimensional hydrodynamic
model of nuclear collisions

Recently a hydrodynamical description of low energy nuclear collisions
between heavy ions is very popular. Nuclear matter is a symmetric homogeneous
mixture of two kind of nuclear constituents: protons (positively charged)
and neutrons (not charged). In Lagrangian form the Navier-Stokes system
is given by: Let
the specific volume,
the velocity,
the internal energy,
the temperature,
the termal flux and
the stress then the compressible Navier-stokes system reads as follows:
for
and
where
is the conserved mass on a slab. Further, it is necessary to assume the
so-called Clausius-Duhem inequality
where
is the specific entropy. The stress is given by
The first term is the effective pressure and the second is the phenomenological
viscous stress (cf. Hasse, R.W. (1978) *Approaches to nuclear friction,
Reports on Progress in Physics* 41, 1027 - 1101. ). The functions
and
are completely defined by
Here
and
are parameters of the so-called Skyrme interaction.
is the Boltzmann constant for our monoparticular gas and
is the Planck' s constant. The internal energy is given by
is a suitable chosen positive constant such that
for
and

**A late reference:** B. Ducomet *Asymptotic behaviour for a non-monotone
fluid in one dimension: the positive temperature case* (2001) MMAS,
24, ???-???.

**Nächste Seite:**Relativistic
Vlasov-Poisson equation (RVM)**Aufwärts:**Models
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collected and worked out by Wolfgang Sprößig, TU-Bergakademie
Freiberg