Title:
Critical behaviour of a fluid in a random shear flow:
Renormalization group analysis of a simplified model
Abstract:
Critical behaviour of a fluid (binary mixture or liquid crystal),
subjected to strongly anisotropic turbulent mixing, is studied by means
of the field theoretic renormalization group. As a simplified model,
relaxational stochastic dynamics of a non-conserved order parameter,
coupled to a random velocity field with prescribed statistics,
is considered. The velocity is taken Gaussian, white in time, with a
correlation function of the form \delta(t-t') / |k_{perp}|^{d+\xi}
where k_{perp} is the component of the wave vector, perpendicular to
the distinguished direction ("direction of the flow") and d the space
dimensionality. It is shown that, depending on the relation between d
and \xi, the system exhibits various types of self-similar (scaling)
behaviour, associated with infrared-attractive fixed points of the
corresponding RG equations. In addition to well-known asymptotic regimes
(like model A of equilibrium critical dynamics) the existence of a new,
non-equilibrium and anisotropic type of critical behaviour
("universality class") is established. The corresponding critical
dimensions are calculated to second order (two-loop approximation) of the
double expansion in \epsilon = 4-d and \xi.
References: N V Antonov and A A Ignatieva, J.Phys.A: Math.Gen 39 (2006)
13593; cond-mat/0607019.