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.