,
Directed Percolation Criticality in Turbulent Liquid Crystals \\-Static and Dynamic Scaling-
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Аннотация
Focusing on the transition between two turbulent states
of electrohydrodynamic convection in nematic liquid crystals,
we present the first clear experimental evidence of an absorbing
phase transition in the directed percolation class 1.
This puts an end to a long-standing puzzle where overwhelming
theoretical and numerical evidence for the ubiquity of this basic
non-equilibrium universality class contrasted strongly with the absence
of any fully-convincing experimental study.
Directed percolation (DP) is an archetypical model
of phase transitions into an absorbing state,
i.e. a state from which a system can never escape,
whose universality class is well established
both in theory and in simulations.
Numerical examples abound in a wide variety of situations,
ranging from epidemic spreading and granular flows
to catalytic reactions and interface roughening in porous media.
From the theoretical side,
it is conjectured that phase transitions into a single absorbing state,
without extra symmetries or conservation laws, fall into the DP class.
It thus comes as a surprise that no experiments could have shown
convincing evidence of the DP critical behavior,
which has been recognized
as an outstanding open problem 2.
Since the existence of an absorbing state inevitably implies
violation of detailed balance,
a genuine non-equilibrium character of the phase transitions,
it is fundamental to experimentally examine the robustness of the DP class
for better understanding of non-equilibrium critical phenomena,
where even the relevant ingredients determining the class are not known.
In our study, focusing on the Pomeau's conjecture 3 that
spatiotemporal intermittency (STI) may be described by DP,
we investigate STI between two turbulent states (DSM1-DSM2)
observed in electrohydrodynamic convection of nematic liquid crystals.
At first glance it behaves qualitatively similarly to DP models (Fig. 1A).
Performing two sets of experiments,
namely steady-state experiment under constant applied voltages
and critical-quench experiment where voltage is suddenly decreased,
we observed algebraic scaling laws and
measured a complete set of independent critical exponents.
Their values all precisely agree with those defining the DP class.
Furthermore, data collapse is achieved with the universal scaling function
in agreement (Fig. 1B).
This constitutes the first complete and satisfactory experimental realization
of a DP class transition.
In the talk we also mention why the DP critical behavior
can be clearly observed in the electrohydrodynamic convection
when it has not been the case for other experiments,
where only partial results have been obtained often with non-DP scaling laws.
References\\
Takeuchi K., Kuroda M., Chaté H., Sano M., to be published.\\
Hinrichsen H., Adv. Phys. 49, 815 (2000).\\
Pomeau Y., Physica D 23, 3 (1986).
тэги
- convection
- critical
- crystal
- directed
- electrohydrodynamic
- liquid
- percolation
- phenomena
- statphys23
- topic-3
- turbulence
