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6ŒŽ7“úi–Ĝj 16:30-

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Directed Percolation Universality in Turbulent Liquid Crystals

ŠT—v(abstract)
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. Although the corresponding universality class 
is well established both in theory and in simulations with plenty of examples, such as in 
epidemics, forest fires, catalytic reactions, interface grouwth, synchronization and calcium 
dynamics in living cells, surprisingly, no experiments could show convincing evidence of the DP 
critical behavior, which has been recognized as an outstanding open problem [1].

In this study, we investigate a transition to spatiotemporal intermittency between two turbulent 
states (DSM1-DSM2) observed in electrohydrodynamic convection of nematic liquid crystals. 
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. This constitutes the first complete and satisfactory 
experimental realization of a DP class transition [2].

Furthuermore, I show a novel aspect of the DP universality, namely universal scaling of hysteresis 
loops. The DSM1-DSM2 transition is accompanied by hysteresis, whose width algebraically depends on 
the ramp rate of the applied voltage [3]. This scaling has been unexplained since it was found, 
but in fact, it is an outcome of the DP universality under the presence of a very rare spontaneous 
nucleation [2]. We obtained the power of the scaling which quantitatively agrees with experiments, 
not only in numerical simulations but also by a simple theoretical calculation, where the power of 
the scaling turns out to be simply related to a critical exponent of DP. These results show that 
the scaling of the hysteresis loops is universal among transitions into a quasi-absorbing state, 
suggesting that it can be observed in a variety of other systems.

[1] H. Hinrichsen, Adv. Phys. 49, 815 (2000).
[2] K. Takeuchi, M. Kuroda, H. Chate and M. Sano, to be published.
[3] S. Kai, W. Zimmermann, M. Andoh, and N. Chizumi, Phys. Rev. Lett. 64, 1111 (1990).


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