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Hidaka, Y.

Ishibashi, Y.

Miyazaki, Y.

Nagaya, T.

Orihara, H.

Kyoto University Research Information Repository

TitleTEMPORAL EVOLUTION OF THE AMPLITUDE ANDTHE PHASE IN THE FORMATION PROCESS OF THEWILLIAMS DOMAIN(Session IV : Structures & Patterns, The1st Tohwa University International Meeting on StatisticalPhysics Theories, Experiments and Computer Simulations)Author(s)Miyazaki, Y.; Hidaka, Y.; Nagaya, T.; Orihara, H.; Ishibashi,Y.Citation物性研究 (1996), 66(3): 590-591Issue Date1996-06-20URL http://hdl.handle.net/2433/95761RightType Departmental Bulletin PaperTextversionpublisherKyoto UniversityTEMPORAL EVOLUTION OF THE AMPLITUDE AND THE PHASE'IN THE FORMATION PROCESS OF THE WILLIAMS DOMAINY. Miyazaki, Y. Hidaka*, T. Nagaya, H. Oriha~a and Y. IshibashiDepart,ment of Applied Physics, School of Engineering,Nagoya University, Nagoya 464-01, Japan*Department of Applied Science, Faculty of Engineering,Kyushu University, Fukuoka 812-81, JapanIn recent years, much attention has been paid to electro-hydrodynamic convection(EHC) inliquid crystals and, a lot of studies on EHC have been done, but not so many on the transientprocess of pattern formation. In this study, therefore, we have investigated the formationprocess of the one-dimensional periodic pattern called Williams domain' from two differentinitial conditions. In the first condition, a system is set to be a uniform state in the absenceof an applied electric field. In the second, the turbulent state under a strong electric field(V = 30.0 Vrms).We used a cell with large aspect ratios (rx = r 11 = 400), which can be regarded as atwo-dimensional system. Figure 1 shows the formation process of the Williams domain afterapplying an electric field. The formation process consists of the following two stages. In the firststage, some small domains of convective structure appear here and there, a~d then grow up,resulting in the appearance of dislocations. In the second stage, a pair of dislocations becomeclose each other and then annihilate. Finally, the stable structure with no dislocation appears.To analyze this pattern formation process, we calculated the power spectrum images, S(k), bythe fast Fourier transformation. As shown in Fig. 2, an oval spot appears at first, and becomessharp as time goes on. Figure 3 (a) shows the time dependence of the peak width of the powerspectrum,Ek Ik - kI 2S(k)EkS(k) (k: averaged wave number)in a plot of logwk vs. logt. The peak width decreases obeying a power law whose exponent isbetween -1/3 and -1/4 except the initial stage.We simulated Ginzburg-Pitaevskii equation with Euler's method.aw a2 a27ft =W -IWI2W + K(ax2 + ay2)W(IWinil < 0.00001 random, D..t = 0.1, D..x = D..y = 1, K = 0.1)Figure 3 (b) shows the time dependence of the peak width of the power spectrum in thesimulation. This peak width also decreases obeying a power law whose ~xponent is between-1/3 and -1/4. This result agrees with the experiment.- 590-(b)Fig. 1 The fonnation process of the Williams domain; (a).t = 16 sec, (b) t = 380 sec.(a) (b)"Fig. 2 The power spectra of the image intensity; (a) t =16 sec, (b) t = 380 sec.c(a) Time dependence of peak width102.--------~.:-:------___,(Experiment). .(b) Time dependence of peak width101r----.;:...-.------c-:------:-o--:-.......-r:.-.,(Simulation)i~~""• Fro"""'b'~"~~~'~~ "~. 10'o From uniform .~ ...._.~.-_(1/4t· 1/3o 0o Wk-1'1/4-----1'113101 IO·IL--~-.....-....--~~""""""'"":-~~~"'"10° 101 1011 101 101 103Time (sec) TimeFig. 3 The time dependence of the peak width of the power spectrum, Wk.. (a) experiment, (b) simulation.- 591-

TEMPORAL EVOLUTION OF THE AMPLITUDE AND THE PHASE IN THE FORMATION PROCESS OF THE WILLIAMS DOMAIN(Session IV : Structures & Patterns, The 1st Tohwa University International Meeting on Statistical Physics Theories, Experiments and Computer Simulations)

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TEMPORAL EVOLUTION OF THE AMPLITUDE AND THE PHASE IN THE FORMATION PROCESS OF THE WILLIAMS DOMAIN(Session IV : Structures & Patterns, The 1st Tohwa University International Meeting on Statistical Physics Theories, Experiments and Computer Simulations)

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