Fluctuation and distribution of macroscopic order in formation processes of a dissipative structure

Kai, Shoichi; Wakabayashi, Shigenori; Imasaki, Masahide

doi:10.1103/physreva.33.2612

Cited by 53 publications

(11 citation statements)

References 26 publications

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“…, the streamlines and the director field, although time dependent in the form of a standing wave, consist of convection rolls with a maximum of the amplitude in the middle of the cell. This statement does not seem to agree with some experimental observations [6,7]. Moreover, even the qualitative nature of the underlying instability mechansism as proposed in Refs.…”

Section: Introductionmentioning

confidence: 43%

“…In the first one, particle trajectories have been observed. This was done by visual inspection of the flow, looking from the side into the boundary layer of an open cell [6]. At these boundaries, one must expect the director field to be fairly complicated because of inhomogeneities of the electric field.…”

Section: Resultsmentioning

confidence: 99%

“…This oscillatory character of the DR has already been demonstrated qualitatively [5,6]. By stroboscopic illumination [11] it has been shown that for some phase differences between the driving voltage and the flash of the stroboscope the convection patterns show up with good contrast, while for other phase differences the pattern is virtually invisible.…”

Section: Introductionmentioning

confidence: 88%

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Phase shift of dielectric rolls in electroconvection

et al. 1992

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Driving electroconvection in a nematic liquid crystal with an electric ac field leads to dielectric convection rolls if the driving frequency is higher than the cutoff frequency. According to the theory, these rolls have a time-dependent velocity and director field that can be described as standing waves which are phase locked to the driving field. The paper reports on measurements of the phase difference between the driving electric field and the director field by means of a stroboscopic technique. Experimental evidence of a symmetry breaking of the oscillations of the director field with respect to the polarity of the electric field is presented, and the possibility to measure flexoelectric coefficients by examining this asymmetry is discussed.PACS number(s): 61.30.6d, 47.20. -k

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Section: Introductionmentioning

confidence: 43%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 88%

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Phase shift of dielectric rolls in electroconvection

et al. 1992

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“…The oscillatory behaviour of director structures in the dielectric regime was established already in early experiments [7,8]. In a study of DR using stroboscopic illumination, Schneider et al [9] have shown experimentally that the amplitudes of optical contrast are strongly time dependent as a consequence of the dynamics of the director field.…”

Section: Introductionmentioning

confidence: 96%

Spatio-temporal Analysis of Electroconvection in Nematics

Amm

Grigutsch

Stannarius

1998

Zeitschrift Für Naturforschung A

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We investigate electroconvection in nematic liquid crystals by means of optical microscopy. Time resolved optical images are used to study the director dynamics. For the first time we present instant images in the dielectric regime. A numerical simulation of the optical transmission patterns is performed on the basis of Fermat's principle. In the instant images of dielectric rolls, the periodicity of the observed optical pattern is equal to the wavelength Ao of the convection rolls. The well known low contrast 'stationary' optical texture observed in conventional experiments results from time averaging of these instant images; its wavelength is Ao/2.

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“…However, more realistic models of physical systems require considering various noise sources, for example, the laser models [10], the lattice model [11], the structure-formation process in liquid crystals [12], the imperfect pitchfork bifurcation in superfluid turbulence in liquid helium [13], etc. Though various sources are presented simultaneously in some stochastic processes, they are assumed to have different origins and are treated as independent random variables in most of the previous investigations [10 -15].…”

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confidence: 99%

Reentrance Phenomena in a Bistable Kinetic Model Driven by Correlated Noise

Jia

1997

Phys. Rev. Lett.

135

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In this Letter we discuss a bistable model driven by two white noise sources, when the correlation time of the correlations between two sources t is nonzero. We find that there is a critical value of the correlation time t c . For t . t c , the system undergoes a succession of two phase transitions (namely, the reentrance phenomenon) as the strength of the correlations between two noise sources l is varied. However, for t , t c , the system undergoes a (single) phase transition as l is varied.[S0031-9007(96)01943-6] PACS numbers: 05.40.+j, 82.20.Db The study of dynamical systems disturbed by noise is recurrent in many contexts of physics and other sciences. Particularly for nonequilibrium systems, where noise plays a crucial role[1,2], the noise-induced transition has been intensively investigated. The effects of colored noise (i.e., fluctuations of intensity D with a correlation time t) have attracted a great deal of interest in recent years. Different theories have been used to deal with the colored-noise problem, for instance, the conventional small-t theory [3,4], the functional-calculus theory of Fox [5], the decoupling theory (often called Hanggi ansatz) [6], the unified colored-noise theory [7], and the recent interpolation procedure [8].Recently, Castro et al. [9] presented an analysis of a chemical reaction system, when it is forced by one colorednoise source, by using the interpolation procedure which is an extension of the unified colored-noise theory and allows us to study both t ! 0 and t !`cases. They showed that the system undergoes a purely noise-induced transition from a monostable regime to a bistable one, then to the monostable regime as t increases, namely, a succession of two phase transitions when the correlation time is monotonically varied. This type of nonequilibrium transitions phenomenon has been called the reentrance phenomenon [9].The largest amount of work about fluctuations has been referred to the consideration of systems with just one noise source. However, more realistic models of physical systems require considering various noise sources, for example, the laser models [10], the lattice model [11], the structure-formation process in liquid crystals [12], the imperfect pitchfork bifurcation in superfluid turbulence in liquid helium [13], etc. Though various sources are presented simultaneously in some stochastic processes, they are assumed to have different origins and are treated as independent random variables in most of the previous investigations [10 -15]. However, in certain situations they may have a common origin and thus may be correlated with each other as well [16][17][18][19][20][21]. The study of dynamical systems with correlation noise terms has attracted attention in the field of stochastic processes. Some of these investigations were concerned with the steady-state statistical properties of systems [16 -20]; others were concerned with the transient problems [21]. Now a question to be raised is if similar peculiarities studied by Castro et al. [9] can be found in...

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Fluctuation and distribution of macroscopic order in formation processes of a dissipative structure

Cited by 53 publications

References 26 publications

Phase shift of dielectric rolls in electroconvection

Phase shift of dielectric rolls in electroconvection

Spatio-temporal Analysis of Electroconvection in Nematics

Reentrance Phenomena in a Bistable Kinetic Model Driven by Correlated Noise

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