Tomoyuki Nagaya | PubMed Health

PubMed2004

Phase-ordering simulation of one-dimensional conserved kink system.

The kink-antikink kinetics of one-dimensional phase ordering under conserved order parameter dynamics is studied numerically. The average domain size is found to grow logarithmically, and the distribution of domain size and order parameter correlation function are shown to satisfy a scaling relation. The two-time autocorrelation function follows a power law of A (t(0))(t) approximately t(-lambda) , where lambda depends on the start time of the calculation t(0) . If t(0) is in the scaling regime, lambda takes a constant value of 3.0. Thus the scaling functions are sensitive to the initial configuration of domains. When the initial kink positions are given by uniform random numbers, the scaling functions agree with those obtained by cell dynamical system simulation.

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PubMed2004

Experimental study of spinodal decomposition in a 1D conserved order parameter system.

We study the zigzag instability coarsening of splay-bend walls formed in a nematic liquid crystal under external fields. The vertexes of zigzag can be considered as kinks in a one-dimensional order parameter system and the geometrical constraints associated with the necessary equal length sum of zig and zag segments impose a conserved quantity in this Cahn-Hilliard-type problem. In the late stage of coarsening, the characteristic length of the system L(t) shows a logarithmic increase in time and the dynamical scaling law holds. We then try to extract the nontrivial asymptotic scaling exponent lambda of the two-time correlation function, defined by lim( approximately [L(t)/L(t('))](-lambda). The scaling exponents with respective time references, t(')=32 and 64 s, after quench are found to be lambda approximately 2 which is larger than the value with respective time reference t(')=0, predicted by numerical simulation.

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PubMed2002

Experimental study of coarsening dynamics of the zigzag wall in a nematic liquid crystal with negative dielectric anisotropy.

When a homeotropically aligned nematic liquid crystal cell is placed above two permanent magnets forming a magnetic quadrupole, a straight splay-bend wall, or a so-called Ising wall, is formed. With a material of positive dielectric anisotropy, it has been shown that the application of an electric field perpendicular to the plates leads to a zigzag instability of the wall, exclusively related to the elastic anisotropy of the liquid crystal. In this case, the coarsening process of the zigzag is very slow, which in turn leads to experimental difficulties concerning its quantitative investigation. If a material of negative dielectric anisotropy is used under an electric field with low voltage and low frequency, two convective rolls appear along the Ising wall due to the charge focusing effect, which is also responsible, at a higher voltage in the homogenous tilted regions, for the appearance of Williams domains electrohydrodynamic instability. If the voltage is higher than a threshold value, the straight Ising wall spontaneously breaks into a zigzag shape and a fast coarsening of the zigzag proceeds, associated with the annihilation of two neighboring vertices. In the present paper, the coarsening dynamics of this system, which can be considered as a one-dimensional Ising situation, are investigated experimentally. At late times, the average width of the zigzag increases logarithmically with time. This finding is consistent with the theory and also with the numerical simulation of a one-dimensional Cahn-Hilliard situation having a conserved order parameter. The scaling analysis of size distribution of the Ising domain, the shape of the power spectrum, and of the correlation function of the Ising order parameter, as well as the number density correlation functions of kinks also confirms that the dynamical scaling law predicted for one-dimensional conservative systems holds for the coarsening process. As supposed from symmetry arguments, it is confirmed that this experiment constitutes a one-dimensional analog of spinodal decomposition.

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