Dynamical scaling in two-dimensional quenched uniaxial nematic liquid crystals

Abstract

The phase-ordering kinetics of the two-dimensional uniaxial nematic has been studied using a cell dynamic scheme. The system after quench from T=infinity was found to scale dynamically with an asymptotic growth law similar to that of the two-dimensional O(2) model (quenched from above the Kosterlitz-Thouless transition temperature), i.e., L (t) approximately [t/ln (t/ t(0) ) ](1/2) (with nonuniversal time scale t(0) ). We obtained the true asymptotic limit of the growth law by performing our simulation for a sufficiently long time. The presence of topologically stable 1/2 -disclination points is reflected in the observed large-momentum dependence k(-4) of the structure factor. The correlation function was also found to tally with the theoretical prediction of the correlation function for the two-dimensional O(2) system.

Numerical method of lines for the relaxational dynamics of nematic liquid crystals

“…Our numerical results for spinodal decomposition, then, agree both qualitatively and quantitatively with theoretical results and previous numerical work [20]. There are numerical results reported in the literature are conflicting [21,22]. We indicate possible reasons for this discrepancy in the following section.…”

“…There are two alternatives to the MOL discretisation for tensor order parameter descriptions of the nematic phase. These are the cell dynamical scheme of Oono and Puri [29] as implemented by Zapotocky et al [21] and Dutta and Roy [22], and the lattice Boltzmann method of Denniston et al [30]. Our method differs in an important way from both these approaches, in that it provides a direct discretisation of the governing equations of motions.…”

Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model

“…The fact that the system is at the upper critical dimension d * = 4 of its equilibrium critical point only enters into the additive logarithmic corrections to scaling. In this respect, the 4D spherical models shows a different behaviour from those systems [7,9,10,11,12,13,14,15,17,18,32] where logarithmic corrections to non-equilibrium dynamical scaling were seen before.…”

“…L(t) ∼ (t/ ln t) 1/2 for a non-conserved order-parameter, and occurs in many systems where topological defects (e.g. vortices) play a role, such as planar magnets, frustrated spin systems, liquid crystals or superconductor arrays, see [7,8,9,10,11,12,13,14,15,16,17,18]. Recently, for equilibrium critical phenomena, Kenna, Johnston and Janke [19,20] have constructed a systematic theory for these logarithmic factors, based on an analysis of the complex zeroes of the partition function, by which they derive scaling relations between the exponents describing eventual logarithmic correction factors to simple scaling.…”

Antipersistent behavior of defects in a lyotropic liquid crystal during annihilation

“…Introduction -The understanding of ordering processes in condensed matter has been the focus of considerable research over the last decades [1][2][3][4][5][6][7][8][9][10][11]. One of the main aspects of the ordering process is the dynamical behavior of defects present in the material.…”