Dynamic texture scaling of sheared nematic polymers in the large Ericksen number limit

LCP droplet dispersions: a two-phase, diffuse-interface kinetic theory and global droplet defect predictions

“…We will solve these equations in two space dimensions, building a numerical method that we now describe. First, we rewrite the eqn (17) in a form that reveals the basic mathematical structure,…”

“…16 ), Fokker-Planck (FP) equation solvers for the particle orientational probability distribution function (cf. [17][18][19][20][21][22][23][24][25][26][27] ), Landau-deGennes (LdG) mesoscopic model solvers for the second-moment tensor of the particle PDF (cf. [28][29][30][31][32][33][34][35][36][37] ), and Leslie-Ericksen-Frank (LEF) continuum model solvers for the nematic director (cf.…”

Second Order, Linear, and Unconditionally Energy Stable Schemes for a Hydrodynamic Model of Smectic-A Liquid Crystals

“…In nematic phases, the rod-like molecules self-align to have a long-range directional order with their long axes roughly parallel. While maintaining long-range directional order, the molecules are free to flow and their center of mass positions are randomly distributed as in a liquid, see [6,7,13,17,[21][22][23][24]43,50,66,71,[74][75][76][77]84]. In smectic phases, the molecules maintain the general orientational order of nematics, but also tend to align themselves in layers or planes.…”

A Linear, Decoupled and Energy stable scheme for smectic-A Liquid Crystal Flows

“…There are many different smectic phases, all characterized by different types and degrees of positional and orientational order (cf. [3,7,11,12,17,37,39,[42][43][44]44,[47][48][49] and the references therein). In particular, in Smectic-A phase, molecules are oriented along the normal vector of the layers, while in Smectic-C phases they are tilted away from the normal vector of the layer.…”