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Michael P. Allen (auth.), Paolo Pasini, Claudio Zannoni's Advances in the Computer Simulatons of Liquid Crystals PDF

By Michael P. Allen (auth.), Paolo Pasini, Claudio Zannoni (eds.)

Computer simulations offer a necessary set of instruments for knowing the macroscopic homes of liquid crystals and in their part transitions when it comes to molecular types. whereas simulations of liquid crystals are in keeping with an identical basic Monte Carlo and molecular dynamics suggestions as are used for different fluids, they current a couple of particular difficulties and peculiarities attached to the intrinsic houses of those mesophases.
the sphere of machine simulations of anisotropic fluids is interdisciplinary and is evolving very speedily. the current quantity covers various innovations and version platforms, from lattices to difficult particle and Gay-Berne to atomistic, for thermotropics, lyotropics, and a few biologically fascinating liquid crystals. Contributions are written by means of a superb panel of overseas academics and offers a well timed account of the recommendations and difficulties within the field.

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Applying a potential cutoff reduces this number, but not all parts of the potential are short-ranged, and there are some standard tricks to optimize the efficiency: (i) make a neighbour list for each atom, updated at intervals; (ii) use a domain decomposition approach, dividing space into a lattice of cells; (iii) use multiple time step approaches, with longer timesteps for the longer-ranged, more slowly-varying forces. Many other authors in this volume will give further details of molecular dynamics methods, especially concentrating on methods to handle longrange forces and parallel algorithms; additionally one may consult the references [1-4].

This method can be used if the director orientation n is known. This could in principle be achieved in MD, preparing a system with the director along Z, say, and exploiting the much slower time scale for director tumbling compared to molecular reorientation. Alternatively an attempt can be made, even in Me, of pinning the director along the z direction by an 25 external field, for instance adding to the potential energy a term N Uezt = -(Ep2 (cos,Bi). (27) i=l where the positive coupling parameter ( determines the strength of interaction with the field and ,Bi measures the angle between the axis of the i-th molecule and the field.

3 80 ". ", .. T 4 . 00 ~ ~ "- '- ~ ~ ~ Figure 7. 00 phase [18]. 0 (8) ...... 0 Figure 8. 40 (d) [18]. 00 (b), 36 (80) The density g(z) will be sinusoidally varying in a smectic and essentially constant in a nematic, as we see for a Gay-Berne fluid of elongated particles in fig. 8 [18]. 5. Thermodynamic observables The distribution functions introduced earlier on can be used to write down expressions for the various thermodynamic functions. Quite often these will be too complicated to be practically applicable as such but they nevertheless constitute the basis for approximate formulations or for algorithms to be used in computer simulations.

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