Molecular dynamics simulations of a flexible liquid crystal

Molecular dynamics simulations have been performed for a liquid crystal composed of a Gay—Berne core site with two alkyl chains of different length (C₇ and C₃) at either end of the molecule. Calculations have been carried out for 512 molecules in the NVT ensemble for simulation times of up to 8.0ns at two distinct densities. The liquid crystal phases of the material have been fully characterized by measurements of orientational order parameters and radial distribution functions in each phase. Results are also presented for conformational distributions and effective torsional potentials of the system. We conclude that models of this nature represent a powerful approach to the study of flexibility in mesogenic systems and open up possibilities for predicting both the phase behaviour and bulk properties of liquid crystals based solely on a prior knowledge of intermolecular interactions.     

On Namias's Fractional Fourier Transforms

The objective of this paper is to make rigorous a formal study(Namias, 1980) of fractional powers for the Fourier transform.To make the theory unambiguous, it is found necessary to modifyNamias's fractional operators. Some theorems are then provedfor the modified operators and an operational calculus is developed.Finally, an application to an ordinary differential equationis considered.