A numerical method for generalized exponential integrals

Abstract We present a method for evaluation of the exponential integral, E s ( x ), generalized to an arbitrary order s > 0. The algorithm is valid whatever s > 0 and x > 0. In the region x ⩾ 1, we start from a proper initial value, obtained by asymptotic calculation, and then compute the required E s ( x ) by means of a suitable combination of Taylor's expansions and recurrences, whatever s > 0. When x s 0 ( x ) (0 s 0 ⩽ 1), which is obtained by the means of suitable expansions. A forward recursion finally yields the required E s ( x ). Numerical stability and accuracy of the proposed algorithm are discussed and some results given

Hybridly Aligned Liquid Crystal Films. A Monte Carlo Study of Molecular Organization and Thermodynamics

Abstract A Monte Cario simulation of a nematic Lebwohl-Lasher hybrid liquid crystal film, confined between two surfaces with antagonistic anchoring alignment, is presented. We have calculated the ordering and the molecular organization inside the film for different lateral sizes. The influence of these boundary conditions on the nematic isotropic phase transition is also investigated

Recent results for generalized exponential integrals

Abstract Basic properties of the exponential-integral function of real order, Ev(x), and relevant expressions for evaluating this special function are presented. The mathematical results have been essentially obtained by generalizing known formulae valid for the usual exponential-integral, En(x)

Computer simulations of nematic droplets with toroidal boundary conditions

We present Monte Carlo simulations of nematic droplets with toroidal boundary conditions (TBC) and various anchoring strengths and we investigate the orientational order and the molecular organizations in these systems that mimic polymer dispersed liquid crystals (PDLC). PACS: 02.50 Monte Carlo studies PACS: 61.30.Jf Defects in liquid crystals PACS: 61.30.Gd Orientational order of liquid crystals PACS: 64.70.M Liquid Crystals phase transition

Monte Carlo Simulations of Model Nematic Droplets

Abstract We present Monte Carlo computer simulations of model nematic droplets with radial boundary conditions and various anchoring strengths and we investigate the orientational order and the molecular organizations in these systems that mimic polymer dispersed liquid crystals (PDLC). We find a hedgehog organization at high anchoring strengths and that an ordered domain is created in the droplet center at lower strengths

NMR spectra from Monte Carlo simulations of polymer dispersed liquid crystals

We present the calculation of NMR line shapes, including dynamical effects, of polymer dispersed liquid crystals starting from the Monte Carlo configurations simulated for a lattice spin model. We consider droplets with radial, bipolar, and random boundary conditions and examine to what extent their predicted deuterium NMR spectra differ in the presence of molecular motion

Dynamical and field effects in polymer-dispersed liquid crystals: monte carlo simulations of NMR spectra

We analyze the dynamical aspects of molecular ordering in nematic droplets with radial and bipolar boundary conditions---as encountered in polymer-dispersed liquid crystals---by calculating and interpreting the corresponding ${}^{2}\mathrm{H}$ NMR spectra. In particular, we focus on effects of molecular motion such as fluctuations of molecular long axes and translational diffusion, and on external field ordering effects. As in our previous paper [Phys. Rev. E 60, 4219 (1999)], where field effects were not considered, equilibrium configurations inside nematic droplets are obtained from Monte Carlo simulations of the Lebwohl-Lasher lattice spin model

Polymer network-induced ordering in a nematogenic liquid: a Monte Carlo study.

In this Monte Carlo study we investigate molecular ordering in a nematogenic liquid with dispersed polymer networks. The polymer network fibers are assumed to have rough surface morphology resulting in a partial randomness in anchoring conditions, while the fiber direction is assumed to be well defined. In particular, we focus on the loss of long-range aligning capability of the network when the degree of disorder in anchoring is increased. This process is monitored by calculating relevant order parameters and the corresponding ${}^{2}\mathrm{H}$ nuclear magnetic resonance spectra, showing that the aligning ability of the network is lost only for completely disordering anchoring conditions. Moreover, above the nematic-isotropic transition temperature surface-induced paranematic order is detected. In addition, for perfectly smooth fiber surfaces with homeotropic anchoring conditions topological line defects can be observed

A Unified Point of View on the Theory of Generalized Bessel Functions

Abstract Bessel functions have been generalized in a number of ways and many of these generalizations have been proved to be important tools in applications. In this paper we present a unified treatment, thus proving that many of the seemingly different generalizations may be viewed as particular cases of a two-variable function of the type introduced by Miller during the sixties

Nematics with dispersed polymer fibrils: a Monte Carlo study of the external-field-induced switching.

We present a Monte Carlo study of molecular ordering in nematics with dispersed regular and random arrays of straight and distorted polymer fibrils. We focus on the collective molecular reorientation--the switching--resulting from the competing aligning effects of fibrils and of a progressively applied transversal external field, and for straight fibrils identify structural Fréedericksz and saturation transitions. The role of fibril topography in the switching is monitored by simulating electric capacitance Slightly distorted fibrils are shown to give a sharper switching at a lower threshold