Statics and kinetics at the nematic­-isotropic interface: effects of biaxiality

We use the Landau-de Gennes theory of a nematic liquid crystal to investigate anew aspects of the properties of the interface between the isotropic and nematic liquid crystal phases of the same fluid. The equations of the static interface have been solved, both numerically and using asymptotic analysis, with an emphasis on the effect of inclusion of the order parameter biaxiality on the physical properties. We have compared the results of the exact solutions to the commonly used de Gennes ansatz, which assumes positive and uniform unixiality through the interface. Although the de Gennes ansatz in general gives good results, when bend and splay elastic constants dominate over the twist constants, it can lead to errors of up to 10% in the surface energy. The asymptotic analysis also shows that, by contrast with the de Gennes ansatz, the order parameter wings in the isotropic phase exhibit negative order parameter, with principal axis perpendicular to the surface. For moving interfaces, using an approximation which at this stage does not yet include hydrodynamic coupling, we have compared our results with the analogue of the de Gennes ansatz used by the present authors in an earlier paper. We find that including biaxiality leads to larger effects in the dynamic than in the static properties, and that whereas this is essentially a perturbation to the energy, the velocity of the moving interface can be significantly slowed down. The slowing down effects are strongly correlated with surface biaxiality, but both effects seem to be diminished when the isotropic phase is advancing

Light scattering by optically anisotropic scatterers II: T--matrix computations for radially and uniformly anisotropic droplets

This is the second paper in a series on light scattering from optically anisotropic scatterers embedded in an isotropic medium. The apparently complex T-matrix theory involving mixing of angular momentum components turns out to be an efficient approach to calculating scattering in these systems. We present preliminary results of numerical calculations of the scattering by spherical droplets in some simple cases. The droplets contain optically anisotropic material with local radial or uniform anisotropy. We concentrate on cases in which the scattering is due only to the local optical anisotropy within the scatterer. For radial anisotropy we find non-monotonic dependence of the scattering cross-section on the degree of anisotropy can occur in a regime for which both the Rayleigh and semi-classical theories are inapplicable. For uniform anisotropy the cross-section is strongly dependent on the angle between the incident light and the optical axis, and for larger droplets this dependence is non-monotonic.Comment: 14 pages, 6 figures, uses RevTex

Modeling Smectic Layers in Confined Geometries: Order Parameter and Defects

We identify problems with the standard complex order parameter formalism for smectic-A (SmA) liquid crystals, and discuss possible alternative descriptions of smectic order. In particular, we suggest an approach based on the real smectic density variation rather than a complex order parameter. This approach gives reasonable numerical results for the smectic layer configuration and director field in sample geometries, and can be used to model smectic liquid crystals under nanoscale confinement for technological applications.Comment: 8 page

Large effect of a small bias field in liquid-crystal magnetic transitions

Most liquid crystals show low sensitivity to magnetic field. However, in this paper we show that a small bias magnetic field not only breaks the symmetry of the ground state, but also plays a crucial role in facilitating the reorientation induced by a large test magnetic field. In particular, a small bias field may alter significantly the strength of the test field needed to observe a given reorientation of the liquid crystal. Moreover, the bias field interacts with other symmetry breaking features of the cell, e.g., pretilt, to change also the qualitative features of the equilibrium state

Long-range dispersal, stochasticity and the broken accelerating wave of advance.

Rare long distance dispersal events are thought to have a disproportionate impact on the spread of invasive species. Modelling using integrodifference equations suggests that, when long distance contacts are represented by a fat-tailed dispersal kernel, an accelerating wave of advance can ensue. Invasions spreading in this manner could have particularly dramatic effects. Recently, various authors have suggested that demographic stochasticity disrupts wave acceleration. Integrodifference models have been widely used in movement ecology, and as such a clearer understanding of stochastic effects is needed. Here, we present a stochastic non-linear one-dimensional lattice model in which demographic stochasticity and the dispersal regime can be systematically varied. Extensive simulations show that stochasticity has a profound effect on model behaviour, and usually breaks acceleration for fat-tailed kernels. Exceptions are seen for some power law kernels, K(l)∝|l|-β with β<3, for which acceleration persists despite stochasticity. Such kernels lack a second moment and are important in 'accelerating' phenomena such as Lévy flights. Furthermore, for long-range kernels the approach to the continuum limit behaviour as stochasticity is reduced is generally slow. Given that real-world populations are finite, stochastic models may give better predictive power when long-range dispersal is important. Insights from mean-field models such as integrodifference equations should be applied with caution in such circumstances

Locative inversion in Germanic and Romance : A conspiracy theory

Peer reviewe

Nonequivalence of updating rules in evolutionary games under high mutation rates.

Moran processes are often used to model selection in evolutionary simulations. The updating rule in Moran processes is a birth-death process, i. e., selection according to fitness of an individual to give birth, followed by the death of a random individual. For well-mixed populations with only two strategies this updating rule is known to be equivalent to selecting unfit individuals for death and then selecting randomly for procreation (biased death-birth process). It is, however, known that this equivalence does not hold when considering structured populations. Here we study whether changing the updating rule can also have an effect in well-mixed populations in the presence of more than two strategies and high mutation rates. We find, using three models from different areas of evolutionary simulation, that the choice of updating rule can change model results. We show, e. g., that going from the birth-death process to the death-birth process can change a public goods game with punishment from containing mostly defectors to having a majority of cooperative strategies. From the examples given we derive guidelines indicating when the choice of the updating rule can be expected to have an impact on the results of the model