Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects.

We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in the full-anisotropy limit. We show that a comprehensive understanding of the dynamic behavior of systems with quenched defects requires a generalized definition of the dynamic order parameter. By doing so, we demonstrate that the inclusion of quenched defects lowers the dynamic critical temperature as well, with a linear trend across the range of defect fractions considered. We also explore if and how it is possible to predict the dynamic behavior of specific magnetic systems with quenched randomness. Various geometric quantities, such as a defect potential index, the defect dipole moment, and the properties of the defect Delaunay triangulation, prove useful for this purpose.

Sequencing era methods for identifying signatures of selection in the genome.

Insights into genetic loci which are under selection and their functional roles contribute to increased understanding of the patterns of phenotypic variation we observe today. The availability of whole-genome sequence data, for humans and other species, provides opportunities to investigate adaptation and evolution at unprecedented resolution. Many analytical methods have been developed to interrogate these large data sets and characterize signatures of selection in the genome. We review here recently developed methods and consider the impact of increased computing power and data availability on the detection of selection signatures. Consideration of demography, recombination and other confounding factors is important, and use of a range of methods in combination is a powerful route to resolving different forms of selection in genome sequence data. Overall, a substantial improvement in methods for application to whole-genome sequencing is evident, although further work is required to develop robust and computationally efficient approaches which may increase reproducibility across studies.

Evidence of Early-Stage Selection on EPAS1 and GPR126 Genes in Andean High Altitude Populations.

The aim of this study is to identify genetic variants that harbour signatures of recent positive selection and may facilitate physiological adaptations to hypobaric hypoxia. To achieve this, we conducted whole genome sequencing and lung function tests in 19 Argentinean highlanders (>3500 m) comparing them to 16 Native American lowlanders. We developed a new statistical procedure using a combination of population branch statistics (PBS) and number of segregating sites by length (nSL) to detect beneficial alleles that arose since the settlement of the Andes and are currently present in 15-50% of the population. We identified two missense variants as significant targets of selection. One of these variants, located within the GPR126 gene, has been previously associated with the forced expiratory volume/forced vital capacity ratio. The other novel missense variant mapped to the EPAS1 gene encoding the hypoxia inducible factor 2α. EPAS1 is known to be the major selection candidate gene in Tibetans. The derived allele of GPR126 is associated with lung function in our sample of highlanders (p < 0.05). These variants may contribute to the physiological adaptations to hypobaric hypoxia, possibly by altering lung function. The new statistical approach might be a useful tool to detect selected variants in population studies.

Computational studies of history dependence in nematic liquid crystals in random environments.

Glassy liquid crystalline systems are expected to show significant history-dependent effects. Two model glassy systems are the RAN and SSS (sprinkled silica spin) lattice models. The RAN model is a Lebwohl-Lasher lattice model with locally coupled nematic spins, together with uncorrelated random anisotropy fields at each site, while the SSS model has a finite concentration of impurity spins frozen in random directions. Here Brownian simulation is used to study the effect of different sample histories in the low temperature regime in a three-dimensional (d = 3) model intermediate between SSS and RAN, in which a finite concentration p < p(c) (p(c) the percolation threshold) of frozen spins interacts with neighboring nematic spins with coupling W. Simulations were performed at temperature T ∼ T(NI)/2 (T(NI) the bulk nematic-isotropic transition temperature) for temperature-quenched and field-quenched histories (TQH and FQH, respectively), as well as for temperature-annealed histories (AH). The first two of these limits represent extreme histories encountered in typical experimental studies. Using long-time averages for equilibrated systems, we calculate orientational order parameters and two-point correlation functions. Finite-size scaling was used to determine the range of the orientational ordering, as a function of coupling strength W,p and sample history. Sample history plays a significant role; for given concentration p, as disorder strength W is increased, TQH systems sustain quasi-long-range order (QLRO) and short-range order (SRO). The data are also consistent with a long-range order (LRO) phase at very low disorder strength. By contrast, for FQH and p ≤ 0.1, only LRO and QLRO occur within the range of parameters investigated. The crossover between regimes depends on history, but in general, the FQH phase is more ordered than the AH phase, which is more ordered than the TQH phase. However, at temperatures close to the isotropic-nematic phase transition of pure samples we observe SRO for p = 0.1 even for FQH. We detect also in the QLRO phase a domain-type structural pattern, consistent with ideas introduced by Giamarchi and Doussal [Phys. Rev. B 52, 1242 (1995)] on superconducting flux lattices. In the weak-disorder limit the orientational correlation length obeys the Larkin-Imry-Ma scaling ξ ∼ D(-2/(4-d)).

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.

Magnetite nanorod thermotropic liquid crystal colloids: synthesis, optics and theory.

We have developed a facile method for preparing magnetic nanoparticles which couple strongly with a liquid crystal (LC) matrix, with the aim of preparing ferronematic liquid crystal colloids for use in magneto-optical devices. Magnetite nanoparticles were prepared by oxidising colloidal Fe(OH)(2) with air in aqueous media, and were then subject to alkaline hydrothermal treatment with 10 mol dm(-3) NaOH at 100°C, transforming them into a polydisperse set of domain magnetite nanorods with maximal length ~500 nm and typical diameter ~20 nm. The nanorods were coated with 4-n-octyloxybiphenyl-4-carboxylic acid (OBPh) and suspended in nematic liquid crystal E7. As compared to the conventional oleic acid coating, this coating stabilizes LC-magnetic nanorod suspensions. The suspension acts as a ferronematic system, using the colloidal particles as intermediaries to amplify magnetic field-LC director interactions. The effective Frederiks magnetic threshold field of the magnetite nanorod-liquid crystal composite is reduced by 20% as compared to the undoped liquid crystal. In contrast with some previous work in this field, the magneto-optical effects are reproducible on time scales of months. Prospects for magnetically switched liquid crystal devices using these materials are good, but a method is required to synthesize single magnetic domain nanorods.

Molecular-field-theory approach to the Landau theory of liquid crystals: uniaxial and biaxial nematics.

Nematic liquid crystal phase diagrams in temperature-biaxiality space are usually complex. We construct a Landau theory based on the analogous molecular-field theory for orthorhombic biaxial nematic fluids. A formal procedure yields coefficients (some of which, unusually, can be tensorial) in this Landau expansion, correctly predicts the complete set of invariants formed from the ordering tensors, and avoids ad hoc parametrization of the molecular biaxiality. By regularizing the Landau expansion to avoid unwanted order parameter divergences at low temperatures, we predict phase behavior over the whole range of biaxiality. The resulting phase diagrams have the same topology as those of molecular-field theory.

Molecular field theory for biaxial nematic liquid crystals composed of molecules with C(2h) point group symmetry.

The biaxial nematic phase is generally taken, either explicitly or implicitly, to have D(2h) point group symmetry. However, it is possible for the biaxial phase to have a lower symmetry depending on that of its constituent molecules. Here we develop a molecular field theory for a nematogen composed of C(2h) molecules in terms of the nine independent second rank orientational order parameters defining the C(2h) biaxial nematic. In addition, there is a rank one order parameter constructed from two pseudovectors which is only nonzero in the C(2h) phase. The theory is simplified by removing all but the three dominant order parameters. The predicted phase behavior is found to be rich with three possible biaxial nematic phases and with the transitions involving a biaxial nematic phase exhibiting tricritical points.

Frederiks transition in ferroelectric liquid-crystal nanosuspensions.

We construct a theoretical model of the dielectric properties of a ferroelectric LC nanosuspension (FLCNS), using a generalized Maxwell-Garnett picture. The theory supposes that an FLCNS may as a first approximation be considered as a complex homogeneous dielectric ceramic, thus neglecting positional correlations of the colloidal particles. The FLCNS then consists of an anisotropic matrix with a very low concentration (<1% by volume) of impurity particles. The impurity particles possess both shape and dielectric anisotropy, as well as a permanent electric polarization and strong liquid-crystal director anchoring on the particle surface. We show that the effective dielectric properties for capacitance properties and for effective liquid-crystal free energies do not coincide. We calculate the effect of doping a liquid crystal with ferroelectric impurities on the Frederiks transition. The theory takes account of inclusion shape, dielectric susceptibility, and local field effects. We neglect the possibility of dielectric particle chaining, which appears experimentally not to occur in general. Our calculations suggest, in qualitative agreement with experiment, that doping a nematic liquid crystal with ferroelectric particles, even at very low particle concentration, can in some cases significantly decrease the electric Frederiks threshold field.

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.

Orientational coupling amplification in ferroelectric nematic colloids.

We investigated the physical properties of low concentration ferroelectric nematic colloids, using calorimetry, optical methods, infrared spectroscopy, and capacitance studies. The resulting homogeneous colloids possess a significantly amplified nematic orientational coupling. We find that the nematic orientation coupling increases by approximately 10% for particle concentrations of 0.2%. A manifestation of the increased orientational order is that the clearing temperature of a nematic colloid increases by up to 40 degrees C compared to the pure liquid crystal host. A theoretical model is proposed in which the ferroelectric particles induce local dipoles whose effective interaction is proportional to the square of the orientational order parameter.