The role of attractive interactions in rod-sphere mixtures

We present a computer simulation study of binary mixtures of prolate Gay-Berne particles and Lennard-Jones spheres. Results are presented for three such rod-sphere systems which differ from each other only in the interaction between unlike particles. Both the mixing-demixing behavior and the transitions between the isotropic and any liquid crystalline phases are studied for each system, as a function of temperature and concentration ratio. For systems which show macroscopic demixing, the rod-sphere interaction is shown to give direct control over interfacial anchoring properties, giving rise to the possibility of micellar phase formation in the case of homeotropic anchoring. Additionally, it is shown that on incorporating high concentrations of spheres into a system of rods with weak demixing properties, microphase-separated structures can be induced, including bicontinuous and lamellar arrangements.</p

Computer simulation of liquid crystals

A review is presented of molecular and mesoscopic computer simulations of liquid crystalline systems. Molecular simulation approaches applied to such systems are described and the key findings for bulk phase behaviour are reported. Following this, recently developed lattice Boltzmann (LB) approaches to the mesoscale modelling of nemato-dynamics are reviewed. The article concludes with a discussion of possible areas for future development in this field.</p

Flat Directions in Flipped SU(5) I: All-Order Analysis

We present a systematic classification of field directions for the string-derived flipped SU(5) model that are D- and F-flat to all orders. Properties of the flipped SU(5) model with field values in these directions are compared to those associated with other flat directions that have been shown to be F-flat to specific finite orders in the superpotential. We discuss the phenomenological Higgs spectrum, and quark and charged-lepton mass textures.Comment: 22 pages. Late

Seeding of the nematic-isotropic phase transition by an electric field

In this paper, we use a relatively simple continuum model to investigate the effects of dielectric inhomogeneity within confined liquid crystal cells. Specifically, we consider, in planar, cylindrical and spherical geometries, the stability of a nematic-isotropic interface subject to an applied voltage. Depending on the magnitude of this voltage, the temperature and the geometry of the cell, the nematic region may shrink until the material is completely isotropic within the cell, grow until the nematic phase cells the cell or, in certain geometries, coexist with the isotropic phase. For planar geometry, no coexistence is found, but we are able to give analytical expressions for the critical voltage for an electric-field-induced phase transition as well as the critical wetting layer thickness for arbitrary applied voltage. In cells with cylindrical and spherical geometries, however, stable nematic-isotropic coexistence is predicted, the thickness of the nematic region being controllable by alteration of the applied voltage.</p

Investigation of Quasi--Realistic Heterotic String Models with Reduced Higgs Spectrum

Quasi--realistic heterotic-string models in the free fermionic formulation typically contain an anomalous U(1), which gives rise to a Fayet-Iliopolous term that breaks supersymmetry at the one--loop level in string perturbation theory. Supersymmetry is restored by imposing F- and D-flatness on the vacuum. In Phys. Rev. D 78 (2008) 046009, we presented a three generation free fermionic standard-like model which did not admit stringent F- and D-flat directions, and argued that the all the moduli in the model are fixed. The particular property of the model was the reduction of the untwisted Higgs spectrum by a combination of symmetric and asymmetric boundary conditions with respect to the internal fermions associated with the compactified dimensions. In this paper we extend the analysis of free fermionic models with reduced Higgs spectrum to the cases in which the SO(10) symmetry is left unbroken, or is reduced to the flipped SU(5) subgroup. We show that all the models that we study in this paper do admit stringent flat directions. The only examples of models that do not admit stringent flat directions remain the strandard-like models of reference Phys. Rev. D 78 (2008) 046009.Comment: 38 pages, 1 figur

On the Possibility of Optical Unification in Heterotic Strings

Recently J. Giedt discussed a mechanism, entitled optical unification, whereby string scale unification is facilitated via exotic matter with intermediate scale mass. This mechanism guarantees that a virtual MSSM unification below the string scale is extrapolated from the running of gauge couplings upward from M_Z^o when an intermediate scale desert is assumed. In this letter we explore the possibility of optical unification within the context of weakly coupled heterotic strings. In particular, we investigate this for models of free fermionic construction containing the NAHE set of basis vectors. This class is of particular interest for optical unification, because it provides a standard hypercharge embedding within SO(10), giving the standard k_Y = 5/3 hypercharge level, which was shown necessary for optical unification. We present a NAHE model for which the set of exotic SU(3)_C triplet/anti-triplet pairs, SU(2)_L doublets, and non-Abelian singlets with hypercharge offers the possibility of optical unification. Whether this model can realize optical unification is conditional upon these exotics not receiving Fayet-Iliopoulos (FI) scale masses when a flat direction of scalar vacuum expectation values is non-perturbatively chosen to cancel the FI D-term, xi, generated by the anomalous U(1)-breaking Green-Schwarz-Dine-Seiberg-Wittten mechanism. A study of perturbative flat directions and their phenomenological implications for this model is underway. This paper is a product of the NFS Research Experiences for Undergraduates and the NSF High School Summer Science Research programs at Baylor University.Comment: 16 pages. Standard Late

Using particle shape to induce tilted and bistable liquid crystal anchoring

We use Monte Carlo simulations of hard Gaussian overlap (HGO) particles symmetrically confined in slab geometry to investigate the role of particle-substrate interactions on liquid crystalline anchoring. Despite the restriction here to purely steric interactions and smooth substrates, a range of behaviours are captured, including tilted anchoring and homeotropic-planar bistability. These macroscopic behaviours are all achieved through appropriate tuning of the microscopics of the HGO-substrate interaction, based upon non-additive descriptions for the HGO-substrate shape parameter.</p

Classification of the chiral Z2XZ2 fermionic models in the heterotic superstring

The first particle physics observable whose origin may be sought in string theory is the triple replication of the matter generations. The class of Z2XZ2 orbifolds of six dimensional compactified tori, that have been most widely studied in the free fermionic formulation, correlate the family triplication with the existence of three twisted sectors in this class. In this work we seek an improved understanding of the geometrical origin of the three generation free fermionic models. Using fermionic and orbifold techniques we classify the Z2XZ2 orbifold with symmetric shifts on six dimensional compactified internal manifolds. We show that perturbative three generation models are not obtained in the case of Z2XZ2 orbifolds with symmetric shifts on complex tori, and that the perturbative three generation models in this class necessarily employ an asymmetric shift. We present a class of three generation models in which the SO(10) gauge symmetry cannot be broken perturbatively, while preserving the Standard Model matter content. We discuss the potential implications of the asymmetric shift for strong-weak coupling duality and moduli stabilization. We show that the freedom in the modular invariant phases in the N=1 vacua that control the chiral content, can be interpreted as vacuum expectation values of background fields of the underlying N=4 theory, whose dynamical components are projected out by the Z2-fermionic projections. In this class of vacua the chiral content of the models is determined by the underlying N=4 mother theory.Comment: 36 pages. Standard LaTe

A lattice spring model of heterogeneous materials with plasticity

A three-dimensional lattice spring model of a heterogeneous material is presented. For small deformations, the model is shown to recover the governing equations for an isotropic elastic medium. The model gives reasonable agreement with theoretical predictions for the elastic fields generated by a spherical inclusion, although for small particle sizes the discretization of the underlying lattice causes some departures from the predicted values. Plasticity is introduced by decreasing the elastic moduli locally whilst maintaining stress continuity. Results are presented for a spherical inclusion in a plastic matrix and are found to be in good agreement with the predictions of Wilner (1988 J. Mech. Phys. Solids 36 141-65).</p

Competing Alignments of Nematic Liquid Crystals on Square Patterned Substrates

A theoretical analysis is presented of a nematic liquid crystal confined between substrates pat- terned with squares that promote vertical and planar alignment. Two approaches are used to eluci- date the behavior across a wide range of length scales: Monte Carlo simulation of hard particles and Frank-Oseen continuum theory. Both approaches predict bistable degenerate azimuthal alignment in the bulk along the edges of the squares; the continuum calculation additionally reveals the possi- bility of an anchoring transition to diagonal alignment if the polar anchoring energy associated with the pattern is sufficiently weak. Unlike the striped systems previously analyzed, the Monte Carlo simulations suggest that there is no "bridging" transition for sufficiently thin cells. The extent to which these geometrically patterned systems resemble topographically patterned substrates, such as square wells, is also discussed.Comment: 11 pages, 12 figure