150 research outputs found
Molecular organization of nematic liquid crystals between concentric cylinders: Role of the elastic anisotropy
The orientational order in a nematic liquid crystal sample confined to an annular region between two concentric cylinders is investigated by means of lattice Monte Carlo simulations. Strong anchoring and homeotropic orientations, parallel to the radial direction, are implemented at the confining surfaces. The elastic anisotropy is taken into account in the bulk interactions by using the pair potential introduced by Gruhn and Hess [T. Gruhn and S. Hess, Z. Naturforsch. A 51, 1 (1996)] and parametrized by Romano and Luckhurst [S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998)IJPBEV0217-979210.1142/S0217979298001344; Phys. Lett. A 302, 203 (2002)PYLAAG0375-960110.1016/S0375-9601(02)01042-3; G. R. Luckhurst and S. Romano, Liq. Cryst. 26, 871 (1999)LICRE60267-829210.1080/026782999204561], i.e., the so-called GHRL potential. In the case of equal elastic constants, a small but appreciable deformation along the cylinder axis direction is observed, whereas when the values of K11/K33 if K22=K33 are low enough, all the spins in the bulk follow the orientation imposed by the surfaces. For larger values of K11/K33, spontaneous deformations, perpendicular to the polar plane, increase significantly. Our findings indicate that the onset of these deformations also depends on the ratio K22/K33 and on the radius of the cylindrical surfaces. Although expected from the elastic theory, no tangential component of the deformations was observed in the simulations for the set of parameters analyzed
Concerning some integrals of the generalized exponential-integral function
AbstractThis paper deals with some integrals involving the generalized exponential integral, EΜ(x), which are of interest for applications. New relations have been derived by generalizing known expressions valid for Μ = n integer. Numerical results are also given, which extend existing tables to the entire real domain
Multivariable Hermite polynomials and phase-space dynamics
The phase-space approach to classical and quantum systems demands for advanced analytical tools. Such an approach characterizes the evolution of a physical system through a set of variables, reducing to the canonically conjugate variables in the classical limit. It often happens that phase-space distributions can be written in terms of quadratic forms involving the above quoted variables. A significant analytical tool to treat these problems may come from the generalized many-variables Hermite polynomials, defined on quadratic forms in R(exp n). They form an orthonormal system in many dimensions and seem the natural tool to treat the harmonic oscillator dynamics in phase-space. In this contribution we discuss the properties of these polynomials and present some applications to physical problems
Differential cross sections for muonic atom scattering from hydrogenic molecules
The differential cross sections for low-energy muonic hydrogen atom
scattering from hydrogenic molecules are directly expressed by the
corresponding amplitudes for muonic atom scattering from hydrogen-isotope
nuclei. The energy and angular dependence of these three-body amplitudes is
thus taken naturally into account in scattering from molecules, without
involving any pseudopotentials. Effects of the internal motion of nuclei inside
the target molecules are included for every initial rotational-vibrational
state. These effects are very significant as the considered three-body
amplitudes often vary strongly within the energy interval eV.
The differential cross sections, calculated using the presented method, have
been successfully used for planning and interpreting many experiments in
low-energy muon physics. Studies of nuclear capture in and the
measurement of the Lamb shift in atoms created in H gaseous targets
are recent examples.Comment: 21 pages, 13 figures, submitted to Phys. Rev.
Nematics with quenched disorder: pinning out the origin of memory
Memory effects and glassy behavior have been repeatedly observed in disordered nematic liquid crystals but the connection between these effects and the system topology remained unrevealed. We present an analysis of the local and global topology of the nematic ordering in the presence of quenched disorder and we show that nematics with quenched disorder can be mapped into a system of pinned defect lines and that the memory of the system stems from the pinning of these strings
External and intrinsic anchoring in nematic liquid crystals: A Monte Carlo study
We present a Monte Carlo study of external surface anchoring in nematic cells
with partially disordered solid substrates, as well as of intrinsic anchoring
at free nematic interfaces. The simulations are based on the simple hexagonal
lattice model with a spatially anisotropic intermolecular potential. We
estimate the corresponding extrapolation length by imposing an elastic
deformation in a hybrid cell-like nematic sample. Our estimates for
increase with increasing surface disorder and are essentially
temperature--independent. Experimental values of are approached only when
both the coupling of nematic molecules with the substrate and the anisotropy of
nematic--nematic interactions are weak.Comment: Revisions primarily in section I
Analysis of Nematic Liquid Crystals with Disclination Lines
We investigate the structure of nematic liquid crystal thin films described
by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary
conditions of nonzero degree. We prove that as the elasticity constant goes to
zero a limiting uniaxial texture forms with disclination lines corresponding to
a finite number of defects, all of degree 1/2 or all of degree -1/2. We also
state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs
model without magnetic field that follows from a similar proof.Comment: 40 pages, 1 figur
O(N) and RP^{N-1} Models in Two Dimensions
I provide evidence that the 2D model for is equivalent
to the -invariant non-linear -model in the continuum limit. To
this end, I mainly study particular versions of the models, to be called
constraint models. I prove that the constraint and models are
equivalent for sufficiently weak coupling. Numerical results for their
step-scaling function of the running coupling are
presented. The data confirm that the constraint model is in the samei
universality class as the model with standard action. I show that the
differences in the finite size scaling curves of i and models
observed by Caracciolo et al. can be explained as a boundary effect. It is
concluded, in contrast to Caracciolo et al., that and models
share a unique universality class.Comment: 14 pages (latex) + 1 figure (Postscript) ,uuencode
Topological Defects in Nematic Droplets of Hard Spherocylinders
Using computer simulations we investigate the microscopic structure of the
singular director field within a nematic droplet. As a theoretical model for
nematic liquid crystals we take hard spherocylinders. To induce an overall
topological charge, the particles are either confined to a two-dimensional
circular cavity with homeotropic boundary or to the surface of a
three-dimensional sphere. Both systems exhibit half-integer topological point
defects. The isotropic defect core has a radius of the order of one particle
length and is surrounded by free-standing density oscillations. The effective
interaction between two defects is investigated. All results should be
experimentally observable in thin sheets of colloidal liquid crystals.Comment: 13 pages, 16 figures, Phys. Rev.
High-Temperature series for the lattice spin model (generalized Maier-Saupe model of nematic liquid crystals) in two space dimensions and with general spin dimensionality n
High temperature series expansions of the spin-spin correlation functions of
the RP^{n-1} spin model on the square lattice are computed through order
beta^{8} for general spin dimensionality n. Tables are reported for the
expansion coefficients of the energy per site, the susceptibility and the
second correlation moment.Comment: 6 pages, revtex, IFUM 419/FT, 2 figures not include
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