40 research outputs found
Smectic Liquid Crystals: Materials with One-Dimensional, Periodic Order
Smectic liquid crystals are materials formed by stacking deformable, fluid
layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary
conditions can impose curvature on the layers. Since the layer spacing and
curvature are intertwined, the problem of finding minimal configurations for
the layers becomes highly nontrivial. We discuss various topological and
geometrical aspects of these materials and present recent progress on finding
some exact layer configurations. We also exhibit connections to the study of
certain embedded minimal surfaces and briefly summarize some important open
problems.Comment: 16 page
Smectic blue phases: layered systems with high intrinsic curvature
We report on a construction for smectic blue phases, which have quasi-long
range smectic translational order as well as three dimensional crystalline
order. Our proposed structures fill space by adding layers on top of a minimal
surface, introducing either curvature or edge defects as necessary. We find
that for the right range of material parameters, the favorable saddle-splay
energy of these structures can stabilize them against uniform layered
structures. We also consider the nature of curvature frustration between mean
curvature and saddle-splay.Comment: 15 pages, 11 figure
Weirdest Martensite: Smectic Liquid Crystal Microstructure And Weyl-poincaré Invariance
Smectic liquid crystals are remarkable, beautiful examples of materials microstructure, with ordered patterns of geometrically perfect ellipses and hyperbolas. The solution of the complex problem of filling three-dimensional space with domains of focal conics under constraining boundary conditions yields a set of strict rules, which are similar to the compatibility conditions in a martensitic crystal. Here we present the rules giving compatible conditions for the concentric circle domains found at two-dimensional smectic interfaces with planar boundary conditions. Using configurations generated by numerical simulations, we develop a clustering algorithm to decompose the planar boundaries into domains. The interfaces between different domains agree well with the smectic compatibility conditions. We also discuss generalizations of our approach to describe the full three-dimensional smectic domains, where the variant symmetry group is the Weyl-Poincaré group of Lorentz boosts, translations, rotations, and dilatations. © 2016 American Physical Society.1161
Rotational Invariance and the Theory of Directed Polymer Nematics
The consequences of rotational invariance in a recent theory of fluctuations
in dilute polymer nematics are explored. A correct rotationally invariant free
energy insures that anomalous couplings are not generated in a one-loop
renormalization group calculation.Comment: 4 Pages, latex file (requires REVTEX 3.0), two postscript figures
(attached), IASSNS-HEP-93/2
The electroclinic effect and modulated phases in smectic liquid crystals
We explore the possibility that the large electroclinic effect observed in
ferroelectric liquid crystals arises from the presence of an ordered array of
disclination lines and walls. If the spacing of these defects is in the
subvisible range, this modulated phase would be similar macroscopically to a
smectic A phase. The application of an electric field distorts the array,
producing a large polarization, and hence a large electroclinic effect. We show
that with suitable elastic parameters and sufficiently large chirality, the
modulated phase is favored over the smectic A and helically twisted smectic C*
phases. We propose various experimental tests of this scenario.Comment: 9 pages, 7 figures; new version includes dipolar interactions and
bend-twist couplin
Random close packing of granular matter
We propose an interpretation of the random close packing of granular
materials as a phase transition, and discuss the possibility of experimental
verification.Comment: 6 page
Bulk Universality and Related Properties of Hermitian Matrix Models
We give a new proof of universality properties in the bulk of spectrum of the
hermitian matrix models, assuming that the potential that determines the model
is globally and locally function (see Theorem \ref{t:U.t1}).
The proof as our previous proof in \cite{Pa-Sh:97} is based on the orthogonal
polynomial techniques but does not use asymptotics of orthogonal polynomials.
Rather, we obtain the -kernel as a unique solution of a certain non-linear
integro-differential equation that follows from the determinant formulas for
the correlation functions of the model. We also give a simplified and
strengthened version of paper \cite{BPS:95} on the existence and properties of
the limiting Normalized Counting Measure of eigenvalues. We use these results
in the proof of universality and we believe that they are of independent
interest
Fluctuating Filaments I: Statistical Mechanics of Helices
We examine the effects of thermal fluctuations on thin elastic filaments with
non-circular cross-section and arbitrary spontaneous curvature and torsion.
Analytical expressions for orientational correlation functions and for the
persistence length of helices are derived, and it is found that this length
varies non-monotonically with the strength of thermal fluctuations. In the weak
fluctuation regime, the local helical structure is preserved and the
statistical properties are dominated by long wavelength bending and torsion
modes. As the amplitude of fluctuations is increased, the helix ``melts'' and
all memory of intrinsic helical structure is lost. Spontaneous twist of the
cross--section leads to resonant dependence of the persistence length on the
twist rate.Comment: 5 figure
Level-Spacing Distributions and the Bessel Kernel
The level spacing distributions which arise when one rescales the Laguerre or
Jacobi ensembles of hermitian matrices is studied. These distributions are
expressible in terms of a Fredholm determinant of an integral operator whose
kernel is expressible in terms of Bessel functions of order . We derive
a system of partial differential equations associated with the logarithmic
derivative of this Fredholm determinant when the underlying domain is a union
of intervals. In the case of a single interval this Fredholm determinant is a
Painleve tau function.Comment: 18 pages, resubmitted to make postscript compatible, no changes to
manuscript conten
Statistical mechanics of triangulated ribbons
We use computer simulations and scaling arguments to investigate statistical
and structural properties of a semiflexible ribbon composed of isosceles
triangles. We study two different models, one where the bending energy is
calculated from the angles between the normal vectors of adjacent triangles,
the second where the edges are viewed as semiflexible polymers so that the
bending energy is related to the angles between the tangent vectors of
next-nearest neighbor triangles. The first model can be solved exactly whereas
the second is more involved. It was recently introduced by Liverpool and
Golestanian Phys.Rev.Lett. 80, 405 (1998), Phys.Rev.E 62, 5488 (2000) as a
model for double-stranded biopolymers such as DNA. Comparing observables such
as the autocorrelation functions of the tangent vectors and the bond-director
field, the probability distribution functions of the end-to-end distance, and
the mean squared twist we confirm the existence of local twist correlation, but
find no indications for other predicted features such as twist-stretch
coupling, kinks, or oscillations in the autocorrelation function of the
bond-director field.Comment: 10 pages, 13 figures. submitted to PRE, revised versio