154 research outputs found
Flory Exponents from a Self-Consistent Renormalization Group
The wandering exponent for an isotropic polymer is predicted remarkably
well by a simple argument due to Flory. By considering oriented polymers living
in a one-parameter family of background tangent fields, we are able to relate
the wandering exponent to the exponent in the background field through an
-expansion. We then choose the background field to have the same
correlations as the individual polymer, thus self-consistently solving for
. We find for and for , which is
exactly the Flory result.Comment: 11 pages, Plain Tex (macros included), IASSNS-HEP-93/1
Smectic Order in Double-Twist Cylinders
I propose a double-twist texture with local smectic order, which may have
been seen in recent experiments. As in the Renn-Lubensky TGB phase, the smectic
order is broken only through a lattice of screw dislocations. A melted lattice
of screw dislocations can produce a double-twist texture as can an unmelted
lattice. In the latter case I show that geometry only allows for certain angles
between smectic regions. I discuss the possibility of connecting these
double-twist tubes together to form a smectic blue phase.Comment: 12 pages, plain TeX (macros included), 5 postscript figures
(included). Revised version has some more text and a new figure. To appear in
J. Phys. II France (1997
Poisson Bracket Formulation of Nematic Polymer Dynamics
We formulate the dynamical theory of nematic polymers, starting from a
microscopic Poisson bracket approach. We find that the Poisson bracket between
the nematic director and momentum depends on the (Maier-Saupe) order parameter
of the nematic phase. We use this to derive reactive couplings of the nematic
director to the strain rates. Additionally, we find that local dynamics breaks
down as the polymers begin to overlap. We offer a physical picture for both
results.Comment: Harvmac, 17 pages, 1 postscript figur
Local Writhing Dynamics
We present an alternative local definition of the writhe of a self-avoiding
closed loop which differs from the traditional non-local definition by an
integer. When studying dynamics this difference is immaterial. We employ a
formula due to Aldinger, Klapper and Tabor for the change in writhe and propose
a set of local, link preserving dynamics in an attempt to unravel some puzzles
about actin.Comment: plain TeX, harvmac + epsf, 11 pages, 1 included eps figure. Reference
adde
Liquids with Chiral Bond Order
I describe new phases of a chiral liquid crystal with nematic and hexatic
order. I find a conical phase, similar to that of a cholesteric in an applied
magnetic field for Frank elastic constants . I discuss the role of
fluctuations in the context of this phase and the possibility of satisfying the
inequality for sufficiently long polymers. In addition I discuss the
topological constraint relating defects in the bond order field to textures of
the nematic and elucidate its physical meaning. Finally I discuss the analogy
between smectic liquid crystals and chiral hexatics and propose a
defect-riddled ground state, akin to the Renn-Lubensky twist grain boundary
phase of chiral smectics.Comment: plain TeX, 19 Pages, four figures, uufiled and included. Minor
correction and clarificatio
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