883 research outputs found
Anomalous Elasticity of Polymer Cholesterics
We show that polymer cholesterics have much longer pitches than comparable
short molecule cholesterics, due to their anomalous elasticity. The pitch
of a chiral mixture with concentration near the racemic (non-chiral)
concentration diverges like with (for short molecule cholesterics ). The short molecule law is
recovered for polymers of finite molecular length once the pitch is
longer than a length that diverges like with . Our predictions could be tested by measurements of the pitch in DNA.Comment: 12 pages, Plain TeX, (1 postscript figure, compressed, uuencoded and
appended to paper), minor corrections, IASSNS-HEP-94/4
Sliding Columnar Phase of DNA-Lipid Complexes
We introduce a simple model for DNA-cationic-lipid complexes in which
galleries between planar bilayer lipid lamellae contain DNA 2D smectic lattices
that couple orientationally and positionally to lattices in neighboring
galleries. We identify a new equilibrium phase in which there are long-range
orientational but not positional correlations between DNA lattices. We discuss
properties of this new phase such as its X-ray structure factor S(r), which
exhibits unusual exp(- const.ln^2 r) behavior as a function of in-plane
separation r.Comment: This file contains 4 pages of double column text and one postscript
figure. This version includes interactions between dislocations in a given
gallery and presents an improved estimate of the decoupling temperature. It
is the published versio
Ground state properties of solid-on-solid models with disordered substrates
We study the glassy super-rough phase of a class of solid-on-solid models
with a disordered substrate in the limit of vanishing temperature by means of
exact ground states, which we determine with a newly developed minimum cost
flow algorithm. Results for the height-height correlation function are compared
with analytical and numerical predictions. The domain wall energy of a boundary
induced step grows logarithmically with system size, indicating the marginal
stability of the ground state, and the fractal dimension of the step is
estimated. The sensibility of the ground state with respect to infinitesimal
variations of the quenched disorder is analyzed.Comment: 4 pages RevTeX, 3 eps-figures include
Non-Ergodic Dynamics of the 2D Random-phase Sine-Gordon Model: Applications to Vortex-Glass Arrays and Disordered-Substrate Surfaces
The dynamics of the random-phase sine-Gordon model, which describes 2D
vortex-glass arrays and crystalline surfaces on disordered substrates, is
investigated using the self-consistent Hartree approximation. The
fluctuation-dissipation theorem is violated below the critical temperature T_c
for large time t>t* where t* diverges in the thermodynamic limit. While above
T_c the averaged autocorrelation function diverges as Tln(t), for T<T_c it
approaches a finite value q* proportional to 1/(T_c-T) as q(t) = q* -
c(t/t*)^{-\nu} (for t --> t*) where \nu is a temperature-dependent exponent. On
larger time scales t > t* the dynamics becomes non-ergodic. The static
correlations behave as Tln{x} for T>T_c and for T<T_c when x < \xi* with \xi*
proportional to exp{A/(T_c-T)}. For scales x > \xi*, they behave as (T/m)ln{x}
where m is approximately T/T_c near T_c, in general agreement with the
variational replica-symmetry breaking approach and with recent simulations of
the disordered-substrate surface. For strong- coupling the transition becomes
first-order.Comment: 12 pages in LaTeX, Figures available upon request, NSF-ITP 94-10
A variational study of the random-field XY model
A disorder-dependent Gaussian variational approach is applied to the
-dimensional ferromagnetic XY model in a random field. The randomness yields
a non extensive contribution to the variational free energy, implying a random
mass term in correlation functions. The Imry-Ma low temperature result,
concerning the existence () or absence () of long-range order is
obtained in a transparent way. The physical picture which emerges below
is that of a marginally stable mixture of domains. We also calculate within
this variational scheme, disorder dependent correlation functions, as well as
the probability distribution of the Imry-Ma domain size.Comment: 14 pages, latex fil
Sliding Phases in XY-Models, Crystals, and Cationic Lipid-DNA Complexes
We predict the existence of a totally new class of phases in weakly coupled,
three-dimensional stacks of two-dimensional (2D) XY-models. These ``sliding
phases'' behave essentially like decoupled, independent 2D XY-models with
precisely zero free energy cost associated with rotating spins in one layer
relative to those in neighboring layers. As a result, the two-point spin
correlation function decays algebraically with in-plane separation. Our
results, which contradict past studies because we include higher-gradient
couplings between layers, also apply to crystals and may explain recently
observed behavior in cationic lipid-DNA complexes.Comment: 4 pages of double column text in REVTEX format and 1 postscript
figur
Kinetic Roughening in Surfaces of Crystals Growing on Disordered Substrates
Substrate disorder effects on the scaling properties of growing crystalline
surfaces in solidification or epitaxial deposition processes are investigated.
Within the harmonic approach there is a phase transition into a low-temperature
(low-noise) superrough phase with a continuously varying dynamic exponent z>2
and a non-linear response. In the presence of the KPZ nonlinearity the disorder
causes the lattice efects to decay on large scales with an intermediate
crossover behavior. The mobility of the rough surface hes a complex dependence
on the temperature and the other physical parameters.Comment: 13 pages, 2 figures (not included). Submitted to Phys. Rev. Letts.
Use Latex twic
Nonlinear Elasticity of the Sliding Columnar Phase
The sliding columnar phase is a new liquid-crystalline phase of matter
composed of two-dimensional smectic lattices stacked one on top of the other.
This phase is characterized by strong orientational but weak positional
correlations between lattices in neighboring layers and a vanishing shear
modulus for sliding lattices relative to each other. A simplified elasticity
theory of the phase only allows intralayer fluctuations of the columns and has
three important elastic constants: the compression, rotation, and bending
moduli, , , and . The rotationally invariant theory contains
anharmonic terms that lead to long wavelength renormalizations of the elastic
constants similar to the Grinstein-Pelcovits renormalization of the elastic
constants in smectic liquid crystals. We calculate these renormalizations at
the critical dimension and find that , where is a wavenumber. The behavior of
, , and in a model that includes fluctuations perpendicular to the
layers is identical to that of the simple model with rigid layers. We use
dimensional regularization rather than a hard-cutoff renormalization scheme
because ambiguities arise in the one-loop integrals with a finite cutoff.Comment: This file contains 18 pages of double column text in REVTEX format
and 6 postscript figure
Iterated Moire Maps and Braiding of Chiral Polymer Crystals
In the hexagonal columnar phase of chiral polymers a bias towards cholesteric
twist competes with braiding along an average direction. When the chirality is
strong, screw dislocations proliferate, leading to either a tilt grain boundary
phase or a new "moire state" with twisted bond order. Polymer trajectories in
the plane perpendicular to their average direction are described by iterated
moire maps of remarkable complexity.Comment: 10 pages (plain tex) 3 figures uufiled and appende
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