129 research outputs found
Phases and Transitions in Phantom Nematic Elastomer Membranes
Motivated by recently discovered unusual properties of bulk nematic
elastomers, we study a phase diagram of liquid-crystalline polymerized phantom
membranes, focusing on in-plane nematic order. We predict that such membranes
should enerically exhibit five phases, distinguished by their conformational
and in-plane orientational properties, namely isotropic-crumpled,
nematic-crumpled, isotropic-flat, nematic-flat and nematic-tubule phases. In
the nematic-tubule phase, the membrane is extended along the direction of {\em
spontaneous} nematic order and is crumpled in the other. The associated
spontaneous symmetries breaking guarantees that the nematic-tubule is
characterized by a conformational-orientational soft (Goldstone) mode and the
concomitant vanishing of the in-plane shear modulus. We show that long-range
orientational order of the nematic-tubule is maintained even in the presence of
harmonic thermal luctuations. However, it is likely that tubule's elastic
properties are ualitatively modified by these fluctuations, that can be studied
using a nonlinear elastic theory for the nematic tubule phase that we derive at
the end of this paper.Comment: 12 pages, 4 eps figures. To appear in PR
The shape of invasion perclation clusters in random and correlated media
The shape of two-dimensional invasion percolation clusters are studied
numerically for both non-trapping (NTIP) and trapping (TIP) invasion
percolation processes. Two different anisotropy quantifiers, the anisotropy
parameter and the asphericity are used for probing the degree of anisotropy of
clusters. We observe that in spite of the difference in scaling properties of
NTIP and TIP, there is no difference in the values of anisotropy quantifiers of
these processes. Furthermore, we find that in completely random media, the
invasion percolation clusters are on average slightly less isotropic than
standard percolation clusters. Introducing isotropic long-range correlations
into the media reduces the isotropy of the invasion percolation clusters. The
effect is more pronounced for the case of persisting long-range correlations.
The implication of boundary conditions on the shape of clusters is another
subject of interest. Compared to the case of free boundary conditions, IP
clusters of conventional rectangular geometry turn out to be more isotropic.
Moreover, we see that in conventional rectangular geometry the NTIP clusters
are more isotropic than TIP clusters
Fluctuation-Dissipation Theorem for the Microcanonical Ensemble
A derivation of the Fluctuation-Dissipation Theorem for the microcanonical
ensemble is presented using linear response theory. The theorem is stated as a
relation between the frequency spectra of the symmetric correlation and
response functions. When the system is not in the thermodinamic limit, this
result can be viewed as an extension of the fluctuation-dissipation relations
to a situation where dynamical fluctuations determine the response. Therefore,
the relation presented here between equilibrium fluctuations and response can
have a very different physical nature from the usual one in the canonical
ensemble. These considerations imply that the Fluctuation-Dissipation Theorem
is not restricted to the context of thermal equilibrium, where it is usually
derived. Dispersion relations and sum rules are also obtained and discussed in
the present case. Although analogous to the Kramers-Kronig relations, they are
not related to the frequency spectrum but to the energy dependence of the
response function.Comment: 15 pages, v3: final version, new text added, new reference
Conformations of confined biopolymers
Nanoscale and microscale confinement of biopolymers naturally occurs in cells
and has been recently achieved in artificial structures designed for
nanotechnological applications. Here, we present an extensive theoretical
investigation of the conformations and shape of a biopolymer with varying
stiffness confined to a narrow channel. Combining scaling arguments, analytical
calculations, and Monte Carlo simulations, we identify various scaling regimes
where master curves quantify the functional dependence of the polymer
conformations on the chain stiffness and strength of confinement.Comment: 5 pages, 4 figures, minor correction
A New Phase of Tethered Membranes: Tubules
We show that fluctuating tethered membranes with {\it any} intrinsic
anisotropy unavoidably exhibit a new phase between the previously predicted
``flat'' and ``crumpled'' phases, in high spatial dimensions where the
crumpled phase exists. In this new "tubule" phase, the membrane is crumpled in
one direction but extended nearly straight in the other. Its average thickness
is with the intrinsic size of the membrane. This phase
is more likely to persist down to than the crumpled phase. In Flory
theory, the universal exponent , which we conjecture is an exact
result. We study the elasticity and fluctuations of the tubule state, and the
transitions into it.Comment: 4 pages, self-unpacking uuencoded compressed postscript file with
figures already inside text; unpacking instructions are at the top of file.
To appear in Phys. Rev. Lett. November (1995
Effects of Self-Avoidance on the Tubular Phase of Anisotropic Membranes
We study the tubular phase of self-avoiding anisotropic membranes. We discuss
the renormalizability of the model Hamiltonian describing this phase and derive
from a renormalization group equation some general scaling relations for the
exponents of the model. We show how particular choices of renormalization
factors reproduce the Gaussian result, the Flory theory and the Gaussian
Variational treatment of the problem. We then study the perturbative
renormalization to one loop in the self-avoiding parameter using dimensional
regularization and an epsilon-expansion about the upper critical dimension, and
determine the critical exponents to first order in epsilon.Comment: 19 pages, TeX, uses Harvmac. Revised Title and updated references: to
appear in Phys. Rev.
Folding of the Triangular Lattice with Quenched Random Bending Rigidity
We study the problem of folding of the regular triangular lattice in the
presence of a quenched random bending rigidity + or - K and a magnetic field h
(conjugate to the local normal vectors to the triangles). The randomness in the
bending energy can be understood as arising from a prior marking of the lattice
with quenched creases on which folds are favored. We consider three types of
quenched randomness: (1) a ``physical'' randomness where the creases arise from
some prior random folding; (2) a Mattis-like randomness where creases are
domain walls of some quenched spin system; (3) an Edwards-Anderson-like
randomness where the bending energy is + or - K at random independently on each
bond. The corresponding (K,h) phase diagrams are determined in the hexagon
approximation of the cluster variation method. Depending on the type of
randomness, the system shows essentially different behaviors.Comment: uses harvmac (l), epsf, 17 figs included, uuencoded, tar compresse
Folding transition of the triangular lattice in a discrete three--dimensional space
A vertex model introduced by M. Bowick, P. Di Francesco, O. Golinelli, and E.
Guitter (cond-mat/9502063) describing the folding of the triangular lattice
onto the face centered cubic lattice has been studied in the hexagon
approximation of the cluster variation method. The model describes the
behaviour of a polymerized membrane in a discrete three--dimensional space. We
have introduced a curvature energy and a symmetry breaking field and studied
the phase diagram of the resulting model. By varying the curvature energy
parameter, a first-order transition has been found between a flat and a folded
phase for any value of the symmetry breaking field.Comment: 11 pages, latex file, 2 postscript figure
Folding transitions of the triangular lattice with defects
A recently introduced model describing the folding of the triangular lattice
is generalized allowing for defects in the lattice and written as an Ising
model with nearest-neighbor and plaquette interactions on the honeycomb
lattice. Its phase diagram is determined in the hexagon approximation of the
cluster variation method and the crossover from the pure Ising to the pure
folding model is investigated, obtaining a quite rich structure with several
multicritical points. Our results are in very good agreement with the available
exact ones and extend a previous transfer matrix study.Comment: 16 pages, latex, 5 postscript figure
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