1,967 research outputs found
Bethe lattice solution of a model of SAW's with up to 3 monomers per site and no restriction
In the multiple monomers per site (MMS) model, polymeric chains are
represented by walks on a lattice which may visit each site up to K times. We
have solved the unrestricted version of this model, where immediate reversals
of the walks are allowed (RA) for K = 3 on a Bethe lattice with arbitrary
coordination number in the grand-canonical formalism. We found transitions
between a non-polymerized and two polymerized phases, which may be continuous
or discontinuous. In the canonical situation, the transitions between the
extended and the collapsed polymeric phases are always continuous. The
transition line is partly composed by tricritical points and partially by
critical endpoints, both lines meeting at a multicritical point. In the
subspace of the parameter space where the model is related to SASAW's
(self-attracting self-avoiding walks), the collapse transition is tricritical.
We discuss the relation of our results with simulations and previous Bethe and
Husimi lattice calculations for the MMS model found in the literature.Comment: 25 pages, 9 figure
Orientational correlations in confined DNA
We study how the orientational correlations of DNA confined to nanochannels
depend on the channel diameter D by means of Monte Carlo simulations and a
mean-field theory. This theory describes DNA conformations in the
experimentally relevant regime where the Flory-de Gennes theory does not apply.
We show how local correlations determine the dependence of the end-to-end
distance of the DNA molecule upon D. Tapered nanochannels provide the necessary
resolution in D to study experimentally how the extension of confined DNA
molecules depends upon D. Our experimental and theoretical results are in
qualitative agreement.Comment: Revised version including supplemental material, 7 pages, 8 figure
Leadership Statistics in Random Structures
The largest component (``the leader'') in evolving random structures often
exhibits universal statistical properties. This phenomenon is demonstrated
analytically for two ubiquitous structures: random trees and random graphs. In
both cases, lead changes are rare as the average number of lead changes
increases quadratically with logarithm of the system size. As a function of
time, the number of lead changes is self-similar. Additionally, the probability
that no lead change ever occurs decays exponentially with the average number of
lead changes.Comment: 5 pages, 3 figure
Critical Dynamics of Gelation
Shear relaxation and dynamic density fluctuations are studied within a Rouse
model, generalized to include the effects of permanent random crosslinks. We
derive an exact correspondence between the static shear viscosity and the
resistance of a random resistor network. This relation allows us to compute the
static shear viscosity exactly for uncorrelated crosslinks. For more general
percolation models, which are amenable to a scaling description, it yields the
scaling relation for the critical exponent of the shear
viscosity. Here is the thermal exponent for the gel fraction and
is the crossover exponent of the resistor network. The results on the shear
viscosity are also used in deriving upper and lower bounds on the incoherent
scattering function in the long-time limit, thereby corroborating previous
results.Comment: 34 pages, 2 figures (revtex, amssymb); revised version (minor
changes
A two-parameter random walk with approximate exponential probability distribution
We study a non-Markovian random walk in dimension 1. It depends on two
parameters eps_r and eps_l, the probabilities to go straight on when walking to
the right, respectively to the left. The position x of the walk after n steps
and the number of reversals of direction k are used to estimate eps_r and
eps_l. We calculate the joint probability distribution p_n(x,k) in closed form
and show that, approximately, it belongs to the exponential family.Comment: 12 pages, updated reference to companion paper cond-mat/060126
Charge renormalization and phase separation in colloidal suspensions
We explore the effects of counterion condensation on fluid-fluid phase
separation in charged colloidal suspensions. It is found that formation of
double layers around the colloidal particles stabilizes suspensions against
phase separation. Addition of salt, however, produces an instability which, in
principle, can lead to a fluid-fluid separation. The instability, however, is
so weak that it should be impossible to observe a fully equilibrated
coexistence experimentally.Comment: 7 pages, Europhysics Letters (in press
Scaling and Crossover to Tricriticality in Polymer Solutions
We propose a scaling description of phase separation of polymer solutions.
The scaling incorporates three universal limiting regimes: the Ising limit
asymptotically close to the critical point of phase separation, the "ideal-gas"
limit for the pure-solvent phase, and the tricritical limit for the
polymer-rich phase asymptotically close to the theta point. We have also
developed a phenomenological crossover theory based on the
near-tricritical-point Landau expansion renormalized by fluctuations. This
theory validates the proposed scaled representation of experimental data and
crossover to tricriticality.Comment: 4 pages, 3 figure
Unicyclic Components in Random Graphs
The distribution of unicyclic components in a random graph is obtained
analytically. The number of unicyclic components of a given size approaches a
self-similar form in the vicinity of the gelation transition. At the gelation
point, this distribution decays algebraically, U_k ~ 1/(4k) for k>>1. As a
result, the total number of unicyclic components grows logarithmically with the
system size.Comment: 4 pages, 2 figure
Multifractal behavior of linear polymers in disordered media
The scaling behavior of linear polymers in disordered media modelled by
self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional
percolation clusters at their critical concentrations p_c is studied. All
possible SAW configurations of N steps on a single backbone configuration are
enumerated exactly. We find that the moments of order q of the total number of
SAWs obtained by averaging over many backbone configurations display
multifractal behavior, i.e. different moments are dominated by different
subsets of the backbone. This leads to generalized coordination numbers \mu_q
and enhancement exponents \gamma_q, which depend on q. Our numerical results
suggest that the relation \mu_1 = p_ c \mu between the first moment \mu_1 and
its regular lattice counterpart \mu is valid.Comment: 11 pages, 12 postscript figures, to be published in Phys. Rev.
Elasticity near the vulcanization transition
Signatures of the vulcanization transition--amorphous solidification induced
by the random crosslinking of macromolecules--include the random localization
of a fraction of the particles and the emergence of a nonzero static shear
modulus. A semi-microscopic statistical-mechanical theory is presented of the
latter signature that accounts for both thermal fluctuations and quenched
disorder. It is found (i) that the shear modulus grows continuously from zero
at the transition, and does so with the classical exponent, i.e., with the
third power of the excess cross-link density and, quite surprisingly, (ii) that
near the transition the external stresses do not spoil the spherical symmetry
of the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change
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