156 research outputs found
Two-dimensional Copolymers and Multifractality: Comparing Perturbative Expansions, MC Simulations, and Exact Results
We analyze the scaling laws for a set of two different species of long
flexible polymer chains joined together at one of their extremities (copolymer
stars) in space dimension D=2. We use a formerly constructed field-theoretic
description and compare our perturbative results for the scaling exponents with
recent conjectures for exact conformal scaling dimensions derived by a
conformal invariance technique in the context of D=2 quantum gravity. A simple
MC simulation brings about reasonable agreement with both approaches. We
analyse the remarkable multifractal properties of the spectrum of scaling
exponents.Comment: 5 page
Entropy-induced separation of star polymers in porous media
We present a quantitative picture of the separation of star polymers in a
solution where part of the volume is influenced by a porous medium. To this
end, we study the impact of long-range-correlated quenched disorder on the
entropy and scaling properties of -arm star polymers in a good solvent. We
assume that the disorder is correlated on the polymer length scale with a
power-law decay of the pair correlation function . Applying
the field-theoretical renormalization group approach we show in a double
expansion in and that there is a range of
correlation strengths for which the disorder changes the scaling
behavior of star polymers. In a second approach we calculate for fixed space
dimension and different values of the correlation parameter the
corresponding scaling exponents that govern entropic effects. We
find that , the deviation of from its mean field value
is amplified by the disorder once we increase beyond a threshold. The
consequences for a solution of diluted chain and star polymers of equal
molecular weight inside a porous medium are: star polymers exert a higher
osmotic pressure than chain polymers and in general higher branched star
polymers are expelled more strongly from the correlated porous medium.
Surprisingly, polymer chains will prefer a stronger correlated medium to a less
or uncorrelated medium of the same density while the opposite is the case for
star polymers.Comment: 14 pages, 7 figure
Enhancing Robustness and Immunization in geographical networks
We find that different geographical structures of networks lead to varied
percolation thresholds, although these networks may have similar abstract
topological structures. Thus, the strategies for enhancing robustness and
immunization of a geographical network are proposed. Using the generating
function formalism, we obtain the explicit form of the percolation threshold
for networks containing arbitrary order cycles. For 3-cycles, the
dependence of on the clustering coefficients is ascertained. The analysis
substantiates the validity of the strategies with an analytical evidence.Comment: 6 pages, 8 figure
Multifractality of Brownian motion near absorbing polymers
We characterize the multifractal behavior of Brownian motion in the vicinity
of an absorbing star polymer. We map the problem to an O(M)-symmetric
phi^4-field theory relating higher moments of the Laplacian field of Brownian
motion to corresponding composite operators. The resulting spectra of scaling
dimensions of these operators display the convexity properties which are
necessarily found for multifractal scaling but unusual for power of field
operators in field theory. Using a field-theoretic renormalization group
approach we obtain the multifractal spectrum for absorbtion at the core of a
polymer star as an asymptotic series. We evaluate these series using
resummation techniques.Comment: 18 pages, revtex, 6 ps-figure
Star copolymers in porous environments: scaling and its manifestations
We consider star polymers, consisting of two different polymer species, in a
solvent subject to quenched correlated structural obstacles. We assume that the
disorder is correlated with a power-law decay of the pair correlation function
g(x)\sim x^{-a}. Applying the field-theoretical renormalization group approach
in d dimensions, we analyze different scenarios of scaling behavior working to
first order of a double \epsilon=4-d, \delta=4-a expansion. We discuss the
influence of the correlated disorder on the resulting scaling laws and possible
manifestations such as diffusion controlled reactions in the vicinity of
absorbing traps placed on polymers as well as the effective short-distance
interaction between star copolymers.Comment: 13 pages, 3 figure
Two-Dimensional Copolymers and Exact Conformal Multifractality
We consider in two dimensions the most general star-shaped copolymer, mixing
random (RW) or self-avoiding walks (SAW) with specific interactions thereof.
Its exact bulk or boundary conformal scaling dimensions in the plane are all
derived from an algebraic structure existing on a random lattice (2D quantum
gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW
are conformal dimensions of certain star copolymers, here calculated exactly as
non rational algebraic numbers. The associated multifractal function f(alpha)
are found to be identical for a random walk or a SAW in 2D. These are the first
examples of exact conformal multifractality in two dimensions.Comment: 4 pages, 2 figures, revtex, to appear in Phys. Rev. Lett., January
199
Polydisperse star polymer solutions
We analyze the effect of polydispersity in the arm number on the effective
interactions, structural correlations and the phase behavior of star polymers
in a good solvent. The effective interaction potential between two star
polymers with different arm numbers is derived using scaling theory. The
resulting expression is tested against monomer-resolved molecular dynamics
simulations. We find that the theoretical pair potential is in agreement with
the simulation data in a much wider polydispersity range than other proposed
potentials. We then use this pair potential as an input in a many-body theory
to investigate polydispersity effects on the structural correlations and the
phase diagram of dense star polymer solutions. In particular we find that a
polydispersity of 10%, which is typical in experimental samples, does not
significantly alter previous findings for the phase diagram of monodisperse
solutions.Comment: 14 pages, 7 figure
Wavelet treatment of the intra-chain correlation functions of homopolymers in dilute solutions
Discrete wavelets are applied to parametrization of the intra-chain two-point
correlation functions of homopolymers in dilute solutions obtained from Monte
Carlo simulation. Several orthogonal and biorthogonal basis sets have been
investigated for use in the truncated wavelet approximation. Quality of the
approximation has been assessed by calculation of the scaling exponents
obtained from des Cloizeaux ansatz for the correlation functions of
homopolymers with different connectivities in a good solvent. The resulting
exponents are in a better agreement with those from the recent renormalisation
group calculations as compared to the data without the wavelet denoising. We
also discuss how the wavelet treatment improves the quality of data for
correlation functions from simulations of homopolymers at varied solvent
conditions and of heteropolymers.Comment: RevTeX, 19 pages, 7 PS figures. Accepted for publication in PR
Effective interactions between star polymers and colloidal particles
Using monomer-resolved Molecular Dynamics simulations and theoretical
arguments based on the radial dependence of the osmotic pressure in the
interior of a star, we systematically investigate the effective interactions
between hard, colloidal particles and star polymers in a good solvent. The
relevant parameters are the size ratio q between the stars and the colloids, as
well as the number of polymeric arms f (functionality) attached to the common
center of the star. By covering a wide range of q's ranging from zero (star
against a flat wall) up to about 0.75, we establish analytical forms for the
star-colloid interaction which are in excellent agreement with simulation
results. A modified expression for the star-star interaction for low
functionalities, f < 10 is also introduced.Comment: 37 pages, 14 figures, preprint-versio
Scaling in DNA unzipping models: denaturated loops and end-segments as branches of a block copolymer network
For a model of DNA denaturation, exponents describing the distributions of
denaturated loops and unzipped end-segments are determined by exact enumeration
and by Monte Carlo simulations in two and three dimensions. The loop
distributions are consistent with first order thermal denaturation in both
cases. Results for end-segments show a coexistence of two distinct power laws
in the relative distributions, which is not foreseen by a recent approach in
which DNA is treated as a homogeneous network of linear polymer segments. This
unexpected feature, and the discrepancies with such an approach, are explained
in terms of a refined scaling picture in which a precise distinction is made
between network branches representing single stranded and effective double
stranded segments.Comment: 8 pages, 8 figure
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