146 research outputs found
Dragging a polymer chain into a nanotube and subsequent release
We present a scaling theory and Monte Carlo (MC) simulation results for a
flexible polymer chain slowly dragged by one end into a nanotube. We also
describe the situation when the completely confined chain is released and
gradually leaves the tube. MC simulations were performed for a self-avoiding
lattice model with a biased chain growth algorithm, the pruned-enriched
Rosenbluth method. The nanotube is a long channel opened at one end and its
diameter is much smaller than the size of the polymer coil in solution. We
analyze the following characteristics as functions of the chain end position
inside the tube: the free energy of confinement, the average end-to-end
distance, the average number of imprisoned monomers, and the average stretching
of the confined part of the chain for various values of and for the number
of monomers in the chain, . We show that when the chain end is dragged by a
certain critical distance into the tube, the polymer undergoes a
first-order phase transition whereby the remaining free tail is abruptly sucked
into the tube. This is accompanied by jumps in the average size, the number of
imprisoned segments, and in the average stretching parameter. The critical
distance scales as . The transition takes place when
approximately 3/4 of the chain units are dragged into the tube. The theory
presented is based on constructing the Landau free energy as a function of an
order parameter that provides a complete description of equilibrium and
metastable states. We argue that if the trapped chain is released with all
monomers allowed to fluctuate, the reverse process in which the chain leaves
the confinement occurs smoothly without any jumps. Finally, we apply the theory
to estimate the lifetime of confined DNA in metastable states in nanotubes.Comment: 13pages, 14figure
Screening by symmetry of long-range hydrodynamic interactions of polymers confined in sheets
Hydrodynamic forces may significantly affect the motion of polymers. In
sheet-like cavities, such as the cell's cytoplasm and microfluidic channels,
the hydrodynamic forces are long-range. It is therefore expected that that
hydrodynamic interactions will dominate the motion of polymers in sheets and
will be manifested by Zimm-like scaling. Quite the opposite, we note here that
although the hydrodynamic forces are long-range their overall effect on the
motion of polymers vanishes due to the symmetry of the two-dimensional flow. As
a result, the predicted scaling of experimental observables such as the
diffusion coefficient or the rotational diffusion time is Rouse-like, in accord
with recent experiments. The effective screening validates the use of the
non-interacting blobs picture for polymers confined in a sheet.Comment: http://www.weizmann.ac.il/complex/tlusty/papers/Macromolecules2006.pdf
http://pubs.acs.org/doi/abs/10.1021/ma060251
Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional -Model: Autocorrelations and Interface Tension
We discuss the recently proposed multicanonical multigrid Monte Carlo method
and apply it to the scalar -model on a square lattice. To investigate
the performance of the new algorithm at the field-driven first-order phase
transitions between the two ordered phases we carefully analyze the
autocorrelations of the Monte Carlo process. Compared with standard
multicanonical simulations a real-time improvement of about one order of
magnitude is established. The interface tension between the two ordered phases
is extracted from high-statistics histograms of the magnetization applying
histogram reweighting techniques.Comment: 49 pp. Latex incl. 14 figures (Fig.7 not included, sorry) as
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Speckle from phase ordering systems
The statistical properties of coherent radiation scattered from
phase-ordering materials are studied in detail using large-scale computer
simulations and analytic arguments. Specifically, we consider a two-dimensional
model with a nonconserved, scalar order parameter (Model A), quenched through
an order-disorder transition into the two-phase regime. For such systems it is
well established that the standard scaling hypothesis applies, consequently the
average scattering intensity at wavevector _k and time t' is proportional to a
scaling function which depends only on a rescaled time, t ~ |_k|^2 t'. We find
that the simulated intensities are exponentially distributed, with the
time-dependent average well approximated using a scaling function due to Ohta,
Jasnow, and Kawasaki. Considering fluctuations around the average behavior, we
find that the covariance of the scattering intensity for a single wavevector at
two different times is proportional to a scaling function with natural
variables mt = |t_1 - t_2| and pt = (t_1 + t_2)/2. In the asymptotic large-pt
limit this scaling function depends only on z = mt / pt^(1/2). For small values
of z, the scaling function is quadratic, corresponding to highly persistent
behavior of the intensity fluctuations. We empirically establish a connection
between the intensity covariance and the two-time, two-point correlation
function of the order parameter. This connection allows sensitive testing,
either experimental or numerical, of existing theories for two-time
correlations in systems undergoing order-disorder phase transitions. Comparison
between theory and our numerical results requires no adjustable parameters.Comment: 18 pgs RevTeX, to appear in PR
Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model
This paper describes the application of finite-size scaling concepts to
domain growth in systems with a non-conserved order parameter. A finite-size
scaling ansatz for the time-dependent order parameter distribution function is
proposed, and tested with extensive Monte-Carlo simulations of domain growth in
the 2-D spin-flip kinetic Ising model. The scaling properties of the
distribution functions serve to elucidate the configurational self-similarity
that underlies the dynamic scaling picture. Moreover, it is demonstrated that
the application of finite-size-scaling techniques facilitates the accurate
determination of the bulk growth exponent even in the presence of strong
finite-size effects, the scale and character of which are graphically exposed
by the order parameter distribution function. In addition it is found that one
commonly used measure of domain size--the scaled second moment of the
magnetisation distribution--belies the full extent of these finite-size
effects.Comment: 13 pages, Latex. Figures available on request. Rep #9401
Phonon Localization in One-Dimensional Quasiperiodic Chains
Quasiperiodic long range order is intermediate between spatial periodicity
and disorder, and the excitations in 1D quasiperiodic systems are believed to
be transitional between extended and localized. These ideas are tested with a
numerical analysis of two incommensurate 1D elastic chains: Frenkel-Kontorova
(FK) and Lennard-Jones (LJ). The ground state configurations and the
eigenfrequencies and eigenfunctions for harmonic excitations are determined.
Aubry's "transition by breaking the analyticity" is observed in the ground
state of each model, but the behavior of the excitations is qualitatively
different. Phonon localization is observed for some modes in the LJ chain on
both sides of the transition. The localization phenomenon apparently is
decoupled from the distribution of eigenfrequencies since the spectrum changes
from continuous to Cantor-set-like when the interaction parameters are varied
to cross the analyticity--breaking transition. The eigenfunctions of the FK
chain satisfy the "quasi-Bloch" theorem below the transition, but not above it,
while only a subset of the eigenfunctions of the LJ chain satisfy the theorem.Comment: This is a revised version to appear in Physical Review B; includes
additional and necessary clarifications and comments. 7 pages; requires
revtex.sty v3.0, epsf.sty; includes 6 EPS figures. Postscript version also
available at
http://lifshitz.physics.wisc.edu/www/koltenbah/koltenbah_homepage.htm
Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: Molecular Dynamics Simulation
The scission kinetics of bottle-brush molecules in solution and on an
adhesive substrate is modeled by means of Molecular Dynamics simulation with
Langevin thermostat. Our macromolecules comprise a long flexible polymer
backbone with segments, consisting of breakable bonds, along with two side
chains of length , tethered to each segment of the backbone. In agreement
with recent experiments and theoretical predictions, we find that bond cleavage
is significantly enhanced on a strongly attractive substrate even though the
chemical nature of the bonds remains thereby unchanged.
We find that the mean bond life time decreases upon adsorption by
more than an order of magnitude even for brush molecules with comparatively
short side chains $N=1 \div 4$. The distribution of scission probability along
the bonds of the backbone is found to be rather sensitive regarding the
interplay between length and grafting density of side chains. The life time
declines with growing contour length as ,
and with side chain length as . The probability
distribution of fragment lengths at different times agrees well with
experimental observations. The variation of the mean length of the
fragments with elapsed time confirms the notion of the thermal degradation
process as a first order reaction.Comment: 15 pages, 7 figure
Early Stages of Homopolymer Collapse
Interest in the protein folding problem has motivated a wide range of
theoretical and experimental studies of the kinetics of the collapse of
flexible homopolymers. In this Paper a phenomenological model is proposed for
the kinetics of the early stages of homopolymer collapse following a quench
from temperatures above to below the theta temperature. In the first stage,
nascent droplets of the dense phase are formed, with little effect on the
configurations of the bridges that join them. The droplets then grow by
accreting monomers from the bridges, thus causing the bridges to stretch.
During these two stages the overall dimensions of the chain decrease only
weakly. Further growth of the droplets is accomplished by the shortening of the
bridges, which causes the shrinking of the overall dimensions of the chain. The
characteristic times of the three stages respectively scale as the zeroth, 1/5
and 6/5 power of the the degree of polymerization of the chain.Comment: 11 pages, 3 figure
A review of Monte Carlo simulations of polymers with PERM
In this review, we describe applications of the pruned-enriched Rosenbluth
method (PERM), a sequential Monte Carlo algorithm with resampling, to various
problems in polymer physics. PERM produces samples according to any given
prescribed weight distribution, by growing configurations step by step with
controlled bias, and correcting "bad" configurations by "population control".
The latter is implemented, in contrast to other population based algorithms
like e.g. genetic algorithms, by depth-first recursion which avoids storing all
members of the population at the same time in computer memory. The problems we
discuss all concern single polymers (with one exception), but under various
conditions: Homopolymers in good solvents and at the point, semi-stiff
polymers, polymers in confining geometries, stretched polymers undergoing a
forced globule-linear transition, star polymers, bottle brushes, lattice
animals as a model for randomly branched polymers, DNA melting, and finally --
as the only system at low temperatures, lattice heteropolymers as simple models
for protein folding. PERM is for some of these problems the method of choice,
but it can also fail. We discuss how to recognize when a result is reliable,
and we discuss also some types of bias that can be crucial in guiding the
growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011
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