17 research outputs found
Crossover from reptation to Rouse dynamics in a one-dimensional model
A simple one-dimensional model is constructed for polymer motion. It exhibits
the crossover from reptation to Rouse dynamics through gradually allowing
hernia creation and annihilation. The model is treated by the density matrix
technique which permits an accurate finite-size-scaling analysis of the
behavior of long polymers.Comment: 5 Pages RevTeX and 5 PostScript figures included (to appear in
Physical Review E
Crossover from Reptation to Rouse dynamics in the Extended Rubinstein-Duke Model
The competition between reptation and Rouse Dynamics is incorporated in the
Rubinstein-Duke model for polymer motion by extending it with sideways motions,
which cross barriers and create or annihilate hernias. Using the Density-Matrix
Renormalization-Group Method as solver of the Master Equation, the renewal time
and the diffusion coefficient are calculated as function of the length of the
chain and the strength of the sideways motion. These new types of moves have a
strong and delicate influence on the asymptotic behavior of long polymers. The
effects are analyzed as function of the chain length in terms of effective
exponents and crossover scaling functions.Comment: 16 Pages RevTeX and 13 PostScript figures included, accepted for
publication in Phys. Rev.
Reptation in the Rubinstein-Duke model: the influence of end-reptons dynamics
We investigate the Rubinstein-Duke model for polymer reptation by means of
density-matrix renormalization group techniques both in absence and presence of
a driving field. In the former case the renewal time \tau and the diffusion
coefficient D are calculated for chains up to N=150 reptons and their scaling
behavior in N is analyzed. Both quantities scale as powers of N: and with the asymptotic exponents z=3 and x=2, in agreement
with the reptation theory. For an intermediate range of lengths, however, the
data are well-fitted by some effective exponents whose values are quite
sensitive to the dynamics of the end reptons. We find 2.7 <z< 3.3 and 1.8 <x<
2.1 for the range of parameters considered and we suggest how to influence the
end reptons dynamics in order to bring out such a behavior. At finite and not
too small driving field, we observe the onset of the so-called band inversion
phenomenon according to which long polymers migrate faster than shorter ones as
opposed to the small field dynamics. For chains in the range of 20 reptons we
present detailed shapes of the reptating chain as function of the driving field
and the end repton dynamics.Comment: RevTeX 12 Pages and 14 figure
Stochastic lattice models for the dynamics of linear polymers
Linear polymers are represented as chains of hopping reptons and their motion
is described as a stochastic process on a lattice. This admittedly crude
approximation still catches essential physics of polymer motion, i.e. the
universal properties as function of polymer length. More than the static
properties, the dynamics depends on the rules of motion. Small changes in the
hopping probabilities can result in different universal behavior. In particular
the cross-over between Rouse dynamics and reptation is controlled by the types
and strength of the hoppings that are allowed. The properties are analyzed
using a calculational scheme based on an analogy with one-dimensional spin
systems. It leads to accurate data for intermediately long polymers. These are
extrapolated to arbitrarily long polymers, by means of finite-size-scaling
analysis. Exponents and cross-over functions for the renewal time and the
diffusion coefficient are discussed for various types of motion.Comment: 60 pages, 19 figure
Coexistence of excited states in confined Ising systems
Using the density-matrix renormalization-group method we study the
two-dimensional Ising model in strip geometry. This renormalization scheme
enables us to consider the system up to the size 300 x infinity and study the
influence of the bulk magnetic field on the system at full range of
temperature. We have found out the crossover in the behavior of the correlation
length on the line of coexistence of the excited states. A detailed study of
scaling of this line is performed. Our numerical results support and specify
previous conclusions by Abraham, Parry, and Upton based on the related bubble
model.Comment: 4 Pages RevTeX and 4 PostScript figures included; the paper has been
rewritten without including new result
Cumulant ratios and their scaling functions for Ising systems in strip geometries
We calculate the fourth-order cumulant ratio (proposed by Binder) for the
two-dimensional Ising model in a strip geometry L x oo. The Density Matrix
Renormalization Group method enables us to consider typical open boundary
conditions up to L=200. Universal scaling functions of the cumulant ratio are
determined for strips with parallel as well as opposing surface fields.Comment: 4 pages, RevTex, one .eps figure; references added, format change
Effect of Gravity and Confinement on Phase Equilibria: A Density Matrix Renormalization Approach
The phase diagram of the 2D Ising model confined between two infinite walls
and subject to opposing surface fields and to a bulk "gravitational" field is
calculated by means of density matrix renormalization methods. In absence of
gravity two phase coexistence is restricted to temperatures below the wetting
temperature. We find that gravity restores the two phase coexistence up to the
bulk critical temperature, in agreement with previous mean-field predictions.
We calculate the exponents governing the finite size scaling in the temperature
and in the gravitational field directions. The former is the exponent which
describes the shift of the critical temperature in capillary condensation. The
latter agrees, for large surface fields, with a scaling assumption of Van
Leeuwen and Sengers. Magnetization profiles in the two phase and in the single
phase region are calculated. The profiles in the single phase region, where an
interface is present, agree well with magnetization profiles calculated from a
simple solid-on-solid interface hamiltonian.Comment: 4 pages, RevTeX and 4 PostScript figures included. Final version as
published. To appear in Phys. Rev. Let
Crossover behavior for long reptating polymers
We analyze the Rubinstein-Duke model for polymer reptation by means of
density matrix renormalization techniques. We find a crossover behavior for a
series of quantities as function of the polymer length. The crossover length
may become very large if the mobility of end groups is small compared to that
of the internal reptons. Our results offer an explanation to a controversy
between theory, experiments and simulations on the leading and subleading
scaling behavior of the polymer renewal time and diffusion constant.Comment: 4 Pages, RevTeX, and 4 PostScript figures include