arXiv subjects

Andrzej Drzewinski

Publications and source records attributed to Andrzej Drzewinski.

14 recordsLinked to original sources

arXiv2010

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.

cond-mat.stat-mech↗

arXiv2008

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.

cond-mat.stat-mech↗

arXiv2006

Crossover from Reptation to Rouse dynamics in the Cage Model

The two-dimensional cage model for polymer motion is discussed with an emphasis on the effect of sideways motions, which cross the barriers imposed by the lattice. Using the Density Matrix Method as a solver of the Master Equation, the renewal time and the diffusion coefficient are calculated as a function of the strength of the barrier crossings. A strong crossover influence of the barrier crossings is found and it is analyzed in terms of effective exponents for a given chain length. The crossover scaling functions and the crossover scaling exponents are calculated.

cond-mat.stat-mech↗

arXiv2006

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.

cond-mat.stat-mech↗

arXiv2006

Exact Solution for a 1-dimensional model for Reptation

We discuss the exact solution for the properties of the recently introduced ``necklace'' model for reptation. The solution gives the drift velocity, diffusion constant and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.

cond-mat.stat-mech↗

arXiv2004

Scaling in the Rubinstein-Duke Model for Reptation

We consider an arbitrarily charged polymer driven by a weak field through a gel according to the rules of the Rubinstein-Duke model. The probability distribution in the stationary state is related to that of the model in which only the head is charged. Thereby drift velocity, diffusion constant and orientation of any charged polymers are expressed in terms of those of the central model. Mapping the problem on a random walk of a tagged particle along a one-dimenional chain, leads to a unified scaling expression for the local orientation. It provides also an elucidation of the role of corrections to scaling.

cond-mat.stat-mech↗

arXiv2003

Polymer Dynamics in Repton Model at Large Fields

Polymer dynamics at large fields in Rubinstein-Duke repton model is investigated theoretically. Simple diagrammatic approach and analogy with asymmetric simple exclusion models are used to analyze the reptation dynamics of polymers. It is found that for polyelectrolytes the drift velocity decreases exponentially as a function of the external field with an exponent depending on polymer size and parity, while for polyampholytes the drift velocity is independent of polymer chain size. However, for polymers, consisting of charged and neutral blocks, the drift velocity approaches the constant limit which is determined by the size of the neutral block. The theoretical arguments are supported by extensive numerical calculations by means of density-matrix renormalization group techniques.

cond-mat.stat-mech↗

arXiv2002

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 τand 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: $τ\sim N^z$ and $D \sim 1/N^x$ 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.

cond-mat.stat-mech↗

arXiv2000

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.

cond-mat.stat-mech↗

arXiv2000

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.

cond-mat.stat-mech↗

arXiv1999

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.

cond-mat↗

arXiv1998

Anomalous corrections to the Kelvin equation at complete wetting

We consider an Ising model confined in an $L \times \infty$ geometry with identical surface fields at the boundaries. According to the Kelvin equation the bulk coexistence field scales as 1/L for large L; thermodynamics and scaling arguments predict higher order corrections of the type $1/L^2$ and $1/L^{5/3}$ at partial and complete wetting respectively. Our numerical results, obtained by density-matrix renormalization techniques for systems of widths up to L = 144, are in agreement with a $1/L^2$ correction in the partial wet regime. However at complete wetting we find a large range of surface fields and temperatures with a correction to scaling of type $1/L^{4/3}$. We show that this term is generated by a {\it thin} wetting layer whose free energy is dominated by the contacts with the wall. For $L$ sufficiently large we expect a crossover to a $1/L^{5/3}$ correction as predicted by the theory for a {\it thick} wetting layer. This crossover is indeed found in a solid-on-solid model which provides a simplified description of the wetting layer and allows the study of much larger systems than those available in a density-matrix renormalization calculation.

cond-mat.stat-mech↗

arXiv1998

Critical point shift in a fluid confined between opposing walls

The properties of a fluid, or Ising magnet, confined in a $L \times \infty$ geometry with opposing surface fields at the walls are studied by density matrix renormalization techniques. In particular we focus on the effect of gravity on the system, which is modeled by a bulk field whose strength varies linearly with the distance from the walls. It is well known that in the absence of gravity phase coexistence is restricted to temperatures below the wetting temperature. We find that gravity restores phase coexistence up to the bulk critical temperature, in agreement with previous mean field results. A detailed study of the scaling to the critical point, as $L \to \infty$, is performed. The temperature shift scales as $1/L^{y_T}$, while the gravitational constant scales as $1/L^{1+y_H}$, with $y_T$ and $y_H$ the bulk thermal and magnetic exponents respectively. For weak surface fields and $L$ not too large, we also observe a regime where the gravitational constant scales as $1/L^{1+y_H - Δ_1 y_T}$ ($Δ_1$ is the surface gap exponent) with a crossover, for sufficiently large $L$, to a scaling of type $1/L^{1+y_H}$.

cond-mat.stat-mech↗

arXiv1997

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.

cond-mat.stat-mech↗