Unexpected crossover dynamics of single polymer in a corrugated tube

We present molecular dynamics study of a generic (coarse-grained) model for single-polymer diffusion confined in a corrugated cylinder. For a narrow tube, i.e., diameter of the cylinder $\delta < 2.3$, the axial diffusion coefficient $D_{||}$ scales as $D_{||} \propto N^{-3/2}$, with chain length $N$, up to $N \approx 100$ then crosses over to Rouse scaling for the larger $N$ values. The $N^{-3/2}$ scaling is due to the large fluctuation of the polymer chain along its fully stretched equilibrium conformation. The stronger scaling, namely $N^{-3/2}$, is not observed for an atomistically smooth tube and/or for a cylinder with larger diameter.Comment: 10 pages, 3 figures, LaTeX, version accepted by J. Chem. Phy

Reunion of random walkers with a long range interaction: applications to polymers and quantum mechanics

We use renormalization group to calculate the reunion and survival exponents of a set of random walkers interacting with a long range $1/r^2$ and a short range interaction. These exponents are used to study the binding-unbinding transition of polymers and the behavior of several quantum problems.Comment: Revtex 3.1, 9 pages (two-column format), 3 figures. Published version (PRE 63, 051103 (2001)). Reference corrections incorporated (PRE 64, 059902 (2001) (E

Reunion of Vicious Walkers: Results from ϵ\epsilon-Expansion -

The anomalous exponent, $\eta_{p}$, for the decay of the reunion probability of $p$ vicious walkers, each of length $N$, in $d$ $(=2-\epsilon)$ dimensions, is shown to come from the multiplicative renormalization constant of a $p$ directed polymer partition function. Using renormalization group(RG) we evaluate $\eta_{p}$ to $O(\epsilon^2)$. The survival probability exponent is $\eta_{p}/2$. For $p=2$, our RG is exact and $\eta_p$ stops at $O(\epsilon)$. For $d=2$, the log corrections are also determined. The number of walkers that are sure to reunite is 2 and has no $\epsilon$ expansion.Comment: No of pages: 11, 1figure on request, Revtex3,IP/BBSR/929

Finite Size Correction In A Disordered System - A New Divergence

We show that the amplitude of the finite size correction term for the $n$th moment of the partition function, for randomly interacting directed polymers, diverges (on the high temperature side) as $(n_c - n)^{-r}$, as a critical moment $n_c$ is approached. The exponent $r$ is independent of temperature but does depend on the effective dimensionality. There is no such divergence on the low temperature side ($n>n_c)$.Comment: 8 pages, Revtex, 5 figures. For figs, send mail to [email protected]

Shocks in asymmetric simple exclusion processes of interacting particles

In this paper, we study shocks and related transitions in asymmetric simple exclusion processes of particles with nearest neighbor interactions. We consider two kinds of inter-particle interactions. In one case, the particle-hole symmetry is broken due to the interaction. In the other case, particles have an effective repulsion due to which the particle-current-density drops down near the half filling. These interacting particles move on a one dimensional lattice which is open at both the ends with injection of particles at one end and withdrawal of particles at the other. In addition to this, there are possibilities of attachments or detachments of particles to or from the lattice with certain rates. The hydrodynamic equation that involves the exact particle current-density of the particle conserving system and additional terms taking care of the attachment-detachment kinetics is studied using the techniques of boundary layer analysis.Comment: 10 pages, 8 figure

Dynamical study of the hyperextended scalar-tensor theory in the empty Bianchi type I model

The dynamics of the hyperextended scalar-tensor theory in the empty Bianchi type I model is investigated. We describe a method giving the sign of the first and second derivatives of the metric functions whatever the coupling function. Hence, we can predict if a theory gives birth to expanding, contracting, bouncing or inflationary cosmology. The dynamics of a string inspired theory without antisymetric field strength is analysed. Some exact solutions are found.Comment: 18 pages, 3 figure

Bulk and surface transitions in asymmetric simple exclusion process: Impact on boundary layers

In this paper, we study boundary-induced phase transitions in a particle non-conserving asymmetric simple exclusion process with open boundaries. Using boundary layer analysis, we show that the key signatures of various bulk phase transitions are present in the boundary layers of the density profiles. In addition, we also find possibilities of surface transitions in the low- and high- density phases. The surface transition in the low-density phase provides a more complete description of the non-equilibrium critical point found in this system.Comment: 9 pages including figure

Phase-plane analysis of driven multi-lane exclusion models

We show how a fixed point based boundary-layer analysis technique can be used to obtain the steady-state particle density profiles of driven exclusion processes on two-lane systems with open boundaries. We have considered two distinct two-lane systems. In the first, particles hop on the lanes in one direction obeying exclusion principle and there is no exchange of particles between the lanes. The hopping on one lane is affected by the particle occupancies on the other, which thereby introduces an indirect interaction among the lanes. Through a phase plane analysis of the boundary layer equation, we show why the bulk density undergoes a sharp change as the interaction between the lanes is increased. The second system involves one lane with driven exclusion process and the other with biased diffusion of particles. In contrast to the previous model, here there is a direct interaction between the lanes due to particle exchange between them. In this model, we have looked at two possible scenarios with constant (flat) and non-constant bulk profiles. The fixed point based boundary layer method provides a new perspective on several aspects including those related to maximal/minimal current phases, possibilities of shocks under very restricted boundary conditions for the flat profile but over a wide range of boundary conditions for the non-constant profile.Comment: 13 pages, 17 figure

Multi-shocks in asymmetric simple exclusions processes: Insights from fixed-point analysis of the boundary-layers

The boundary-induced phase transitions in an asymmetric simple exclusion process with inter-particle repulsion and bulk non-conservation are analyzed through the fixed points of the boundary layers. This system is known to have phases in which particle density profiles have different kinds of shocks. We show how this boundary-layer fixed-point method allows us to gain physical insights on the nature of the phases and also to obtain several quantitative results on the density profiles especially on the nature of the boundary-layers and shocks.Comment: 12 pages, 8 figure