1,351 research outputs found
Polymers with Randomness: Phases and Phase Transitions
We discuss various aspects of the randomly interacting directed polymers with
emphasis on the phases and phase transition. We also discuss the behaviour of
overlaps of directed paths in a random medium.Comment: Invited talk at StatPhys, Calcutta 1995, to appear in Physica A;
REVTEX, 2 figures on request (email: [email protected]
Nonequilibrium Growth problems
We discuss the features of nonequilibrium growth problems, their scaling
description and their differences from equilibrium problems. The emphasis is on
the Kardar-Parisi-Zhang equation and the renormalization group point of view.
Some of the recent developments along these lines are mentioned.Comment: 9 pages, revtex, A brief overview as published in Current Science 77,
394 (1999
Incommensuration in quantum antiferromagnetic chain
A dimerized quantum Heisenberg or XY antiferromagnetic chain has a gap in the
spectrum. We show that a weak incommensurate modulation around a dimerized
chain produces a zero temperature quantum critical point. As the
incommensuration wavelength is varied, there is a transition to a modulated
gapless state. The critical behaviour is in the universality class of the
classical commensurate-incommensurate (Pokrovsky-Talapov) transition. An
analogous metal-insulator transition can also take place for an incommensurate
chain.Comment: 5 pages, revtex, no figures, to appear in J. Phys A Letter
Infinite number of exponents for a spin glass transition
We consider the behavior of the overlap of paths at the spin
glass transition for a directed polymer in a random medium. We show that an
infinite number of exponents is required to describe these overlaps. This is
done in an expansion without using the replica trick.Comment: Revtex, 1 postscript figure available on request (email:
[email protected]). To appear in Phys. Rev. B1 Rapid Communicatio
Dynamics of unbinding of polymers in a random medium
We have studied the aging effect on the dynamics of unbinding of a double
stranded directed polymer in a random medium. By using the Monte Carlo dynamics
of a lattice model in two dimensions, for which disorder is known to be
relevant, the unbinding dynamics is studied by allowing the bound polymer to
relax in the random medium for a waiting time and then allowing the two strands
to unbind. The subsequent dynamics is formulated in terms of the overlap of the
two strands and also the overlap of each polymer with the configuration at the
start of the unbinding process. The interrelations between the two and the
nature of the dependence on the waiting time are studied.Comment: 7 pages, latex, 3 figures, To appear in J. Chem. Phy
Reunion of Vicious Walkers: Results from -Expansion -
The anomalous exponent, , for the decay of the reunion probability
of vicious walkers, each of length , in dimensions,
is shown to come from the multiplicative renormalization constant of a
directed polymer partition function. Using renormalization group(RG) we
evaluate to . The survival probability exponent is
. For , our RG is exact and stops at .
For , the log corrections are also determined. The number of walkers that
are sure to reunite is 2 and has no expansion.Comment: No of pages: 11, 1figure on request, Revtex3,IP/BBSR/929
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 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
Finite Size Correction In A Disordered System - A New Divergence
We show that the amplitude of the finite size correction term for the th
moment of the partition function, for randomly interacting directed polymers,
diverges (on the high temperature side) as , as a critical
moment is approached. The exponent is independent of temperature but
does depend on the effective dimensionality. There is no such divergence on the
low temperature side (.Comment: 8 pages, Revtex, 5 figures. For figs, send mail to [email protected]
Co-non-solvency: Mean-field polymer theory does not describe polymer collapse transition in a mixture of two competing good solvents
Smart polymers are a modern class of polymeric materials that often exhibit
unpredictable behavior in mixtures of solvents. One such phenomenon is
co-non-solvency. Co-non-solvency occurs when two (perfectly) miscible and
competing good solvents, for a given polymer, are mixed together. As a result,
the same polymer collapses into a compact globule within intermediate mixing
ratios. More interestingly, polymer collapses when the solvent quality remains
good and even gets increasingly better by the addition of the better cosolvent.
This is a puzzling phenomenon that is driven by strong local concentration
fluctuations. Because of the discrete particle based nature of the
interactions, Flory-Huggins type mean field arguments become unsuitable. In
this work, we extend the analysis of the co-non-solvency effect presented
earlier [Nature Communications 5, 4882 (2014)]. We explain why co-non-solvency
is a generic phenomenon that can be understood by the thermodynamic treatment
of the competitive displacement of (co)solvent components. This competition can
result in a polymer collapse upon improvement of the solvent quality. Specific
chemical details are not required to understand these complex conformational
transitions. Therefore, a broad range of polymers are expected to exhibit
similar reentrant coil-globule-coil transitions in competing good solvents
Model for the unidirectional motion of a dynein molecule
Cytoplasmic dyneins transport cellular organelles by moving on a microtubule
filament. It has been found recently that depending on the applied force and
the concentration of the adenosine triphosphate (ATP) molecules, dynein's step
size varies. Based on these studies, we propose a simple model for dynein's
unidirectional motion taking into account the variations in its step size. We
study how the average velocity and the relative dispersion in the displacement
vary with the applied load. The model is amenable to further extensions by
inclusion of details associated with the structure and the processivity of the
molecule.Comment: 10 pages, 5 figure
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