38 research outputs found
Operator Spectrum and Exact Exponents of the Fully Packed Loop Model
We develop a Coulomb gas description of the critical fluctuations in the
fully packed loop model on the honeycomb lattice. We identify the complete
operator spectrum of this model in terms of electric and magnetic {\em
vector}-charges, and we calculate the scaling dimensions of these operators
exactly. We also study the geometrical properties of loops in this model, and
we derive exact results for the fractal dimension and the loop size
distribution function. A review of the many different representations of this
model that have recently appeared in the literature, is given.Comment: 17 pages latex, 3 postscript figures, IOP style files include
Landau theory of glassy dynamics
An exact solution of a Landau model of an order-disorder transition with
activated critical dynamics is presented. The model describes a funnel-shaped
topography of the order parameter space in which the number of energy lowering
trajectories rapidly diminishes as the ordered ground-state is approached. This
leads to an asymmetry in the effective transition rates which results in a
non-exponential relaxation of the order-parameter fluctuations and a
Vogel-Fulcher-Tammann divergence of the relaxation times, typical of a glass
transition. We argue that the Landau model provides a general framework for
studying glassy dynamics in a variety of systems.Comment: 4 pages, 2 figure
A First Exposure to Statistical Mechanics for Life Scientists
Statistical mechanics is one of the most powerful and elegant tools in the
quantitative sciences. One key virtue of statistical mechanics is that it is
designed to examine large systems with many interacting degrees of freedom,
providing a clue that it might have some bearing on the analysis of the
molecules of living matter. As a result of data on biological systems becoming
increasingly quantitative, there is a concomitant demand that the models set
forth to describe biological systems be themselves quantitative. We describe
how statistical mechanics is part of the quantitative toolkit that is needed to
respond to such data. The power of statistical mechanics is not limited to
traditional physical and chemical problems and there are a host of interesting
ways in which these ideas can be applied in biology. This article reports on
our efforts to teach statistical mechanics to life science students and
provides a framework for others interested in bringing these tools to a
nontraditional audience in the life sciences.Comment: 27 pages, 16 figures. Submitted to American Journal of Physic
Force steps during viral DNA packaging?
Biophysicists and structural biologists increasingly acknowledge the role played by the mechanical properties of macromolecules as a critical element in many biological processes. This change has been brought about, in part, by the advent of single molecule biophysics techniques that have made it possible to exert piconewton forces on key macromolecules and observe their deformations at nanometer length scales, as well as to observe the mechanical action of macromolecules such as molecular motors. This has opened up immense possibilities for a new generation of mechanical investigations that will respond to such measurements in an attempt to develop a coherent theory for the mechanical behavior of macromolecules under conditions where thermal and chemical effects are on an equal footing with deterministic forces. This paper presents an application of the principles of mechanics to the problem of DNA packaging, one of the key events in the life cycle of bacterial viruses with special reference to the nature of the internal forces that are built up during the DNA packaging process
Kac-Moody Symmetries of Critical Ground States
The symmetries of critical ground states of two-dimensional lattice models
are investigated. We show how mapping a critical ground state to a model of a
rough interface can be used to identify the chiral symmetry algebra of the
conformal field theory that describes its scaling limit. This is demonstrated
in the case of the six-vertex model, the three-coloring model on the honeycomb
lattice, and the four-coloring model on the square lattice. These models are
critical and they are described in the continuum by conformal field theories
whose symmetry algebras are the , , and the
Kac-Moody algebra, respectively. Our approach is based on the
Frenkel--Kac--Segal vertex operator construction of level one Kac--Moody
algebras.Comment: 42 pages, RevTex, 14 ps figures, Submitted to Nucl. Phys. B. [FS
Stretching short biopolymers by fields and forces
We study the mechanical properties of semiflexible polymers when the contour
length of the polymer is comparable to its persistence length. We compute the
exact average end-to-end distance and shape of the polymer for different
boundary conditions, and show that boundary effects can lead to significant
deviations from the well-known long-polymer results. We also consider the case
of stretching a uniformly charged biopolymer by an electric field, for which we
compute the average extension and the average shape, which is shown to be
trumpetlike. Our results also apply to long biopolymers when thermal
fluctuations have been smoothed out by a large applied field or force.Comment: 10 pages, 7 figure
Secondary Structures in Long Compact Polymers
Compact polymers are self-avoiding random walks which visit every site on a
lattice. This polymer model is used widely for studying statistical problems
inspired by protein folding. One difficulty with using compact polymers to
perform numerical calculations is generating a sufficiently large number of
randomly sampled configurations. We present a Monte-Carlo algorithm which
uniformly samples compact polymer configurations in an efficient manner
allowing investigations of chains much longer than previously studied. Chain
configurations generated by the algorithm are used to compute statistics of
secondary structures in compact polymers. We determine the fraction of monomers
participating in secondary structures, and show that it is self averaging in
the long chain limit and strictly less than one. Comparison with results for
lattice models of open polymer chains shows that compact chains are
significantly more likely to form secondary structure.Comment: 14 pages, 14 figure
A First Exposure to Statistical Mechanics for Life Scientists: Applications to Binding
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a clue that it might have some bearing on the analysis of the molecules of living matter. As a result of data on biological systems becoming increasingly quantitative, there is a concomitant demand that the models set forth to describe biological systems be themselves quantitative. We describe how statistical mechanics is part of the quantitative toolkit that is needed to respond to such data. The power of statistical mechanics is not limited to traditional physical and chemical problems and there are a host of interesting ways in which these ideas can be applied in biology. This article reports on our efforts to teach statistical mechanics to life science students with special reference to binding problems in biology and provides a framework for others interested in bringing these tools to a nontraditional audience in the life sciences. 1 1 Does Statistical Mechanics Matter in Biology
Conformational Entropy of Compact Polymers
Exact results for the scaling properties of compact polymers on the square
lattice are obtained from an effective field theory. The entropic exponent
\gamma=117/112 is calculated, and a line of fixed points associated with
interacting chains is identified; along this line \gamma varies continuously.
Theoretical results are checked against detailed numerical transfer matrix
calculations, which also yield a precise estimate for the connective constant
\kappa=1.47280(1).Comment: 4 pages, 1 figur
Correlated quantum percolation in the lowest Landau level
Our understanding of localization in the integer quantum Hall effect is
informed by a combination of semi-classical models and percolation theory.
Motivated by the effect of correlations on classical percolation we study
numerically electron localization in the lowest Landau level in the presence of
a power-law correlated disorder potential. Careful comparisons between
classical and quantum dynamics suggest that the extended Harris criterion is
applicable in the quantum case. This leads to a prediction of new localization
quantum critical points in integer quantum Hall systems with power-law
correlated disorder potentials. We demonstrate the stability of these critical
points to addition of competing short-range disorder potentials, and discuss
possible experimental realizations.Comment: 15 pages, 12 figure