1,634 research outputs found
Interacting Elastic Lattice Polymers: a Study of the Free-Energy of Globular Rings
We introduce and implement a Monte Carlo scheme to study the equilibrium
statistics of polymers in the globular phase. It is based on a model of
"interacting elastic lattice polymers" and allows a sufficiently good sampling
of long and compact configurations, an essential prerequisite to study the
scaling behaviour of free energies. By simulating interacting self-avoiding
rings at several temperatures in the collapsed phase, we estimate both the bulk
and the surface free energy. Moreover from the corresponding estimate of the
entropic exponent we provide evidence that, unlike for swollen and
-point rings, the hyperscaling relation is not satisfied for globular
rings.Comment: 8 pages; v2: typos removed, published versio
Topological and geometrical entanglement in a model of circular DNA undergoing denaturation
The linking number (topological entanglement) and the writhe (geometrical
entanglement) of a model of circular double stranded DNA undergoing a thermal
denaturation transition are investigated by Monte Carlo simulations. By
allowing the linking number to fluctuate freely in equilibrium we see that the
linking probability undergoes an abrupt variation (first-order) at the
denaturation transition, and stays close to 1 in the whole native phase. The
average linking number is almost zero in the denatured phase and grows as the
square root of the chain length, N, in the native phase. The writhe of the two
strands grows as the square root of N in both phases.Comment: 7 pages, 11 figures, revte
Phase Ordering in Nematic Liquid Crystals
We study the kinetics of the nematic-isotropic transition in a
two-dimensional liquid crystal by using a lattice Boltzmann scheme that couples
the tensor order parameter and the flow consistently. Unlike in previous
studies, we find the time dependences of the correlation function, energy
density, and the number of topological defects obey dynamic scaling laws with
growth exponents that, within the numerical uncertainties, agree with the value
1/2 expected from simple dimensional analysis. We find that these values are
not altered by the hydrodynamic flow. In addition, by examining shallow
quenches, we find that the presence of orientational disorder can inhibit
amplitude ordering.Comment: 21 pages, 14 eps figures, revte
Spinodal decomposition to a lamellar phase: effects of hydrodynamic flow
Results are presented for the kinetics of domain growth of a two-dimensional
fluid quenched from a disordered to a lamellar phase. At early times when a
Lifshitz-Slyozov mechanism is operative the growth process proceeds
logarithmically in time to a frozen state with locked-in defects. However when
hydrodynamic modes become important, or the fluid is subjected to shear, the
frustration of the system is alleviated and the size and orientation of the
lamellae attain their equilibrium values.Comment: 4 Revtex pages, 4 figures, to appear in Physical Review Letter
Ranking knots of random, globular polymer rings
An analysis of extensive simulations of interacting self-avoiding polygons on
cubic lattice shows that the frequencies of different knots realized in a
random, collapsed polymer ring decrease as a negative power of the ranking
order, and suggests that the total number of different knots realized grows
exponentially with the chain length. Relative frequencies of specific knots
converge to definite values because the free energy per monomer, and its
leading finite size corrections, do not depend on the ring topology, while a
subleading correction only depends on the crossing number of the knots.Comment: 4 pages, 5 figure
A Lattice Boltzmann Model of Binary Fluid Mixture
We introduce a lattice Boltzmann for simulating an immiscible binary fluid
mixture. Our collision rules are derived from a macroscopic thermodynamic
description of the fluid in a way motivated by the Cahn-Hilliard approach to
non-equilibrium dynamics. This ensures that a thermodynamically consistent
state is reached in equilibrium. The non-equilibrium dynamics is investigated
numerically and found to agree with simple analytic predictions in both the
one-phase and the two-phase region of the phase diagram.Comment: 12 pages + 4 eps figure
Lattice Boltzmann Algorithm for three-dimensional liquid crystal hydrodynamics
We describe a lattice Boltzmann algorithm to simulate liquid crystal
hydrodynamics in three dimensions. The equations of motion are written in terms
of a tensor order parameter. This allows both the isotropic and the nematic
phases to be considered. Backflow effects and the hydrodynamics of topological
defects are naturally included in the simulations, as are viscoelastic effects
such as shear-thinning and shear-banding. We describe the implementation of
velocity boundary conditions and show that the algorithm can be used to
describe optical bounce in twisted nematic devices and secondary flow in
sheared nematics with an imposed twist.Comment: 12 pages, 3 figure
Rheology of cholesteric blue phases
Blue phases of cholesteric liquid crystals offer a spectacular example of
naturally occurring disclination line networks. Here we numerically solve the
hydrodynamic equations of motion to investigate the response of three types of
blue phases to an imposed Poiseuille flow. We show that shear forces bend and
twist and can unzip the disclination lines. Under gentle forcing the network
opposes the flow and the apparent viscosity is significantly higher than that
of an isotropic liquid. With increased forcing we find strong shear thinning
corresponding to the disruption of the defect network. As the viscosity starts
to drop, the imposed flow sets the network into motion. Disclinations break-up
and re-form with their neighbours in the flow direction. This gives rise to
oscillations in the time-dependent measurement of the average stress.Comment: 4 pages, 4 figure
- âŠ