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 $\alpha-2$ we provide evidence that, unlike for swollen and $\Theta$-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

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