Dewetting hydrodynamics in 1+1 dimensions

A model for the phase transition between partial wetting and dewetting of a substrate has been formulated that explicitly incorporates the hydrodynamic flow during the dewetting process in 1 + 1 dimensions. The model simulates a fluid layer of finite thickness on a substrate in coexistence with a dry part of the substrate and a gas phase above the substrate. Under nonequilibrium ''dewetting'' conditions, the front between the dry part and the wet part of the surface moves towards the wet part inducing hydrodynamic flow inside the wet layer. In more general terms, the model handles two immiscible fluids with a freely movable interface in an inhomogeneous external force field. Handling the interface by a new variant of the phase-field model, we obtain an efficient code with well-defined interfacial properties. In particular, the (free) energy can be chosen at will. We demonstrate that our model works well in the viscosity range of creeping flow and we give qualitative results for the higher Reynolds numbers. Connections to experimental realizations are discussed

A polarizable interatomic force field for TiO2_2 parameterized using density functional theory

We report a classical interatomic force field for TiO$_2$, which has been parameterized using density functional theory forces, energies, and stresses in the rutile crystal structure. The reliability of this new classical potential is tested by evaluating the structural properties, equation of state, phonon properties, thermal expansion, and some thermodynamic quantities such as entropy, free energy, and specific heat under constant volume. The good agreement of our results with {\em ab initio} calculations and with experimental data, indicates that our force-field describes the atomic interactions of TiO$_2$ in the rutile structure very well. The force field can also describe the structures of the brookite and anatase crystals with good accuracy.Comment: Accepted for publication in Phys. Rev. B; Changes from v1 include multiple minor revisions and a re-write of the description of the force field in Section II

Influence of external flows on crystal growth: numerical investigation

We use a combined phase-field/lattice-Boltzmann scheme [D. Medvedev, K. Kassner, Phys. Rev. E {\bf 72}, 056703 (2005)] to simulate non-facetted crystal growth from an undercooled melt in external flows. Selected growth parameters are determined numerically. For growth patterns at moderate to high undercooling and relatively large anisotropy, the values of the tip radius and selection parameter plotted as a function of the Peclet number fall approximately on single curves. Hence, it may be argued that a parallel flow changes the selected tip radius and growth velocity solely by modifying (increasing) the Peclet number. This has interesting implications for the availability of current selection theories as predictors of growth characteristics under flow. At smaller anisotropy, a modification of the morphology diagram in the plane undercooling versus anisotropy is observed. The transition line from dendrites to doublons is shifted in favour of dendritic patterns, which become faster than doublons as the flow speed is increased, thus rendering the basin of attraction of dendritic structures larger. For small anisotropy and Prandtl number, we find oscillations of the tip velocity in the presence of flow. On increasing the fluid viscosity or decreasing the flow velocity, we observe a reduction in the amplitude of these oscillations.Comment: 10 pages, 7 figures, accepted for Physical Review E; size of some images had to be substantially reduced in comparison to original, resulting in low qualit

Percolation and Critical Behaviour in SU(2) Gauge Theory

The paramagnetic-ferromagnetic transition in the Ising model can be described as percolation of suitably defined clusters. We have tried to extend such picture to the confinement-deconfinement transition of SU(2) pure gauge theory, which is in the same universality class of the Ising model. The cluster definition is derived by approximating SU(2) by means of Ising-like effective theories. The geometrical transition of such clusters turns out to describe successfully the thermal counterpart for two different lattice regularizations of (3+1)-d SU(2).Comment: Lattice 2000 (Finite Temperature), 4 pages, 4 figures, 2 table

Comments on Sweeny and Gliozzi dynamics for simulations of Potts models in the Fortuin-Kasteleyn representation

We compare the correlation times of the Sweeny and Gliozzi dynamics for two-dimensional Ising and three-state Potts models, and the three-dimensional Ising model for the simulations in the percolation prepresentation. The results are also compared with Swendsen-Wang and Wolff cluster dynamics. It is found that Sweeny and Gliozzi dynamics have essentially the same dynamical critical behavior. Contrary to Gliozzi's claim (cond-mat/0201285), the Gliozzi dynamics has critical slowing down comparable to that of other cluster methods. For the two-dimensional Ising model, both Sweeny and Gliozzi dynamics give good fits to logarithmic size dependences; for two-dimensional three-state Potts model, their dynamical critical exponent z is 0.49(1); the three-dimensional Ising model has z = 0.37(2).Comment: RevTeX, 4 pages, 5 figure

Simulations of a single membrane between two walls using a Monte Carlo method

Quantitative theory of interbilayer interactions is essential to interpret x-ray scattering data and to elucidate these interactions for biologically relevant systems. For this purpose Monte Carlo simulations have been performed to obtain pressure P and positional fluctuations sigma. A new method, called Fourier Monte-Carlo (FMC), that is based on a Fourier representation of the displacement field, is developed and its superiority over the standard method is demonstrated. The FMC method is applied to simulating a single membrane between two hard walls, which models a stack of lipid bilayer membranes with non-harmonic interactions. Finite size scaling is demonstrated and used to obtain accurate values for P and sigma in the limit of a large continuous membrane. The results are compared with perturbation theory approximations, and numerical differences are found in the non-harmonic case. Therefore, the FMC method, rather than the approximations, should be used for establishing the connection between model potentials and observable quantities, as well as for pure modeling purposes.Comment: 10 pages, 10 figure

Correlated percolation and the correlated resistor network

We present some exact results on percolation properties of the Ising model, when the range of the percolating bonds is larger than nearest-neighbors. We show that for a percolation range to next-nearest neighbors the percolation threshold Tp is still equal to the Ising critical temperature Tc, and present the phase diagram for this type of percolation. In addition, we present Monte Carlo calculations of the finite size behavior of the correlated resistor network defined on the Ising model. The thermal exponent t of the conductivity that follows from it is found to be t = 0.2000 +- 0.0007. We observe no corrections to scaling in its finite size behavior.Comment: 16 pages, REVTeX, 6 figures include

Thermal roughening of an SOS-model with elastic interaction

We analyze the effects of a long-ranged step-step interaction on thermal roughening within the framework of a solid-on-solid model of a crystal surface by means of Monte Carlo simulation. A repulsive step-step interaction is modeled by elastic dipoles located on sites adjacent to the steps. In order to reduce the computational effort involved in calculating interaction energy based on long-ranged potentials, we employ a multi-grid scheme. As a result of the long-range character of the step interaction, the roughening temperature increases drastically compared to a system with short-range cutoff as a consequence of anti-correlations between surface defects

Nonequilibrium relaxation of the two-dimensional Ising model: Series-expansion and Monte Carlo studies

We study the critical relaxation of the two-dimensional Ising model from a fully ordered configuration by series expansion in time t and by Monte Carlo simulation. Both the magnetization (m) and energy series are obtained up to 12-th order. An accurate estimate from series analysis for the dynamical critical exponent z is difficult but compatible with 2.2. We also use Monte Carlo simulation to determine an effective exponent, z_eff(t) = - {1/8} d ln t /d ln m, directly from a ratio of three-spin correlation to m. Extrapolation to t = infinity leads to an estimate z = 2.169 +/- 0.003.Comment: 9 pages including 2 figure

Metastable lifetimes in a kinetic Ising model: Dependence on field and system size

The lifetimes of metastable states in kinetic Ising ferromagnets are studied by droplet theory and Monte Carlo simulation, in order to determine their dependences on applied field and system size. For a wide range of fields, the dominant field dependence is universal for local dynamics and has the form of an exponential in the inverse field, modified by universal and nonuniversal power-law prefactors. Quantitative droplet-theory predictions are numerically verified, and small deviations are shown to depend nonuniversally on the details of the dynamics. We identify four distinct field intervals in which the field dependence and statistical properties of the lifetimes are different. The field marking the crossover between the weak-field regime, in which the decay is dominated by a single droplet, and the intermediate-field regime, in which it is dominated by a finite droplet density, vanishes logarithmically with system size. As a consequence the slow decay characteristic of the former regime may be observable in systems that are macroscopic as far as their equilibrium properties are concerned.Comment: 18 pages single spaced. RevTex Version 3. FSU-SCRI-94-1