171 research outputs found
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 TiO parameterized using density functional theory
We report a classical interatomic force field for TiO, 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 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
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