203 research outputs found
A necklace of Wulff shapes
In a probabilistic model of a film over a disordered substrate, Monte-Carlo
simulations show that the film hangs from peaks of the substrate. The film
profile is well approximated by a necklace of Wulff shapes. Such a necklace can
be obtained as the infimum of a collection of Wulff shapes resting on the
substrate. When the random substrate is given by iid heights with exponential
distribution, we prove estimates on the probability density of the resulting
peaks, at small density
Simulations of Solid-on-Solid Models of Spreading of Viscous Droplets
We have studied the dynamics of spreading of viscous non-volatile fluids on
surfaces by MC simulations of SOS models. We have concentrated on the complete
wetting regime, with surface diffusion barriers neglected for simplicity.
First, we have performed simulations for the standard SOS model. Formation of a
single precursor layer, and a density profile with a spherical cap shaped
center surrounded by Gaussian tails can be reproduced with this model.
Dynamical layering (DL), however, only occurs with a very strongly attractive
van der Waals type of substrate potential. To more realistically describe the
spreading of viscous liquid droplets, we introduce a modified SOS model. In the
new model, tendency for DL and the effect of the surface potential are in part
embedded into the dynamics of the model. This allows a relatively simple
description of the spreading under different conditions, with a temperature
like parameter which strongly influences the droplet morphologies. Both rounded
droplet shapes and DL can easily be reproduced with the model. Furthermore, the
precursor width increases proportional to the square root of time, in
accordance with experimental observations. PACS: 68.10.Gw, 05.70.Ln, 61.20.Ja.Comment: to appear in Physica A (1994), standard LaTex, 20 page
Dynamics of Spreading of Chainlike Molecules with Asymmetric Surface Interactions
In this work we study the spreading dynamics of tiny liquid droplets on solid
surfaces in the case where the ends of the molecules feel different
interactions with respect to the surface. We consider a simple model of dimers
and short chainlike molecules that cannot form chemical bonds with the surface.
We use constant temperature Molecular Dynamics techniques to examine in detail
the microscopic structure of the time dependent precursor film. We find that in
some cases it can exhibit a high degree of local order that can persist even
for flexible chains. Our model also reproduces the experimentally observed
early and late-time spreading regimes where the radius of the film grows
proportional to the square root of time. The ratios of the associated transport
coefficients are in good overall agreement with experiments. Our density
profiles are also in good agreement with measurements on the spreading of
molecules on hydrophobic surfaces.Comment: 12 pages, LaTeX with APS macros, 21 figures available by contacting
[email protected], to appear in Phys. Rev.
Molecular ordering of precursor films during spreading of tiny liquid droplets
In this work we address a novel feature of spreading dynamics of tiny liquid
droplets on solid surfaces, namely the case where the ends of the molecules
feel different interactions to the surface. We consider a simple model of
dimers and short chain--like molecules which cannot form chemical bonds with
the surface. We study the spreading dynamics by Molecular Dynamics techniques.
In particular, we examine the microscopic structure of the time--dependent
precursor film and find that in some cases it can exhibit a high degree of
local order. This order persists even for flexible chains. Our results suggest
the possibility of extracting information about molecular interactions from the
structure of the precursor film.Comment: 4 pages, revtex, no figures, complete file available from
ftp://rock.helsinki.fi/pub/preprints/tft/ or at
http://www.physics.helsinki.fi/tft/tft_preprints.html (to appear in Phys.
Rev. E Rapid Comm.
Force-velocity relation and density profiles for biased diffusion in an adsorbed monolayer
In this paper, which completes our earlier short publication [Phys. Rev.
Lett. 84, 511 (2000)], we study dynamics of a hard-core tracer particle (TP)
performing a biased random walk in an adsorbed monolayer, composed of mobile
hard-core particles undergoing continuous exchanges with a vapor phase. In
terms of an approximate approach, based on the decoupling of the third-order
correlation functions, we obtain the density profiles of the monolayer
particles around the TP and derive the force-velocity relation, determining the
TP terminal velocity, V_{tr}, as the function of the magnitude of external bias
and other system's parameters. Asymptotic forms of the monolayer particles
density profiles at large separations from the TP, and behavior of V_{tr} in
the limit of small external bias are found explicitly.Comment: Latex, 31 pages, 3 figure
Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes
The rigorous microscopic theory of equilibrium crystal shapes has made
enormous progress during the last decade. We review here the main results which
have been obtained, both in two and higher dimensions. In particular, we
describe how the phenomenological Wulff and Winterbottom constructions can be
derived from the microscopic description provided by the equilibrium
statistical mechanics of lattice gases. We focus on the main conceptual issues
and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical
Physics on Probabilistic Methods in Statistical Physic
Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
We reconsider the conceptual foundations of the renormalization-group (RG)
formalism, and prove some rigorous theorems on the regularity properties and
possible pathologies of the RG map. Regarding regularity, we show that the RG
map, defined on a suitable space of interactions (= formal Hamiltonians), is
always single-valued and Lipschitz continuous on its domain of definition. This
rules out a recently proposed scenario for the RG description of first-order
phase transitions. On the pathological side, we make rigorous some arguments of
Griffiths, Pearce and Israel, and prove in several cases that the renormalized
measure is not a Gibbs measure for any reasonable interaction. This means that
the RG map is ill-defined, and that the conventional RG description of
first-order phase transitions is not universally valid. For decimation or
Kadanoff transformations applied to the Ising model in dimension ,
these pathologies occur in a full neighborhood of the low-temperature part of the first-order
phase-transition surface. For block-averaging transformations applied to the
Ising model in dimension , the pathologies occur at low temperatures
for arbitrary magnetic-field strength. Pathologies may also occur in the
critical region for Ising models in dimension . We discuss in detail
the distinction between Gibbsian and non-Gibbsian measures, and give a rather
complete catalogue of the known examples. Finally, we discuss the heuristic and
numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also
ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.
Environmental Policy Design and the Fragmentation of International Markets for Innovation
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