436 research outputs found
Monte-Carlo simulation of string-like colloidal assembly
We study structural phase transition of polymer-grafted colloidal particles
by Monte Carlo simulations on hard spherical particles. The interaction
potential, which has a weak repulsive step outside the hard core, was validated
with use of the self-consistent field calculations. With this potential,
canonical Monte Carlo simulations have been carried out in two and three
dimensions using the Metropolis algorithm. At low temperature and high density,
we find that the particles start to self-assemble and finally align in strings.
By analyzing the cluster size distribution and string length distribution, we
construct a phase diagram and find that this string-like assembly is related to
the percolation phenomena. The average string length diverges in the region
where the melting transition line and the percolation transition line cross,
which is similar to Ising spin systems where the percolation transition line
and the order-disorder line meet on the critical point.Comment: 7 pages, 6 figures, Accepted for Europhysics Letter
Particle Monte Carlo simulation of string-like colloidal assembly in 2 dimensions
We simulate structural phase behavior of polymer-grafted colloidal particles
by molecular Monte Carlo technique. Interparticle potential, which has a finite
repulsive square-step outside a rigid core of the colloid, was previously
confirmed via numerical self-consistent field calculation. This model potential
is purely repulsive. We simulate these model colloids in the canonical ensemble
in 2 dimensions and find that these particles containing no interparticle
attraction self-assemble and align in a string-like assembly, at low
temperature and high density. This string-like colloidal assembly is related to
percolation phenomena. Analyzing the cluster size distribution and the average
string length, we build phase diagrams and discover that the average string
length diverges around the region where the melting transition line and the
percolation transition line cross. This result is similar to Ising spin
systems, in which the percolation transition line and the order-disorder line
meet at a critical point.Comment: 11 pages, 14 figure
Deformation of Equilibrium Shape of a Vesicle Induced by Injected Flexible Polymers
Using field theoretic approach, we study equilibrium shape deformation of a
vesicle induced by the presence of enclosed flexible polymers, which is a
simple model of drug delivery system or endocytosis. To evaluate the total free
energy of this system, it is necessary to calculate the bending elastic energy
of the membrane, the conformation entropy of the polymers and their
interactions. For this purpose, we combine phase field theory for the membrane
and self-consistent field theory for the polymers. Simulations on this coupled
model system for axiosymmetric shapes show a shape deformation of the vesicle
induced by introducing polymers into it. We examined the dependence of the
stability of the vesicle shape on the chain length of the polymers and the
packing ratio of the vesicle. We present a simple model calculation that shows
the relative stability of the prolate shape compared to the oblate shape.Comment: 5 pages, 3 figure
Phase ordering and shape deformation of two-phase membranes
Within a coupled-field Ginzburg-Landau model we study analytically phase
separation and accompanying shape deformation on a two-phase elastic membrane
in simple geometries such as cylinders, spheres and tori. Using an exact
periodic domain wall solution we solve for the shape and phase ordering field,
and estimate the degree of deformation of the membrane. The results are
pertinent to a preferential phase separation in regions of differing curvature
on a variety of vesicles.Comment: 4 pages, submitted to PR
Lattice-Gas Simulations of Minority-Phase Domain Growth in Binary Immiscible and Ternary Amphiphilic Fluid
We investigate the growth kinetics of binary immiscible fluids and emulsions
in two dimensions using a hydrodynamic lattice-gas model. We perform
off-critical quenches in the binary fluid case and find that the domain size
within the minority phase grows algebraically with time in accordance with
theoretical predictions. In the late time regime we find a growth exponent n =
0.45 over a wide range of concentrations, in good agreement with other
simluations. In the early time regime we find no universal growth exponent but
a strong dependence on the concentration of the minority phase. In the ternary
amphiphilic fluid case the kinetics of self assembly of the droplet phase are
studied for the first time. At low surfactant concentrations, we find that,
after an early algebraic growth, a nucleation regime dominates the late-time
kinetics, which is enhanced by an increasing concentration of surfactant. With
a further increase in the concentration of surfactant, we see a crossover to
logarithmically slow growth, and finally saturation of the oil droplets, which
we fit phenomenologically to a stretched exponential function. Finally, the
transition between the droplet and the sponge phase is studied.Comment: 22 pages, 13 figures, submitted to PR
Time-reversal method and cross-correlation techniques by normal mode theory: a three-point problem
International audienceSince its beginning in acoustics, the Time-Reversal method (hereafter referred as TR) has been explored by different studies to locate and characterize seismic sources in elastic media. But few authors have proposed an analytical analysis of the method, especially in the case of an elastic medium and for a finite body such as the Earth. In this paper, we use a normal mode approach (for general 3-D case and degenerate modes in 1-D reference model) to investigate the convergence properties of the TR method. We first investigate a three-point problem, with two fixed points which are the source and the receiver and a third one corresponding to a changing observation point. We extend the problem of a single channel TR experiment to a multiple channel and multiple station TR experiment. We show as well how this problem relates to the retrieval of Green's function with a multiple source cross-correlation and also the differences between TR method and cross-correlation techniques. Since most of the noise sources are located close to the surface of the Earth, we show that the time derivative of the cross-correlation of long-period seismograms with multiple sources at the surface is different from the Green's function. Next, we show the importance of a correct surface-area weighting of the signal resent by the stations according to a Voronoi tessellation of the Earth surface. We use arguments based on the stationary phase approximation to argue that phase-information is more important than amplitude information for getting a good focusing in TR experiment. Finally, by using linear relationships between the time-reversed displacement (resp. strain wavefields) and the components of a vector force source (resp. a moment tensor source), we show how to retrieve force (or moment tensor components) of any long period tectonic or environmental sources by time reversal
Lattice-gas simulations of Domain Growth, Saturation and Self-Assembly in Immiscible Fluids and Microemulsions
We investigate the dynamical behavior of both binary fluid and ternary
microemulsion systems in two dimensions using a recently introduced
hydrodynamic lattice-gas model of microemulsions. We find that the presence of
amphiphile in our simulations reduces the usual oil-water interfacial tension
in accord with experiment and consequently affects the non-equilibrium growth
of oil and water domains. As the density of surfactant is increased we observe
a crossover from the usual two-dimensional binary fluid scaling laws to a
growth that is {\it slow}, and we find that this slow growth can be
characterized by a logarithmic time scale. With sufficient surfactant in the
system we observe that the domains cease to grow beyond a certain point and we
find that this final characteristic domain size is inversely proportional to
the interfacial surfactant concentration in the system.Comment: 28 pages, latex, embedded .eps figures, one figure is in colour, all
in one uuencoded gzip compressed tar file, submitted to Physical Review
Topography and instability of monolayers near domain boundaries
We theoretically study the topography of a biphasic surfactant monolayer in
the vicinity of domain boundaries. The differing elastic properties of the two
phases generally lead to a nonflat topography of ``mesas'', where domains of
one phase are elevated with respect to the other phase. The mesas are steep but
low, having heights of up to 10 nm. As the monolayer is laterally compressed,
the mesas develop overhangs and eventually become unstable at a surface tension
of about K(dc)^2 (dc being the difference in spontaneous curvature and K a
bending modulus). In addition, the boundary is found to undergo a
topography-induced rippling instability upon compression, if its line tension
is smaller than about K(dc). The effect of diffuse boundaries on these features
and the topographic behavior near a critical point are also examined. We
discuss the relevance of our findings to several experimental observations
related to surfactant monolayers: (i) small topographic features recently found
near domain boundaries; (ii) folding behavior observed in mixed phospholipid
monolayers and model lung surfactants; (iii) roughening of domain boundaries
seen under lateral compression; (iv) the absence of biphasic structures in
tensionless surfactant films.Comment: 17 pages, 9 figures, using RevTeX and epsf, submitted to Phys Rev
The Energy-Scaling Approach to Phase-Ordering Growth Laws
We present a simple, unified approach to determining the growth law for the
characteristic length scale, , in the phase ordering kinetics of a system
quenched from a disordered phase to within an ordered phase. This approach,
based on a scaling assumption for pair correlations, determines
self-consistently for purely dissipative dynamics by computing the
time-dependence of the energy in two ways. We derive growth laws for conserved
and non-conserved models, including two-dimensional XY models and
systems with textures. We demonstrate that the growth laws for other systems,
such as liquid-crystals and Potts models, are determined by the type of
topological defect in the order parameter field that dominates the energy. We
also obtain generalized Porod laws for systems with topological textures.Comment: LATeX 18 pages (REVTeX macros), one postscript figure appended,
REVISED --- rearranged and clarified, new paragraph on naive dimensional
analysis at end of section I
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