12,782 research outputs found
Growth in systems of vesicles and membranes
We present a theoretical study for the intermediate stages of the growth of
membranes and vesicles in supersaturated solutions of amphiphilic molecules.
The problem presents important differences with the growth of droplets in the
classical theory of Lifshitz-Slyozov-Wagner, because the aggregates are
extensive only in two dimensions, but still grow in a three dimensional bath.
The balance between curvature and edge energy favours the nucleation of small
planar membranes, but as they grow beyond a critical size they close themselves
to form vesicles. We obtain a system of coupled equations describing the growth
of planar membranes and vesicles, which is solved numerically for different
initial conditions. Finally, the range of parameters relevant in experimental
situations is discussed.Comment: 13 pages and 5 postscript figures. To appear in Phys. Rev
Driven low density granular mixtures
We study the steady state properties of a 2D granular mixture in the presence
of energy driving by employing simple analytical estimates and Direct
Simulation Monte Carlo. We adopt two different driving mechanisms: a) a
homogeneous heat bath with friction and b) a vibrating boundary (thermal or
harmonic) in the presence of gravity. The main findings are: the appearance of
two different granular temperatures, one for each species; the existence of
overpopulated tails in the velocity distribution functions and of non trivial
spatial correlations indicating the spontaneous formation of cluster
aggregates. In the case of a fluid subject to gravity and to a vibrating
boundary, both densities and temperatures display non uniform profiles along
the direction normal to the wall, in particular the temperature profiles are
different for the two species while the temperature ratio is almost constant
with the height. Finally, we obtained the velocity distributions at different
heights and verified the non gaussianity of the resulting distributions.Comment: 19 pages, 12 figures, submitted for publicatio
Critical properties of Ising model on Sierpinski fractals. A finite size scaling analysis approach
The present paper focuses on the order-disorder transition of an Ising model
on a self-similar lattice. We present a detailed numerical study, based on the
Monte Carlo method in conjunction with the finite size scaling method, of the
critical properties of the Ising model on some two dimensional deterministic
fractal lattices with different Hausdorff dimensions. Those with finite
ramification order do not display ordered phases at any finite temperature,
whereas the lattices with infinite connectivity show genuine critical behavior.
In particular we considered two Sierpinski carpets constructed using different
generators and characterized by Hausdorff dimensions d_H=log 8/log 3 = 1.8927..
and d_H=log 12/log 4 = 1.7924.., respectively.
The data show in a clear way the existence of an order-disorder transition at
finite temperature in both Sierpinski carpets.
By performing several Monte Carlo simulations at different temperatures and
on lattices of increasing size in conjunction with a finite size scaling
analysis, we were able to determine numerically the critical exponents in each
case and to provide an estimate of their errors.
Finally we considered the hyperscaling relation and found indications that it
holds, if one assumes that the relevant dimension in this case is the Hausdorff
dimension of the lattice.Comment: 21 pages, 7 figures; a new section has been added with results for a
second fractal; there are other minor change
Steady state properties of a mean field model of driven inelastic mixtures
We investigate a Maxwell model of inelastic granular mixture under the
influence of a stochastic driving and obtain its steady state properties in the
context of classical kinetic theory. The model is studied analytically by
computing the moments up to the eighth order and approximating the
distributions by means of a Sonine polynomial expansion method. The main
findings concern the existence of two different granular temperatures, one for
each species, and the characterization of the distribution functions, whose
tails are in general more populated than those of an elastic system. These
analytical results are tested against Monte Carlo numerical simulations of the
model and are in general in good agreement. The simulations, however, reveal
the presence of pronounced non-gaussian tails in the case of an infinite
temperature bath, which are not well reproduced by the Sonine method.Comment: 23 pages, 10 figures, submitted for publicatio
Which is the temperature of granular systems? A mean field model of free cooling inelastic mixtures
We consider a mean field model describing the free cooling process of a two
component granular mixture, a generalization of so called Maxwell model. The
cooling is viewed as an ordering process and the scaling behavior is attributed
to the presence of an attractive fixed point at for the dynamics. By
means of asymptotic analysis of the Boltzmann equation and of numerical
simulations we get the following results: 1)we establish the existence of two
different partial granular temperatures, one for each component, which violates
the Zeroth Law of Thermodynamics; 2) we obtain the scaling form of the two
distribution functions; 3) we prove the existence of a continuous spectrum of
exponents characterizing the inverse-power law decay of the tails of the
velocity, which generalizes the previously reported value 4 for the pure model;
4) we find that the exponents depend on the composition, masses and restitution
coefficients of the mixture; 5) we also remark that the reported distributions
represent a dynamical realization of those predicted by the Non Extensive
Statistical Mechanics, in spite of the fact that ours stem from a purely
dynamical approach.Comment: 23 pages, 9 figures. submitted for publicatio
Interface pinning and slow ordering kinetics on infinitely ramified fractal structures
We investigate the time dependent Ginzburg-Landau (TDGL) equation for a non
conserved order parameter on an infinitely ramified (deterministic) fractal
lattice employing two alternative methods: the auxiliary field approach and a
numerical method of integration of the equations of evolution. In the first
case the domain size evolves with time as , where is
the anomalous random walk exponent associated with the fractal and differs from
the normal value 2, which characterizes all Euclidean lattices. Such a power
law growth is identical to the one observed in the study of the spherical model
on the same lattice, but fails to describe the asymptotic behavior of the
numerical solutions of the TDGL equation for a scalar order parameter. In fact,
the simulations performed on a two dimensional Sierpinski Carpet indicate that,
after an initial stage dominated by a curvature reduction mechanism \`a la
Allen-Cahn, the system enters in a regime where the domain walls between
competing phases are pinned by lattice defects.
The lack of translational invariance determines a rough free energy
landscape, the existence of many metastable minima and the suppression of the
marginally stable modes, which in translationally invariant systems lead to
power law growth and self similar patterns. On fractal structures as the
temperature vanishes the evolution is frozen, since only thermally activated
processes can sustain the growth of pinned domains.Comment: 16 pages+14 figure
Velocity fluctuations in a one dimensional Inelastic Maxwell model
We consider the velocity fluctuations of a system of particles described by
the Inelastic Maxwell Model. The present work extends the methods, previously
employed to obtain the one-particle velocity distribution function, to the
study of the two particle correlations. Results regarding both the homogeneous
cooling process and the steady state driven regime are presented. In particular
we obtain the form of the pair correlation function in the scaling region of
the homogeneous cooling process and show that some of its moments diverge. This
fact has repercussions on the behavior of the energy fluctuations of the model.Comment: 16 pages, 1 figure, to be published on Journal of Statistical
Mechanics: Theory and Experiment
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