194 research outputs found
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
A Soluble Phase Field Model
The kinetics of an initially undercooled solid-liquid melt is studied by
means of a generalized Phase Field model, which describes the dynamics of an
ordering non-conserved field phi (e.g. solid-liquid order parameter) coupled to
a conserved field (e.g. thermal field). After obtaining the rules governing the
evolution process, by means of analytical arguments, we present a discussion of
the asymptotic time-dependent solutions. The full solutions of the exact
self-consistent equations for the model are also obtained and compared with
computer simulation results. In addition, in order to check the validity of the
present model we confronted its predictions against those of the standard Phase
field model and found reasonable agreement. Interestingly, we find that the
system relaxes towards a mixed phase, depending on the average value of the
conserved field, i.e. on the initial condition. Such a phase is characterized
by large fluctuations of the phi field.Comment: 13 pages, 8 figures, RevTeX 3.1, submitted to Physical Review
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
Phase separation in systems with absorbing states
We study the problem of phase separation in systems with a positive definite
order parameter, and in particular, in systems with absorbing states. Owing to
the presence of a single minimum in the free energy driving the relaxation
kinetics, there are some basic properties differing from standard phase
separation. We study analytically and numerically this class of systems; in
particular we determine the phase diagram, the growth laws in one and two
dimensions and the presence of scale invariance. Some applications are also
discussed.Comment: Submitted to Europhysics Let
Dynamics of vibrofluidized granular gases in periodic structures
The behavior of a driven granular gas in a container consisting of
connected compartments is studied employing a microscopic kinetic model. After
obtaining the governing equations for the occupation numbers and the granular
temperatures of each compartment we consider the various dynamical regimes. The
system displays interesting analogies with the ordering processes of phase
separating mixtures quenched below the their critical point. In particular, we
show that below a certain value of the driving intensity the populations of the
various compartments become unequal and the system clusterizes. Such a
phenomenon is not instantaneous, but is characterized by a time scale, ,
which follows a Vogel-Vulcher exponential behavior. On the other hand, the
reverse phenomenon which involves the ``evaporation'' of a cluster due to the
driving force is also characterized by a second time scale which diverges at
the limit of stability of the cluster.Comment: 11 pages, 17 figure
Multiple time-scale approach for a system of Brownian particles in a non-uniform temperature field
The Smoluchowsky equation for a system of interacting Brownian particles in a
temperature gradient is derived from the Kramers equation by means of a
multiple time-scale method. The interparticle interactions are assumed to be
represented by a mean-field description. We present numerical results that
compare well with the theoretical prediction together with an extensive
discussion on the prescription of the Langevin equation in overdamped systems.Comment: 8 pages, 2 figure
Dynamics of Fluid Mixtures in Nanospaces
A multicomponent extension of our recent theory of simple fluids [ U.M.B.
Marconi and S. Melchionna, Journal of Chemical Physics, 131, 014105 (2009) ] is
proposed to describe miscible and immiscible liquid mixtures under
inhomogeneous, non steady conditions typical of confined fluid flows. We first
derive from a microscopic level the evolution equations of the phase space
distribution function of each component in terms of a set of self consistent
fields, representing both body forces and viscous forces (forces dependent on
the density distributions in the fluid and on the velocity distributions).
Secondly, we solve numerically the resulting governing equations by means of
the Lattice Boltzmann method whose implementation contains novel features with
respect to existing approaches. Our model incorporates hydrodynamic flow,
diffusion, surface tension, and the possibility for global and local viscosity
variations. We validate our model by studying the bulk viscosity dependence of
the mixture on concentration, packing fraction and size ratio. Finally we
consider inhomogeneous systems and study the dynamics of mixtures in slits of
molecular thickness and relate structural and flow properties.Comment: 16 pages, 8 figure
A simulational and theoretical study of the spherical electrical double layer for a size-asymmetric electrolyte: the case of big coions
Monte Carlo simulations of a spherical macroion, surrounded by a
size-asymmetric electrolyte in the primitive model, were performed. We
considered 1:1 and 2:2 salts with a size ratio of 2 (i.e., with coions twice
the size of counterions), for several surface charge densities of the
macrosphere. The radial distribution functions, electrostatic potential at the
Helmholtz surfaces, and integrated charge are reported. We compare these
simulational data with original results obtained from the Ornstein-Zernike
integral equation, supplemented by the hypernetted chain/hypernetted chain
(HNC/HNC) and hypernetted chain/mean spherical approximation (HNC/MSA)
closures, and with the corresponding calculations using the modified
Gouy-Chapman and unequal-radius modified Gouy-Chapman theories. The HNC/HNC and
HNC/MSA integral equations formalisms show good concordance with Monte Carlo
"experiments", whereas the notable limitations of point-ion approaches are
evidenced. Most importantly, the simulations confirm our previous theoretical
predictions of the non-dominance of the counterions in the size-asymmetric
spherical electrical double layer [J. Chem. Phys. 123, 034703 (2005)], the
appearance of anomalous curvatures at the outer Helmholtz plane and the
enhancement of charge reversal and screening at high colloidal surface charge
densities due to the ionic size asymmetry.Comment: 11 pages, 7 figure
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