240 research outputs found
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
Noise Rectification and Fluctuations of an Asymmetric Inelastic Piston
We consider a massive inelastic piston, whose opposite faces have different
coefficients of restitution, moving under the action of an infinitely dilute
gas of hard disks maintained at a fixed temperature. The dynamics of the piston
is Markovian and obeys a continuous Master Equation: however, the asymmetry of
restitution coefficients induces a violation of detailed balance and a net
drift of the piston, as in a Brownian ratchet. Numerical investigations of such
non-equilibrium stationary state show that the velocity fluctuations of the
piston are symmetric around the mean value only in the limit of large piston
mass, while they are strongly asymmetric in the opposite limit. Only taking
into account such an asymmetry, i.e. including a third parameter in addition to
the mean and the variance of the velocity distribution, it is possible to
obtain a satisfactory analytical prediction for the ratchet drift velocity.Comment: 6 pages, 5 figures, to be published on Europhysics Letters; some
references have been adde
Non-equilibrium fluctuations in a driven stochastic Lorentz gas
We study the stationary state of a one-dimensional kinetic model where a
probe particle is driven by an external field E and collides, elastically or
inelastically, with a bath of particles at temperature T. We focus on the
stationary distribution of the velocity of the particle, and of two estimates
of the total entropy production \Delta s_tot. One is the entropy production of
the medium \Delta s_m, which is equal to the energy exchanged with the
scatterers, divided by a parameter \theta, coinciding with the particle
temperature at E=0. The other is the work W done by the external field, again
rescaled by \theta. At small E, a good collapse of the two distributions is
found: in this case the two quantities also verify the Fluctuation Relation
(FR), indicating that both are good approximations of \Delta s_tot.
Differently, for large values of E, the fluctuations of W violate the FR, while
\Delta s_m still verifies it.Comment: 6 pages, 4 figure
Models of granular ratchets
We study a general model of granular Brownian ratchet consisting of an
asymmetric object moving on a line and surrounded by a two-dimensional granular
gas, which in turn is coupled to an external random driving force. We discuss
the two resulting Boltzmann equations describing the gas and the object in the
dilute limit and obtain a closed system for the first few moments of the system
velocity distributions. Predictions for the net ratchet drift, the variance of
its velocity fluctuations and the transition rates in the Markovian limit, are
compared to numerical simulations and a fair agreement is observed.Comment: 15 pages, 4 figures, to be published on Journal of Statistical
Mechanics: Theory and Experiment
The inelastic hard dimer gas: a non-spherical model for granular matter
We study a two-dimensional gas of inelastic smooth hard dimers. Since the
collisions between dimers are dissipative, being characterized by a coefficient
of restitution , and no external driving force is present, the energy
of the system decreases in time and no stationary state is achieved. However,
the resulting non equilibrium state of the system displays several interesting
properties in close analogy with systems of inelastic hard spheres, whose
relaxational dynamics has been thoroughly explored. We generalise to inelastic
systems a recently method introduced [G.Ciccotti and G.Kalibaeva, J. Stat.
Phys. {\bf 115}, 701 (2004)] to study the dynamics of rigid elastic bodies made
up of different spheres hold together by rigid bonds. Each dimer consists of
two hard disks of diameter , whose centers are separated by a fixed distance
. By describing the rigid bonds by means of holonomic constraints and
deriving the appropriate collision rules between dimers, we reduce the dynamics
to a set of equations which can be solved by means of event driven simulation.
After deriving the algorithm we study the decay of the total kinetic energy,
and of the ratio between the rotational and the translational kinetic energy of
inelastic dimers. We show numerically that the celebrated Haff's homogeneous
cooling law , describing how the kinetic energy of an inelastic hard
sphere system with constant coefficient of restitution decreases in time, holds
even in the case of these non spherical particles. We fully characterize this
homogeneous decay process in terms of appropriate decay constants and confirm
numerically the scaling behavior of the velocity distributions.Comment: 21 pages, 6 figures and 2 tables, submitted to JC
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
Nonequilibrium steady states in fluids of platelike colloidal particles
Nonequilibrium steady states in an open system connecting two reservoirs of
platelike colloidal particles are investigated by means of a recently proposed
phenomenological dynamic density functional theory [M. Bier and R. van Roij,
Phys. Rev. E 76, 021405 (2007)]. The platelike colloidal particles are
approximated within the Zwanzig model of restricted orientations, which
exhibits an isotropic-nematic bulk phase transition. Inhomogeneities of the
local chemical potential generate a diffusion current which relaxes to a
nonvanishing value if the two reservoirs coupled to the system sustain
different chemical potentials. The relaxation process of initial states towards
the steady state turns out to comprise two regimes: a smoothening of initial
steplike structures followed by an ultimate relaxation of the slowest diffusive
mode. The position of a nonequilibrium interface and the particle current of
steady states depend nontrivially on the structure of the reservoirs due to the
coupling between translational and orientational degrees of freedom of the
fluid
Fluctuation-Induced Casimir Forces in Granular Fluids
We have numerically investigated the behavior of driven non-cohesive granular
media and found that two fixed large intruder particles, immersed in a sea of
small particles, experience, in addition to a short range depletion force, a
long range repulsive force. The observed long range interaction is
fluctuation-induced and we propose a mechanism similar to the Casimir effect
that generates it: the hydrodynamic fluctuations are geometrically confined
between the intruders, producing an unbalanced renormalized pressure. An
estimation based on computing the possible Fourier modes explains the repulsive
force and is in qualitative agreement with the simulations.Comment: 4 pages, 3 figures. Accepted in Phys. Rev. Letter
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
Recherches sur les derives du 1,4-benzodioxan. Note VII 2-Amino-methylbenzodioxan substitues en 71
Les recherches de Fourneau et ses collaiborateurs sur les proprietes pharmacodynamiques et en particulier sur l\u27activite sympatholytique manifestee par le 2-diethylaminomethyl-1,4-benzodioxan et le 2-piperidinomethyl- 1,4-benzodioxan ont ouvert la voie a une serie d\u27irrvestigations sur les amide-amines correspondantes sur les piperazines bis-2-(methyl-1,4-benzodioxan) et les amides derives de l\u27acide-1,4-benzodioxan-2-carboxyliqu
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