477 research outputs found
Random sequential adsorption on a dashed line
We study analytically and numerically a model of random sequential adsorption
(RSA) of segments on a line, subject to some constraints suggested by two kinds
of physical situations:
- deposition of dimers on a lattice where the sites have a spatial extension;
- deposition of extended particles which must overlap one (or several)
adsorbing sites on the substrate.
Both systems involve discrete and continuous degrees of freedom, and, in one
dimension, are equivalent to our model, which depends on one length parameter.
When this parameter is varied, the model interpolates between a variety of
known situations : monomers on a lattice, "car-parking" problem, dimers on a
lattice. An analysis of the long-time behaviour of the coverage as a function
of the parameter exhibits an anomalous 1/t^2 approach to the jamming limit at
the transition point between the fast exponential kinetics, characteristic of
the lattice model, and the 1/t law of the continuous one.Comment: 14 pages (Latex) + 4 Postscript figure
Jamming coverage in competitive random sequential adsorption of binary mixture
We propose a generalized car parking problem where cars of two different
sizes are sequentially parked on a line with a given probability . The free
parameter interpolates between the classical car parking problem of only
one car size and the competitive random sequential adsorption (CRSA) of a
binary mixture. We give an exact solution to the CRSA rate equations and find
that the final coverage, the jamming limit, of the line is always larger for a
binary mixture than for the uni-sized case. The analytical results are in good
agreement with our direct numerical simulations of the problem.Comment: 4 pages 2-column RevTeX, Four figures, (there was an error in the
previous version. We replaced it (including figures) with corrected and
improved version that lead to new results and conclusions
Adsorption of Line Segments on a Square Lattice
We study the deposition of line segments on a two-dimensional square lattice.
The estimates for the coverage at jamming obtained by Monte-Carlo simulations
and by -order time-series expansion are successfully compared. The
non-trivial limit of adsorption of infinitely long segments is studied, and the
lattice coverage is consistently obtained using these two approaches.Comment: 19 pages in Latex+5 postscript files sent upon request ; PTB93_
Critical Behavior of the Ferromagnetic Ising Model on a Sierpinski Carpet: Monte Carlo Renormalization Group Study
We perform a Monte Carlo Renormalization Group analysis of the critical
behavior of the ferromagnetic Ising model on a Sierpi\'nski fractal with
Hausdorff dimension . This method is shown to be relevant to
the calculation of the critical temperature and the magnetic
eigen-exponent on such structures. On the other hand, scaling corrections
hinder the calculation of the temperature eigen-exponent . At last, the
results are shown to be consistent with a finite size scaling analysis.Comment: 16 pages, 7 figure
Irreversible Deposition of Line Segment Mixtures on a Square Lattice: Monte Carlo Study
We have studied kinetics of random sequential adsorption of mixtures on a
square lattice using Monte Carlo method. Mixtures of linear short segments and
long segments were deposited with the probability and , respectively.
For fixed lengths of each segment in the mixture, the jamming limits decrease
when increases. The jamming limits of mixtures always are greater than
those of the pure short- or long-segment deposition.
For fixed and fixed length of the short segments, the jamming limits have
a maximum when the length of the long segment increases. We conjectured a
kinetic equation for the jamming coverage based on the data fitting.Comment: 7 pages, latex, 5 postscript figure
Simulation study of random sequential adsorption of mixtures on a triangular lattice
Random sequential adsorption of binary mixtures of extended objects on a
two-dimensional triangular lattice is studied numerically by means of Monte
Carlo simulations. The depositing objects are formed by self-avoiding random
walks on the lattice. We concentrate here on the influence of the symmetry
properties of the shapes on the kinetics of the deposition processes in
two-component mixtures. Approach to the jamming limit in the case of mixtures
is found to be exponential, of the form: and the values of the parameter
are determined by the order of symmetry of the less symmetric object
in the mixture. Depending on the local geometry of the objects making the
mixture, jamming coverage of a mixture can be either greater than both
single-component jamming coverages or it can be in between these values.
Results of the simulations for various fractional concentrations of the objects
in the mixture are also presented.Comment: 11 figures, 2 table
Fractal formation and ordering in random sequential adsorption
We reveal the fractal nature of patterns arising in random sequential
adsorption of particles with continuum power-law size distribution, , . We find that the patterns become more and
more ordered as increases, and that the Apollonian packing is obtained
at limit. We introduce the entropy production rate as a
quantitative criteria of regularity and observe a transition from an irregular
regime of the pattern formation to a regular one. We develop a scaling theory
that relates kinetic and structural properties of the system.Comment: 4 pages, RevTex, 4 postscript figures. To appear in Phys.Rev.Let
Fractal dimension and degree of order in sequential deposition of mixture
We present a number models describing the sequential deposition of a mixture
of particles whose size distribution is determined by the power-law , . We explicitly obtain the scaling function in
the case of random sequential adsorption (RSA) and show that the pattern
created in the long time limit becomes scale invariant. This pattern can be
described by an unique exponent, the fractal dimension. In addition, we
introduce an external tuning parameter beta to describe the correlated
sequential deposition of a mixture of particles where the degree of correlation
is determined by beta, while beta=0 corresponds to random sequential deposition
of mixture. We show that the fractal dimension of the resulting pattern
increases as beta increases and reaches a constant non-zero value in the limit
when the pattern becomes perfectly ordered or non-random
fractals.Comment: 16 pages Latex, Submitted to Phys. Rev.
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