69 research outputs found
New cellular automaton designed to simulate epitaxial films growth
In this paper a simple (2+1) solid-on-solid model of the epitaxial films
growth based on random deposition followed by breaking particle-particle
lateral bonds and particles surface diffusion is introduced. The influence of
the critical number of the particle-particle lateral bonds and the
deposition rate on the surface roughness dynamics and possible surface
morphology anisotropy is presented. The roughness exponent and the
growth exponent are , ,
and for , 2, 3 and 4, respectively. Snapshots from
simulations of the growth process are included.Comment: 10 pages, elsart, 5 figures in 20 file
Truth seekers in opinion dynamics models
We modify the model of Deffuant et al. to distinguish true opinion among
others in the fashion of Hegselmann and Krause
. The basic features of both models
modified to account for truth seekers are qualitatively the same.Comment: RevTeX4, 2 pages, 1 figure in 6 eps file
Majority-vote model on (3,4,6,4) and (3^4,6) Archimedean lattices
On Archimedean lattices, the Ising model exhibits spontaneous ordering. Two
examples of these lattices of the majority-vote model with noise are considered
and studied through extensive Monte Carlo simulations. The order/disorder phase
transition is observed in this system. The calculated values of the critical
noise parameter are q_c=0.091(2) and q_c=0.134(3) for (3,4,6,4) and (3^4,6)
Archimedean lattices, respectively. The critical exponents beta/nu, gamma/nu
and 1/nu for this model are 0.103(6), 1.596(54), 0.872(85) for (3,4,6,4) and
0.114(3), 1.632(35), 0.978(104) for (3^4,6) Archimedean lattices. These results
differs from the usual Ising model results and the majority-vote model on
so-far studied regular lattices or complex networks. The effective
dimensionality of the system [D_{eff}(3,4,6,4)=1.802(55) and
D_{eff}(3^4,6)=1.860(34)] for these networks are reasonably close to the
embedding dimension two.Comment: 6 pages, 7 figures in 12 eps files, RevTex
Square lattice site percolation at increasing ranges of neighbor interactions
We report site percolation thresholds for square lattice with neighbor
interactions at various increasing ranges. Using Monte Carlo techniques we
found that nearest neighbors (N), next nearest neighbors (N), next next
nearest neighbors (N) and fifth nearest neighbors (N) yield the same
. At odds, fourth nearest neighbors (N) give .
These results are given an explanation in terms of symmetry arguments. We then
consider combinations of various ranges of interactions with (N+N),
(N+N), (N+N+N) and (N+N). The calculated associated
thresholds are respectively . The
existing Galam--Mauger universal formula for percolation thresholds does not
reproduce the data showing dimension and coordination number are not sufficient
to build a universal law which extends to complex lattices.Comment: 4 pages, revtex
How pairs of partners emerge in an initially fully connected society
A social group is represented by a graph, where each pair of nodes is
connected by two oppositely directed links. At the beginning, a given amount
of resources is assigned randomly to each node . Also, each link
is initially represented by a random positive value, which means the
percentage of resources of node which is offered to node . Initially
then, the graph is fully connected, i.e. all non-diagonal matrix elements
are different from zero. During the simulation, the amounts of
resources change according to the balance equation. Also, nodes
reorganise their activity with time, going to give more resources to those
which give them more. This is the rule of varying the coefficients .
The result is that after some transient time, only some pairs of nodes
survive with non-zero and , each pair with symmetric and positive
. Other coefficients vanish. Unpaired nodes remain
with no resources, i.e. their , and they cease to be active, as they
have nothing to offer. The percentage of survivors (i.e. those with with
positive) increases with the velocity of varying the numbers , and it
slightly decreases with the size of the group. The picture and the results can
be interpreted as a description of a social algorithm leading to marriages.Comment: 7 pages, 3 figure
Average distance in growing trees
Two kinds of evolving trees are considered here: the exponential trees, where
subsequent nodes are linked to old nodes without any preference, and the
Barab\'asi--Albert scale-free networks, where the probability of linking to a
node is proportional to the number of its pre-existing links. In both cases,
new nodes are linked to nodes. Average node-node distance is
calculated numerically in evolving trees as dependent on the number of nodes
. The results for not less than a thousand are averaged over a thousand
of growing trees. The results on the mean node-node distance for large
can be approximated by for the exponential trees, and
for the scale-free trees, where the are constant. We
derive also iterative equations for and its dispersion for the exponential
trees. The simulation and the analytical approach give the same results.Comment: 6 pages, 3 figures, Int. J. Mod. Phys. C14 (2003) - in prin
Restoring site percolation on a damaged square lattice
We study how to restore site percolation on a damaged square lattice with
nearest neighbor (N) interactions. Two strategies are suggested for a
density of destroyed sites by a random attack at . In the first one, a
density of new sites are created with longer range interactions, either
next nearest neighbor (N) or next next nearest neighbor (N). In the
second one, new longer range interactions N or N are created for a
fraction of the remaining sites in addition to their N
interactions. In both cases, the values of and are tuned in order to
restore site percolation which then occurs at new percolation thresholds,
respectively , , and . Using Monte Carlo
simulations the values of the pairs , and , are calculated for the whole range . Our schemes are applicable to all regular lattices.Comment: 5 pages, revtex
Spreading gossip in social networks
We study a simple model of information propagation in social networks, where
two quantities are introduced: the spread factor, which measures the average
maximal fraction of neighbors of a given node that interchange information
among each other, and the spreading time needed for the information to reach
such fraction of nodes. When the information refers to a particular node at
which both quantities are measured, the model can be taken as a model for
gossip propagation. In this context, we apply the model to real empirical
networks of social acquaintances and compare the underlying spreading dynamics
with different types of scale-free and small-world networks. We find that the
number of friendship connections strongly influences the probability of being
gossiped. Finally, we discuss how the spread factor is able to be applied to
other situations.Comment: 10 pages, 16 figures, Revtex; Virt.J. of Biol. Phys., Oct.1 200
Exact Curie temperature for the Ising model on Archimedean and Laves lattices
Using the Feynman-Vdovichenko combinatorial approach to the two dimensional
Ising model, we determine the exact Curie temperature for all two dimensional
Archimedean lattices. By means of duality, we extend our results to cover all
two dimensional Laves lattices. For those lattices where the exact critical
temperatures are not exactly known yet, we compare them with Monte Carlo
simulations.Comment: 10 pages, 1 figures, 3 table
Clusterization, frustration and collectivity in random networks
We consider the random Erd{\H o}s--R\'enyi network with enhanced
clusterization and Ising spins at the network nodes. Mutually linked
spins interact with energy . Magnetic properties of the system as dependent
on the clustering coefficient are investigated with the Monte Carlo heat
bath algorithm. For the Curie temperature increases from 3.9 to 5.5
when increases from almost zero to 0.18. These results deviate only
slightly from the mean field theory. For the spin-glass phase appears
below ; this temperature decreases with , on the contrary to the
mean field calculations. The results are interpreted in terms of social
systems.Comment: 10 pages, 6 figures; serious change of result
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