325 research outputs found
Analytical results for the Sznajd model of opinion formation
The Sznajd model, which describes opinion formation and social influence, is
treated analytically on a complete graph. We prove the existence of the phase
transition in the original formulation of the model, while for the Ochrombel
modification we find smooth behaviour without transition. We calculate the
average time to reach the stationary state as well as the exponential tail of
its probability distribution. An analytical argument for the observed
dependence in the distribution of votes in Brazilian elections is provided.Comment: 10 pages 5 figure
Loop expansion around the Bethe-Peierls approximation for lattice models
We develop an effective field theory for lattice models, in which the only
non-vanishing diagrams exactly reproduce the topology of the lattice. The
Bethe-Peierls approximation appears naturally as the saddle point
approximation. The corrections to the saddle-point result can be obtained
systematically. We calculate the lowest loop corrections for magnetisation and
correlation function.Comment: 8 page
Multi-market minority game: breaking the symmetry of choice
Generalization of the minority game to more than one market is considered. At
each time step every agent chooses one of its strategies and acts on the market
related to this strategy. If the payoff function allows for strong fluctuation
of utility then market occupancies become inhomogeneous with preference given
to this market where the fluctuation occured first. There exists a critical
size of agent population above which agents on bigger market behave
collectively. In this regime there always exists a history of decisions for
which all agents on a bigger market react identically.Comment: 15 pages, 12 figures, Accepted to 'Advances in Complex Systems
Statistical properties of stock order books: empirical results and models
We investigate several statistical properties of the order book of three
liquid stocks of the Paris Bourse. The results are to a large degree
independent of the stock studied. The most interesting features concern (i) the
statistics of incoming limit order prices, which follows a power-law around the
current price with a diverging mean; and (ii) the humped shape of the average
order book, which can be quantitatively reproduced using a `zero intelligence'
numerical model, and qualitatively predicted using a simple approximation.Comment: Revised version, 10 pages, 4 .eps figures. to appear in Quantitative
Financ
Van Kampen's expansion approach in an opinion formation model
We analyze a simple opinion formation model consisting of two parties, A and
B, and a group I, of undecided agents. We assume that the supporters of parties
A and B do not interact among them, but only interact through the group I, and
that there is a nonzero probability of a spontaneous change of opinion (A->I,
B->I). From the master equation, and via van Kampen's Omega-expansion approach,
we have obtained the "macroscopic" evolution equation, as well as the
Fokker-Planck equation governing the fluctuations around the deterministic
behavior. Within the same approach, we have also obtained information about the
typical relaxation behavior of small perturbations.Comment: 17 pages, 6 figures, submited to Europ.Phys.J.
A Unified Framework for the Pareto Law and Matthew Effect using Scale-Free Networks
We investigate the accumulated wealth distribution by adopting evolutionary
games taking place on scale-free networks. The system self-organizes to a
critical Pareto distribution (1897) of wealth with (which is in agreement with that of U.S. or Japan). Particularly, the
agent's personal wealth is proportional to its number of contacts
(connectivity), and this leads to the phenomenon that the rich gets richer and
the poor gets relatively poorer, which is consistent with the Matthew Effect
present in society, economy, science and so on. Though our model is simple, it
provides a good representation of cooperation and profit accumulation behavior
in economy, and it combines the network theory with econophysics.Comment: 5 pages, 8 figure
Collective Behavior of Asperities in Dry Friction at Small Velocities
We investigate a simple model of dry friction based on extremal dynamics of
asperities. At small velocities, correlations develop between the asperities,
whose range becomes infinite in the limit of infinitely slow driving, where the
system is self-organized critical. This collective phenomenon leads to
effective aging of the asperities and results in velocity dependence of the
friction force in the form .Comment: 7 pages, 8 figures, revtex, submitted to Phys. Rev.
Infinite-Order Percolation and Giant Fluctuations in a Protein Interaction Network
We investigate a model protein interaction network whose links represent
interactions between individual proteins. This network evolves by the
functional duplication of proteins, supplemented by random link addition to
account for mutations. When link addition is dominant, an infinite-order
percolation transition arises as a function of the addition rate. In the
opposite limit of high duplication rate, the network exhibits giant structural
fluctuations in different realizations. For biologically-relevant growth rates,
the node degree distribution has an algebraic tail with a peculiar rate
dependence for the associated exponent.Comment: 4 pages, 2 figures, 2 column revtex format, to be submitted to PRL 1;
reference added and minor rewording of the first paragraph; Title change and
major reorganization (but no result changes) in response to referee comments;
to be published in PR
Effect of a columnar defect on the shape of slow-combustion fronts
We report experimental results for the behavior of slow-combustion fronts in
the presence of a columnar defect with excess or reduced driving, and compare
them with those of mean-field theory. We also compare them with simulation
results for an analogous problem of driven flow of particles with hard-core
repulsion (ASEP) and a single defect bond with a different hopping probability.
The difference in the shape of the front profiles for excess vs. reduced
driving in the defect, clearly demonstrates the existence of a KPZ-type of
nonlinear term in the effective evolution equation for the slow-combustion
fronts. We also find that slow-combustion fronts display a faceted form for
large enough excess driving, and that there is a corresponding increase then in
the average front speed. This increase in the average front speed disappears at
a non-zero excess driving in agreement with the simulated behavior of the ASEP
model.Comment: 7 pages, 7 figure
Cracking Piles of Brittle Grains
A model which accounts for cracking avalanches in piles of grains subject to
external load is introduced and numerically simulated. The stress is
stochastically transferred from higher layers to lower ones. Cracked areas
exhibit various morphologies, depending on the degree of randomness in the
packing and on the ductility of the grains. The external force necessary to
continue the cracking process is constant in wide range of values of the
fraction of already cracked grains. If the grains are very brittle, the force
fluctuations become periodic in early stages of cracking. Distribution of
cracking avalanches obeys a power law with exponent .Comment: RevTeX, 6 pages, 7 postscript figures, submitted to Phys. Rev.
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