56 research outputs found
Marketing Percolation
A percolation model is presented, with computer simulations for
illustrations, to show how the sales of a new product may penetrate the
consumer market. We review the traditional approach in the marketing
literature, which is based on differential or difference equations similar to
the logistic equation (Bass 1969). This mean field approach is contrasted with
the discrete percolation on a lattice, with simulations of "social percolation"
(Solomon et al 2000) in two to five dimensions giving power laws instead of
exponential growth, and strong fluctuations right at the percolation threshold.Comment: to appear in Physica
Peer-to-Peer and Mass Communication Effect on Revolution Dynamics
Revolution dynamics is studied through a minimal Ising model with three main
influences (fields): personal conservatism (power-law distributed),
inter-personal and group pressure, and a global field incorporating
peer-to-peer and mass communications, which is generated bottom-up from the
revolutionary faction. A rich phase diagram appears separating possible
terminal stages of the revolution, characterizing failure phases by the
features of the individuals who had joined the revolution. An exhaustive
solution of the model is produced, allowing predictions to be made on the
revolution's outcome
From 2000 Bush-Gore to 2006 Italian elections: Voting at fifty-fifty and the Contrarian Effect
A sociophysical model for opinion dynamics is shown to embody a series of
recent western hung national votes all set at the unexpected and very
improbable edge of a fifty-fifty score. It started with the Bush-Gore 2000
American presidential election, followed by the 2002 Stoiber-Schr\H{o}der, then
the 2005 Schr\H{o}der-Merkel German elections, and finally the 2006
Prodi-Berlusconi Italian elections. In each case, the country was facing
drastic choices, the running competing parties were advocating very different
programs and millions of voters were involved. Moreover, polls were given a
substantial margin for the predicted winner. While all these events were
perceived as accidental and isolated, our model suggests that indeed they are
deterministic and obey to one single universal phenomena associated to the
effect of contrarian behavior on the dynamics of opinion forming. The not hung
Bush-Kerry 2005 presidential election is shown to belong to the same universal
frame. To conclude, the existence of contrarians hints at the repetition of
hung elections in the near future.Comment: 17 pages, 8 figure
Statistical physics of the Schelling model of segregation
We investigate the static and dynamic properties of a celebrated model of
social segregation, providing a complete explanation of the mechanisms leading
to segregation both in one- and two-dimensional systems. Standard statistical
physics methods shed light on the rich phenomenology of this simple model,
exhibiting static phase transitions typical of kinetic constrained models,
nontrivial coarsening like in driven-particle systems and percolation-related
phenomena.Comment: 4 pages, 3 figure
Dynamical Scaling from Multi-Scale Measurements
We present a new measure of the Dynamical Critical behavior: the "Multi-scale
Dynamical Exponent (MDE)"Comment: 9 pages,Latex, Request figures from [email protected]
Efficient Monte Carlo algorithm and high-precision results for percolation
We present a new Monte Carlo algorithm for studying site or bond percolation
on any lattice. The algorithm allows us to calculate quantities such as the
cluster size distribution or spanning probability over the entire range of site
or bond occupation probabilities from zero to one in a single run which takes
an amount of time scaling linearly with the number of sites on the lattice. We
use our algorithm to determine that the percolation transition occurs at
occupation probability 0.59274621(13) for site percolation on the square
lattice and to provide clear numerical confirmation of the conjectured
4/3-power stretched-exponential tails in the spanning probability functions.Comment: 8 pages, including 3 postscript figures, minor corrections in this
version, plus updated figures for the position of the percolation transitio
Basic kinetic wealth-exchange models: common features and open problems
We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social
Forces 65 (1986) 293; J. Math. Sociol. 26 (2002) 217], Bennati [E. Bennati,
Rivista Internazionale di Scienze Economiche e Commerciali 35 (1988) 735],
Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B
17 (2000) 167], and of Dragulescu and Yakovenko [A. Dragulescu, V. M.
Yakovenko, Eur. Phys. J. B 17 (2000) 723]. Analytical fitting forms for the
equilibrium wealth distributions are proposed. The influence of heterogeneity
is investigated, the appearance of the fat tail in the wealth distribution and
the relaxation to equilibrium are discussed. A unified reformulation of the
models considered is suggested.Comment: Updated version; 9 pages, 5 figures, 2 table
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