Multidimensional Consensus model on a Barabasi-Albert network

A Consensus Model according to Deffuant on a directed Barabasi-Albert network was simulated. Agents have opinions on different subjects. A multi-component subject vector was used. The opinions are discrete. The analysis regards distribution and clusters of agents which are on agreement in the opinions of the subjects. Remarkable results are on the one hand, that there mostly exists no absolute consens. It determines depending on the ratio of number of agents to the number of subjects, whether the communication ends in a consens or a pluralism. Mostly a second robust cluster remains, in its size depending on the number of subjects. Two agents agree either in (nearly) all or (nearly) no subject. The operative parameter of the consens-formating-process is the tolerance in change of views of the group-members.Comment: 14 pages including all 10 figures, for IJMPC 16, issue

Universality of the Threshold for Complete Consensus for the Opinion Dynamics of Deffuant et al

In the compromise model of Deffuant et al., opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. The opinions of a randomly chosen pair of compatible agents get closer to each other. We provide strong numerical evidence that the threshold value of \epsilon above which all agents share the same opinion in the final configuration is 1/2, independently of the underlying social topology.Comment: 8 pages, 4 figures, to appear in Int. J. Mod. Phys. C 15, issue

Election results and the Sznajd model on Barabasi network

The network of Barabasi and Albert, a preferential growth model where a new node is linked to the old ones with a probability proportional to their connectivity, is applied to Brazilian election results. The application of the Sznajd rule, that only agreeing pairs of people can convince their neighbours, gives a vote distribution in good agreement with reality.Comment: 7 pages including two figures, for Eur. Phys. J.

A generalized spin model of financial markets

We reformulate the Cont-Bouchaud model of financial markets in terms of classical "super-spins" where the spin value is a measure of the number of individual traders represented by a portfolio manager of an investment agency. We then extend this simplified model by switching on interactions among the super-spins to model the tendency of agencies getting influenced by the opinion of other managers. We also introduce a fictitious temperature (to model other random influences), and time-dependent local fields to model slowly changing optimistic or pessimistic bias of traders. We point out close similarities between the price variations in our model with $N$ super-spins and total displacements in an $N$-step Levy flight. We demonstrate the phenomena of natural and artificially created bubbles and subsequent crashes as well as the occurrence of "fat tails" in the distributions of stock price variations.Comment: 11 pages LATEX, 7 postscript figures; longer text with theoretical analysis, more accurate numerical data, better terminology, additional references. Accepted for publication in European Physical Journal

Number of spanning clusters at the high-dimensional percolation thresholds

A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions for d>6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review

Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model

The long-time behavior of transport coefficients in a model for spatially heterogeneous media in two and three dimensions is investigated by Molecular Dynamics simulations. The behavior of the velocity auto-correlation function is rationalized in terms of a competition of the critical relaxation due to the underlying percolation transition and the hydrodynamic power-law anomalies. In two dimensions and in the absence of a diffusive mode, another power law anomaly due to trapping is found with an exponent -3 instead of -2. Further, the logarithmic divergence of the Burnett coefficient is corroborated in the dilute limit; at finite density, however, it is dominated by stronger divergences.Comment: Full-length paragraph added that exemplifies the relevance for dense fluids and makes a connection to recently observed, novel long-time tails in a hard-sphere flui

Applications and Sexual Version of a Simple Model for Biological Ageing

We use a simple model for biological ageing to study the mortality of the population, obtaining a good agreement with the Gompertz law. We also simulate the same model on a square lattice, considering different strategies of parental care. The results are in agreement with those obtained earlier with the more complicated Penna model for biological ageing. Finally, we present the sexual version of this simple model.Comment: For Int.J.Mod.Phys.C Dec. 2001; 11 pages including 6 fig

Network of social groups or Let's have a party

We present a simple model for growing up and depletion of parties due to the permanent communication between the participants of the events. Because of the rapid exchange of information, everybody is able to evaluate its own and and all other parties by means of the list of its friends. Therefore the number of participants at different parties can be changed incessantly. Depending on the deepness of the social contacts, which will be characterized by a parameter $\alpha$, a stable distribution of party members emerges. At a critical $\alpha_c$ an abrupt depletion of almost all parties is observed and as the consequence all the peoples are assembled at a single party. The model is based on a hierarchical social network. The probability that a certain person is contacted to another one depends on the social distance introduced within the network and homophily parameter $\alpha$.Comment: 15 pages, 6 figure