The mechanism of double exponential growth in hyper-inflation

Analyzing historical data of price indices we find an extraordinary growth phenomenon in several examples of hyper-inflation in which price changes are approximated nicely by double-exponential functions of time. In order to explain such behavior we introduce the general coarse-graining technique in physics, the Monte Carlo renormalization group method, to the price dynamics. Starting from a microscopic stochastic equation describing dealers' actions in open markets we obtain a macroscopic noiseless equation of price consistent with the observation. The effect of auto-catalytic shortening of characteristic time caused by mob psychology is shown to be responsible for the double-exponential behavior.Comment: 9 pages, 5 figures and 2 tables, submitted to Physica

The Grounds For Time Dependent Market Potentials From Dealers' Dynamics

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.Comment: 9 pages, 3 figures, proceedings of APFA

Precise calculation of a bond percolation transition and survival rates of nodes in a complex network

<p><b>(a) Cumulative distributions of the survival rate at the critical point (<i>f</i>_c = 0.994) of nodes belonging to the largest shell, <i>k</i>_<i>s</i> = 25, in the initial state. (b) Schematic figure of calculating the survival rate</b>. Each link is supposed to be removed with the same probability and we compare the sizes of separated clusters. The gray nodes belong to the largest cluster. <b>(c) Cumulative distribution of link numbers at the critical point in a log-log plot</b>. The solid line is calculated only in the largest cluster, and a superposition of 100 trials. The dotted line is calculated for all clusters, and we take superposition of 10 trials. The guide line shows the slope of 1.5, the same slope as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0119979#pone.0119979.g001" target="_blank">Fig 1(a)</a>.</p

Nonequilibrium Phase Transitions in Models of Aggregation, Adsorption, and Dissociation

We study nonequilibrium phase transitions in a mass-aggregation model which allows for diffusion, aggregation on contact, dissociation, adsorption and desorption of unit masses. We analyse two limits explicitly. In the first case mass is locally conserved whereas in the second case local conservation is violated. In both cases the system undergoes a dynamical phase transition in all dimensions. In the first case, the steady state mass distribution decays exponentially for large mass in one phase, and develops an infinite aggregate in addition to a power-law mass decay in the other phase. In the second case, the transition is similar except that the infinite aggregate is missing.Comment: Major revision of tex