Mixed phase and bound states in the phase diagram of the extended Hubbard model

The paper examines part of the ground state diagram of the extended Hubbard model, with the on-site attraction U0 in the presence of charge density waves, superconducting and $\eta$-superconducting order parameters. We show the possibility of the stabilization of the mixed state, with all three nonzero order parameters, in the model with nearest neighbor interactions. The other result of the paper is application of the exact solution of the Schrodinger equation for the two electron bound state, as an additional bound for the phase diagram of the model, resulting in the partial suppression of the superconducting state of the s-wave symmetry, in favor of the normal state phase.Comment: submitted to Acta Physica Polonica

Price Variations in a Stock Market With Many Agents

Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large variations may be due to a crowd effect, where agents imitate each other's behavior. The variations over different time scales can be related to each other in a systematic way, similar to the Levy stable distribution proposed by Mandelbrot to describe real market indices. In the simplest, least realistic case, exact results for the statistics of the variations are derived by mapping onto a model of diffusing and annihilating particles, which has been solved by quantum field theory methods. When the agents imitate each other and respond to recent market volatility, different scaling behavior is obtained. In this case the statistics of price variations is consistent with empirical observations. The interplay between ``rational'' traders whose behavior is derived from fundamental analysis of the stock, including dividends, and ``noise traders'', whose behavior is governed solely by studying the market dynamics, is investigated. When the relative number of rational traders is small, ``bubbles'' often occur, where the market price moves outside the range justified by fundamental market analysis. When the number of rational traders is larger, the market price is generally locked within the price range they define.Comment: 39 pages (Latex) + 20 Figures and missing Figure 1 (sorry), submitted to J. Math. Eco

Self-organization of structures and networks from merging and small-scale fluctuations

We discuss merging-and-creation as a self-organizing process for scale-free topologies in networks. Three power-law classes characterized by the power-law exponents 3/2, 2 and 5/2 are identified and the process is generalized to networks. In the network context the merging can be viewed as a consequence of optimization related to more efficient signaling.Comment: Physica A: Statistical Mechanics and its Applications, In Pres

Spatial-temporal correlations in the process to self-organized criticality

A new type of spatial-temporal correlation in the process approaching to the self-organized criticality is investigated for the two simple models for biological evolution. The change behaviors of the position with minimum barrier are shown to be quantitatively different in the two models. Different results of the correlation are given for the two models. We argue that the correlation can be used, together with the power-law distributions, as criteria for self-organized criticality.Comment: 3 pages in RevTeX, 3 eps figure

A Heavenly Example of Scale Free Networks and Self-Organized Criticality

The sun provides an explosive, heavenly example of self-organized criticality. Sudden bursts of intense radiation emanate from rapid rearrangements of the magnetic field network in the corona. Avalanches are triggered by loops of flux that reconnect or snap into lower energy configurations when they are overly stressed. Our recent analysis of observational data reveals that the loops (links) and footpoints (nodes), where they attach on the photosphere, embody a scale free network. The statistics of the avalanches and of the network structure are unified through a simple dynamical model where the avalanches and network co-generate each other into a complex, critical state. This particular example points toward a general dynamical mechanism for self-generation of complex networks.Comment: Submitted to proceedings for the Latin American Workshop on Nonlinear Phenomena, Salvador, Brazil (2003

A Monte Carlo Renormalization Group Approach to the Bak-Sneppen model

A recent renormalization group approach to a modified Bak-Sneppen model is discussed. We propose a self-consistency condition for the blocking scheme to be essential for a successful RG-method applied to self-organized criticality. A new method realizing the RG-approach to the Bak-Sneppen model is presented. It is based on the Monte-Carlo importance sampling idea. The new technique performs much faster than the original proposal. Using this technique we cross-check and improve previous results.Comment: 11 pages, REVTex, 2 Postscript figures include

Restriction of Fourier transforms to curves, II: Some classes with vanishing torsion

We consider the Fourier restriction operators associated to certain degenerate curves in R^d for which the highest torsion vanishes. We prove estimates with respect to affine arclength and with respect to the Euclidean arclength measure on the curve. The estimates have certain uniform features, and the affine arclength results cover families of flat curves.Comment: 26 pages, Final version to appear in the Journal of the Australian Mathematical Societ

Self-Organized Criticality and Stock Market Dynamics: an Empirical Study

The Stock Market is a complex self-interacting system, characterized by an intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically about the possibility that the market is in a self-organized critical state (SOC). A wavelet transform method is used in order to separate high activity periods, related to the avalanches of sandpile models, from quiescent. A statistical analysis of the filtered data show a power law behaviour in the avalanche size, duration and laminar times. The memory process, implied by the power law distribution, of the laminar times is not consistent with classical conservative models for self-organized criticality. We argue that a ``near-SOC'' state or a time dependence in the driver, which may be chaotic, can explain this behaviour.Comment: 16 pages, 13 figures. In press: Physica

Randmoness and Step-like Distribution of Pile Heights in Avalanche Models

The paper develops one-parametric family of the sand-piles dealing with the grains' local losses on the fixed amount. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean height of the pile is destined to describe the crossover. The height's densities corresponding to the models with relaxation of the both types tend one to another as the parameter increases. These densities follow a step-like behaviour in contrast to the peaked shape found in the models with the local loss of the grains down to the fixed level [S. Lubeck, Phys. Rev. E, 62, 6149, (2000)]. A spectral approach based on the long-run properties of the pile height considers the models with deterministic and random relaxation more accurately and distinguishes the both cases up to admissible parameter values.Comment: 5 pages, 5 figure