Search

The article discusses the physical example of a particular style of random walk, a surprise discovery that was uncovered when authorities conducted a circulation tracking of U.S. currency through a Web site. The tracking was originally meant to determine the pattern of the human travel in the country.

Focuses on random walks, a phenomenon involved in particle trajectories that exhibit fractal, chaotic and turbulent behavior. Overview of studies made about random walks; Examples of a non-brownian random walk; Description of the chaos paradigm.

Examples are given of scaling relationships governed by fractional exponents. Additional examples are presented with heavy tail probability distributions governed by a fractional exponent. This includes the analysis of the Boltzmann–Gibbs entropy, subject to an appropriate constraint, to generate long-tailed probability distributions. The stretched exponential distribution is employed to derive a time scale for the glass transition that contains an essential singularity at a critical temperature. These examples demonstrate that there are many routes to producing fractional exponents in physical systems. [Copyright &y& Elsevier]

Anomalous diffusion is employed to model defect motion in materials near their glass transition temperature. Even though the motion of a single defect possesses no characteristic time scale the overall effect of a concentration of defects is to produce stretched exponential relaxation in the glass. This function has a well-defined time scale that depends on the concentration of mobile defects. In our model, the time scale diverges as the temperature is lowered, as well as, increasing with increasing pressure. We use the manner in which this time scale diverges to derive equations for conductivity, dielectric relaxation and viscosity as a function of temperature and pressure that are in good agreement with experimental data that we have checked for polymeric glassy materials. [Copyright &y& Elsevier]

The similarity of documents in a large database of published Fractals articles was examined for redundancy. Three different text matching techniques were used on published Abstracts to identify redundancy candidates, and predictions were verified by reading full text versions of the redundancy candidate articles. A small fraction of the total articles in the database was judged to be redundant. This was viewed as a lower limit, because it excluded cases where the concepts remained the same, but the text was altered substantially. Far more pervasive than redundant publications were publications that did not violate the letter of redundancy but rather violated the spirit of redundancy. There appeared to be widespread publication maximization strategies. Studies that resulted in one comprehensive paper decades ago now result in multiple papers that focus on one major problem, but are differentiated by parameter ranges, or other stratifying variables. This 'paper inflation' is due in large part to the increasing use of metrics (publications, patents, citations, etc) to evaluate research performance, and the researchers' motivation to maximize the metrics. [ABSTRACT FROM AUTHOR]