Minding impacting events in a model of stochastic variance

We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold and another one when the local standard deviation outnumbers it. In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterised by large values of the Hurst exponent is greater than 0.8, which are ubiquitous features in complex systems.Comment: 18 pages, 5 figures, 1 table. To published in PLoS on

Magnetic multiparticle systems and symbolic dynamics

The aim of this review is to describe some aspects of the dynamic properties of magnetic multiparticle systems in the micrometer range. These particles include monodisperse magnetic microspheres, and magnetic holes, i.e. nonmagnetic particles dispersed in ferrofluids.The complementary use of analogue simulations and computer simulations to explore the dynamic properties is demonstrated.The ability to describe the complex dynamics of magnetic holes in quantitative symbolic dynamic terms using the notion of knot- and braid theory will be discussed. In particular, statistical analysis of braid words, diffusion, memory effects and correlations for the complex dynamics is illustrated