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Competitive random sequential adsorption of point and fixed-sized particles: analytical results
(2001)
In den letzten 2 Jahrzehnten des 20. Jahrhunderts hat sich mit der rasanten Entwicklung der Nichtlinearen Wissenschaften ein weiterer Umbruch vollzogen, der eine ausgepraegte Nachhaltigkeit in Wissenschaft und Technik ebenso wie in der Gesellschaft erwarten laesst. Die Nichtlinearen Wissenschaften werden auch als Nichtlineare Dynamik, Wissenschaft Komplexer Systeme oder etwas eingegrenzt Chaostheorie bezeichnet.
We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal structures in CRPs. The CRP analysis of prototypical model systems with nonlinear interactions demonstrates that this technique enables to find these nonlinear interrelations from bivariate time series, whereas linear correlation tests do not. Applying the CRP analysis to climatological data, we find a complex relationship between rainfall and El Nino data.
The rescaling of geological data series to a geological reference time series is of major interest in many investigations. For example, geophysical borehole data should be correlated to a given data series whose time scale is known in order to achieve an age-depth function or the sedimentation rate for the borehole data. Usually this synchronization is performed visually and by hand. Instead of using this wiggle matching by eye, we present the application of cross recurrence plots for such tasks. Using this method, the synchronization and rescaling of geological data to a given time scale is much easier and faster than by hand.
The 300 year record of the yearly sunspot numbers and numerically generated trajectory of the solar inertial motion (SIM) were subjects of a synchronization analysis. Phase synchronization of the sunspot cycle and a fast component of the SIM have been found and confirmed with statistical significance in three epochs (1727-1757, 1802-1832 and 1863-1922) of the entire 1700-1997 record. This result can be considered as a quantitative support for the hypothesis that there is a weak interaction of gravity and solar activity.