TY - JOUR A1 - Kurths, Jürgen A1 - Schwarz, Udo T1 - Application of techniques of nonlinear dynamics to SS Cyg N2 - We look for structural properties in the light curve of the dwarf nova SS Cyg by means of techniques from nonlinear dynamics. Applying the popular Grassberger-Procaccia procedure, Cannizzo and Goddings (1988) showed that there is no evidence for a low-dimensional attractor underlying this record. Because there are some hints for order in the light curve, we search for other signatures of deterministic systems. Therefore, we use other methods recently developed in this theory, such as local linear prediction and recurrence maps. Our main findings are: i] the prediction error grows exponentially during outburst phases, but via a power law in the quiescent states, ii] there are some rather regular patterns in this light curve which sometimes recur, but the recurrence is not regular. This leads to the following conclusions: i] The outburst dynamics shows a higher degree of order than the quiescent one. There are some hints for deterministic chaos in the outburst behavior. ii] The light curve is a complex mixture of deterministic and stochastic structures. The analysis presented in this paper shows that methods of nonlinear dynamics can be an efficient tool for the study of complex processes, even if there is no evidence for a low-dimensional attractor. Y1 - 1993 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/SS_Cyg_AIP.ps.gz SN - 0-7503-0282-8 ER - TY - JOUR A1 - Schwarz, udo A1 - Benz, Arnold O. A1 - Kurths, Jürgen A1 - Witt, Annette T1 - Analysis of solar spike events by means of symbolic dynamics methods N2 - Using quantities of symbolic dynamics, such as mutual information, Shannon information and algorithmic complexity, we have searched for interrelations of spikes emitted simultaneously at different frequencies during the impulsive phase of a flare event. As the spikes are related to the flare energy release and are interpreted as emissions originating at different sites having different magnetic field strengths, any relation in frequency is interpretated as a relation in space. This approach is appropriate to characterize such spatio-temporal patterns, whereas the popular estimate of fractal dimensions can be applied to low-dimensional systems only. Depending on the energy release and emission processes, two types of fragmentation are possible: a scenario of global organization (spikes are emitted in a succession of similar events by the same system) or a scenario of local organization (many systems triggered by an initial event). Mutual information which is a generalization of correlation indicates a relation in frequency beyond the bandwidth of individual spikes. The scans in the spectrograms with large mutual information also show a low level of Shannon information and algorithmic complexity, indicating that the simultaneous appearance of spikes at other frequencies is not a completely stochastic phenomenon (white noise). It may be caused by a nonlinear deterministic system or by a Markov process. By means of mutual information we find a memory over frequency intervals up to 60 MHz. Shannon information and algorithmic complexity concern the mbox{whole} frequency region, i.e. the global source region. A global organization is also apparent in quasi-periodic changes of the Shannon information and algorithmic complexity in the range of 2 - 8 seconds. The finding is compatible with a scenario of local organization in which the information of one event spreads spatially and triggers further events at different places. The region is not an ensemble of independently flashing sources, each representing a system that cascades in energy after an initial trigger. On the contrary, there is a causal connection between the sources at any time. The analysis of the four spike events suggests that the structure in frequency is not stochastic but a process in which spikes at nearby locations are simultaneously triggered by a common exciter. Y1 - 1993 UR - http://www.astro.phys.ethz.ch/papers/benz/schwarz/schwarz/schwarz.html SN - 004-6361 ER - TY - JOUR A1 - Schwarz, Udo T1 - Das Maunder-Minimum : alles sonnenklar, oder? N2 - Im vorletzten Absatz des o.g. Kurzberichtes befindet sich eine falsche Aussage zur C14-Produktion waehrend des Maunder-Minimums. Wie aus der in meiner Abbildung gezeigten Delta C14-Haeufigkeit fuer den Zeitraum des Maunder-Minimums hervorgeht, war die C14-Produktion zu dieser Zeit erhoeht statt, wie von Herrn Buehrke und anderen Autoren in der Literatur behauptet, erniedrigt. Die allgemein akzeptierte Begruendung fuer die erhoehte C14-Produktion lautet: Der geringere Sonnenwind schirmt die Erde weniger stark von der kosmischen Strahlung ab. Y1 - 1994 ER - TY - JOUR A1 - Kurths, Jürgen A1 - Schwarz, Udo T1 - Chaos theory and radio emission N2 - The application of chaos theory has become popular to understand the nature of various features of solar activity because most of them are far from regular. The usual approach, however, that is basing on finding low- dimensional structures of the underlying processes seems to be successful only in a few exceptional cases, such as in rather coherent phenomena as coronal pulsations. It is important to note that most phenomena in solar radio emission are more complex. We present two kinds of techniques from nonlinear dynamics which can be useful to analyse such phenomena: i] Fragmentation processes observed in solar spike events are studied by means of symbolic dynamics methods. Different measures of complexity calculated from such observations reveal that there is some order in this fragmentation. ii] Bursts are a typical transient phenomenon. To study energization processes causing impulsive microwave bursts, the wavelet analysis is applied. It exhibits structural differences of the pre- and post-impulsive phase in cases where the power spectra of both are not distinct. Y1 - 1994 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/Review.ps.gz ER - TY - JOUR A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Parlitz, Ulrich A1 - Sonett, Charles P. T1 - Testing for nonlinearity in radiocarbon data N2 - The radiocarbon record that has been extended from 7199 BC to 1891 AD is of fundamental importance to understand century-scale variations of solar activity. We have, therefore, studied how to extract information from dynamic reconstructions of this observational record. Using some rather unusual methods of nonlinear dynamics, we have found that the data are significantly different from linear colored noise and that there is some evidence of nonlinear behavior. The method of recurrence plots exhibits that the grand minima of solar activity are quite different in their recurrence. Most remarkably, it suggests that the recent epoch seems to be similar to the Medieval maximum. Y1 - 1994 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/n.ps.gz SN - 1023-5809 ER - TY - JOUR A1 - Meister, Claudia-Veronika A1 - Liperovsky, Viktor A. A1 - Schlegel, K. A1 - Haldoupis, Ch. T1 - Currents and turbulence in and near mid-latitude sporadic e-layers caused by strong acoustic impulses JF - Preprint NLD Y1 - 1995 VL - 11 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Witt, Annette T1 - Non-linear data analysis in solar radio astronomy N2 - We have discussed some tools from nonlinear dynamics which may help to analyze transient phenomena, such as solar bursts. The structure function known from turbulence theory is an appropriate method to find out some scaling behavior of fluctuations in time. More generally, the wavelet analysis, which is some generalization of the power spectrum, exhibits information on the location as well as the size of hidden characteristic features. Applying both techniques to microwave bursts, we have found some scaling properties that refer to the existence of hierarchic time structures. This is in good accordance with the electric circuit model for describing the flare-particle energization process. Y1 - 1995 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/lnp.ps.gz ER - TY - JOUR A1 - Voss, Henning U. A1 - Kurths, Jürgen A1 - Schwarz, Udo T1 - Reconstruction of grand minima of solar activity from radiocarbon data : linear and nonlinear signal analysis N2 - Using a special technique of data analysis, we have found out 34 grand minima of solar activity in a 7,700 years long C14 record. The method used rests on a proper filtering of the C14 record and the extrapolation of verifiable results for the later history back in time. Additionally, we have applied a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of grand minima by Eddy, but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested esp. the model of Barnes et al. There are hints for that the grand minima might solely be driven by the 209--year period found in the C14 record. Y1 - 1996 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/vks.ps.gz ER - TY - JOUR A1 - Feudel, Fred A1 - Seehafer, Norbert A1 - Rüdiger, Sten T1 - Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing JF - Preprint NLD Y1 - 1996 VL - 31 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Maaß, Peter A1 - Pereverzev, Sergei V. A1 - Ramlau, Ronny A1 - Solodky, Sergei G. T1 - An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection JF - Preprint NLD Y1 - 1998 SN - 1432-2935 VL - 48 PB - Univ. Potsdam CY - Potsdam ER - TY - JOUR A1 - Liperovsky, Viktor A. A1 - Pochotelov, O. A. A1 - Liperovskaya, E. V. A1 - Parrot, M. A1 - Meister, Claudia-Veronika A1 - Alimov, O. A. T1 - Modifications of sporadic E-layers caused by seismic activity JF - Preprint NLD Y1 - 1998 SN - 1432-2935 VL - 49 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Witt, Annette A1 - Feudel, Fred A1 - Gebogi, C. A1 - Kurths, Jürgen A1 - Braun, Robert T1 - Tracer dynamics in a flow of driven vortices JF - Preprint NLD Y1 - 1998 SN - 1432-2935 VL - 51 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Fatkullin, Mars N. A1 - Förster, Matthias A1 - Schwarz, Udo T1 - Irregularities of electron density and temperature in the day sector of the plasmasphere base during the summer season at high solar activity by observations of the aktivnyi satellite N2 - Based on the data of the Magion2 subsatellite of the Intercosmos24 satellite, an example of small-scale irregularities of the electron concentration with linear dimensions l ~ 100-300 m in the polar ion- osphere of the morning sector under field-aligned currents at altitudes of 1800-2030 km during the main phase of the magnetic storm of June 13, 1990 is presented. The dependence of the spectral index of the above small-scale irregularities on latitude is determined for the first time. Certain mechanisms of the generation of these small-scale irregularities are also qualitatively discussed. Y1 - 1999 UR - http://www.maik.rssi.ru/cgi-bin/search.pl?type=abstract&name=cosres&number=3&year=97&page=226 ER - TY - JOUR A1 - Timmer, Jens A1 - Schwarz, Udo A1 - Voss, Henning U. A1 - Wardinski, Ingo A1 - Belloni, Tomaso A1 - Hasinger, Günther A1 - VanDerKlis, Michael A1 - Kurths, Jürgen T1 - Linear and Nonlinear Time Series Analysis of the Black Hole Candidate Cygnus X-1 N2 - We analyze the variability in the x-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the overall second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear and nonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data. Y1 - 2000 UR - http://pre.aps.org/ ER - TY - JOUR A1 - Palus, Milan A1 - Kurths, Jürgen A1 - Schwarz, Udo A1 - Novotná, Dagmar A1 - Charvátová, Ivanka T1 - Is the solar activity cycle synchronized with the solar inertial motion? N2 - 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. Y1 - 2001 UR - http://ejournals.wspc.com.sg/ijbc/10/1011/S0218127400001766.html ER - TY - JOUR A1 - Kurths, Jürgen A1 - Schwarz, Udo T1 - Nichtlineare Wissenschaften - neue Paradigmen und Konzepte N2 - 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. Y1 - 2001 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/2001ArtChaos.pdf SN - 0177- 3674 ER - TY - JOUR A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Lange, Holger A1 - Hauhs, M. T1 - Conceptual model of runoff from a forested catchment N2 - We investigate the relationship between precipitation and runoff data from a small forested catchment in the Harz mountains (Germany). For this purpose, we develop a conceptual model including memory effects to predict the runoff signal using the precipitation data as input. An enhanced variant of the model also includes air temperature as input variable. We show in terms of correlation functions that this model describes main dynamical properties of the runoff, especially the delay between rain event and runoff response as the annual persistence in the runoff data. Y1 - 2001 UR - http://journals.worldscientific.com.sg/ijbc/11/1110/S0218127401003619.html ER - TY - JOUR A1 - Sitz, Andre A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Maus, Doris A1 - Wiese, Michael A1 - Warnecke, Günter T1 - Signatures of acoustic emission signals generated during high speed cutting N2 - Acoustic emission signals generated during high speed cutting of steel are investigated. The data are represen ted in time-folded form. Several methods from linear and nonlinear data analysis based on time- and frequency- domain are applied to the data and reveal signatures of the observed acoustic emission signal. These investiga tions are necessary for modeling the cutting process by means of differential equations. Y1 - 2001 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/21618.pdf ER - TY - JOUR A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Hasinger, Günther A1 - Belloni, Tomaso T1 - Nonlinear Time series analysis of the X-ray flux of compact objects N2 - We analyse the X-ray light curves of compact objects using linear and nonlinear time series analysis methods. A Power Density Spectrum (PDS) describes the overall second order properties of the observed data well. To look beyond we propose the nonlinear Q-statistic to detect an asymmetry of the time series. This allows us to find relevant time scales. This method even grants a subclassification of the known states of X-ray sources. Y1 - 2001 SN - 0004-640x ER - TY - JOUR A1 - Cser, Adrienn A1 - Donner, Reik Volker A1 - Schwarz, Udo A1 - Feudel, Ulrike A1 - Otto, Andreas H. T1 - Statistical parameters of a control strategy of laser beam melt ablation N2 - Laser beam melt ablation - a contact-free machining process - offers several advantages compared to conventional processing mechanisms: there exists no tool wear and even extremely hard or brittle materials can be processed. During ablation the workpiece is molten by a CO2-laser beam, this melt is then driven out by the impulse of a process gas. The idea behind laser ablation is rather simple, but it has a major limitation in practical applications: with increasing ablation rates surface quality of the workpiece processed declines rapidly. At high ablation rates, depending on the process parameters different periodic-like structures can be observed on the ablated surface. These structures show a dependence on the line energy, which has been identified as a fundamental control parameter. In dependence on this parameter several regimes with different behaviours of the process have been separated. These regimes are distinguishable as well in the surfaces obtained as in the signals gained by the measurement of the process emissions. Further aim is to identify the different modes of the system and reach a deeper understanding of the dynamics of the molten material in order to understand the formation of these surface structures. With this it should be possible to influence the system in the direction of avoiding structure formation even at high ablation rates. Relying on the results on-line monitoring and control of the process should be studied. Y1 - 2001 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/2001-EIS.ps ER -