@book{AbelHolschneider2009, author = {Abel, Markus and Holschneider, Matthias}, title = {Modellierung und Datenbankanalyse komplexer Systeme Teil 1 : Vorlesung 2009-04-23}, publisher = {Univ.-Bibl.}, address = {Potsdam}, year = {2009}, abstract = {Komplexe Systeme reichen von "harten", physikalischen, wie Klimaphysik, Turbulenz in Fluiden oder Plasmen bis zu so genannten "weichen", wie man sie in der Biologie, der Physik weicher Materie, Soziologie oder {\"O}konomie findet. Die Ausbildung von Verst{\"a}ndnis zu einem solchen System beinhaltet eine Beschreibung in Form von Statistiken und schlussendlich mathematischen Gleichungen. Moderne Datenanalyse stellt eine große Menge von Werkzeugen zur Analyse von Komplexit{\"a}t auf verschiedenen Beschreibungsebenen bereit. In diesem Kurs werden statistische Methoden mit einem Schwerpunkt auf dynamischen Systemen diskutiert und einge{\"u}bt. Auf der methodischen Seite werden lineare und nichtlineare Ans{\"a}tze behandelt, inklusive der Standard-Werkzeuge der deskriptiven und schlussfolgernden Statistik, Wavelet Analyse, Nichtparametrische Regression und der Sch{\"a}tzung nichtlinearer Maße wie fraktaler Dimensionen, Entropien und Komplexit{\"a}tsmaßen. Auf der Modellierungsseite werden deterministische und stochastische Systeme, Chaos, Skalierung und das Entstehen von Komplexit{\"a}t durch Wechselwirkung diskutiert - sowohl f{\"u}r diskrete als auch f{\"u}r ausgedehnte Systeme. Die beiden Ans{\"a}tze werden durch Systemanalyse jeweils passender Beispiele vereint.}, language = {de} } @article{AbelFlachPikovskij1998, author = {Abel, Markus and Flach, S. and Pikovskij, Arkadij}, title = {Localisation in a coupled standard map lattice}, year = {1998}, abstract = {We study spatially localized excitations in a lattice of coupled standard maps. Time-periodic solutions (breathers) exist in a range of coupling that is shown to shrink as the period grows to infinity, thus excluding the possibility of time-quasiperiodic breathers. The evolution of initially localized chaotic and quasiperiodic states in a lattice is studied numerically. Chaos is demonstrated to spread}, language = {en} } @article{AbelFlachPikovskij1998, author = {Abel, Markus and Flach, S. and Pikovskij, Arkadij}, title = {Localization in a coupled standard map lattice}, year = {1998}, language = {en} } @article{AbelCelaniVergenietal.2001, author = {Abel, Markus and Celani, A. and Vergeni, D. and Vulpiani, A.}, title = {Front propagation in laminar flows}, year = {2001}, abstract = {The Problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius type are considered under the assumption of no feedback of the concentration on the velocity. Numerical simulations of advection-reaction-diffusion equations have been performed by an algorithm based on discrete-time maps. The results show a generic enhancement of the speed of front propagation by the underlying flow. For small molecular diffusivity, the front speed Vf depends on the typical flow velocity U as a power law with an exponent depending on the topological properties of the flow, and on the ratio of reactive and advective time scales. For open-streamline flows we find always Vf~U, whereas for cellular flows we observe Vf~U1/4 for fast advection and Vf~U3/4 for slow advection.}, language = {en} } @article{AbelCelaniErgnietal.2002, author = {Abel, Markus and Celani, A. and Ergni, V. and Vulpiani, A.}, title = {Front speed enhancement in cellular flows}, issn = {1054-1500}, year = {2002}, language = {en} } @article{AbelBergweilerGerhard2006, author = {Abel, Markus and Bergweiler, Steffen and Gerhard, Reimund}, title = {Synchronization of organ pipes : experimental observations and modeling}, issn = {0001-4966}, doi = {10.1121/1.217044}, year = {2006}, abstract = {We report measurements on the synchronization properties of organ pipes. First, we investigate influence of an external acoustical signal from a loudspeaker on the sound of an organ pipe. Second, the mutual influence of two pipes with different pitch is analyzed. In analogy to the externally driven, or mutually coupled self-sustained oscillators, one observes a frequency locking, which can be explained by synchronization theory. Further, we measure the dependence of the frequency of the signals emitted by two mutually detuned pipes with varying distance between the pipes. The spectrum shows a broad '' hump '' structure, not found for coupled oscillators. This indicates a complex coupling of the two organ pipes leading to nonlinear beat phenomena.}, language = {en} } @article{AbelAhnertKurthsetal.2005, author = {Abel, Markus and Ahnert, Karsten and Kurths, R. and Mandelj, S.}, title = {Additive nonparametric reconstruction of dynamical systems from time series}, issn = {1063-651X}, year = {2005}, abstract = {We present a nonparametric way to retrieve an additive system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long-term predictions. We apply our method to a modified chaotic Chua oscillator in order to demonstrate its potential}, language = {en} } @phdthesis{Abel2005, author = {Abel, Markus}, title = {Turbulent flows : transport, analysis and modeling}, address = {Potsdam}, pages = {Getr. Z{\"a}hlung}, year = {2005}, language = {en} } @article{Abel2004, author = {Abel, Markus}, title = {Nonparametric modeling and spatiotemporal dynamical systems}, issn = {0218-1274}, year = {2004}, abstract = {This article describes how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by means of backfitting or more general algorithms, like the alternating conditional expectation value one. The method is illustrated by numerically generated data. As an application, the example of vortex ripple dynamics, a highly complex fluid-granular system, is treated}, language = {en} } @phdthesis{Abel1998, author = {Abel, Markus}, title = {Localization in driven nonlinear lattices}, address = {Potsdam}, pages = {100 S. : graph. Darst.}, year = {1998}, language = {en} }