TY - JOUR A1 - Abel, Markus A1 - Ahnert, Karsten A1 - Kurths, R. A1 - Mandelj, S. T1 - Additive nonparametric reconstruction of dynamical systems from time series N2 - 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 Y1 - 2005 SN - 1063-651X ER - TY - JOUR A1 - Ahnert, Karsten A1 - Abel, Markus A1 - Kollosche, Matthias A1 - Jorgensen, Per Jorgen A1 - Kofod, Guggi T1 - Soft capacitors for wave energy harvesting JF - Journal of materials chemistry N2 - Wave energy harvesting could be a substantial renewable energy source without impact on the global climate and ecology, yet practical attempts have struggled with the problems of wear and catastrophic failure. An innovative technology for ocean wave energy harvesting was recently proposed, based on the use of soft capacitors. This study presents a realistic theoretical and numerical model for the quantitative characterization of this harvesting method. Parameter regions with optimal behavior are found, and novel material descriptors are determined, which dramatically simplify analysis. The characteristics of currently available materials are evaluated, and found to merit a very conservative estimate of 10 years for raw material cost recovery. Y1 - 2011 U6 - https://doi.org/10.1039/c1jm12454d SN - 0959-9428 SN - 1364-5501 VL - 21 IS - 38 SP - 14492 EP - 14497 PB - Royal Society of Chemistry CY - Cambridge ER - TY - THES A1 - Ahnert, Karsten T1 - Compactons in strongly nonlinear lattices T1 - Kompaktonen in stark nichtlinearen Gittern N2 - In the present work, we study wave phenomena in strongly nonlinear lattices. Such lattices are characterized by the absence of classical linear waves. We demonstrate that compactons – strongly localized solitary waves with tails decaying faster than exponential – exist and that they play a major role in the dynamics of the system under consideration. We investigate compactons in different physical setups. One part deals with lattices of dispersively coupled limit cycle oscillators which find various applications in natural sciences such as Josephson junction arrays or coupled Ginzburg-Landau equations. Another part deals with Hamiltonian lattices. Here, a prominent example in which compactons can be found is the granular chain. In the third part, we study systems which are related to the discrete nonlinear Schrödinger equation describing, for example, coupled optical wave-guides or the dynamics of Bose-Einstein condensates in optical lattices. Our investigations are based on a numerical method to solve the traveling wave equation. This results in a quasi-exact solution (up to numerical errors) which is the compacton. Another ansatz which is employed throughout this work is the quasi-continuous approximation where the lattice is described by a continuous medium. Here, compactons are found analytically, but they are defined on a truly compact support. Remarkably, both ways give similar qualitative and quantitative results. Additionally, we study the dynamical properties of compactons by means of numerical simulation of the lattice equations. Especially, we concentrate on their emergence from physically realizable initial conditions as well as on their stability due to collisions. We show that the collisions are not exactly elastic but that a small part of the energy remains at the location of the collision. In finite lattices, this remaining part will then trigger a multiple scattering process resulting in a chaotic state. N2 - In der hier vorliegenden Arbeit werden Wellenphänomene in stark nichtlinearen Gittern untersucht. Diese Gitter zeichnen sich vor allem durch die Abwesenheit von klassischen linearen Wellen aus. Es wird gezeigt, dass Kompaktonen – stark lokalisierte solitäre Wellen, mit Ausläufern welche schneller als exponentiell abfallen – existieren, und dass sie eine entscheidende Rolle in der Dynamik dieser Gitter spielen. Kompaktonen treten in verschiedenen diskreten physikalischen Systemen auf. Ein Teil der Arbeit behandelt dabei Gitter von dispersiv gekoppelten Oszillatoren, welche beispielsweise Anwendung in gekoppelten Josephsonkontakten oder gekoppelten Ginzburg-Landau-Gleichungen finden. Ein weiterer Teil beschäftigt sich mit Hamiltongittern, wobei die granulare Kette das bekannteste Beispiel ist, in dem Kompaktonen beobachtet werden können. Im dritten Teil werden Systeme, welche im Zusammenhang mit der Diskreten Nichtlinearen Schrödingergleichung stehen, studiert. Diese Gleichung beschreibt beispielsweise Arrays von optischen Wellenleitern oder die Dynamik von Bose-Einstein-Kondensaten in optischen Gittern. Das Studium der Kompaktonen basiert hier hauptsächlich auf dem numerischen Lösen der dazugehörigen Wellengleichung. Dies mündet in einer quasi-exakten Lösung, dem Kompakton, welches bis auf numerische Fehler genau bestimmt werden kann. Ein anderer Ansatz, der in dieser Arbeit mehrfach verwendet wird, ist die Approximation des Gitters durch ein kontinuierliches Medium. Die daraus resultierenden Kompaktonen besitzen einen im mathematischen Sinne kompakten Definitionsbereich. Beide Methoden liefern qualitativ und quantitativ gut übereinstimmende Ergebnisse. Zusätzlich werden die dynamischen Eigenschaften von Kompaktonen mit Hilfe von direkten numerischen Simulationen der Gittergleichungen untersucht. Dabei wird ein Hauptaugenmerk auf die Entstehung von Kompaktonen unter physikalisch realisierbaren Anfangsbedingungen und ihre Kollisionen gelegt. Es wird gezeigt, dass die Wechselwirkung nicht exakt elastisch ist, sondern dass ein Teil ihrer Energie an der Position der Kollision verharrt. In endlichen Gittern führt dies zu einem multiplen Streuprozess, welcher in einem chaotischen Zustand endet. KW - Gitterdynamik KW - Hamilton KW - Compacton KW - Soliton KW - granulare Kette KW - Lattice dynamics KW - Hamiltonian KW - Compacton KW - Soliton KW - Granular chain Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-48539 ER - TY - JOUR A1 - Ahnert, Karsten A1 - Pikovskij, Arkadij T1 - Compactons and chaos in strongly nonlinear lattices N2 - We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are superexponentially localized and present an accurate numerical method allowing one to find them for an arbitrary nonlinearity index. Compactons evolve from rather general initially localized perturbations and collide nearly elastically. Nevertheless, on a long time scale for finite lattices an extensive chaotic state is generally observed. Because of the system's scaling, these dynamical properties are valid for any energy. Y1 - 2009 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.79.026209 SN - 1539-3755 ER - TY - JOUR A1 - Mulansky, Mario A1 - Ahnert, Karsten A1 - Pikovskij, Arkadij A1 - Shepelyansky, Dima L. T1 - Dynamical thermalization of disordered nonlinear lattices N2 - We study numerically how the energy spreads over a finite disordered nonlinear one-dimensional lattice, where all linear modes are exponentially localized by disorder. We establish emergence of dynamical thermalization characterized as an ergodic chaotic dynamical state with a Gibbs distribution over the modes. Our results show that the fraction of thermalizing modes is finite and grows with the nonlinearity strength. Y1 - 2009 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.80.056212 SN - 1539-3755 ER - TY - JOUR A1 - Mulansky, Mario A1 - Ahnert, Karsten A1 - Pikovskij, Arkadij A1 - Shepelyansky, Dima L. T1 - Strong and weak chaos in weakly nonintegrable many-body hamiltonian systems JF - Journal of statistical physics N2 - We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear oscillators by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the measure of chaos is found to be proportional to the coupling strength and lattice length, with the typical maximal Lyapunov exponent being proportional to the square root of coupling. This strong chaos appears as a result of triplet resonances between nearby modes. In addition to strong chaos we observe a weakly chaotic component having much smaller Lyapunov exponent, the measure of which drops approximately as a square of the coupling strength down to smallest couplings we were able to reach. We argue that this weak chaos is linked to the regime of fast Arnold diffusion discussed by Chirikov and Vecheslavov. In disordered lattices of large size we find a subdiffusive spreading of initially localized wave packets over larger and larger number of modes. The relations between the exponent of this spreading and the exponent in the dependence of the fast Arnold diffusion on coupling strength are analyzed. We also trace parallels between the slow spreading of chaos and deterministic rheology. KW - Lyapunov exponent KW - Arnold diffusion KW - Chaos spreading Y1 - 2011 U6 - https://doi.org/10.1007/s10955-011-0335-3 SN - 0022-4715 VL - 145 IS - 5 SP - 1256 EP - 1274 PB - Springer CY - New York ER - TY - JOUR A1 - Mulansky, Mario A1 - Ahnert, Karsten A1 - Pikovskij, Arkadij T1 - Scaling of energy spreading in strongly nonlinear disordered lattices JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - To characterize a destruction of Anderson localization by nonlinearity, we study the spreading behavior of initially localized states in disordered, strongly nonlinear lattices. Due to chaotic nonlinear interaction of localized linear or nonlinear modes, energy spreads nearly subdiffusively. Based on a phenomenological description by virtue of a nonlinear diffusion equation, we establish a one-parameter scaling relation between the velocity of spreading and the density, which is confirmed numerically. From this scaling it follows that for very low densities the spreading slows down compared to the pure power law. Y1 - 2011 U6 - https://doi.org/10.1103/PhysRevE.83.026205 SN - 1539-3755 VL - 83 IS - 2 PB - American Physical Society CY - College Park ER -