TY - JOUR A1 - Seehafer, Norbert A1 - Gellert, Marcus A1 - Kuzanyan, Kirill M. A1 - Pipin, V. V. T1 - Helicity and the solar dynamo Y1 - 2003 ER - TY - JOUR A1 - Feudel, Fred A1 - Gellert, Marcus A1 - Rüdiger, Sten A1 - Witt, Annette A1 - Seehafer, Norbert T1 - Dynamo effect in a driven helical flow Y1 - 2003 UR - http://link.aps.org/abstract/PRE/v68/e046302 ER - TY - JOUR A1 - Feudel, Fred A1 - Witt, Annette A1 - Gellert, Marcus A1 - Kurths, Jürgen A1 - Grebogi, Celso A1 - Sanjuan, Miguel Angel Fernandez T1 - Intersections of stable and unstable manifolds : the skeleton of Lagrangian chaos N2 - We study Hamiltonian chaos generated by the dynamics of passive tracers moving in a two-dimensional fluid flow and describe the complex structure formed in a chaotic layer that separates a vortex region from the shear flow. The stable and unstable manifolds of unstable periodic orbits are computed. It is shown that their intersections in the Poincare map as an invariant set of homoclinic points constitute the backbone of the chaotic layer. Special attention is paid to the finite time properties of the chaotic layer. In particular, finite time Lyapunov exponents are computed and a scaling law of the variance of their distribution is derived. Additionally, the box counting dimension as an effective dimension to characterize the fractal properties of the layer is estimated for different duration times of simulation. Its behavior in the asymptotic time limit is discussed. By computing the Lyapunov exponents and by applying methods of symbolic dynamics, the formation of the layer as a function of the external forcing strength, which in turn represents the perturbation of the originally integrable system, is characterized. In particular, it is shown that the capture of KAM tori by the layer has a remarkable influence on the averaged Lyapunov exponents. (C) 2004 Elsevier Ltd. All rights reserved Y1 - 2005 ER - TY - JOUR A1 - Feudel, Fred A1 - Bergemann, Kay A1 - Tuckerman, Laurette S. A1 - Egbers, C. A1 - Futterer, B. A1 - Gellert, Marcus A1 - Hollerbach, Rainer T1 - Convection patterns in a spherical fluid shell JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Symmetry-breaking bifurcations have been studied for convection in a nonrotating spherical shell whose outer radius is twice the inner radius, under the influence of an externally applied central force field with a radial dependence proportional to 1/r(5). This work is motivated by the GeoFlow experiment, which is performed under microgravity condition at the International Space Station where this particular central force can be generated. In order to predict the observable patterns, simulations together with path-following techniques and stability computations have been applied. Branches of axisymmetric, octahedral, and seven-cell solutions have been traced. The bifurcations producing them have been identified and their stability ranges determined. At higher Rayleigh numbers, time-periodic states with a complex spatiotemporal symmetry are found, which we call breathing patterns. Y1 - 2011 U6 - https://doi.org/10.1103/PhysRevE.83.046304 SN - 1539-3755 VL - 83 IS - 4 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Feudel, Fred A1 - Seehafer, Norbert A1 - Tuckerman, Laurette S. A1 - Gellert, Marcus T1 - Multistability in rotating spherical shell convection JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - The multiplicity of stable convection patterns in a rotating spherical fluid shell heated from the inner boundary and driven by a central gravity field is presented. These solution branches that arise as rotating waves (RWs) are traced for varying Rayleigh number while their symmetry, stability, and bifurcations are studied. At increased Rayleigh numbers all the RWs undergo transitions to modulated rotating waves (MRWs) which are classified by their spatiotemporal symmetry. The generation of a third frequency for some of the MRWs is accompanied by a further loss of symmetry. Eventually a variety of MRWs, three-frequency solutions, and chaotic saddles and attractors control the dynamics for higher Rayleigh numbers. Y1 - 2013 U6 - https://doi.org/10.1103/PhysRevE.87.023021 SN - 1539-3755 VL - 87 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Feudel, Fred A1 - Tuckerman, L. S. A1 - Gellert, Marcus A1 - Seehafer, Norbert T1 - Bifurcations of rotating waves in rotating spherical shell convection JF - Physical Review E N2 - The dynamics and bifurcations of convective waves in rotating and buoyancy-driven spherical Rayleigh-Benard convection are investigated numerically. The solution branches that arise as rotating waves (RWs) are traced by means of path-following methods, by varying the Rayleigh number as a control parameter for different rotation rates. The dependence of the azimuthal drift frequency of the RWs on the Ekman and Rayleigh numbers is determined and discussed. The influence of the rotation rate on the generation and stability of secondary branches is demonstrated. Multistability is typical in the parameter range considered. KW - nonsymmetric linear-systems KW - thermal-convection KW - fluid shells KW - hopf-bifurcation KW - onset KW - magnetoconvection KW - number KW - flow Y1 - 2015 U6 - https://doi.org/10.1103/PhysRevE.92.053015 SN - 1539-3755 SN - 1550-2376 VL - 92 IS - 5 PB - American Physical Society CY - Woodbury ER -