TY - JOUR A1 - Zienicke, Egbert A1 - Seehafer, Norbert A1 - Feudel, Fred T1 - Bifurcations in two-dimensional Rayleigh-Bénard convection Y1 - 1998 ER - TY - BOOK A1 - Zienicke, Egbert A1 - Seehafer, Norbert A1 - Feudel, Fred T1 - Bifurcations in two-dimensional Rayleigh-Bénard convection T3 - Preprint NLD Y1 - 1997 SN - 1432-2935 VL - 42 PB - Univ. Potsdam 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 - Seehafer, Norbert A1 - Zienicke, Egbert A1 - Feudel, Fred T1 - Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch Y1 - 1996 ER - TY - BOOK A1 - Seehafer, Norbert A1 - Zienicke, Egbert A1 - Feudel, Fred T1 - Absence of magnetohydrodynamic activity in the voltage-driven sheet T3 - Preprint NLD Y1 - 1996 VL - 32 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Seehafer, Norbert A1 - Galanti, B. A1 - Feudel, Fred A1 - Rüdiger, Sten T1 - Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing Y1 - 1996 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Feudel, Fred A1 - Schmidtmann, Olaf T1 - Nonlinear dynamo with ABC forcing Y1 - 1996 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Feudel, Fred A1 - Galanti, B. T1 - Bifurcations in a magnetofluid with helical forcing Y1 - 1998 SN - 1-563-47284-8 ER - TY - JOUR A1 - Seehafer, Norbert A1 - Demircan, Ayhan A1 - Feudel, Fred T1 - Fluid helicity and dynamo effect N2 - Using the incompressible magnetohydrodynamic equations, we have numerically studied the dynamo effect in electrically conducting fluids. The necessary energy input into the system was modeled either by an explicit forcing term in the Navier-Stokes equation or fully selfconsistently by thermal convection in a fluid layer heated from below. If the fluid motion is capable of dynamo action, the dynamo effect appears in the form of a phase transition or bifurcation at some critical strength of the forcing. Both the dynamo bifurcation and subsequent bifurcations that occur when the strength of the forcing is further raised were studied, including the transition to chaotic states. Special attention was paid to the helicity of the flow as well as to the symmetries of the system and symmetry breaking in the bifurcations. The magnetic field tends to be accumulated in special regions of the flow, notably in the vicinity of stagnation points or near the boundaries of convection cells. Y1 - 2001 ER - TY - JOUR A1 - Schmidtmann, Olaf A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Nonlinear Galerkin methods based on the concept of determining modes for the magnetohydrodynamic equations Y1 - 1998 ER - TY - JOUR A1 - Schmidtmann, Olaf A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations Y1 - 1997 ER - TY - BOOK A1 - Schmidtmann, Olaf A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations T3 - Preprint NLD Y1 - 1997 SN - 1432-2935 VL - 35 PB - Univ. Potsdam CY - Potsdam ER - TY - JOUR A1 - Rüdiger, Sten A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Dynamo bifurcations in an array of driven convectionlike rolls Y1 - 1998 ER - TY - BOOK A1 - Rüdiger, Sten A1 - Feudel, Fred A1 - Seehafer, Norbert T1 - Dynamo bifurcations in an array of driven convectionlike rolls T3 - Preprint NLD Y1 - 1998 SN - 1432-2935 VL - 43 PB - Univ. CY - Potsdam 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 - Tuckerman, Laurette S. A1 - Zaks, Michael A1 - Hollerbach, Rainer T1 - Hysteresis of dynamos in rotating spherical shell convection JF - Physical review fluids / American Physical Society N2 - Bifurcations of dynamos in rotating and buoyancy-driven spherical Rayleigh-Benard convection in an electrically conducting fluid are investigated numerically. Both nonmagnetic and magnetic solution branches comprised of rotating waves are traced by path-following techniques, and their bifurcations and interconnections for different Ekman numbers are determined. In particular, the question of whether the dynamo branches bifurcate super- or sub-critically and whether a direct link to the primary pure convective states exists is answered. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevFluids.2.053902 SN - 2469-990X VL - 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 - TY - JOUR A1 - Feudel, Fred A1 - Tuckerman, L. S. A1 - Gellert, M. A1 - Seehafer, Norbert T1 - Bifurcations of rotating waves in rotating spherical shell convection JF - Physical review : E, Statistical, nonlinear and soft matter physics 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. 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 - 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 - Seehafer, Norbert A1 - Tuckerman, Laurette S. T1 - Multistability in rotating spherical shell convection Y1 - 2013 UR - http://link.aps.org/doi/10.1103/PhysRevE.87.023021 (9.9.2013) SN - 1539-3755 ER -