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Fluid Helicity and Dynamo Bifurcations
 Phys. Lett. A
"... The bifurcation behaviour of the 3D magnetohydrodynamic equations has been studied for external forcings of varying degree of helicity. With increasing strength of the forcing a primary nonmagnetic steady state loses stability to a magnetic periodic state if the helicity exceeds a threshold value a ..."
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The bifurcation behaviour of the 3D magnetohydrodynamic equations has been studied for external forcings of varying degree of helicity. With increasing strength of the forcing a primary nonmagnetic steady state loses stability to a magnetic periodic state if the helicity exceeds a threshold value
c © World Scientific Publishing Company The dynamo bifurcation in rotating spherical shells
, 2009
"... ar ..."
Fluid helicity and dynamo effect
"... 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 NavierStokes equation or fully selfconsistently by thermal convec ..."
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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
The dynamo effect
 In Peyresq Lectures on Nonlinear Phenomena, vol. II (2003
"... We first present basic results about advection, diffusion and amplification of a magnetic field by the flow of an electrically conducting fluid. This topic has been initially motivated by the study of possible mechanisms to explain the magnetic fields of astrophysical objects. However, selfgenerati ..."
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generation of a magnetic field by an electrically conducting fluid, the socalled dynamo effect, is also a typical bifurcation problem that involves many interesting aspects from the viewpoint of dynamical system theory: the effect of the flow geometry on the nature of the bifurcation, the effect of turbulent
Lowdimensional dynamo modelling and symmetrybreaking bifurcations
"... Motivated by the successful Karlsruhe dynamo experiment, a relatively lowdimensional dynamo model is proposed. It is based on a strong truncation of the magnetohydrodynamic (MHD) equations with an external forcing of the Roberts type and the requirement that the model system satisfies the symmetri ..."
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the symmetries of the full MHD system, so that the first symmetrybreaking bifurcations can be captured. The backbone of the Roberts dynamo is formed by the Roberts flow, a helical mean magnetic field and another part of the magnetic field coupled to these two by triadic mode interactions. A minimum truncation
Bifurcation Phenomena and Dynamo Effect in Electrically Conducting Fluids
"... Electrically conducting uids in motion can act as selfexcited dynamos. The magnetic fields of celestial bodies like the Earth and the Sun are generated by such dynamos. Their theory aims at modeling and understanding both the kinematic and dynamic aspects of the underlying processes. Kinematic dyna ..."
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Electrically conducting uids in motion can act as selfexcited dynamos. The magnetic fields of celestial bodies like the Earth and the Sun are generated by such dynamos. Their theory aims at modeling and understanding both the kinematic and dynamic aspects of the underlying processes. Kinematic
NONLINEAR SPACEPERIODIC DYNAMO IN AN ABCFORCED
, 2001
"... Nonlinear behavior of an MHD system with ABC forcing under periodic boundary conditions is considered. Most computations are performed for a fixed kinematic Reynolds number and magnetic Reynolds numbers increasing from 0 to 60. The kinematic Reynolds number is small enough for the trivial solution ..."
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with a zero magnetic field to be stable to velocity perturbations. At the critical magnetic Reynolds number for the onset of instability of the trivial solution the dominant eigenvalue of the kinematic dynamo problem is real. In agreement with the bifurcation theory new steady states with non
Chaos in Accretion Disk Dynamos?
, 1995
"... Accretion disks appear to be favourable places for dynamo action, because of their strong differential rotation. A simple estimate of the strength of an accretion disk dynamo indicates that it will be highly nonlinear. In spite of this, most studies hitherto have assumed a linear model for the dyna ..."
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for the dynamo. Here we investigate nonlinear, axisymmetric meanfield dynamos in accretion disks in order to study the route to chaotic solutions in certain parameter regimes. We find a sequence of bifurcations that lead eventually to chaos. Finally, the physical significance of these results is discussed.
On a Codimension Three Bifurcation Arising in a Simple Dynamo Model
"... In this paper we investigate the dynamics associated with a degenerate codimension two TakensBogdanov bifurcation which arises in a recently derived model for selfexciting dynamo action introduced by Hide et al. [1]. The general unfolding of such a codimension three bifurcation has already been di ..."
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In this paper we investigate the dynamics associated with a degenerate codimension two TakensBogdanov bifurcation which arises in a recently derived model for selfexciting dynamo action introduced by Hide et al. [1]. The general unfolding of such a codimension three bifurcation has already been
On a Codimension Three Bifurcation Arising in a Simple Dynamo Model
"... On a codimension three bifurcation arising in a ..."
Results 1  10
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33