5,107 research outputs found
Random Field XY Model in Three Dimensions: The Role of Vortices
We study vortex states in a 3d random-field XY model of up to one billion
lattice spins. Starting with random spin orientations, the sample freezes into
the vortex-glass state with a stretched-exponential decay of spin correlations,
having short correlation length and a low susceptibility, compared to
vortex-free states. In a field opposite to the initial magnetization, peculiar
topological objects -- walls of spins still opposite to the field -- emerge
along the hysteresis curve. On increasing the field strength, the walls develop
cracks bounded by vortex loops. The loops then grow in size and eat the walls
away. Applications to magnets and superconductors are discussed.Comment: 5 pages, 8 figure
Oscillations and secondary bifurcations in nonlinear magnetoconvection
Complicated bifurcation structures that appear in nonlinear systems governed by partial differential equations (PDEs) can be explained by studying appropriate low-order amplitude equations. We demonstrate the power of this approach by considering compressible magnetoconvection. Numerical experiments reveal a transition from a regime with a subcritical Hopf bifurcation from the static solution, to one where finite-amplitude oscillations persist although there is no Hopf bifurcation from the static solution. This transition is associated with a codimension-two bifurcation with a pair of zero eigenvalues. We show that the bifurcation pattern found for the PDEs is indeed predicted by the second-order normal form equation (with cubic nonlinearities) for a Takens-Bogdanov bifurcation with Z2 symmetry. We then extend this equation by adding quintic nonlinearities and analyse the resulting system. Its predictions provide a qualitatively accurate description of solutions of the full PDEs over a wider range of parameter values. Replacing the reflecting (Z2) lateral boundary conditions with periodic [O(2)] boundaries allows stable travelling wave and modulated wave solutions to appear; they could be described by a third-order system
Magnetic diffusivity tensor and dynamo effects in rotating and shearing turbulence
The turbulent magnetic diffusivity tensor is determined in the presence of
rotation or shear. The question is addressed whether dynamo action from the
shear-current effect can explain large-scale magnetic field generation found in
simulations with shear. For this purpose a set of evolution equations for the
response to imposed test fields is solved with turbulent and mean motions
calculated from the momentum and continuity equations. The corresponding
results for the electromotive force are used to calculate turbulent transport
coefficients. The diagonal components of the turbulent magnetic diffusivity
tensor are found to be very close together, but their values increase slightly
with increasing shear and decrease with increasing rotation rate. In the
presence of shear, the sign of the two off-diagonal components of the turbulent
magnetic diffusion tensor is the same and opposite to the sign of the shear.
This implies that dynamo action from the shear--current effect is impossible,
except perhaps for high magnetic Reynolds numbers. However, even though there
is no alpha effect on the average, the components of the alpha tensor display
Gaussian fluctuations around zero. These fluctuations are strong enough to
drive an incoherent alpha--shear dynamo. The incoherent shear--current effect,
on the other hand, is found to be subdominant.Comment: 12 pages, 13 figures, improved version, accepted by Ap
Analysis of the shearing instability in nonlinear convection and magnetoconvection
Numerical experiments on two-dimensional convection with or without a vertical magnetic field reveal a bewildering variety of periodic and aperiodic oscillations. Steady rolls can develop a shearing instability, in which rolls turning over in one direction grow at the expense of rolls turning over in the other, resulting in a net shear across the layer. As the temperature difference across the fluid is increased, two-dimensional pulsating waves occur, in which the direction of shear alternates. We analyse the nonlinear dynamics of this behaviour by first constructing appropriate low-order sets of ordinary differential equations, which show the same behaviour, and then analysing the global bifurcations that lead to these oscillations by constructing one-dimensional return maps. We compare the behaviour of the partial differential equations, the models and the maps in systematic two-parameter studies of both the magnetic and the non-magnetic cases, emphasising how the symmetries of periodic solutions change as a result of global bifurcations. Much of the interesting behaviour is associated with a discontinuous change in the leading direction of a fixed point at a global bifurcation; this change occurs when the magnetic field is introduced
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