ABSTRACT
In this work, we study numerically the periodicity of regular regions embedded in chaotic states for the case of an anisotropic magnetic particle. The particle is in the monodomain regime and subject to an applied magnetic field that depends on time. The dissipative Landau-Lifshitz-Gilbert equation models the particle. To perform the characterization, we compute several two-dimensional phase diagrams in the parameter space for the Lyapunov exponents and the isospikes. We observe multiple transitions among periodic states, revealing complex topological structures in the parameter space typical of dynamic systems. To show the finer details of the regular structures, iterative zooms are performed. In particular, we find islands of synchronization for the magnetization and the driven field and several shrimp structures with different periods.
ABSTRACT
We compare the dynamics obtained in two intermediate aspect ratio (diameter over height) experiments. These systems have rotational symmetry and consist of fluid layers that are destabilized using two different methods. The first one is a classical Bénard-Marangoni experiment, where the destabilizing forces, buoyancy and surface tension, are created by temperature gradients. The second system consists of a large drop of liquid metal destabilized using oscillating magnetic fields. In this configuration, the instability is generated by a radial Lorentz force acting on the conducting fluid. Although there are many important differences between the two configurations, the dynamics are quite similar: the patterns break the rotational symmetry, and different azimuthal and radial wavenumbers appear depending on the experimental control parameters. These patterns in most cases are stationary, but for some parameters they exhibit different dynamical behaviours: rotations, transitions between different solutions or cyclic connections between different patterns.
ABSTRACT
An experimental study of pattern formation in Bénard-Marangoni convection with small aspect ratio containers and high Prandtl number fluids is presented. The observed stationary patterns complete previous experimental works performed at different values of aspect ratio and supercriticality. Detailed experimental studies of the flow in some single structures are described, and spatial bifurcations between different stationary planforms for a fixed aspect ratio are shown. These experimental results agree qualitatively with linear theory analysis and with some previous numerical works about boundary conditions effects.
