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Register a new userBoundary between Stable and Unstable Regimes of Accretion. Ordered and Chaotic Unstable Regimes
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We present a study of the Rayleigh-Taylor unstable regime of accretion onto rotating magnetized stars in a set of high grid resolution three-dimensional (3D) magnetohydrodynamic (MHD) simulations performed in low-viscosity discs. We find that the boundary between the stable and unstable regimes is determined almost entirely by the fastness parameter omega_s=Omega_star/Omega_K(r_m), where Omega_star is the angular velocity of the star and Omega_K(r_m) is the angular velocity of the Keplerian disc at the disc-magnetosphere boundary r=r_m. We found that accretion is unstable if omega_s < 0.6. Accretion through instabilities is present in stars with different magnetospheric sizes. However, only in stars with relatively small magnetospheres, r_m/R_star < 7, do the unstable tongues produce chaotic hot spots on the stellar surface and irregular light-curves. At even smaller values of the fastness parameter, omega_s < 0.45, multiple irregular tongues merge, forming one or two ordered unstable tongues that rotate with the angular frequency of the inner disc. This transition occurs in stars with even smaller magnetospheres, r_m/R_star < 4.2. Most of our simulations were performed at a small tilt of the dipole magnetosphere, Theta=5 degrees, and a small viscosity parameter alpha=0.02. Test simulations at higher alpha values show that many more cases become unstable, and the light-curves become even more irregular. Test simulations at larger tilts of the dipole Theta show that instability is present, however, accretion in two funnel streams dominates if Theta > 15 degrees. The results of these simulations can be applied to accreting magnetized stars with relatively small magnetospheres: Classical T Tauri stars, accreting millisecond X-ray pulsars, and cataclysmics variables.
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We investigated the boundary between stable and unstable regimes of accretion and its dependence on different parameters. Simulations were performed using a cubed sphere code with high grid resolution (244 grid points in the azimuthal direction), which is twice as high as that used in our earlier studies. We chose a very low viscosity value, with alpha-parameter alpha=0.02. We observed from the simulations that the boundary strongly depends on the ratio between magnetospheric radius r_m (where the magnetic stress in the magnetosphere matches the matter stress in the disk) and corotation radius r_cor (where the Keplerian velocity in the disk is equal to the angular velocity of the star). For a small misalignment angle of the dipole field, Theta=5 degrees, accretion is unstable if r_cor/r_m>1.35, and is stable otherwise. In cases of a larger misalignment angle of the dipole, Theta=20 degrees, instability occurs at slightly larger values, r_cor/r_m>1.41.
Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading e.g. to the formation of spatial and temporal solitons, rogue waves and chaotic dynamics. Here we experimentally demonstrate the existence of a modulational instability in condensates of cavity polaritons, arising from the strong coupling of cavity photons with quantum well excitons. For this purpose we investigate the spatiotemporal coherence properties of polariton condensates in GaAs-based microcavities under continuous-wave pumping. The chaotic behavior of the instability results in a strongly reduced spatial and temporal coherence and a significantly inhomogeneous density. Additionally we show how the instability can be tamed by introducing a periodic potential so that condensation occurs into negative mass states, leading to largely improved coherence and homogeneity. These results pave the way to the exploration of long-range order in dissipative quantum fluids of light within a controlled platform.
An update is given on the current status of solar and stellar dynamos. At present, it is still unclear why stellar cycle frequencies increase with rotation frequency in such a way that their ratio increases with stellar activity. The small-scale dynamo is expected to operate in spite of a small value of the magnetic Prandtl number in stars. Whether or not the global magnetic activity in stars is a shallow or deeply rooted phenomenon is another open question. Progress in demonstrating the presence and importance of magnetic helicity fluxes in dynamos is briefly reviewed, and finally the role of nonlocality is emphasized in modeling stellar dynamos using the mean-field approach. On the other hand, direct numerical simulations have now come to the point where the models show solar-like equatorward migration that can be compared with observations and that need to be understood theoretically.
To determine the stability and instability of a given steady galaxy configuration is one of the fundamental problems in the Vlasov theory for galaxy dynamics. In this article, we study the stability of isotropic spherical symmetric galaxy models $f_{0}(E)$, for which the distribution function $f_{0}$ depends on the particle energy $E$ only. In the first part of the article, we derive the first sufficient criterion for linear instability of $f_{0}(E):$ $f_{0}(E)$ is linearly unstable if the second-order operator [ A_{0}equiv-Delta+4piint f_{0}^{prime}(E){I-mathcal{P}}dv ] has a negative direction, where $mathcal{P}$ is the projection onto the function space ${g(E,L)},$ $L$ being the angular momentum [see the explicit formula (ref{A0-radial})]. In the second part of the article, we prove that for the important King model, the corresponding $A_{0}$ is positive definite. Such a positivity leads to the nonlinear stability of the King model under all spherically symmetric perturbations.
We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian, and possesses stable and unstable regimes. The dynamics of the whole system is shown to be strongly influenced by the quantum subsystem. In particular, chaos is seen to arise in the vicinity of a quantum critical case, which separates the stable and unstable regimes of the bosonic system.
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