Axisymmetric Magnetorotational Instability in Viscous Accretion Disks

Axisymmetric magnetorotational instability (MRI) in viscous accretion disks is investigated by linear analysis and two-dimensional nonlinear simulations. The linear growth of the viscous MRI is characterized by the Reynolds number defined as $R_{\rm MRI} \equiv v_A^2/\nu\Omega$, where $v_A$ is the Alfv{\'e}n velocity, $\nu$ is the kinematic viscosity, and $\Omega$ is the angular velocity of the disk. Although the linear growth rate is suppressed considerably as the Reynolds number decreases, the nonlinear behavior is found to be almost independent of $R_{\rm MRI}$. At the nonlinear evolutionary stage, a two-channel flow continues growing and the Maxwell stress increases until the end of calculations even though the Reynolds number is much smaller than unity. A large portion of the injected energy to the system is converted to the magnetic energy. The gain rate of the thermal energy, on the other hand, is found to be much larger than the viscous heating rate. Nonlinear behavior of the MRI in the viscous regime and its difference from that in the highly resistive regime can be explained schematically by using the characteristics of the linear dispersion relation. Applying our results to the case with both the viscosity and resistivity, it is anticipated that the critical value of the Lundquist number $S_{\rm MRI} \equiv v_A^2/\eta\Omega$ for active turbulence depends on the magnetic Prandtl number $S_{{\rm MRI},c} \propto Pm^{1/2}$ in the regime of $Pm \gg 1$ and remains constant when $Pm \ll 1$, where $Pm \equiv S_{\rm MRI}/R_{\rm MRI} = \nu/\eta$ and $\eta$ is the magnetic diffusivity.Comment: Accepted for publication in ApJ -- 18 pages, 9 figures, 1 tabl

Local Simulations of the Magneto-rotational Instability in Core-Collapse Supernovae

Bearing in mind the application to core-collapse supernovae, we study nonlinear properties of the magneto-rotational instability (MRI) by means of three- dimensional simulations in the framework of a local shearing box approximation. By changing systematically the shear rates that symbolize the degree of differential rotation in nascent proto-neutron stars (PNSs), we derive a scaling relation between the turbulent stress sustained by the MRI and the shear- vorticity ratio. Our parametric survey shows a power-law scaling between the turbulent stress ($>$) and the shear- vorticity ratio ($g_q$) as $> \propto g_q^{\delta}$ with its index $\delta \sim 0.5$. The MRI-amplified magnetic energy has a similar scaling relative to the turbulent stress, while the Maxwell stress has slightly smaller power-law index ($\sim 0.36$). By modeling the effect of viscous heating rates due to the MRI turbulence, we show that the stronger magnetic fields or the larger shear rates initially imposed lead to the higher dissipation rates. For a rapidly rotating PNS with the spin period in milliseconds and with strong magnetic fields of $10^{15}$ G, the energy dissipation rate is estimated to exceed $10^{51} {\rm erg\ sec^{-1}}$. Our results suggest that the conventional magnetohydrodynamic (MHD) mechanism of core-collapse supernovae is likely to be affected by the MRI-driven turbulence, which we speculate, on one hand, could harm the MHD-driven explosions due to the dissipation of the shear rotational energy at the PNS surface, on the other hand the energy deposition there might be potentially favorable for the working of the neutrino-heating mechanism.Comment: 12 pages, 8 figures, Accepted for publication in Ap

Australia\u27s Most Extreme Case : A New Alternative for U.S. Medical Malpractice Liability Reform

The United States currently confronts a severe increase in medical costs and a simultaneous decrease in the availability of health care services. A nearly identical situation recently emerged in the Commonwealth of Australia. This phenomenon, often labeled the medical malpractice crisis, results in part from an increasing litigious trend spurred on by the appeal of potentially enormous damage awards. More lawsuits filed and increased award amounts raise the liability of health care providers and generate uncertainty in the medical malpractice insurance market. This in turn drives up the costs of insurance policy premiums and ultimately forces health care providers to diminish their delivery of health services. In response, many states implement reform initiatives that cap the maximum amount recoverable for an injured patient\u27s non-economic loss. Australian jurisdictions, by contrast, take a more comprehensive approach to liability reform that incorporates a minimum loss requirement and a calculation scheme that proportions non-economics damage awards based on a hypothetical most extreme case. The Australian approach not only limits the quantum of damages available to plaintiffs, but also produces more consistent damage awards than the U.S. cap approach. That is, Australian-style reform reduces the uncertainty posed to insurers in estimating their policyholders\u27 liability. In turn, insurers can more accurately set rates. The reform model followed by Australia is appropriate for the United States. If implemented, it would alleviate inefficiencies created by certain features unique to the U.S. legal system, including civil jury trials and contingency fee agreements. The regulation of non-economic damage awards in a manner consistent with Australia\u27s reform thus presents a desirable model for U.S. policymakers, state legislatures, and the federal government to emulate in the current medical malpractice crisis

Special Relativistic Magnetohydrodynamic Simulation of Two-Component Outflow Powered by Magnetic Explosion on Compact Stars

The nonlinear dynamics of outflows driven by magnetic explosion on the surface of a compact star is investigated through special relativistic magnetohydrodynamic simulations. We adopt, as the initial equilibrium state, a spherical stellar object embedded in hydrostatic plasma which has a density $\rho(r) \propto r^{- \alpha}$ and is threaded by a dipole magnetic field. The injection of magnetic energy at the surface of compact star breaks the equilibrium and triggers a two-component outflow. At the early evolutionary stage, the magnetic pressure increases rapidly around the stellar surface, initiating a magnetically driven outflow. A strong forward shock driven outflow is then excited. The expansion velocity of the magnetically driven outflow is characterized by the Alfv\'en velocity on the stellar surface, and follows a simple scaling relation $v_{\rm mag} \propto {v_{\rm A}}^{1/2}$. When the initial density profile declines steeply with radius, the strong shock is accelerated self-similarly to relativistic velocity ahead of the magnetically driven component. We find that it evolves according to a self-similar relation $\Gamma_{\rm sh} \propto r_{\rm sh}$, where $\Gamma_{\rm sh}$ is the Lorentz factor of the plasma measured at the shock surface $r_{\rm sh}$. Purely hydrodynamic process would be responsible for the acceleration mechanism of the shock driven outflow. Our two-component outflow model, which is the natural outcome of the magnetic explosion, can provide a better understanding of the magnetic active phenomena on various magnetized compact stars.Comment: Accepted for publication in ApJ. 15 pages, 2 tables, 17 figure