Unstable magnetohydrodynamical continuous spectrum of accretion disks. A new route to magnetohydrodynamical turbulence in accretion disks

We present a detailed study of localised magnetohydrodynamical (MHD) instabilities occuring in two--dimensional magnetized accretion disks. We model axisymmetric MHD disk tori, and solve the equations governing a two--dimensional magnetized accretion disk equilibrium and linear wave modes about this equilibrium. We show the existence of novel MHD instabilities in these two--dimensional equilibria which do not occur in an accretion disk in the cylindrical limit. The disk equilibria are numerically computed by the FINESSE code. The stability of accretion disks is investigated analytically as well as numerically. We use the PHOENIX code to compute all the waves and instabilities accessible to the computed disk equilibrium. We concentrate on strongly magnetized disks and sub--Keplerian rotation in a large part of the disk. These disk equilibria show that the thermal pressure of the disk can only decrease outwards if there is a strong gravitational potential. Our theoretical stability analysis shows that convective continuum instabilities can only appear if the density contours coincide with the poloidal magnetic flux contours. Our numerical results confirm and complement this theoretical analysis. Furthermore, these results show that the influence of gravity can either be stabilizing or destabilizing on this new kind of MHD instability. In the likely case of a non--constant density, the height of the disk should exceed a threshold before this type of instability can play a role. This localised MHD instability provides an ideal, linear route to MHD turbulence in strongly magnetized accretion disk tori.Comment: 20 pages, 10 figures, accepted for publication in Astronomy & Astrophysic

Pressure-driven Instabilities in Cylindrical Geometry: A New General Criterion

A new criterion for pressure-driven interchange instabilities in cylindrical geometry is derived, based on an alternate use of the Energy Principle. This criterion is inequivalent to Suydam's criterion and does not contain the magnetic shear. In fact, it is shown that Suydam's criterion relates to the instability of the slow magnetosonic branch, while the present criterion relates to the Alfv\'enic one, which is the most dangerous of the two. These findings explain why pressure-driven modes nearly always exist even if Suydam's criterion is satisfied by a large margin.Comment: 4 pages. Submitted to Phys. Rev. Let

Toward detailed prominence seismology - II. Charting the continuous magnetohydrodynamic spectrum

Starting from accurate MHD flux rope equilibria containing prominence condensations, we initiate a systematic survey of their linear eigenoscillations. To quantify the full spectrum of linear MHD eigenmodes, we require knowledge of all flux-surface localized modes, charting out the continuous parts of the MHD spectrum. We combine analytical and numerical findings for the continuous spectrum for realistic prominence configurations. The equations governing all eigenmodes for translationally symmetric, gravitating equilibria containing an axial shear flow, are analyzed, along with their flux-surface localized limit. The analysis is valid for general 2.5D equilibria, where either density, entropy, or temperature vary from one flux surface to another. We analyze the mode couplings caused by the poloidal variation in the flux rope equilibria, by performing a small gravity parameter expansion. We contrast the analytical results with continuous spectra obtained numerically. For equilibria where the density is a flux function, we show that continuum modes can be overstable, and we present the stability criterion for these convective continuum instabilities. Furthermore, for all equilibria, a four-mode coupling scheme between an Alfvenic mode of poloidal mode number m and three neighboring (m-1, m, m+1) slow modes is identified, occurring in the vicinity of rational flux surfaces. For realistically prominence equilibria, this coupling is shown to play an important role, from weak to stronger gravity parameter g values. The analytic predictions for small g are compared with numerical spectra, and progressive deviations for larger g are identified. The unstable continuum modes could be relevant for short-lived prominence configurations. The gaps created by poloidal mode coupling in the continuous spectrum need further analysis, as they form preferred frequency ranges for global eigenoscillations.Comment: Accepted by Astronmy & Astrophysics, 21 pages, 15 figure

Numerical simulations of stellar winds: polytropic models

We discuss steady-state transonic outflows obtained by direct numerical solution of the hydrodynamic and magnetohydrodynamic equations. We make use of the Versatile Advection Code, a software package for solving systems of (hyperbolic) partial differential equations. We proceed stepwise from a spherically symmetric, isothermal, unmagnetized, non-rotating Parker wind to arrive at axisymmetric, polytropic, magnetized, rotating models. These represent 2D generalisations of the analytical 1D Weber-Davis wind solution, which we obtain in the process. Axisymmetric wind solutions containing both a `wind' and a `dead' zone are presented. Since we are solving for steady-state solutions, we efficiently exploit fully implicit time stepping. The method allows us to model thermally and/or magneto-centrifugally driven stellar outflows. We particularly emphasize the boundary conditions imposed at the stellar surface. For these axisymmetric, steady-state solutions, we can use the knowledge of the flux functions to verify the physical correctness of the numerical solutions.Comment: 11 pages, 6 figures, accepted for Astron. Astrophys. 342, to appear 199

Adhesion and patterning of cortical neurons on polyethylenimine and fluorocarbon-coated surfaces

Adhesion and patterning of cortical neurons was investigated on isolated islands of neuron-adhesive polyethylenimine (PEI) surrounded by a neuron-repellent fluorocarbon (FC) layer. In addition, the development of fasciculated neurites between the PEI-coated areas was studied over a time period of 15 days. The patterns consisted of PEI-coated wells (diameter 150 /spl mu/m, depth 0.5 /spl mu/m) which were etched in a coating of fluorocarbon (FC) on top of polyimide (PI) coated glass. The separation distance between the PEI-coated wells were varied between 10 and 90 /spl mu/m. This paper shows that chemical patterns of PEI and FC result in highly compliant patterns of adhering cortical neurons after 1 day in vitro. Interconnecting neurite fascicles between PEI-coated wells were especially present on patterns with a separation distance of 10 /spl mu/m after 8 days in vitro. A significant lower number of interconnecting neurite fascicles was observed on 20 /spl mu/m separated patterns. Effective isolation of neurons into PEI-coated wells was achieved on patterns with a separation distance of 80 /spl mu/m as no interconnecting neurite fascicles were observed

Adhesion and patterning of cortical neurons on polyethylenimine and fluorcarboncoated surfaces

In this study adhesion and patterning of cortical neurons on modified glass surfaces was investigated. Patterns of cortical neurons were prepared with a combination of polyethylenimine (PEI) and plasma-deposited fluorocarbon (FC). In addition neurite\ud development and fasciculation of interconnecting neurites between PEI-coated areas was studied. The patterns consisted of PEI-coated circular holes (diameter 150 pm) which were initially etched in a Fluorocarbon (FC) layer. The separation distance between the PEI-coated circular holes was varied from 10 up to 90 pm. This paper shows that the chemical patterns, prepared with a combination of polyethylenimine (PEI) and plasma deposited Fluorocarbon\ud (FC), results in highly compliant patterns of adhering cortical neurons. Furthermore it was shown that interconnecting neurite bundles between neurons on the PEI-coated circular holes were especially present on the pattern with a minimal separation distance (10 pm) between the PEI-coated circular holes. In contrast\ud interconnecting neurite bundles were hardly observed on patterns with a maximal separation distance (90 pm) between the PEI-coated\ud circular holes

Toward detailed prominence seismology - I. Computing accurate 2.5D magnetohydrodynamic equilibria

Context. Prominence seismology exploits our knowledge of the linear eigenoscillations for representative magnetohydro- dynamic models of filaments. To date, highly idealized models for prominences have been used, especially with respect to the overall magnetic configurations. Aims. We initiate a more systematic survey of filament wave modes, where we consider full multi-dimensional models with twisted magnetic fields representative of the surrounding magnetic flux rope. This requires the ability to compute accurate 2.5 dimensional magnetohydrodynamic equilibria that balance Lorentz forces, gravity, and pressure gradients, while containing density enhancements (static or in motion). Methods. The governing extended Grad-Shafranov equation is discussed, along with an analytic prediction for circular flux ropes for the Shafranov shift of the central magnetic axis due to gravity. Numerical equilibria are computed with a finite element-based code, demonstrating fourth order accuracy on an explicitly known, non-trivial test case. Results. The code is then used to construct more realistic prominence equilibria, for all three possible choices of a free flux-function. We quantify the influence of gravity, and generate cool condensations in hot cavities, as well as multi- layered prominences. Conclusions. The internal flux rope equilibria computed here have the prerequisite numerical accuracy to allow a yet more advanced analysis of the complete spectrum of linear magnetohydrodynamic perturbations, as will be demonstrated in the companion paper.Comment: Accepted by Astronomy & Astrophysics, 15 pages, 15 figure

Adhesion and neurite development of cortical neurons on micropatterns of polyethylenimine and fluorcarbon

This study aims on the preparation of isolated islands of cortical neurons on modified glass surfaces. Isolated islands of cortical neurons were obtained with a combination of neuron-adhesive polyethylenimine (PEI) and neuron-repellent plasma-deposited fluorocarbon (FC). Neurite development and fasciculation of interconnecting neurites between PEI-coated areas was studied. The patterns consisted of PEI-coated wells (diameter 150 ¿m) which were initially etched in a Fluorocarbon (FC) layer. The separation distance between the PEI-coated wells was varied from 10 up to 90 ¿m. This paper shows that the chemical patterns, prepared with a combination of polyethylenimine (PEI) and plasma deposited Fluorocarbon (FC), results in highly compliant patterns of adhering cortical neurons. Furthermore, it was shown that the occurrence of connecting neurite fascicles between neurons on PEI-coated wells is inversely proportional to the separation distance between the wells. Interconnecting fascicles were especially present on the pattern with a minimal separation distance (10 ¿m) between the PEI-coated wells. In contrast, interconnecting neurite fascicles were not observed on patterns with a minimal separation distance of 80 ¿m between the well

Three dimensional evolution of differentially rotating magnetized neutron stars

We construct a new three-dimensional general relativistic magnetohydrodynamics code, in which a fixed mesh refinement technique is implemented. To ensure the divergence-free condition as well as the magnetic flux conservation, we employ the method by Balsara (2001). Using this new code, we evolve differentially rotating magnetized neutron stars, and find that a magnetically driven outflow is launched from the star exhibiting a kink instability. The matter ejection rate and Poynting flux are still consistent with our previous finding (Shibata et al., 2011) obtained in axisymmetric simulations.Comment: 12 pages, 14 figures, accepted by PR