Jacobi-like bar mode instability of relativistic rotating bodies

We perform some numerical study of the secular triaxial instability of rigidly rotating homogeneous fluid bodies in general relativity. In the Newtonian limit, this instability arises at the bifurcation point between the Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by viscous dissipation. We locate the onset of instability along several constant baryon mass sequences of uniformly rotating axisymmetric bodies for compaction parameter $M/R = 0-0.275$. We find that general relativity weakens the Jacobi like bar mode instability, but the stabilizing effect is not very strong. According to our analysis the critical value of the ratio of the kinetic energy to the absolute value of the gravitational potential energy $(T/|W|)_{\rm crit}$ for compaction parameter as high as 0.275 is only 30% higher than the Newtonian value. The critical value of the eccentricity depends very weakly on the degree of relativity and for $M/R=0.275$ is only 2% larger than the Newtonian value at the onset for the secular bar mode instability. We compare our numerical results with recent analytical investigations based on the post-Newtonian expansion.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

Health Care Utilization and Comorbidity History of North Carolina Medicaid Beneficiaries in a Controlled Substance "Lock-in" Program

BACKGROUND Medicaid "lock-in" programs (MLIPs) are a widely used strategy for addressing potential misuse of prescription drugs among beneficiary populations. However, little is known about the health care needs and attributes of beneficiaries selected into these programs. Our goal was to understand the characteristics of those eligible, enrolled, and retained in a state MLIP. METHODS Demographics, comorbidities, and health care utilization were extracted from Medicaid claims from June 2009 through June 2013. Beneficiaries enrolled in North Carolina's MLIP were compared to those who were MLIP-eligible, but not enrolled. Among enrolled beneficiaries, those completing the 12-month MLIP were compared to those who exited prior to 12 months. RESULTS Compared to beneficiaries who were eligible for, but not enrolled in the MLIP (N = 11,983), enrolled beneficiaries (N = 5,424) were more likely to have: 1) substance use (23% versus 14%) and mental health disorders, 2) obtained controlled substances from multiple pharmacies, and 3) visited more emergency departments (mean: 8.3 versus 4.2 in the year prior to enrollment). One-third (N = 1,776) of those enrolled in the MLIP exited the program prior to completion. LIMITATIONS Accurate information on unique prescribers visited by beneficiaries was unavailable. Time enrolled in Medicaid differed for beneficiaries, which may have led to underestimation of covariate prevalence. CONCLUSIONS North Carolina's MLIP appears to be successful in identifying subpopulations that may benefit from provision and coordination of services, such as substance abuse and mental health services. However, there are challenges in retaining this population for the entire MLIP duration

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Dynamic observations of vesiculation reveal the role of silicate crystals in bubble nucleation and growth in andesitic magmas

Bubble nucleation and growth control the explosivity of volcanic eruptions, and the kinetics of these processes are generally determined from examinations of natural samples and quenched experimental run products. These samples, however, only provide a view of the final state, from which the initial conditions of a time-evolving magmatic system are then inferred. The interpretations that follow are inexact due to the inability of determining the exact conditions of nucleation and the potential detachment of bubbles from their nucleation sites, an uncertainty that can obscure their nucleation location \u2013 either homogeneously within the melt or heterogeneously at the interface between crystals and melts. We present results of a series of dynamic, real-time 4D X-ray tomographic microscopy experiments where we observed the development of bubbles in crystal bearing silicate magmas. Experimentally synthesized andesitic glasses with 0.25\u20130.5 wt% H2O and seed silicate crystals were heated at 1 atm to induce bubble nucleation and track bubble growth and movement. In contrast to previous studies on natural and experimentally produced samples, we found that bubbles readily nucleated on plagioclase and clinopyroxene crystals, that their contact angle changes during growth and that they can grow to sizes many times that of the silicate on whose surface they originated. The rapid heterogeneous nucleation of bubbles at low degrees of supersaturation in the presence of silicate crystals demonstrates that silicates can affect when vesiculation ensues, influencing subsequent permeability development and effusive vs. explosive transition in volcanic eruptions

Magnetic Braking in Differentially Rotating, Relativistic Stars

We study the magnetic braking and viscous damping of differential rotation in incompressible, uniform density stars in general relativity. Differentially rotating stars can support significantly more mass in equilibrium than nonrotating or uniformly rotating stars. The remnant of a binary neutron star merger or supernova core collapse may produce such a "hypermassive" neutron star. Although a hypermassive neutron star may be stable on a dynamical timescale, magnetic braking and viscous damping of differential rotation will ultimately alter the equilibrium structure, possibly leading to delayed catastrophic collapse. Here we consider the slow-rotation, weak-magnetic field limit in which E_rot << E_mag << W, where E_rot is the rotational kinetic energy, E_mag is the magnetic energy, and W is the gravitational binding energy of the star. We assume the system to be axisymmetric and solve the MHD equations in both Newtonian gravitation and general relativity. Toroidal magnetic fields are generated whenever the angular velocity varies along the initial poloidal field lines. We find that the toroidal fields and angular velocities oscillate independently along each poloidal field line, which enables us to transform the original 2+1 equations into 1+1 form and solve them along each field line independently. The incoherent oscillations on different field lines stir up turbulent-like motion in tens of Alfven timescales ("phase mixing"). In the presence of viscosity, the stars eventually are driven to uniform rotation, with the energy contained in the initial differential rotation going into heat. Our evolution calculations serve as qualitative guides and benchmarks for future, more realistic MHD simulations in full 3+1 general relativity.Comment: 26 pages, 27 graphs, 1 table, accepted for publication by Phys. Rev.