376 research outputs found
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 . 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 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 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.
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