Self-Similar Force-Free Wind From an Accretion Disk

We consider a self-similar force-free wind flowing out of an infinitely thin disk located in the equatorial plane. On the disk plane, we assume that the magnetic stream function $P$ scales as $P\propto R^\nu$, where $R$ is the cylindrical radius. We also assume that the azimuthal velocity in the disk is constant: $v_\phi = Mc$, where $M<1$ is a constant. For each choice of the parameters $\nu$ and $M$, we find an infinite number of solutions that are physically well-behaved and have fluid velocity $\leq c$ throughout the domain of interest. Among these solutions, we show via physical arguments and time-dependent numerical simulations that the minimum-torque solution, i.e., the solution with the smallest amount of toroidal field, is the one picked by a real system. For $\nu \geq 1$, the Lorentz factor of the outflow increases along a field line as \gamma \approx M(z/\Rfp)^{(2-\nu)/2} \approx R/R_{\rm A}, where \Rfp is the radius of the foot-point of the field line on the disk and R_{\rm A}=\Rfp/M is the cylindrical radius at which the field line crosses the Alfven surface or the light cylinder. For $\nu < 1$, the Lorentz factor follows the same scaling for z/\Rfp < M^{-1/(1-\nu)}, but at larger distances it grows more slowly: \gamma \approx (z/\Rfp)^{\nu/2}. For either regime of $\nu$, the dependence of $\gamma$ on $M$ shows that the rotation of the disk plays a strong role in jet acceleration. On the other hand, the poloidal shape of a field line is given by z/\Rfp \approx (R/\Rfp)^{2/(2-\nu)} and is independent of $M$. Thus rotation has neither a collimating nor a decollimating effect on field lines, suggesting that relativistic astrophysical jets are not collimated by the rotational winding up of the magnetic field.Comment: 21 pages, 15 figures, accepted to MNRA

The effect of manganese oxide on the sinterability of hydroxyapatite

The sinterability of manganese oxide (MnO2) doped hydroxyapatite (HA) ranging from 0.05 to 1 wt% was investigated. Green samples were prepared and sintered in air at temperatures ranging from 1000 to 1400 °C. Sintered bodies were characterized to determine the phase stability, grain size, bulk density, hardness, fracture toughness and Young's modulus. XRD analysis revealed that the HA phase stability was not disrupted throughout the sintering regime employed. In general, samples containing less than 0.5 wt% MnO2 and when sintered at lower temperatures exhibited higher mechanical properties than the undoped HA. The study revealed that all the MnO2-doped HA achieved >99% relative density when sintered at 1100–1250 °C as compared to the undoped HA which could only attained highest value of 98.9% at 1150 °C. The addition of 0.05 wt% MnO2 was found to be most beneficial as the samples exhibited the highest hardness of 7.58 GPa and fracture toughness of 1.65 MPam1/2 as compared to 5.72 GPa and 1.22 MPam1/2 for the undoped HA when sintered at 1000 °C. Additionally, it was found that the MnO2-doped samples attained E values above 110 GPa when sintered at temperature as low as 1000 °C if compared to 1050 °C for the undoped HA