A mathematical form of force-free magnetosphere equation around Kerr black holes and its application to Meissner effect

Based on the Lagrangian of the steady axisymmetric force-free magnetosphere (FFM) equation around Kerr black holes(KBHs), we find that the FFM equation can be rewritten in a new form as $f_{,rr} / (1-\mu^{2}) + f_{,\mu\mu} / \Delta + K(f(r,\mu),r,\mu) = 0$, where $\mu = -\cos\theta$. By coordinate transformation, the form of the above equation can be given by $s_{,yy} + s_{,zz} + D(s(y,z),y,z) = 0$. Based on the form, we prove finally that the Meissner effect is not possessed by a KBH-FFM with the condition where $d\omega/d A_{\phi} \leqslant 0$ and $H_{\phi}(dH_{\phi}/dA_{\phi}) \geqslant 0$, here $A_{\phi}$ is the $\phi$ component of the vector potential $\vec{A}$, $\omega$ is the angular velocity of magnetic fields and ${H_{\phi}}$ corresponds to twice the poloidal electric current

Consistency of Perfect Fluidity and Jet Quenching in semi-Quark-Gluon Monopole Plasmas

We utilize a new framework, CUJET3.0, to deduce the energy and temperature dependence of jet transport parameter, $\hat{q}(E>10\; {\rm GeV},T)$, from a combined analysis of available data on nuclear modification factor and azimuthal asymmetries from RHIC/BNL and LHC/CERN on high energy nuclear collisions. Extending a previous perturbative-QCD based jet energy loss model (known as CUJET2.0) with (2+1)D viscous hydrodynamic bulk evolution, this new framework includes three novel features of nonperturbative physics origin: (1) the Polyakov loop suppression of color-electric scattering (aka "semi-QGP" of Pisarski et al) and (2) the enhancement of jet scattering due to emergent magnetic monopoles near $T_c$ (aka "magnetic scenario" of Liao and Shuryak) and (3) thermodynamic properties constrained by lattice QCD data. CUJET3.0 reduces to v2.0 at high temperatures $T > 400$ MeV, but greatly enhances $\hat{q}$ near the QCD deconfinement transition temperature range. This enhancement accounts well for the observed elliptic harmonics of jets with $p_T>10$ GeV. Extrapolating our data-constrained $\hat{q}$ down to thermal energy scales, $E \sim 2$ GeV, we find for the first time a remarkable consistency between high energy jet quenching and bulk perfect fluidity with $\eta/s\sim T^3/\hat{q} \sim 0.1$ near $T_c$.Comment: 6 pages, 4 figures; v2: major text revisions, title and abstract modified, typos corrected, references adde

Do peaked solitary water waves indeed exist?

Many models of shallow water waves admit peaked solitary waves. However, it is an open question whether or not the widely accepted peaked solitary waves can be derived from the fully nonlinear wave equations. In this paper, a unified wave model (UWM) based on the symmetry and the fully nonlinear wave equations is put forward for progressive waves with permanent form in finite water depth. Different from traditional wave models, the flows described by the UWM are not necessarily irrotational at crest, so that it is more general. The unified wave model admits not only the traditional progressive waves with smooth crest, but also a new kind of solitary waves with peaked crest that include the famous peaked solitary waves given by the Camassa-Holm equation. Besides, it is proved that Kelvin's theorem still holds everywhere for the newly found peaked solitary waves. Thus, the UWM unifies, for the first time, both of the traditional smooth waves and the peaked solitary waves. In other words, the peaked solitary waves are consistent with the traditional smooth ones. So, in the frame of inviscid fluid, the peaked solitary waves are as acceptable and reasonable as the traditional smooth ones. It is found that the peaked solitary waves have some unusual and unique characteristics. First of all, they have a peaked crest with a discontinuous vertical velocity at crest. Especially, the phase speed of the peaked solitary waves has nothing to do with wave height. In addition, the kinetic energy of the peaked solitary waves either increases or almost keeps the same from free surface to bottom. All of these unusual properties show the novelty of the peaked solitary waves, although it is still an open question whether or not they are reasonable in physics if the viscosity of fluid and surface tension are considered.Comment: 53 pages, 13 figures, 7 tables. Accepted by Communications in Nonlinear Science and Numerical Simulatio