Global evolution in spherical symmetry for self-gravitating massive fields

We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation with quadratic potential. For the initial value problem we establish a global existence theory when initial data are prescribed on a future light cone with vertex at the center of symmetry. A suitably generalized solution in Bondi coordinates is sought which has low regularity and possibly large but finite Bondi mass. A similar result was established first by Christodoulou for massless fields. In order to deal with massive fields, we must overcome several challenges and significantly modify Christodoulou's original method. First of all, we formulate the Einstein-Klein-Gordon system in spherical symmetry as a non-local and nonlinear hyperbolic equation and, by carefully investigating the global dynamical behavior of the massive field, we establish various estimates concerning the Einstein operator, the Hawking mass, and the Bondi mass, including positivity and monotonicity properties. Importantly, in addition to a regularization at the center of symmetry we find it necessary to also introduce a regularization at null infinity. We also establish new energy and decay estimates for, both, regularized and generalized solutions.Comment: 43 page

Inhomogeneity driven by Higgs instability in gapless superconductor

The fluctuations of the Higgs and pseudo Nambu-Goldstone fields in the 2SC phase with mismatched pairing are described in the nonlinear realization framework of the gauged Nambu--Jona-Lasinio model. In the gapless 2SC phase, not only Nambu-Goldstone currents can be spontaneously generated, but the Higgs field also exhibits instablity. The Nambu-Goldstone currents generation indicates the formation of the single plane wave LOFF state and breaks rotation symmetry, while the Higgs instability favors spatial inhomogeneity and breaks translation invariance. In this paper, we focus on the Higgs instability which has not drawn much attention yet. The Higgs instability cannot be removed without a long range force, thus it persists in the gapless superfluidity and induces phase separation. In the case of g2SC state, the Higgs instability can only be partially removed by the electric Coulomb energy. However, it is not excluded that the Higgs instability might be completely removed in the charge neutral gCFL phase by the color Coulomb energy.Comment: 21 pages, 5 figure

Heavy Quarkonium States with the Holographic Potential

The quarkonium states in a quark-gluon plasma is examined with the heavy quark potential implied by the holographic principle. Both the vanila AdS-Schwarzschild metric and the one with an infrared cutoff are considered. The dissociation temperature is calculated by solving the Schr\"o dinger equation of the potential model. In the case of the AdS-Schwarzschild metric with a IR cutoff, the dissociation temperatures for $J/\psi$ and $\Upsilon$ with the U-ansatz of the potential are found to agree with the lattice results within a factor of two.Comment: 9 pages with 2 figues in Revte

Joint Deployment and Resource Management for VLC-enabled RISs-assisted UAV Networks

In this paper, the problem of the deployment and resource management for visible light communication (VLC)-enabled, reconfigurable intelligent surfaces (RISs)-assisted unmanned aerial vehicle (UAV) networks is investigated. In the considered model, UAVs provide terrestrial users with wireless services and illumination simultaneously. Moreover, RISs are utilized to further improve the channel quality between UAVs and users. This joint placement and resource management problem is constructed aiming at acquiring the optimal UAV deployment, RISs phase shift, user and RIS association that satisfies the users’ needs with minimum consumption of the UAVs’ energy. An iterative algorithm that alternately optimizes continuous and binary variables is proposed to solve this mixed-integer programming problem. Specifically, RISs phase shift optimization is solved by phases alignment method and semidefinite program algorithm. Next, the successive convex approximation algorithm is proposed to settle the UAV deployment problem. The user and RIS association variables are relaxed to the continuous ones before adopting the dual method to find the optimal solution. Moreover, a greedy algorithm is proposed as an alternative to RIS association optimization with low complexity. Simulation results show that the proposed two schemes harvest the superior performance of 34.85% and 32.11% energy consumption reduction over the case without RIS, respectively

Path integral solution for an angle-dependent anharmonic oscillator

We have given a straightforward method to solve the problem of noncentral anharmonic oscillator in three dimensions. The relative propagator is presented by means of path integrals in spherical coordinates. By making an adequate change of time we were able to separate the angular motion from the radial one. The relative propagator is then exactly calculated. The energy spectrum and the corresponding wave functions are obtained.Comment: Corrected typos and mistakes, To appear in Communications in Theoretical Physic

Microwave assisted heterogeneous catalysis: effects of varying oxygen concentrations on the oxidative coupling of methane

The oxidative coupling of methane was investigated over alumina supported La2O3/CeO2 catalysts under microwave dielectric heating conditions at different oxygen concentrations. It was observed that, at a given temperature using microwave heating, selectivities for both ethane and ethylene were notably higher when oxygen was absent than that in oxygen/methane mixtures. The differences were attributed to the localised heating of microwave radiation resulting in temperature inhomogeneity in the catalyst bed. A simplified model was used to estimate the temperature inhomogeneity; the temperature at the centre of the catalyst bed was 85 °C greater than that at the periphery when the catalyst was heated by microwaves in a gas mixture with an oxygen concentration of 12.5% (v/v), and the temperature difference was estimated to be 168 °C in the absence of oxygen

Precise determination of stellar parameters of the ZZ Ceti and DAZ white dwarf GD 133 through asteroseismology

An increasing number of white dwarf stars show atmospheric chemical composition polluted by heavy elements accreted from debris disk material. The existence of such debris disks strongly suggests the presence of one or more planet(s) whose gravitational interaction with rocky planetesimals is responsible for their disruption by tidal effect. The ZZ Ceti pulsator and polluted DAZ white dwarf GD 133 is a good candidate for searching for such a potential planet. We started in 2011 a photometric follow-up of its pulsations. As a result of this work in progress, we used the data gathered from 2011 to 2015 to make an asteroseismological analysis of GD 133, providing the star parameters from a best fit model with $M$/$M_{\odot}$ = 0.630 $\pm$ 0.002, $T_{\rm eff}$ = 12400 K $\pm$ 70 K, log($M_{\rm He}/M$) = -2.00 $\pm$ 0.02, log($M_{\rm H}/M$) = -4.50 $\pm$ 0.02 and determining a rotation period of $\approx$ 7 days.Comment: 10 pages, 13 figures, accepted by MNRA