Hydrodynamical and radio evolution of young supernova remnant G1.9+0.3 based on the model of diffusive shock acceleration

The radio evolution of, so far the youngest known, Galactic supernova remnant (SNR) G1.9+0.3 is investigated by using three-dimensional (3D) hydrodynamic modelling and non-linear kinetic theory of cosmic ray (CR) acceleration in SNRs. We include consistent numerical treatment of magnetic field amplification (MFA) due to resonant streaming instability. Under the assumption that SNR G1.9+0.3 is the result of a Type Ia supernova explosion located near the Galactic Centre, using widely accepted values for explosion energy 10$^{51}$ erg and ejecta mass 1.4 $M_{\odot}$, the non-thermal continuum radio emission is calculated. The main purpose of this paper is to explain radio flux brightening measured over recent decades and also predict its future temporal evolution. We estimate that the SNR is now $\sim$ 120 yr old, expanding in an ambient density of 0.02 cm$^{-3}$, and explain its steep radio spectral index only by means of efficient non-linear diffusive shock acceleration (NLDSA). We also make comparison between simulations and observations of this young SNR, in order to test the models and assumptions suggested. Our model prediction of a radio flux density increase of $\sim$ 1.8 per cent yr$^{-1}$ during the past two decades agrees well with the measured values. We synthesize the synchrotron spectrum from radio to X-ray and it fits well the VLA, MOST, Effelsberg, Chandra and NuSTAR measurements. We also propose a simplified evolutionary model of the SNR in gamma rays and suggest it may be a promising target for gamma-ray observations at TeV energies with the future generation of instruments like Cherenkov Telescope Array. SNR G1.9+0.3 is the only known Galactic SNR with the increasing flux density and we present here the prediction that the flux density will start to decrease approximately 500 yr from now. We conclude that this is a general property of SNRs in free expansion phase.Comment: 16 pages, 11 figures, 1 table; corrected typos, updated reference

Wormholes in viable f(R)f(R) modified theories of gravity and Weak Energy Condition

In this work wormholes in viable $f(R)$ gravity models are analysed. We are interested in exact solutions for stress-energy tensor components depending on different shape and redshift functions. Several solutions of gravitational equations for different $f(R)$ models are examined. Found solutions imply no need for exotic material, while this need is implied in the standard general theory of relativity. Simple expression for WEC violation near the throat is derived and analysed. High curvature regime is also discussed, as well as the question of the highest possible values of Ricci scalar for which WEC is not violated near the throat, and corresponding functions are calculated for the several models. The approach here differs from the one that has been common since no additional assumptions to simplify the equations are made, and functions in $f(R)$ models are not taken to be arbitrary functions, but rather a feature of the theory that has to be evaluated on the basis of consistency with observations for the Solar System and cosmological evolution.Comment: 8 pages, 10 figures, accepted by the European Physical Journal

On the Cauchy problem for focusing and defocusing Gross-Pitaevskii hierarchies

We consider the dynamical Gross-Pitaevskii (GP) hierarchy on $\R^d$, $d\geq1$, for cubic, quintic, focusing and defocusing interactions. For both the focusing and defocusing case, and any $d\geq1$, we prove local existence and uniqueness of solutions in certain Sobolev type spaces \cH_\xi^\alpha of sequences of marginal density matrices. The regularity is accounted for by \alpha>\frac12& if d=1$,$\alpha>\frac d2-\frac{1}{2(p-1)} $if$d\geq2$and$(d,p)\neq(3,2)$, and$\alpha\geq1$if$(d,p)=(3,2)$, where$p=2$for the cubic, and$p=4$for the quintic GP hierarchy; the parameter$\xi>0$is arbitrary and determines the energy scale of the problem. This result includes the proof of an a priori spacetime bound conjectured by Klainerman and Machedon for the cubic GP hierarchy in$d=3$. In the defocusing case, we prove the existence and uniqueness of solutions globally in time for the cubic GP hierarchy for$1\leq d\leq3$, and of the quintic GP hierarchy for$1\leq d\leq 2$, in an appropriate space of Sobolev type, and under the assumption of an a priori energy bound. For the focusing GP hierarchies, we prove lower bounds on the blowup rate. Also pseudoconformal invariance is established in the cases corresponding to$L^2$ criticality, both in the focusing and defocusing context. All of these results hold without the assumption of factorized initial conditions.Comment: AMS Latex, 28 page