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We study here the arising of Kelvin--Helmholtz Instability (KHI) in one fast jet of 2014 April 16 observed by the Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO) in different UV and EUV wavelengths. The evolution of jet indicates the blob like structure at its boundary which could be the observational evidence of the KHI. We model the jet as a moving cylindrical magnetic flux tube of radius $a$ embedded in a magnetic field B_i and surrounded by rest magnetized plasma with magnetic field B_e. We explore the propagation of the kink MHD mode along the jet that can become unstable against the KHI if its speed exceeds a critical value. Concerning magnetic fields topology we consider three different configurations, notably of (i) spatially homogeneous magnetic fields (untwisted magnetic flux tube), (ii) internal (label `i') twisted magnetic field and external homogeneous one (label `e') (single-twisted flux tube), and (iii) both internal and external twisted magnetic fields (double-twisted magnetic flux tube). Plasma densities in the two media rho_i and rho_e are assumed to be homogeneous. The density contrast is defined in two ways: first as rho_e/rho_i and second as rho_e/(rho_i + rho_e). Computations show that the KHI can occur at accessible flow velocities in all the cases of untwisted and single-twisted flux tubes. It turns out, however, that in the case of a double-twisted flux tube the KHI can merge at an accessible jet speed only when the density contrast is calculated from the ratio rho_e/(rho_i} + rho_e). Evaluated KHI developing times and kink mode wave phase velocities at wavelength of 4 Mm lie in the ranges of 1--6.2 min and 202--271 km/s, respectively---all being reasonable for the modeled jet., Comment: 35 pages, 11 figures

We follow the eruption of two related intermediate filaments observed in H$\alpha$ (from GONG) and in EUV (from SDO/AIA) and the resulting large-amplitude longitudinal oscillations of the plasma in the filament channels. The events occurred in and around the decayed active region AR12486 on 2016 January 26. Our detailed study of the oscillation reveals that the periods of the oscillations are about one hour. In H$\alpha$ the period decreases with time and exhibits strong damping. The analysis of 171~\AA\ images shows that the oscillation has two phases, an initial long period phase and a subsequent oscillation with a shorter period. In this wavelength the damping appears weaker than in H$\alpha$. The velocity is the largest ever detected in a prominence oscillation, approximately 100 $\mathrm{\, km \, s^{-1}}$. Using SDO/HMI magnetograms we reconstruct the magnetic field of the filaments modeled as flux ropes by using a flux-rope insertion method. Applying seismological techniques we determine that the radii of curvature of the field lines in which cool plasma is condensed are in the range 75-120~Mm, in agreement with the reconstructed field. In addition, we infer a field strength of $\ge7$ to 30 gauss, depending on the electron density assumed; that is also in agreement with the values from the reconstruction (8-20 gauss). The poloidal flux is zero and the axis flux is of the order of 10$^{20}$ to 10$^{21}$ Mx, confirming the high shear existing even in a non-active filament., Comment: Accepted for publication in The Astrophysical Journal

We present and discuss here the observations of a small long duration GOES B- class flare associated with a quiescent filament eruption, a global EUV wave and a CME on 2011 May 11. The event was well observed by the Solar Dynamics Observatory (SDO), GONG H{\alpha}, STEREO and HiRAS spectrograph. As the fil- ament erupted, ahead of the filament we observed the propagation of EIT wave fronts, as well as two flare ribbons on both sides of the polarity inversion line (PIL) on the solar surface. The observations show the co-existence of two types of EUV waves, i.e., a fast and a slow one. A type II radio burst with up to the third harmonic component was also associated with this event. The evolution of pho- tospheric magnetic field showed flux emergence and cancellation at the filament site before its eruption., Comment: 17 pages, 6 figures, accepted for the publication in Adv. Space Research

Within the PHFB approach, the $0^{+}\rightarrow 2^{+}$ transition of two neutrino double-$\beta $ decay of $^{94,96}$Zr, $^{100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes is studied employing wave functions generated with four different parametrizations of the pairing plus multipole type of two-nucleon interaction and the summation method. In comparison to the $0^{+}\rightarrow 0^{+}$ transition, the nuclear transition matrix elements $M_{2\nu }(2^{+})$ are quite sensitive to the deformation of the yrast 2$^{+}$ state. Consideration of the available theoretical and experimental results suggest that the observation of the 0$% ^{+}\rightarrow $2$^{+}$ transition of $2\nu \beta ^{-}\beta ^{-}$ decay may be possible in $^{96}$Zr, $^{100}$Mo, $^{130}$Te and $^{150}$Nd isotopes. The effect of deformation on the $M_{2\nu }(2^{+})$ is also studied.

The columnwise Khatri-Rao product of two matrices is an important matrix type, reprising its role as a structured sensing matrix in many fundamental linear inverse problems. Robust signal recovery in such inverse problems is often contingent on proving the restricted isometry property (RIP) of a certain system matrix expressible as a Khatri-Rao product of two matrices. In this work, we analyze the RIP of a generic columnwise Khatri-Rao product matrix by deriving two upper bounds for its $k^{\text{th}}$ order Restricted Isometry Constant ($k$-RIC) for different values of $k$. The first RIC bound is computed in terms of the individual RICs of the input matrices participating in the Khatri-Rao product. The second RIC bound is probabilistic, and is specified in terms of the input matrix dimensions. We show that the Khatri-Rao product of a pair of $m \times n$ sized random matrices comprising independent and identically distributed subgaussian entries satisfies $k$-RIP with arbitrarily high probability, provided $m$ exceeds $O(k \log n)$. Our RIC bounds confirm that the Khatri-Rao product exhibits stronger restricted isometry compared to its constituent matrices for the same RIP order. The proposed RIC bounds are potentially useful in the sample complexity analysis of several sparse recovery problems., Comment: The probabilistic RIC bounds presented as Theorems 2 and 3 in the earlier version (v1 and v2) could be potentially incorrect and have been restated with new proofs in this revised manuscript

In this study, we present the investigation of eleven recurring solar jets originated from two different sites (site 1 and site 2) close to each other (~ 11 Mm) in the NOAA active region (AR) 12035 during 15--16 April 2014. The jets were observed by the Atmospheric Imaging Assembly (AIA) telescope onboard the Solar Dynamics Observatory (SDO) satellite. Two jets were observed by the Aryabhatta Research Institute of Observational Sciences (ARIES), Nainital, India telescope in H-alpha. On 15 April flux emergence is important in site 1 while on 16 April flux emergence and cancellation mechanisms are involved in both sites. The jets of both sites have parallel trajectories and move to the south with a speed between 100 and 360 km/s. We observed some connection between the two sites with some transfer of brightening. The jets of site 2 occurred during the second day and have a tendency to move towards the jets of site 1 and merge with them. We conjecture that the slippage of the jets could be explained by the complex topology of the region with the presence of a few low-altitude null points and many quasi-separatrix layers (QSLs), which could intersect with one another., Comment: 27 pages, 27 figures, accepted for publication in Solar Physics

Employing the PHFB model, nuclear transition matrix elements $M^{\left( K\right) }$ for the neutrinoless double-$\beta^{-} $ decay of $\ ^{76}$Ge and $^{82}$Se isotopes are calculated within mechanisms involving light as well as heavy Majorana neutrinos, and classical Majorons by considering the spin-tensor decomposition of realistic KUO and empirical JUN45 effective two-body interaction. It is noticed that the effects due to the SRC on NTMEs $M^{\left( 0\nu \right) }$ and $M^{\left( 0N\right) }$ due to the exchange of light and heavy Majorana neutrinos, respectively, is maximally incorporated by the central part of the effective two-body interaction, which varies by a small amount with the inclusion of spin-orbit and tensor components. The maximum uncertainty in the average NTMEs $\overline{M}^{(0\nu)}$ and $\overline{M}^{(0N)}$ turns out to be about 10\% and 37\%, respectively.

In this paper, we consider a point-to-point link between an energy harvesting transmitter and receiver, where neither node has the information about the battery state or energy availability at the other node. We consider a model where data is successfully delivered only in slots where both nodes are active. Energy loss occurs whenever one node turns on while the other node is in sleep mode. In each slot, based on their own energy availability, the transmitter and receiver need to independently decide whether or not to turn on, with the aim of maximizing the long-term time-average throughput. We present an upper bound on the throughput achievable by analyzing a genie-aided system that has noncausal knowledge of the energy arrivals at both the nodes. Next, we propose an online policy requiring an occasional one-bit feedback whose throughput is within one bit of the upper bound, asymptotically in the battery size. In order to further reduce the feedback required, we propose a time-dilated version of the online policy. As the time dilation gets large, this policy does not require any feedback and achieves the upper bound asymptotically in the battery size. Inspired by this, we also propose a near-optimal fully uncoordinated policy. We use Monte Carlo simulations to validate our theoretical results and illustrate the performance of the proposed policies., Comment: 8 pages

We investigate the conditions under which the fluting ($m = 2$), $m = 3$, and $m = 12$ magnetohydrodynamic (MHD) modes in a uniformly twisted flux tube moving along its axis become unstable in order to model the Kelvin--Helmholtz (KH) instability in a twisting solar coronal hole jet near the northern pole of the Sun. Using a twisting jet of 2010 August 21 by \emph{SDO}/AIA and other observations of coronal jets we set the parameters of our theoretical model and have obtained that in a twisted magnetic flux tube of radius of $9.8$~Mm, at a density contrast of $0.474$ and fixed Alfv\'en Mach number of ${\cong}0.76$, for three MHD modes there exist instability windows whose width crucially depends upon the internal magnetic field twist. It is found that for the considered modes an azimuthal magnetic field of $1.3$--$1.4$~G (computed at the tube boundary) makes the width of the instability windows equal to zero, that is, it suppress the KH instability onset. On the other hand, the times for developing KH instability of the $m = 12$ MHD mode at instability wavelengths between $15$ and $12$~Mm turn out to be in the range of $1.9$ to $4.7$~minutes that is in agreement with the growth rates estimated from the temporal evolution of the observed unstable jet's blobs in their initial stage., Comment: 23 pages, 6 figures, 1 movie

We present here an interesting two-step filament eruption during 14-15 March 2015. The filament was located in NOAA AR 12297 and associated with a halo Coronal Mass Ejection (CME). We use observations from the Atmospheric Imaging Assembly (AIA) and Heliospheric Magnetic Imager (HMI) instruments onboard the Solar Dynamics Observatory (SDO), and from the Solar and Heliospheric Observatory (SOHO) Large Angle and Spectrometric Coronagraph (LASCO). We also use H-alpha data from the Global Oscillation Network Group (GONG) telescope and the Kanzelhoehe Solar Observatory. The filament shows a first step eruption on 14 March 2015 and it stops its rise at a projected altitude ~ 125 Mm on the solar disk. It remains at this height for ~ 12 hrs. Finally it eruptes on 15 March 2015 and produced a halo CME. We also find jet activity in the active region during both days, which could help the filament de-stabilization and eruption. The decay index is calculated to understand this two-step eruption. The eruption could be due to the presence of successive instability-stability-instability zones as the filament is rising., Comment: 11 pages, 7 figures, accepted for the publication in Solar Physics

In this work, we provide non-asymptotic, probabilistic guarantees for successful recovery of the common nonzero support of jointly sparse Gaussian sources in the multiple measurement vector (MMV) problem. The support recovery problem is formulated as the marginalized maximum likelihood (or type-II ML) estimation of the variance hyperparameters of a joint sparsity inducing Gaussian prior on the source signals. We derive conditions under which the resulting nonconvex constrained optimization perfectly recovers the nonzero support of a joint-sparse Gaussian source ensemble with arbitrarily high probability. The support error probability decays exponentially with the number of MMVs at a rate that depends on the smallest restricted singular value and the nonnegative null space property of the self Khatri-Rao product of the sensing matrix. Our analysis confirms that nonzero supports of size as high as O($m^2$) are recoverable from $m$ measurements per sparse vector. Our derived sufficient conditions for support consistency of the proposed constrained type-II ML solution also guarantee the support consistency of any global solution of the multiple sparse Bayesian learning (M-SBL) optimization whose nonzero coefficients lie inside a bounded interval. For the case of noiseless measurements, we further show that a single MMV is sufficient for perfect recovery of the $k$-sparse support by M-SBL, provided all subsets of $k + 1$ columns of the sensing matrix are linearly independent.

Solar flares are sudden and violent releases of magnetic energy in the solar atmosphere that can be divided in eruptive flares, when plasma is ejected from the solar atmosphere, resulting in a coronal mass ejection (CME), and confined flares when no CME is associated with the flare. We present a case-study showing the evolution of key topological structures, such as spines and fans which may determine the eruptive versus non-eruptive behavior of the series of eruptive flares, followed by confined flares, which are all originating from the same site. To study the connectivity of the different flux domains and their evolution, we compute a potential magnetic field model of the active region. Quasi-separatrix layers are retrieved from the magnetic field extrapolation. The change of behavior of the flares from one day to the next -eruptive to confined- can be attributed to the change of orientation of the magnetic field below the fan with respect to the orientation of the overlaying spine, rather than an overall change in the stability of the large scale field. Flares tend to be more-and-more confined when the field that supports the filament and the overlying field gradually become less-and-less anti-parallel, as a direct result of changes in the photospheric flux distribution, being themselves driven by continuous shearing motions of the different magnetic flux concentrations., Comment: 11 pages, 8 figures accepted for publication in Astronomy and Astrophysics

Context: A subclass of broad EUV and X-ray jets, called blowout jets, have become a topic of research since they could be the link between standard collimated jets and CMEs.} Aim: Our aim is to understand the origin of a series of broad jets, some accompanied by flares and associated with narrow and jet-like CMEs. Methods: We analyze observations of a series of recurrent broad jets observed in AR 10484 on 21-24 October 2003. In particular, one of them occurred simultaneously with an M2.4 flare on 23 October at 02:41 UT (SOLA2003-10-23). Both events were observed by ARIES H-alpha Solar Tower-Telescope, TRACE, SOHO, and RHESSI instruments. The flare was very impulsive and followed by a narrow CME. A local force-free model of AR 10484 is the basis to compute its topology. We find bald patches (BPs) at the flare site. This BP topology is present for at least two days before. Large-scale field lines, associated with the BPs, represent open loops. This is confirmed by a global PFSS model. Following the brightest leading edge of the H-alpha and EUV jet emission, we can temporarily associate it with a narrow CME. Results: Considering their characteristics, the observed broad jets appear to be of the blowout class. As the most plausible scenario, we propose that magnetic reconnection could occur at the BP separatrices forced by the destabilization of a continuously reformed flux rope underlying them. The reconnection process could bring the cool flux-rope material into the reconnected open field lines driving the series of recurrent blowout jets and accompanying CMEs. Conclusions: Based on a model of the coronal field, we compute the AR 10484 topology at the location where flaring and blowout jets occurred from 21 to 24 October 2003. This topology can consistently explain the origin of these events.