Scheduling Under Fading and Partial Channel Information

We consider a scheduler for the downlink of a wireless channel when only partial channel-state information is available at the scheduler. We characterize the network stability region and provide two throughput-optimal scheduling policies. We also derive a deterministic bound on the mean packet delay in the network. Finally, we provide a throughput-optimal policy for the network under QoS constraints when real-time and rate-guaranteed data traffic may be present.Comment: 22 pages, 3 figures; Added IEEE Journal submission notic

Implications on accretion flow dynamics from spectral study of Swift~J1357.2-0933

We report a detailed spectral study of Swift~J1357.2-0933 low-mass X-ray binary during its 2017 outburst using {\it Swift} and {\it NuSTAR} observations. We fit the data with two component advective flow (TCAF) model and power-law model. We observe that the source is in hard state during the outburst, where the size of the Compton cloud changes significantly with disc accretion rate. The typical disc accretion rate for this source is $\sim 1.5-2.0~\%$ of the Eddington accretion rate $(\dot M_{Edd})$. The model fitted intermediate shock compression ratio gives an indication of the presence of jet, which is reported in the literature in different energy bands. We also split NuSTAR data into three equal segments and fit with the model. We check spectral stability using color-color diagram and accretion rate ratio (ARR) vs. intensity diagram using different segments of the light curve but do not find any significant variation in the hardness ratio or in the accretion rate ratio. To estimate the mass of the candidate, we use an important characteristics of TCAF that the the model normalization always remains a constant. We found that the mass comes out to be in the range of $4.0-6.8~M_\odot$. From the model fitted results, we study the disc geometry and different physical parameters of the flow in each observation. The count rate of the source appears to decay in a time scale of $\sim 45 day$.Comment: 6 pages, 3 figures, Accepted (21/11/2018) by MNRA

Effect of r averaging on Chiral Anomaly in Lattice QCD with Wilson Fermion: Finite volume and cutoff effects

We demonstrate the effectiveness of averaging over the Wilson parameter r (which has been proposed earlier) in removing the cutoff effects of naive Wilson fermions in both the anomaly term and the pseudoscalar density term in the flavor singlet axial Ward identity at O(g^2) involving slowly varying background gauge fields. We show that it is the physical fermion contribution which is largely influenced by the r averaging. We have studied the possible interplay between finite size and cutoff effects by investigating in detail naive, O(a) improved and OStm Wilson fermion cases for a range of volumes and lattice fermion mass (am). For naive Wilson fermions r averaging is shown to remove the effects of the interplay. We have shown that for the pseudoscalar density term to O (g^2) the lattice result differs from the continuum result by exhibiting considerable am dependence which appears to be a manifestation of cutoff effects with naive Wilson fermion. The pseudoscalar density term to O(g^2) is shown to be almost independent of am when r-averaging is performed.Comment: 14 pages, 13 figures, revise

Spectral signatures of dissipative standing shocks and mass outflow in presence of Comptonization around a black hole

Accretion flows having positive specific energy are known to produce outflows and winds which escape to a large distance. According to Two Component Advective Flow (TCAF) model, centrifugal pressure dominated region of the flow just outside the black hole horizon, with or without shocks, acts as the base of this outflow. Electrons from this region are depleted due to the wind and consequently, energy transfer rate due to inverse Comptonization of low energy photons are affected. Specifically, it becomes easier to cool this region and emerging spectrum is softened. Our main goal is to show spectral softening due to mass outflow in presence of Compton cooling. To achieve this, we modify Rankine-Hugoniot relationships at the shock front when post-shock region suffers mass loss due to winds and energy loss due to inverse Comptonization. We solve two-temperature equations governing an accretion flow around a black hole which include Coulomb exchange between protons and electrons and other major radiative processes such as bremsstrahlung and thermal Comptonization. We then compute emitted spectrum from this post-shock flow. We also show how location of standing shock which forms outer boundary of centrifugal barrier changes with cooling. With an increase in disc accretion rate $(\dot{m_d})$, cooling is enhanced and we find that the shock moves in towards the black hole. With cooling, thermal pressure is reduced, and as a result, outflow rate is decreased. We thus directly correlate outflow rate with spectral state of the disc.Comment: 10 pages, 6 figures, Accepted for publication in Astrophysics and Space Scienc

Spectral study of GX 339-4 with TCAF using Swift/XRT and NuSTAR Observation

We fit spectra of galactic transient source GX~339-4 during its 2013 outburst using Two Component Advective Flow (TCAF) solution. For the first time, we are fitting combined NuSTAR and Swift observation with TCAF. We use TCAF to fit 0.8-9.0~keV Swift and 4-79 keV NuSTAR spectra along with the LAOR model. To fit the data we use disk accretion rate, halo accretion rate, size of the Compton cloud and the density jump of advective flows at this cloud boundary as model parameters. From TCAF fitted flow parameters, and energy spectral index we conclude that the source was in the hard state throughout this particular outburst. The present analysis also gives some idea about the broadening of Fe $K_{\alpha}$ with the accretion rate. Since TCAF does not include Fe line yet, we make use of the `LAOR model' as a phenomenological model and find an estimate of the Kerr parameter to be $\sim 0.99$ for this candidate.Comment: 10 pages, 4 figures, 1 table, Accepted for Publication in Astrophysics and Space Scienc

Spectral properties of NGC 4151 and the Estimation of black hole mass using TCAF solution

We present X-ray spectral analysis of Seyfert 1.5 Active Galactic Nuclei (AGN) NGC~4151 using \textit{NuSTAR} observation during 2012. This is the first attempt to fit an AGN data using the physical Two Component Advective flow (TCAF) solution. We disentangle the continuum emission properties of the source in the energy range $3.0$ to $70.0$~keV using the spectrum obtained from TCAF model. This model was used as an additive local model directly in {\fontfamily{qcr}\selectfont XSPEC}. Additionally, we used a power law (PL) component, to take care of possible X-ray contribution from the jet, which is not incorporated in the present version of TCAF. Our primary aim is to obtain the flow properties and the mass of the central supermassive black hole from the available archival data. Our best estimate of the average mass obtained from spectral fits of three observations, is $M_{BH}=3.03^{+0.26}_{-0.26}\times 10^7 M_\odot$. This is consistent with earlier estimations in the literature such as reverberation mapping, gas kinematics and stellar dynamics around black holes. We also discuss the accretion dynamics and the flow geometry on the basis of model fitted physical parameters. Model fitted disk accretion rate is found to be lower than the low angular momentum halo accretion rate, indicating that the source was in a hard state during the observation.Comment: 15 pages, 5 figures, Accepted for publicatio

Chiral Anomaly in Lattice QCD with Twisted Mass Wilson Fermion

The flavour singlet axial Ward identity with Osterwalder-Seiler twisted mass Wilson fermion action is studied on a finite lattice, with finite fermion mass and the Wilson parameter r up to 1. Approach to the infinite volume chiral limit and emergence of the anomaly is significantly better than that obtained with O(a) and O(a^2) improved fermion actions. We have shown explicitly that up to O(g^2), parity violating terms cancel in the Ward identity even at finite volume and finite lattice spacing.Comment: Typos correcte

Inference on accretion flow dynamics using TCAF solution from the analysis of spectral evolution of H 1743-322 during 2010 outburst

We study accretion flow dynamics of Galactic transient black hole candidate (BHC) H 1743-322 during its 2010 outburst by analyzing spectral data using Two Component (Keplerian and sub-Keplerian) Advective Flow (TCAF) solution, after its inclusion in XSPEC as a local model. We compare our TCAF solution fitted results with combined disk black body and power-law model fitted results and find a similar smooth variation of thermal (Keplerian or disk black body) and non-thermal (power-law or sub-Keplerian) fluxes/rates in two types of model fits. For a spectral analysis, 2.5-25 keV spectral data from RXTE PCA instrument are used. From the TCAF solution fit, accretion flow parameters, such as Keplerian rate, sub-Keplerian rate, location of centrifugal pressure supported shock and strength of the shock are extracted, thus providing a deeper understanding of accretion process and properties of accretion disks around BHC H 1743-322 during its X-ray outburst. Based on the halo to disk accretion rate ratio (ARR), shock properties, accretion rates and nature of quasi-periodic oscillations (QPOs, if observed) entire outburst is classified into four different spectral states, such as, hard, hard-intermediate, soft-intermediate, and soft. From time variation of intrinsic flow parameters it appears that their evolutions in decline phase do not retrace path of rising phase. Since our current model does not include magnetic fields, spectral turnover at energies beyond 500-600 keV cannot be explained.Comment: 7 pages, 4 figures, 1 table; accepted for publication in Ap

Characterization of GX 339-4 outburst of 2010-11: analysis by xspec using two component advective flow model

We study spectral properties of GX 339-4 during its 2010-11 outburst with Two Component Advective Flow (TCAF) model after its inclusion in XSPEC as a table model. We compare results fitted by TCAF model with combined disk black body and power-law model. For a spectral fit, we use 2.5-25 keV spectral data of the PCA instrument onboard RXTE satellite. From our fit, accretion flow parameters such as Keplerian (disk) rate, sub-Keplerian (halo) rate, location and strength of shock are extracted. We quantify how the disk and the halo rates vary during the entire outburst. We study how the halo to disk accretion rate ratio (ARR), quasi-periodic oscillations (QPOs), shock locations and its strength vary when the system passes through hard, hard-intermediate, soft-intermediate, and soft states. We find pieces of evidence of monotonically increasing and decreasing nature of QPO frequencies depending on the variation of ARR during rising and declining phases. Interestingly, on days of transition from hard state to hard-intermediate spectral state (during the rising phase) or vice-versa (during decline phase), ARR is observed to be locally maximum. Non-constancy of ARR while obtaining reasonable fits points to the presence of two independent components in the flow.Comment: 12 Pages, 4 Figures, 1 Table, and 1 Appendix (Table

Many avatars of the Wilson fermion: A perturbative analysis

We explore different branches of the fermion doublers with Wilson fermion in perturbation theory, in the context of additive mass renormalization and chiral anomaly, and show that by appropriately averaging over suitably chosen branches one can reduce cut-off artifacts. Comparing the central branch with all other branches, we find that the central branch, among all the avatars of the Wilson fermion, is the most suitable candidate for exploring near conformal lattice field theories.Comment: 10 pages, 5 figures, one reference added, accepted for publication in JHE