arXiv subjects

Rajiv Kumar

Publications and source records attributed to Rajiv Kumar.

At least 55 records · Page 3Linked to original sources

arXiv2020

Dual link failure survivability with recovery time constraint: A Parallel cross connection backup route recovery strategy

In this paper, we proposed a fast recovery strategy for a dual link failure in elastic optical network. The elastic optical network is a promising solution to meet the next generation higher bandwidth demand. The survivability of high speed network is very crucial. As the network size increases the probability of the dual link failure and node failure also increases. Here, we proposed a parallel cross connection backup recovery strategy for dual link failure in the network. Proposed strategy shows lower bandwidth blocking probability (BBP), fast connection recovery, and bandwidth provisioning ratio when compared with the existing shared path protection (SPP) and dedicated path protection (DPP) approaches. Simulation is performed on ARPANET and COST239 topology networks.

cs.NI↗

arXiv2019

Regularity of Symbolic Powers of Edge Ideals

In this article, we prove that for several classes of graphs, the Castelnuovo-Mumford regularity of symbolic powers of their edge ideals coincide with that of their ordinary powers.

math.AC↗

arXiv2019

Self-similar solutions for finite size advection-dominated accretion flows

We investigated effects on flow variables of transonic advection-dominated accretion flows (ADAFs) for different outer boundary locations (BLs) with a changing energy constant ($E$) of the flow. We used the ADAF solutions and investigated a general power index rule of a radial bulk velocity $(\vr\propto r^{-p})$ with different BLs, but the power index with radius for a rotation velocity and sound speed is unchanged. Here, $p\geq0.5$ is a power index. This power rule gives two types of self-similar solutions; first, when $p=0.5$ gives a self-similar solution of a first kind and exists for infinite length, which has already been discovered for the ADAFs by Narayan \& Yi, and second, when $p>0.5$ gives a self-similar solution of a second kind and exists for finite length, which corresponds to our new solutions for the ADAFs. By using this index rule in fluid equations, we found that the Mach number ($M$) and advection factor ($\fadv$) vary with the radius when $p>0.5$. The local energies of the ADAFs and the Keplerian disk are matched very well at the BLs. So, this theoretical study is supporting a two-zone configuration theory of the accretion disk, and we also discussed other possible hybrid disk geometries. The present study can have two main implications with a variation of the $p$; first, one that can help with the understanding of outflows and non-thermal spectrum variations in black hole candidates, and second, one that can help with solving partial differential equations for any sized advective disk.

astro-ph.HE↗

arXiv2018

Basis Pursuit Denoise with Nonsmooth Constraints

Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. The misfit level is typically measured in the l2 norm, or other smooth metrics. In this paper, we present a new flexible algorithmic framework that targets nonsmooth level-set constraints, including L1, Linf, and even L0 norms. These constraints give greater flexibility for modeling deviations in observation and denoising, and have significant impact on the solution. Measuring error in the L1 and L0 norms makes the result more robust to large outliers, while matching many observations exactly. We demonstrate the approach for basis pursuit denoise (BPDN) problems as well as for extensions of BPDN to matrix factorization, with applications to interpolation and denoising of 5D seismic data. The new methods are particularly promising for seismic applications, where the amplitude in the data varies significantly, and measurement noise in low-amplitude regions can wreak havoc for standard Gaussian error models.

math.OC↗

arXiv2018

Relaxation algorithms for matrix completion, with applications to seismic travel-time data interpolation

Travel time tomography is used to infer the underlying three-dimensional wavespeed structure of the Earth by fitting seismic travel time data collected at surface stations. Data interpolation and denoising techniques are important pre-processing steps that use prior knowledge about the data, including parsimony in the frequency and wavelet domains, low-rank structure of matricizations, and local smoothness. We show how local smoothness structure can be combined with low rank constraints using level-set optimization formulations, and develop a new relaxation algorithm that can efficiently solve these joint problems. In the seismology setting, we use the approach to interpolate missing stations and de-noise observed stations. The new approach is competitive with alternative algorithms, and offers new functionality to interpolate observed data using both smoothness and low rank structure in the presence of data fitting constraints.

math.OC↗

arXiv2018

The 2D disk structure with advective transonic inflow-outflow solutions around black holes

We solved analytically viscous two-dimensional (2D) fluid equations for accretion and outflows in spherical polar coordinates ($r, θ, ϕ$) and obtained explicitly flow variables in $r-$ and $θ-$directions around black holes (BHs). We investigated global transonic advection-dominated accretion flow (ADAF) solutions in $r-$direction on an equatorial plane with using Paczyński-Wiita potential. We used radial flow variables of ADAFs with symmetric conditions on the equatorial plane, as initial values for integration in $θ-$direction. In the study of 2D disk structure, we used two-azimuthal components of viscous stress tensors namely, $τ_{\rm rϕ}$ and $τ_{\rmθϕ}$. Interestingly, we found that the whole advective disk is not participating in outflow generation and the outflows form close to the BHs. Normally, outflow strength increased with increasing viscosity parameter ($α_1$), mass-loss parameter ($s$) and decreasing gas pressure ratio ($β$). Outflow region increased with increasing $s$, $α_1$ for $τ_{\rm rϕ}$ and decreasing $α_2$ for $τ_{\rmθϕ}$. The $τ_{\rmθϕ}$ is effective in angular momentum transportation at high latitude and outflows collimation along an axis of symmetry since it changes polar velocity ($v_{\rmθ}$) of the flow. The outflow emission is also affected by the ADAF size and decreased with decreasing it. Transonic surfaces formed for both inflows ($v_{\rm r}<0$, very close to BH) and outflows ($v_{\rm r}>0$). We also explored no outflows, outflows and failed outflows regions, which mainly depend on the viscosity parameters.

astro-ph.HE↗

arXiv2018

Simultaneous shot inversion for nonuniform geometries using fast data interpolation

Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using 'simultaneous shots', or random superposition of source terms, works very well in simple acquisition geometries where all sources see all receivers, but this rarely occurs in practice. We develop an approach that interpolates data to an ideal acquisition geometry while solving the inverse problem using simultaneous shots. The approach is formulated as a joint inverse problem, combining ideas from low-rank interpolation with full-waveform inversion. Results using synthetic experiments illustrate the flexibility and efficiency of the approach.

math.OC↗

arXiv2018

Certain Classes of Cohen-Macaulay Multipartite Graphs

The Cohen-Macaulay property of a graph arising from a poset has been studied by various authors. In this article, we study the Cohen-Macaulay property of a graph arising from a family of reflexive and antisymmetric relations on a set. We use this result to find classes of multipartite graphs which are Cohen-Macaulay.

math.AC↗

arXiv2018

Compact binary merger and kilonova: outflows from remnant disc

Outflows launched from a remnant disc of compact binary merger may have essential contribution to the kilonova emission. Numerical calculations are conducted in this work to study the structure of accretion flows and outflows. By the incorporation of limited-energy advection in the hyper-accretion discs, outflows occur naturally from accretion flows due to imbalance between the viscous heating and the sum of the advective and radiative cooling. Following this spirit, we revisit the properties of the merger outflow ejecta. Our results show that around $10^{-3} \sim 10^{-1} M_\odot$ of the disc mass can be launched as powerful outflows. The amount of unbound mass varies with the disc mass and the viscosity. The outflow-contributed peak luminosity is around $10^{40} \sim 10^{41}$ erg/s. Such a scenario can account for the observed kilonovae associated with short gamma-ray bursts, including the recent event AT2017gfo (GW170817).

astro-ph.HE↗

arXiv2017

Estimation of bipolar jets from accretion discs around Kerr black holes

We analyse flows around a rotating black hole and obtain self-consistent accretion-ejection solutions in full general relativistic prescription. Entire energy-angular momentum parameter space is investigated in the advective regime to obtain shocked and shock-free accretion solutions. Jet equations of motion are solved along the von-Zeipel surfaces computed from the post-shock disc, simultaneously with the equations of accretion disc along the equatorial plane. For a given spin parameter, the mass outflow rate increases as the shock moves closer to the black hole, but eventually decreases, maximizing at some intermediate value of shock location. Interestingly, we obtain all types of possible jet solutions, for example, steady shock solution with multiple critical points, bound solution with two critical points and smooth solution with single critical point. Multiple critical points may exist in jet solution for spin parameter $a_s\ge 0.5$. The jet terminal speed generally increases if the accretion shock forms closer to the horizon and is higher for corotating black hole than the counter-rotating and the non-rotating one. Quantitatively speaking, shocks in jet may form for spin parameter $a_s>0.6$ and jet shocks range between $6r_g$ and $130r_g$ above the equatorial plane, while the jet terminal speed $v_{{\rm j}\infty} > 0.35{\cm}$ if Bernoulli parameter ${\cal E}\geq1.01$ for $a_s>0.99$.

astro-ph.HE↗

arXiv2017

Modules with Pure Resolutions

We show that the property of a standard graded algebra R being Cohen-Macaulay is characterized by the existence of a pure Cohen-Macaulay R-module corresponding to any degree sequence of length at most depth(R). We also give a relation in terms of graded Betti numbers, called the Herzog-Kuhl equations, for a pure R-module M to satisfy the condition dim(R) - depth(R) = dim(M) - depth(M). When R is Cohen-Macaulay, we prove an analogous result characterizing all graded Cohen-Macaulay R-modules.

math.AC↗

arXiv2016

Simulations of Viscous Accretion Flow around Black Holes in Two-Dimensional Cylindrical Geometry

We simulate shock-free and shocked viscous accretion flow onto a black hole in a two dimensional cylindrical geometry, where initial conditions were chosen from analytical solutions. The simulation code used the Lagrangian Total Variation Diminishing (LTVD) and remap routine, which enabled us to attain high accuracy in capturing shocks and to handle the angular momentum distribution correctly. Inviscid shock-free accretion disk solution produced a thick disk structure, while the viscous shock-free solution attained a Bondi-like structure, but in either case, no jet activity nor any QPO-like activity developed. The steady state shocked solution in the inviscid, as well as, in the viscous regime, matched theoretical predictions well. However, increasing viscosity renders the accretion shock unstable. Large amplitude shock oscillation is accompanied by intermittent, transient inner multiple shocks. Such oscillation of the inner part of disk is interpreted as the source of QPO in hard X-rays observed in micro-quasars. Strong shock oscillation induces strong episodic jet emission. The jets also showed existence of shocks, which are produced as one shell hits the preceding one. The periodicity of jets and shock oscillation were similar. The jets for higher viscosity parameter are evidently stronger and faster.

astro-ph.HE↗

arXiv2016

Beating level-set methods for 3D seismic data interpolation: a primal-dual alternating approach

Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to `fill in' data volumes from critically subsampled data acquired in the field. Tremendous size of seismic data volumes required for seismic processing remains a major challenge for these techniques. We propose a new approach to solve residual constrained formulations for interpolation. We represent the data volume using matrix factors, and build a block-coordinate algorithm with constrained convex subproblems that are solved with a primal-dual splitting scheme. The new approach is competitive with state of the art level-set algorithms that interchange the role of objectives with constraints. We use the new algorithm to successfully interpolate a large scale 5D seismic data volume, generated from the geologically complex synthetic 3D Compass velocity model, where 80% of the data has been removed.

math.OC↗

arXiv2016

Estimation of mass outflow rates from viscous relativistic accretion discs around black holes

We investigated flow in Schwarzschild metric, around a non-rotating black hole and obtained self-consistent accretion - ejection solution in full general relativity. We covered the whole of parameter space in the advective regime to obtain shocked, as well as, shock-free accretion solution. We computed the jet streamline using von - Zeipel surfaces and projected the jet equations of motion on to the streamline and solved them simultaneously with the accretion disc equations of motion. We found that steady shock cannot exist {for $α\gsim0.06$} in the general relativistic prescription, but is lower if mass - loss is considered too. We showed that for fixed outer boundary, the shock moves closer to the horizon with increasing viscosity parameter. The mass outflow rate increases as the shock moves closer to the black hole, but eventually decreases, maximizing at some intermediate value of shock {location}. The jet terminal speed increases with stronger shocks, quantitatively speaking, the terminal speed of jets $v_{{\rm j}\infty} > 0.1$ if $\rsh < 20 \rg$. The maximum of the outflow rate obtained in the general relativistic regime is less than $6\%$ of the mass accretion rate.

astro-ph.HE↗

arXiv2015

Radiatively driven relativistic jets with variable adiabatic index equation of state

We investigate a relativistic fluid jet driven by radiation from a shocked accretion disc around a non-rotating black hole approximated by Paczyński-Wiita potential. The sub-Keplerian and Keplerian accretion rates control the shock location and therefore, the radiation field around the accretion disc. We compute the radiative moments with full special relativistic transformation. The effect of a fraction of radiation absorbed by the black hole has been approximated, over and above the special relativistic transformations. We show that the radiative moments around a super massive black hole are different compared to that around a stellar mass black hole. We show that the terminal speed of jets increases with the mass accretion rates,synchrotron emission of the accretion disc and reduction of proton fraction of the flow composition. To obtain relativistic terminal velocities of jets, both thermal and radiative driving are important. We show for very high accretion rates and pair dominated flow, jets around super massive black holes are truly ultra-relativistic, while for jets around stellar mass black holes, terminal Lorentz factor of about $10$ is achievable.

astro-ph.HE↗

arXiv2014

Dissipative advective accretion disc solutions with variable adiabatic index around black holes

We investigated accretion on to black holes in presence of viscosity and cooling, by employing an equation of state with variable adiabatic index and multi-species fluid. We obtained the expression of generalized Bernoulli parameter which is a constant of motion for an accretion flow in presence of viscosity and cooling. We obtained all possible transonic solutions for a variety of boundary conditions, viscosity parameters and accretion rates. We identified the solutions with their positions in the parameter space of generalized Bernoulli parameter and the angular momentum on the horizon. We showed that a shocked solution is more luminous than a shock-free one. For particular energies and viscosity parameters, we obtained accretion disc luminosities in the range of $10^{-4}-1.2$ times Eddington limit, and the radiative efficiency seemed to increase with the mass accretion rate too. We found steady state shock solutions even for high-viscosity parameters, high accretion rates, and for wide range of composition of the flow, starting from purely electron-proton to lepton-dominated accretion flow. However, similar to earlier studies of inviscid flow, accretion shock was not obtained for electron-positron pair plasma.

astro-ph.HE↗

arXiv2014

Design and considerations of ADC0808 as interleaved ADCs

Here in this paper we are presenting a digital system background technique for correcting the time offset error rate and gain mismatches in a time interleaved analog to digital converter system for N channel communication using 8 bit ADC0808 ICs. A time interleaved A to D converter system is an effective way to implement a high sampling rate ADC with relatively slow circuits. This paper analyses the benefits and derives an upper band on the performance by considering kT/C noise and slewing requirement of the circuit driving the system. In the system, several channel ADCs operate at interleaved sampling times as if they were effectively a single ADC operating at a much higher sampling rate. A timing mismatch calibration technique is proposed that covers linear and non linear channel mismatches, unifies, and extends the channel models. A novel foreground channel mismatch identification method has been developed, which can be used to fully characterize dynamic linear mismatches. A background identification method provides accurate timing mismatch estimates.

cs.OH↗

arXiv2014

Fast methods for denoising matrix completion formulations, with applications to robust seismic data interpolation

Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of rows and columns, paving the way for matrix completion in extremely large-scale applications, such as seismic data interpolation. In this paper, we consider matrix completion formulations designed to hit a target data-fitting error level provided by the user, and propose an algorithm called LR-BPDN that is able to exploit factorized formulations to solve the corresponding optimization problem. Since practitioners typically have strong prior knowledge about target error level, this innovation makes it easy to apply the algorithm in practice, leaving only the factor rank to be determined. Within the established framework, we propose two extensions that are highly relevant to solving practical challenges of data interpolation. First, we propose a weighted extension that allows known subspace information to improve the results of matrix completion formulations. We show how this weighting can be used in the context of frequency continuation, an essential aspect to seismic data interpolation. Second, we propose matrix completion formulations that are robust to large measurement errors in the available data. We illustrate the advantages of LR-BPDN on the collaborative filtering problem using the MovieLens 1M, 10M, and Netflix 100M datasets. Then, we use the new method, along with its robust and subspace re-weighted extensions, to obtain high-quality reconstructions for large scale seismic interpolation problems with real data, even in the presence of data contamination.

stat.ML↗