Studies of electromagnetic counterparts to gravitational-wave sources and the nonlinear gravitational-wave memory effect

In this dissertation, theoretical/computational results are presented from the investigations of three different topics within the general research areas of gravitational wave astrophysics and electromagnetic counterparts. First, general relativistic force-free electromagnetic theory and its application to black hole magnetospheres are discussed. In this connection, simulations of a binary black hole merger are examined using the open-source software, GiRaFFE, which is used to model black holes’ magnetospheres and to study supermassive black-hole binary mergers in an external magnetic field. In the simulations, a helical magnetic field structure around each black hole is observed. Electromagnetic energy flux is observed during the inspiral and the merger phases. The emission becomes stronger as the binary move from inspiral to the merger phase. The electromagnetic emission during binary black hole merger is accompanied by gravitational waves (GW). A better understanding of electromagnetic emissions along with results from gravitational waves provides us with a better understanding of the physics of the source. In this connection, this work investigates the effect of the inclination of binary on electromagnetic emission. The second topic investigated in this work is an interesting prediction of general relativity called the non-linear memory of GW. The effect of black-hole spins on non-linear memory from supermassive black-hole binary mergers is examined and its impact on the timing residuals observed by pulsar timing arrays is analyzed. The non-linear memory contribution to the gravitational waveform is obtained for inspiraling spinning black holes. These results are generalizations of the work by Favata [1] to the spinning case. The memory contribution during the merger is obtained by using the formula by Favata [1] and is applied to publicly available Simulating eXtreme Spacetimes (SXS) [2] data. Further, our results are used to compute the post-fit timing residual growth during a two-week interval of time for supermassive black holes in the mass range from 108 to 1010 M⊙ . This work would be useful for the search of Burst with Memory (BWM) events with the future Pulsar Timing Array (PTA) which would have higher sensitivity. In literature, researchers have modeled the BWM events as step functions but in this dissertation, it have been investigated how the expected results could change if more accurate models for nonlinear memory waveforms are used. The third topic investigated in this work looks at the accuracy of the gravitational wave- iii forms as given by various models using the recently proposed super- momentum balance law on asymptotically flat spacetimes. Some analytical methods to study the violation of balance laws for the Effective-one-body (EOB) and Backward-one-body (BOB) models are investigated. Future gravitational wave observatories will have better sensitivity and hence more accurate waveforms would be required. Supermomentum balance laws can be used to investigate how accurate are the solutions of various waveform models which are just approximations and not exact solutions to Einstein’s equation. The essential problem with the application of supermomentum balance laws is that it requires a time-dependent Weyl scalar and most models such as EOB and BOB do not have a time-dependent evolving background metric. In this dissertation some approximate solutions for the Weyl scalar for EOB and BOB which can be written in terms of Bondi mass and linear momentum of the system are proposed

Optimal Index Codes via a Duality between Index Coding and Network Coding

In Index Coding, the goal is to use a broadcast channel as efficiently as possible to communicate information from a source to multiple receivers which can possess some of the information symbols at the source as side-information. In this work, we present a duality relationship between index coding (IC) and multiple-unicast network coding (NC). It is known that the IC problem can be represented using a side-information graph $G$ (with number of vertices $n$ equal to the number of source symbols). The size of the maximum acyclic induced subgraph, denoted by $MAIS$ is a lower bound on the \textit{broadcast rate}. For IC problems with $MAIS=n-1$ and $MAIS=n-2$, prior work has shown that binary (over ${\mathbb F}_2$) linear index codes achieve the $MAIS$ lower bound for the broadcast rate and thus are optimal. In this work, we use the the duality relationship between NC and IC to show that for a class of IC problems with $MAIS=n-3$, binary linear index codes achieve the $MAIS$ lower bound on the broadcast rate. In contrast, it is known that there exists IC problems with $MAIS=n-3$ and optimal broadcast rate strictly greater than $MAIS$

Index Coding: Rank-Invariant Extensions

An index coding (IC) problem consisting of a server and multiple receivers with different side-information and demand sets can be equivalently represented using a fitting matrix. A scalar linear index code to a given IC problem is a matrix representing the transmitted linear combinations of the message symbols. The length of an index code is then the number of transmissions (or equivalently, the number of rows in the index code). An IC problem ${\cal I}_{ext}$ is called an extension of another IC problem ${\cal I}$ if the fitting matrix of ${\cal I}$ is a submatrix of the fitting matrix of ${\cal I}_{ext}$. We first present a straightforward $m$\textit{-order} extension ${\cal I}_{ext}$ of an IC problem ${\cal I}$ for which an index code is obtained by concatenating $m$ copies of an index code of ${\cal I}$. The length of the codes is the same for both ${\cal I}$ and ${\cal I}_{ext}$, and if the index code for ${\cal I}$ has optimal length then so does the extended code for ${\cal I}_{ext}$. More generally, an extended IC problem of ${\cal I}$ having the same optimal length as ${\cal I}$ is said to be a \textit{rank-invariant} extension of ${\cal I}$. We then focus on $2$-order rank-invariant extensions of ${\cal I}$, and present constructions of such extensions based on involutory permutation matrices

Comparison of post-Newtonian templates for extreme mass ratio inspirals

Extreme mass ratio inspirals (EMRIs), the inspirals of compact objects into supermassive black holes, are important gravitational wave sources for the Laser Interferometer Space Antenna (LISA). We study the performance of various post-Newtonian (PN) template families relative to the high precision numerical waveforms in the context of EMRI parameter estimation with LISA. Expressions for the time domain waveforms TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt are derived up to 22PN order, i.e $\mathcal{O}(v^{44})$ ($v$ is the characteristic velocity of the binary) beyond the Newtonian term, for a test particle in a circular orbit around a Schwarzschild black hole. The phase difference between the above 22PN waveform families and numerical waveforms are evaluated during two-year inspirals for two prototypical EMRI systems with mass ratios $10^{-4}$ and $10^{-5}$. We find that the dephases (in radians) for TaylorT1 and TaylorT2, respectively, are about $10^{-9}$ ($10^{-2}$) and $10^{-9}$ ($10^{-3}$) for mass ratio $10^{-4}$ ($10^{-5}$). This suggests that using 22PN TaylorT1 or TaylorT2 waveforms for parameter estimation of EMRIs will result in accuracies comparable to numerical waveform accuracy for most of the LISA parameter space. On the other hand, from the dephase results, we find that TaylorT3, TaylorT4 and TaylorEt fare relatively poorly as one approaches the last stable orbit. This implies that, as for comparable mass binaries using the 3.5PN phase of waveforms, the 22PN TaylorT3 and TaylorEt approximants do not perform well enough for the EMRIs. The reason underlying the poor performance of TaylorT3, TaylorT4 and TaylorEt relative to TaylorT1 and TaylorT2 is finally examined.Comment: 10 page

Warm mix asphalt: Paves way for energy saving

Road transport sector in India has expanded in the last sixty years after independence, both in terms of capacity and dimensions. Today, India is having thethird largest road network in the world, with over 4.236 million km of roadways spread across the country. Currently, majority of the Indian roads are paved with Hot Mix Asphalt (HMA),which consists of aggregates and bitumen mixed together at high temperature,approximately150-170°C. The production and placement of HMA pavements has evolved over the last 130 years and recognised as a high quality engineered paving material to produce good quality pavement. During all these years, the production of HMA has modernized from manual hand mixing and placement with rakes and shovels to computerized plants feeding, placement, and compaction equipment that track location and material quality.The main concern with the production of HMA is, it requires large amount of energy and also releases enormous amount of emissions into the environment. So, the road construction industry is looking for an alternate material or a technology that reduces the amount of energy required to produce the HMA, in order to combine energy savings and environmental benefits. Warm Mix Asphalt (WMA) technology is one of the solutions. WMA technologies allow producing the asphalt material at 30 to 40°C lower temperatures than conventional HMA. This paper presents a comprehensive literature review on various WMA technologies across the globe and advantages associated with WMA technologies.It also provides details of some of the attempts done with WMA technologies in India till now

Response of okra (Abelmoschus esculentus L. Moench) to vermicompost, mycorrhiza and micronutrients mixture

A field experiments on okra (Abelmoschus esculentus L Moench) cv. Arka Anamika” was conducted at Department of Vegetable Science, College of Horticulture and Forestry, Jhalrapatan city, Jhalawar during the Kharif 2016-17 to study the effect of vermicompost, mycorrhiza and micronutrients mixture of 16 treatment combination i.e. vermicompost with two levels (2 tons/ha and 4 tons /ha), mycorrhiza with one level (Mycorrhiza seed treatment) and micronutrients mixture with two levels (50 ppm and 100 ppm). The observations revealed that the plant height of A. esculentus after 60 DAS (74 cm), plant height after 90 DAS (79.71cm), number of leaves / plant (43.17), main steam diameter (5.52 cm), number of primary branches per plant (5.10) of A. esculentus and lowest days to first flower bud emergence (33.53) of A. esculentus was noted maximum as compared to control. The results indicates that plant height, number of leaves per plant, main stem diameter, stem girth, number of primary branches increased significantly due to application of different levels of vermicompost, mycorrhiza and micronutrients mixture as compared to control. It is postulated that the vermicompost 2tons and 4tons + mycorrhiza seed treatment + micronutrients mixture 50ppm and 100ppm may positively regulate the A. esculentus growth improved. Therefore, application of vermicompost, mycorrhiza along with a mixture of micronutrients played a significant role on enhancing the growth of okra (A. esculentus) and can be applied to obtain the maximum crop yield of okra (A. esculentus)

Constraints faced Panchayat Members in Relation to Agricultural Development Programs in Ujjain District (M.P.)

In india Panchayati Raj now functions as a system of governance in which Gram Panchayats are the basic units of local administration. The system has three levels: Gram Panchayat (village level), Mandal Parishad or Block Samiti or Panchayat Samiti (block level), and Zila Parishad (district level). Panchayat Raj has come to be related with two broad images. First, it is a government by itself and second it is an agency of the state government. In the integrated exercise of planning for social and economic development, co-ordinate roles, the present set up is a three-tier representative structure of government where the administrators, elected leaders and local population participate in the developmental effort. In this regard the members of Panchyat faced many problems there this study confront the constrains faced by members and suggestions to overcome them with 120 sample unit of Ujjain district. The major finding was obtained in this study that the most serious constraint perceived by the Gram Panchayat Members during agriculture development programmes was Insufficient use of communication media  (85.83%) as it was perceived to the highest extent by gram Panchayat Members with major suggestion of them Properly and timely use of communication media. View Article DOI: 10.47856/ijaast.2021.v08i9.01

GiRaFFE: An Open-Source General Relativistic Force-Free Electrodynamics Code

We present GiRaFFE, the first open-source general relativistic force-free electrodynamics (GRFFE) code for dynamical, numerical-relativity generated spacetimes. GiRaFFE adopts the strategy pioneered by McKinney and modified by Paschalidis and Shapiro to convert a GR magnetohydrodynamic (GRMHD) code into a GRFFE code. In short, GiRaFFE exists as a modification of IllinoisGRMHD, a user-friendly, open-source, dynamical-spacetime GRMHD code. Both GiRaFFE and IllinoisGRMHD leverage the Einstein Toolkit's highly-scalable infrastructure to make possible large-scale simulations of magnetized plasmas in strong, dynamical spacetimes on adaptive-mesh refinement (AMR) grids. We demonstrate that GiRaFFE passes a large suite of both flat and curved-spacetime code tests passed by a number of other state-of-the-art GRFFE codes, and is thus ready for production-scale simulations of GRFFE phenomena of key interest to relativistic astrophysics.Comment: 23 pages, 4 figures. Consistent with published versio

Structural, Dielectric and Electrical Characteristic of Bi0.5Pb0.5[Fe0.1La0.4(Zr0.25Ti0.25)]O3

The polycrystalline compound Bi0.5Pb0.5 [Fe0.1La0.4 (Zr0.25Ti0.25)]O3 was synthesized by substituting Pb, La, Zr and Ti ions on perovskite structured bismuth ferrite (BFO) with the help of mixed oxide solid state reaction method. The present work is to observe the effect of off-valence and iso-valence substitution on the dielectric and electric properties of bismuth ferrite (BFO). The room temperature XRD pattern of the calcinated powders of the sample reveals that the crystal structure is tetragonal with space group P4mm, while BFO has rhombohedral structure with space group R3c. The SEM of the sintered pellet of the compound indicates that the small grains are uniformly distributed over the surface. Complex impedance spectroscopy (CIS) was adopted to analyze the dielectric, impedance and conductivity behavior of the compound. The results show that the dielectric loss in the material is significantly less than that of BFO and the dielectric and ferroelectric behavior of the sample get enhanced. The complex impedance plots show the existence of non-Debye type of relaxation phenomena, which is caused by resistive and capacitive effect of the bulk and grain boundaries. The Arrhenius plot for the compound indicates that the material possesses NTCR behavior. The frequency response of ac conductivity obeys Jonschers law and UDR (universal dielectric response).[Key words: off-valence, iso-valence, CIS, non-Debye type relaxation, NTCR, UDR

IN VITRO RESPONSE BY Terminalia arjuna GENOTYPES DURING MICROPROPAGATION

Terminalia arjuna is an important tree of the medicinal and sericulture industry, commonly known as Arjun. It’s bark is rich in secondary metabolites makes this plant highly valuable in medicine industry to treat cardiovascular disease. Overexploitation due to high demand in medicine, low seed germination, limitations of the conventional method of propagation push this plant towards being endangered. To conserve germplasm of such tree species and meet the requirement in medicinal industry, some non-conventional propagation method like micropropagation has been developed. The present work highlighted the effect of three genotypes (G-1, G-2, and G-3) on tissue culture of T. arjuna situated at Jodhpur, Rajasthan, India. In vitro shoot proliferation was achieved on a modified MS medium enriched with BAP + additives. Among the tested genotypes, Genotype -1 showed maximum bud break response (100%) followed by G-3 (93.33 %) and G-2 (86.66%).  Further multiplication of these shoots on modified MS medium containing BAP + NAA + additives gave 11.38±0.26 (G-1), 9.44±0.21 (G-2) and 10.22±0.32 (G-3) shoots. In vitro rooting was done by pulse treatment with IBA for 10 min prior to transfer on hormone free half strength MS medium containing 0.1% activated charcoal. Maximum in vitro rooting was obtained in G-1 (80%) followed by G-3 (71.11%) and G-2 (68.88%). In the present study, it was observed that optimum growth in all three genotypes required different doses of Plant Growth Regulator. Thus, by identifying and multiplying the best performing genotypes the gap between demand and supply of such medicinal plant can be fulfilled