Lakshminath Bezbaroa Central Library Digital Repository
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- This digital archive comprised of the Institutes' intellectual output.
- It manages, preserves & makes available the academic works of faculty and research scholars.
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Recent Submissions
Archaeology of Sikkim Darjeeleing Himalayas
(2025) Chettri, Upasna
This study is undertaken in Sikkim-Darjeeling Himalayas. The archaeological evidences investigated are Megaliths and Pottery. The central objective of the thesis is to explore the material remains and anthropogenic markers of the past found in the study region. The study hypothesises that Sikkim had a megalithic culture and the existence of a pottery tradition in Sikkim and Darjeeling. In order to investigate the objectives of the study, the methodology opted is desk based assessment along with archaeological and ethnographic investigation for the recording and documentation of the archaeological evidences. For the analysis of the evidences, two different approaches were used.
Study of Certain Partition Functions: Arithmetic Properties, Quantitative Estimates, Asymptotic Formulae, and Partition Inequalities
(2025) Singh, Gurinder
In this thesis, along with the ordinary partition function, we investigate certain restricted partition functions such as t-regular partition functions, mex-related partition functions, and PDO_t(n) partition function. We study arithmetic properties of t-regular partition functions, mex-related partition functions, and PDO_t(n) partition function. For these partition functions, we discover infinite families of Ramanujan-type congruences. We also study the distribution of some of these partition functions modulo some positive integers. We use classical q-series techniques, the theory of modular forms, Radu's algorithm, and the theory of Diophantine equations to prove our results. Analogous to Ono's and Radu's work on Subbarao's conjecture, we prove non-congruences for certain t-regular partitions, for some values of t. Motivated by the conjecture of Parkin and Shanks, we obtain some quantitative estimates for the distribution of 6-, 10-, and 14-regular partitions. For mex-related partition functions, we derive Hardy-Ramanujan type asymptotic formulae. We find the generating functions for the number of hooks of particular lengths in some t-regular partitions. Moving to partition inequalities, we completely uncover the hook length biases for the ordinary partition function. We also prove several hook length biases for t-regular partition functions. We use generating functions and several combinatorial tools and techniques for proving these partition inequalities.
Exploring Pole-Skipping in Holographic Systems
(2025) Baishya, Banashree
The thesis consists of five main chapters. Discussion of our work starts from the second chapter. The second chapter comprises two of our research works. In the first work, the holographic phenomena of pole-skipping were studied in the presence of scalar-Gauss-Bonnet interaction in a four-dimensional Anti-de Sitter-Schwarzchild black hole background. We have initiated a novel study to understand the response of those pole-skipping points under the application of external sources. The source is identified with the holographic dual operator of the bulk scalar field with its non-normalizable solutions. We have analysed in detail the dynamics of pole-skipping points in both sound and shear channels, considering linear perturbations in bulk. In the perturbative regime, characteristic parameters for chaos, namely the Lyapunov exponent and butterfly velocity, remain unchanged. However, the momentum values of the pole-skipping points in various modes are found to be affected by the scalar source. Further, the diffusion coefficient has been observed to evolve non-trivially under the application of external sources. In the second work, we have investigated the holographic fermionic pole-skipping phenomena for a class of interacting theories in a charged AdS black hole background. We have studied two types of fermion-scalar interactions in the bulk: Dipole and Yukawa-type interactions. Depending upon the interaction, we have introduced both real and charged scalar fields. We have particularly analysed the effect of scalar condensation on the fermionic pole-skipping points and discussed their behaviour near critical temperatures. In the third chapter, we have analysed the pole-skipping phenomena of finite temperature Yang-Mills theory with quark flavours, which is dual to D3-D7 brane systems in bulk. We have also considered the external electric field in the boundary field theory, which is dual to the world volume electric field on the D7 brane. We have worked in the probe limit where the D7 branes do not back-react to the D3 brane background. In this scenario, we have computed the characteristic parameters of the chaos, namely, Lyapunov exponent  and butterfly velocity  from the pole-skipping points by performing the near-effective horizon analysis of the linearised Einstein equations. Unlike pure Yang-Mills, once charged quarks with a background electric field are added to the system, the characteristic parameters of the chaos show non-trivial dependence on the quark mass and external electric field. We have observed that  and  decreases with increasing electric field. We have further performed the pole-skipping analysis for the gauge invariant sound, shear, and tensor modes of the perturbation in the bulk and discuss their physical importance in the holographic context. In the fourth chapter, we have investigated two salient chaotic features, namely Lyapunov exponent and butterfly velocity, in the context of an asymptotically Lifshitz black hole background with an arbitrary critical exponent. These features are computed using three methods: entanglement wedge method, out-of-time-ordered correlator computation and pole-skipping. We have presented a comparative study of the aforementioned features, where all of these methods yield exactly similar results for the butterfly velocity and Lyapunov exponent. This establishes an equivalence between all three methods for probing chaos in the chosen gravity background. Furthermore, we have evaluated the chaos at the classical level by computing the eikonal phase and Lyapunov exponent from the bulk gravity. These quantities emerge as nontrivial functions of the anisotropy index. By examining the classical eikonal phase, we uncover different scattering scenarios in the near-horizon and near-boundary regimes. We have also discussed potential limitations regarding the choice of the turning point of the null geodesic in our approach.
Industrial Wastewater Treatment with Cavitation based Hybrid Advanced Oxidation Processes
(2025) Verma, Komal
This thesis investigates the advanced treatment and mineralization of industrial wastewater using innovative hybrid advanced oxidation processes (AOPs). Industrial wastewater, characterized by high chemical oxygen demand (COD) and total organic carbon (TOC), was treated through various ternary hybrid AOPs, combining adsorption, Fenton reactions, and sonication or hydrodynamic cavitation (HC).The development and efficacy of advanced oxidation processes (AOPs) employing Fe3O4-based nanocomposites for industrial wastewater (WW) treatment. A ternary hybrid AOP combining sonication, Fenton reactions, and adsorption was employed using Fe3O4@AC nanocomposites, achieving 94.75% COD and 89% TOC removal within 60 min. LC-MS analysis identified the effective degradation of over 25 organic pollutants, including herbicides and pesticides, with a 60% reduction in wastewater toxicity. Synergistic interactions between activated charcoal adsorption, Fenton reactions, and sonication-induced microconvection were responsible for the enhanced mineralization. Next, work extended to sonoenzymatic treatments using laccase immobilized on Fe3O4 nanoparticles (Fe3O4@Laccase), demonstrating 90.3% COD removal with sonication-assisted enzymatic activity. Structural analysis via FTIR revealed enzyme conformational changes contributing to improved kinetics and substrate affinity. Toxicity analysis indicated a 70% reduction, the biocatalyst retained activity over six cycles. Additionally, Fe3O4@AC nanocomposites were incorporated into chitosan-based hydrogel beads (Fe3O4@AC@CH) to develop a floatable hybrid AOP system. Under optimized conditions, COD and TOC removal reached 96.12% and 78.14%, respectively, with significant degradation of major pollutants. Sonication enhanced mass transfer, while the hydrogel's porous structure facilitated adsorption and surface Fenton reactions, resulting in synergistic pollutant degradation. The beads maintained catalytic performance for six reuse cycles. Lastly, a novel combination of hydrodynamic cavitation (HC), Fe3O4@AC nanocomposites, and Fenton reactions was investigated. Optimized conditions yielded 99.37% COD and 88.80% TOC removal. The HC-based process exhibited superior cavitational yields and significantly enhanced reaction kinetics. The Fe3O4@AC nanocomposites demonstrated high stability and reusability. The findings illustrate the potential of these hybrid AOPs for scalable and efficient industrial wastewater treatment, contributing to sustainable environmental management.
Studies Towards Weak Chelation Assisted Regioselective C-H Activation/C-C Bond Formation: Exploration to Functionalized Heterocycles
(2025) Paul, Tripti
The thesis is divided into four chapters. The first chapter describes the recent advances on transition-metal (TM)-catalyzed weak chelation assisted regioselective C-H functionalization and annulation reactions. The second chapter deals with the weak chelation-guided Rh-catalyzed C4-H alkylation of indoles with cyclopropanols via merging C-H/C-C bond activation. The third chapter demonstrates a biorelevant weakly coordinating directing group (DG) assisted arene C-H alkenylation with cyclopropanols. The fourth chapter focuses on weak chelation assisted oxidative C-H/C-H coupling/annulation cascade of aryl/vinyl phosphonic acid monoesters and benzothiophenes to construct benzothieno-fused oxaphosphacycles.