Lakshminath Bezbaroa Central Library Digital Repository
Welcome to the Institutional Digital Repository of Lakshminath Bezbaroa Central Library.
- This digital archive comprised of the Institutes' intellectual output.
- It manages, preserves & makes available the academic works of faculty and research scholars.
- It is established to facilitate deposit of digital content of scholarly or heritage nature.
- Allowing academics & their departments to share & preserve contents in a managed environment.
Communities in Gyan-IR
Select a community to browse its collections.
Recent Submissions
Strichartz Estimates Associated with Certain Self-Adjoint Operators
(2026) Ghosh, Sunit
The main focus of this thesis is the study of Strichartz estimates and their extensions to systems of orthonormal functions associated with certain self-adjoint operators. In addition, we investigate a sharp Heisenberg-Pauli-Weyl uncertainty principle for the fractional Dunkl transform. We begin with the Fourier analysis on the Euclidean space, discuss some well known results, basic definitions, and and recent developments that motivate the problems discussed in the thesis.
Regularity Results for the Schrödinger Equation on Rank-One Symmetric Spaces of Non-Compact Type
(2026) Sajjan, Manali
In this thesis, we investigate the pointwise convergence of solutions to the Schrödinger equation on real rank one symmetric spaces of noncompact type. The study of pointwise convergence of solutions to the Schrödinger equation to their initial data is a classical problem in harmonic analysis and partial differential equations. Given the solution u(x, t) of the Schrödinger equation, a fundamental question is; whether the solution u(x, t) converges pointwise to the given initial data f(x) as t → 0. This problem originated from the question posed by Carleson, which asks how much regularity to be imposed on the initial data to ensure the pointwise convergence. While the Euclidean case has been extensively studied, with sharp results established under various regularity assumptions. However much less is known in non-Euclidean settings. In this context, Sjölin has studied the regularity of the fractional Schrödinger equation in ℝⁿ.
Development of synthetic ionophores for therapeutics and molecular communication
(2026) Srimayee, Soumya
Ion transport across biological membranes plays a fundamental role in maintaining cellular homeostasis and regulating numerous physiological processes, including signal transduction, osmotic balance, pH regulation, and cellular metabolism. Disruption of ion transport is associated with several pathological conditions, making synthetic ion transporters attractive candidates for therapeutic and biomimetic applications. This dissertation focuses on the design, synthesis, and functional investigation of synthetic ion transport systems with applications in therapeutics, molecular communication, and artificial transmembrane signaling. Chapter 1 provides an overview of the biological significance of ion transport and discusses the therapeutic and non-therapeutic applications of natural and synthetic ionophores. The chapter further highlights recent advances in stimuli-responsive ion transport systems and summarizes commonly employed methods for studying ion transport across membranes. Chapter 2 describes the development of a multi-stimuli-responsive ion transporter obtained by conjugating bis-thiourea ion-binding units with an RGD peptide through a carbonate linker for targeted delivery. Mechanistic investigations reveal its ion transport behavior, while in vitro studies demonstrate its ability to induce apoptosis through disruption of cellular ion homeostasis. Chapter 3 presents a salicylaldehyde-based imine system capable of self-assembly in lipophilic environments to selectively transport Zn²⁺ ions across membranes. The transported Zn²⁺ ions subsequently coordinate with tyrosine to catalyze the conversion of non-fluorescent precursors into fluorescent products, thereby generating a transmembrane signal amplification system. The system further operates as a three-input AND molecular logic gate, demonstrating ion transport-assisted molecular communication across membranes. Chapter 4 reports a self-assembled tripodal molecular system that forms ion channel-like assemblies in hydrophobic environments and facilitates Zn²⁺ transport into lipid vesicles. Inside the vesicles, Zn²⁺ ions interact with a photosensitizer that produces reactive oxygen species upon light irradiation. These reactive species subsequently promote enzyme-mimetic oxidation reactions, including the oxidation of tryptophan to N-formyl kynurenine. The studies presented in this dissertation collectively explore the integration of ion transport with targeted delivery, signal amplification, logic gate operations, and photoactivated catalytic transformations in biomimetic membrane systems.
Nonlinear Dynamics of Double Beam Piezoelectric Energy Harvesters under Parametric, Magnetic and Galloping Excitation
(2026) Roy, Ronit
In this research work, three double cantilever beams based nonlinear piezoelectric energy harvesting systems have been thoroughly investigated to enhance the total power output of the systems. The thesis is well written in 6 chapters. While in first two chapters introduction and literature review have been carried out, the main work has been presented in next 3 chapters and finally the thesis is concluded in 6th chapter where the future scope is also highlighted. Three problems have been solved in this work. In the first problem, nonlinear dynamic analysis of a spring coupled double beam based piezoelectric energy harvester under parametric base excitation is carried out. In the second work, the similar spring coupled double beam-based energy harvester under parametric base excitation has been studied with an introduction of magnetic repulsive force, which is induced by two NdFeB permanent magnets. In the first and second problems, comprehensive theoretical frameworks are developed by formulating coupled electro-mechanical model incorporating geometric and inertial nonlinearities, piezoelectric coupling and parametric instability. In the third work, a magnetically coupled double beam-based energy harvester under galloping excitation is investigated both theoretically and experimentally. The governing spatio-temporal second order differential equations of motion of these systems have been formulated by energy method. These equations are then reduced to their temporal forms by using generalized Galerkin’s method.
Improved Localisation and Reconstruction in a Single Molecule Localisation Microscope to Enable Super-resolution Imaging with Lowered Resource Pre-requisites
(2026) Choudhury, Pranjal
Super-resolution microscopy techniques overcome the diffraction limit of conventional optical microscopes, enabling the visualisation of nanometre-scale structures using visible light. Among these, Single Molecule Localisation Microscopy (SMLM) including techniques like PALM, STORM, and PAINT allows super-resolution imaging using minimally modified fluorescence microscopes. By temporally separating the stochastic emission of fluorophores and localising them computationally, SMLM reconstructs images with nanometre-level precision.