Browsing by Author "Pradhan, Chandan"

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    Study of the Process-form Relationships in Continuum of Braided Channel Patterns
    (2022) Pradhan, Chandan
    The braided rivers are governed by complex, unstable river networks formed due to the interaction of high flow energy and intense sediment transport. The generation of complex morphological adjustments over a braided corridor is a response to the changes in flow and sediment supply. Understanding braided river behavior and underlying concepts through field-based studies, modeling, analysis and cloud computing can be beneficial for their effective management. The present thesis provides a comprehensive understanding of the process-form relationships and associated management approaches along the continuum of braided channels.
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    Trace Formulas and Finite Dimensional Approximations
    (2023) Pradhan, Chandan
    The dissertation gives a new proof of some existing second-order trace formulas, namely the Koplienko-Neidhardt trace formula for pair of unitaries in the multiplicative path, the Koplienko-Neidhardt trace formula for pair of contractions via linear path with one of them being normal. Our proofs are based on the idea of the finite-dimensional approximation method introduced by Voiculescu. As a consequence of our results and the Schaffer matrix unitary dilation, we obtained second-order trace formula for a class of pairs of contractions via linear path. Using a different setup of finite dimensional approximations, we extend the Koplienko-Neidhardt trace formula for a class of pairs of contractions via multiplicative path.