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Articles 1 - 3 of 3
Full-Text Articles in Dynamical Systems
Quantum Mechanics As A Framework For Data Assimilation And Its Application To Atmospheric Parameterization, David Freeman
Quantum Mechanics As A Framework For Data Assimilation And Its Application To Atmospheric Parameterization, David Freeman
Dartmouth College Ph.D Dissertations
Quantum mechanics, as a mathematical system, can be understood as a generalization of classical probability theory. Quantum Mechanical Data Assimilation (QMDA) is a method in which classical dynamical systems are embedded into a quantum mechanical setting, with an associated data assimilation scheme leveraging the operator algebraic setting. In this dissertation, the algebraic structure underlying the operator theoretic formulation of QMDA is discussed. A procedure for closure of dynamical systems based on QMDA, known as Quantum Mechanical Closure (QMCl), is then constructed, and the procedures for constructing the quantum embeddings and implementing QMCl in practice are laid out and implemented for …
Effective Non-Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics, Vincent Paul Flynn
Effective Non-Hermiticity And Topology In Markovian Quadratic Bosonic Dynamics, Vincent Paul Flynn
Dartmouth College Ph.D Dissertations
Recently, there has been an explosion of interest in re-imagining many-body quantum phenomena beyond equilibrium. One such effort has extended the symmetry-protected topological (SPT) phase classification of non-interacting fermions to driven and dissipative settings, uncovering novel topological phenomena that are not known to exist in equilibrium which may have wide-ranging applications in quantum science. Similar physics in non-interacting bosonic systems has remained elusive. Even at equilibrium, an "effective non-Hermiticity" intrinsic to bosonic Hamiltonians poses theoretical challenges. While this non-Hermiticity has been acknowledged, its implications have not been explored in-depth. Beyond this dynamical peculiarity, major roadblocks have arisen in the search …
Ecological Complexity And Avoiding Pest Resurgence: Intuitions From Mathematical Ecology, Theresa Ong, John H. Vandermeer
Ecological Complexity And Avoiding Pest Resurgence: Intuitions From Mathematical Ecology, Theresa Ong, John H. Vandermeer
Dartmouth Scholarship
Pest resurgence is defined by a predictable increase in pests following declines resulting from the implementation of pest management practices. This phenomenon is notorious; familiar in biblical references to cyclical plagues of locust and discussions of pesticide treadmills, where pests resurge following the evolution of pesticide resistance. Targeted “silver-bullet” approaches, whether chemical, mechanical, biological, or genetic in nature, apply a reductionist lens toward the removal of a specific target pest, often ignoring ecological context, by application of said silver-bullet. In this review article, we cover how past and recent developments in theoretical ecology and complex systems dynamics provide a general …