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Full-Text Articles in Dynamical Systems
Time-Dependent Amplification Of Growth Rates In A Plankton-Oxygen Model, Rapha Coutin
Time-Dependent Amplification Of Growth Rates In A Plankton-Oxygen Model, Rapha Coutin
Master's Theses
Near-bottom hypoxia occurs when dissolved oxygen levels drop to a level that is harmful to marine biology, creating biological dead zones along the ocean floor. Recent years have seen a dramatic increase in the percentage of coastal, near-bottom, hypoxic water, with the average in 2021 nearly double that of the average from 2009 to 2018 and about twenty-eight times the average from 1950 to 1980. Recent literature has linked this increase in oceanic hypoxia to the increase in upwelling-favorable winds caused by climate change. Upwelling brings low-oxygen, nutrient-rich water up to the surface, leading to plankton blooms and mass consumption …
Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown
Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown
Theses and Dissertations
This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.
Topological Data Analysis For Systems Of Coupled Oscillators, Alec Dunton
Topological Data Analysis For Systems Of Coupled Oscillators, Alec Dunton
HMC Senior Theses
Coupled oscillators, such as groups of fireflies or clusters of neurons, are found throughout nature and are frequently modeled in the applied mathematics literature. Earlier work by Kuramoto, Strogatz, and others has led to a deep understanding of the emergent behavior of systems of such oscillators using traditional dynamical systems methods. In this project we outline the application of techniques from topological data analysis to understanding the dynamics of systems of coupled oscillators. This includes the examination of partitions, partial synchronization, and attractors. By looking for clustering in a data space consisting of the phase change of oscillators over a …