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Full-Text Articles in Applied Mathematics
Border-Collision Bifurcations Of Cardiac Calcium Cycling, Jacob Michael Kahle
Border-Collision Bifurcations Of Cardiac Calcium Cycling, Jacob Michael Kahle
Masters Theses
In this thesis, we study the nonlinear dynamics of calcium cycling within a cardiac cell. We develop piecewise smooth mapping models to describe intracellular calcium cycling in cardiac myocyte. Then, border-collision bifurcations that arise in these piecewise maps are investigated. These studies are carried out using both one-dimensional and two-dimensional models. Studies in this work lead to interesting insights on the stability of cardiac dynamics, suggesting possible mechanisms for cardiac alternans. Alternans is the precursor of sudden cardiac arrests, a leading cause of death in the United States.
Development And Analysis Of Onboard Translunar Injection Targeting Algorithms, Phillippe Lyles Winters Reed
Development And Analysis Of Onboard Translunar Injection Targeting Algorithms, Phillippe Lyles Winters Reed
Masters Theses
Several targeting algorithms are developed and analyzed for possible future use onboard a spacecraft. Each targeter is designed to determine the appropriate propulsive burn for translunar injection to obtain desired orbital parameters upon arrival at the moon. Primary design objectives are to minimize the computational requirements for each algorithm but also to ensure reasonable accuracy, so that the algorithm’s errors do not force the craft to conduct large mid-course corrections. Several levels of accuracy for dynamical models are explored, the convergence range and speed of each algorithm are compared, and the possible benefits of the Broyden and trust-region targeters are …
Nonlinear Acoustics Of Piston-Driven Gas-Column Oscillations, Andrew William Wilson
Nonlinear Acoustics Of Piston-Driven Gas-Column Oscillations, Andrew William Wilson
Masters Theses
The piston-driven oscillator is traditionally modeled by directly applying boundary conditions to the acoustic wave equations; with better models re-deriving the wave equations but retaining nonlinear and viscous effects. These better models are required as the acoustic solution exhibits singularity near the natural frequencies of the cavity, with an unbounded (and therefore unphysical) solution. Recently, a technique has been developed to model general pressure oscillations in propulsion systems and combustion devices. Here, it is shown that this technique applies equally well to the piston-driven gas-column oscillator; and that the piston experiment provides strong evidence for the validity of the general …