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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
On The P-Inner Functions Of ℓPA, James G. Dragas
On The P-Inner Functions Of ℓPA, James G. Dragas
Mathematics & Statistics Theses & Dissertations
Define ℓpA as the space of all functions holomorphic over the unit disk whose Taylor coefficients are p-summable. Despite their classical origins and simple definition, these spaces are not as well understood as one might expect. This is particularly true when compared with the Hardy spaces, which provide a useful road map for the types of questions we might consider reasonable. In this work we examine the zero sets of ℓpA, p ∈ (1;∞), as well as a notion of inner function that is consistent with the approach taken on numerous other function spaces. …
High-Order Positivity-Preserving L2-Stable Spectral Collocation Schemes For The 3-D Compressible Navier-Stokes Equations, Johnathon Keith Upperman
High-Order Positivity-Preserving L2-Stable Spectral Collocation Schemes For The 3-D Compressible Navier-Stokes Equations, Johnathon Keith Upperman
Mathematics & Statistics Theses & Dissertations
High-order entropy stable schemes are a popular method used in simulations with the compressible Euler and Navier-Stokes equations. The strength of these methods is that they formally satisfy a discrete entropy inequality which can be used to guarantee L2 stability of the numerical solution. However, a fundamental assumption that is explicitly or implicitly used in all entropy stability proofs available in the literature for the compressible Euler and Navier-Stokes equations is that the thermodynamic variables (e.g., density and temperature) are strictly positive in the entire space{time domain considered. Without this assumption, any entropy stability proof for a numerical scheme …
Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis
Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis
Mathematics & Statistics Theses & Dissertations
Volterra integral equations arise in a variety of applications in modern physics and engineering, namely in interactions that contain a memory term. Classical formulations of these problems are largely inflexible when considering non-homogeneous media, which can be problematic when considering long term interactions of real-world applications. The use of fractional derivative and integral terms naturally relax these restrictions in a natural way to consider these problems in a more general setting. One major drawback to the use of fractional derivatives and integrals in modeling is the regularity requirement for functions, where we can no longer assume that functions are as …
Electrohydrodynamic Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Scheme, Charles Leland Armstrong
Electrohydrodynamic Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Scheme, Charles Leland Armstrong
Mathematics & Statistics Theses & Dissertations
Capsules are fluid-filled, elastic membranes that serve as a useful model for synthetic and biological membranes. One prominent application of capsules is their use in modeling the response of red blood cells to external forces. These models can be used to study the cell’s material properties and can also assist in the development of diagnostic equipment. In this work we develop a three dimensional model for numerical simulations of red blood cells under the combined influence of hydrodynamic and electrical forces. The red blood cell is modeled as a biconcave-shaped capsule suspended in an ambient fluid domain. Cell deformation occurs …