Physical Sciences and Mathematics Commons^™

Year-2 Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, Steven M. Wise, Evan Habbershaw

Faculty Publications and Other Works -- Mathematics

In this second progress report we expand upon our previous report and preliminary work. Specifically, we review some work on the numerical solution of single- and multi-species BGK-type kinetic equations of particle transport. Such equations model the motion of fluid particles via a density field when the kinetic theory of rarefied gases must be used in place of the continuum limit Navier-Stokes and Euler equations. The BGK-type equations describe the fluid in terms of phase space variables, and, in three space dimensions, require 6 independent phase-space variables (3 for space and 3 for velocity) for each species for accurate simulation. …

A Progress Report On Numerical Methods For Bgk-Type Kinetic Equations, Evan Habbershaw, Steven M. Wise

Faculty Publications and Other Works -- Mathematics

In this report we review some preliminary work on the numerical solution of BGK-type kinetic equations of particle transport. Such equations model the motion of fluid particles via a density field when the kinetic theory of rarefied gases must be used in place of the continuum limit Navier-Stokes and Euler equations. The BGK-type equations describe the fluid in terms of phase space variables, and, in three space dimensions, require 6 independent phase-space variables (3 for space and 3 for velocity) for accurate simulation. This requires sophisticated numerical algorithms and efficient code to realize predictions over desired space and time scales. …

Simple Mathematical Models Do Not Accurately Predict Early Siv Dynamics, Cecilia Noecker, Krista Schaefer, Kelly Zaccheo, Yiding Yang, Judy Day, Vitaly V. Ganusov

Faculty Publications and Other Works -- Mathematics

Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the …

A Southern Hemisphere Origin For Campanulid Angiosperms, With Traces Of The Break-Up Of Gondwana, Jeremy M. Beaulieu, David C. Tank, Michael J. Donoghue

Faculty Publications and Other Works -- Mathematics

Background

New powerful biogeographic methods have focused attention on long-standing hypotheses regarding the influence of the break-up of Gondwana on the biogeography of Southern Hemisphere plant groups. Studies to date have often concluded that these groups are too young to have been influenced by these ancient continental movements. Here we examine a much larger and older angiosperm clade, the Campanulidae, and infer its biogeographic history by combining Bayesian divergence time information with a likelihood-based biogeographic model focused on the Gondwanan landmasses.

Results

Our analyses imply that campanulids likely originated in the middle Albian (~105 Ma), and that a substantial portion …

Stability Analysis Of Fitzhugh-Nagumo With Smooth Periodic Forcing, Tyler Massaro, Benjamin F. Esham

Faculty Publications and Other Works -- Mathematics

Alan Lloyd Hodgkin and Andrew Huxley received the 1963 Nobel Prize in Physiology for their work describing the propagation of action potentials in the squid giant axon. Major analysis of their system of differential equations was performed by Richard FitzHugh, and later by Jin-Ichi Nagumo who created a tunnel diode circuit based upon FitzHugh’s work. The resulting differential model, known as the FitzHugh-Nagumo (FH-N) oscillator, represents a simplification of the Hodgkin-Huxley (H-H) model, but still replicates the original neuronal dynamics (Izhikevich, 2010). We begin by providing a thorough grounding in the physiology behind the equations, then continue by introducing some …