Dynamical Systems Commons^™

Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft

Theses and Dissertations

Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …

Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

Theses and Dissertations

Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.

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.

Analyzing A Method To Determine The Utility Of Adding A Classification System To A Sequence For Improved Accuracy, Kevin S. Pamilagas

Theses and Dissertations

Frequently, ensembles of classification systems are combined into a sequence in order to better enhance the accuracy in classifying objects of interest. However, there is a point in which adding an additional system to a sequence no longer enhances the system as either the increase in operational costs exceeds the benefit of improvements in classification or the addition of the system does not increase accuracy at all. This research will examine a utility measure to determine the valid or invalid nature of adding a classification system to a sequence of such systems based on the ratio of the change in …

Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson

Theses and Dissertations

The modeling focus on serpentine inlet ducts (S-duct), as with any inlet, is to quantify the total pressure recovery and ow distortion after the inlet, which directly impacts the performance of a turbine engine fed by the inlet. Accurate prediction of S-duct ow has yet to be achieved amongst the computational fluid dynamics (CFD) community to improve the reliance on modeling reducing costly testing. While direct numerical simulation of the turbulent ow in an S-duct is too cost prohibitive due to grid scaling with Reynolds number, wall-modeled large eddy simulation (WM-LES) serves as a tractable alternative. US3D, a hypersonic research …

Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan

Theses and Dissertations

We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential.

We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation …

Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher

Theses and Dissertations

This paper uses KAM torus theory and Simplified General Perturbations 4 (SGP4) orbit prediction techniques compiled by Dr. William Wiesel and compares it to Analytical Graphics ® Incorporated (AGI) Satellite Toolkit ® (STK) orbit data. The goal of this paper is to verify KAM torus theory can be used to describe and propagate an Earth satellite orbit with similar accuracy to existing general perturbation techniques. Using SGP4 code including only truncated geopotential effects, KAM torus generating code, and other utilities were used to describe a particular satellite orbit as a torus and then propagate the satellite using traditional and KAM …

Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge

Theses and Dissertations

A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …