Current Search: Differential equations, Nonlinear (x)
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- Title
- ACCURATE HIGH ORDER COMPUTATION OF INVARIANT MANIFOLDS FOR LONG PERIODIC ORBITS OF MAPS AND EQUILIBRIUM STATES OF PDE.
- Creator
- Gonzalez, Jorge L., Mireles-James, Jason, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
-
The study of the long time behavior of nonlinear systems is not effortless, but it is very rewarding. The computation of invariant objects, in particular manifolds provide the scientist with the ability to make predictions at the frontiers of science. However, due to the presence of strong nonlinearities in many important applications, understanding the propagation of errors becomes necessary in order to quantify the reliability of these predictions, and to build sound foundations for future...
Show moreThe study of the long time behavior of nonlinear systems is not effortless, but it is very rewarding. The computation of invariant objects, in particular manifolds provide the scientist with the ability to make predictions at the frontiers of science. However, due to the presence of strong nonlinearities in many important applications, understanding the propagation of errors becomes necessary in order to quantify the reliability of these predictions, and to build sound foundations for future discoveries. This dissertation develops methods for the accurate computation of high-order polynomial approximations of stable/unstable manifolds attached to long periodic orbits in discrete time dynamical systems. For this purpose a multiple shooting scheme is applied to invariance equations for the manifolds obtained using the Parameterization Method developed by Xavier Cabre, Ernest Fontich and Rafael De La Llave in [CFdlL03a, CFdlL03b, CFdlL05].
Show less - Date Issued
- 2020
- PURL
- http://purl.flvc.org/fau/fd/FA00013468
- Subject Headings
- Invariant manifolds, Nonlinear systems, Diffeomorphisms, Parabolic partial differential equations, Differential equations, Partial
- Format
- Document (PDF)
- Title
- Karhunen-Loeve decomposition for non stationary propulsor flow noise.
- Creator
- Kersulec, Jean-Luc., Florida Atlantic University, Glegg, Stewart A. L., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
- Abstract/Description
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The aim of this thesis is to develop a theory for non stationary propulsor flow noise. The model which is proposed is based on Amiet's paper "Acoustic Radiation from an Airfoil in a Turbulent Stream" [1], which describes broad band noise when a simple model of airfoil interacts with a turbulent flow, under the assumption of stationarity. The Karhunen-Loeve method provides a set of modes which describe the turbulent flow without the assumption of stationarity. A method is described to obtain...
Show moreThe aim of this thesis is to develop a theory for non stationary propulsor flow noise. The model which is proposed is based on Amiet's paper "Acoustic Radiation from an Airfoil in a Turbulent Stream" [1], which describes broad band noise when a simple model of airfoil interacts with a turbulent flow, under the assumption of stationarity. The Karhunen-Loeve method provides a set of modes which describe the turbulent flow without the assumption of stationarity. A method is described to obtain broad band noise calculations when the mean turbulent flow varies with time and produces non stationary turbulence. A comparison of the numerical results obtained with the results from the paper of reference [1] shows the characteristics of time varying sound radiation. The various mathematical formulae will give a starting point to the analysis of real time varying flows, which are not considered in this thesis.
Show less - Date Issued
- 2005
- PURL
- http://purl.flvc.org/fcla/dt/13233
- Subject Headings
- Aerodynamic noise, Turbulence, Aerofoils, Unsteady flow (Aerodynamics), Nonlinear control theory, Differential equations, Nonlinear
- Format
- Document (PDF)
- Title
- Stability analysis for singularly perturbed systems with time-delays.
- Creator
- Yang, Yang, Wang, Yuan, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Singularly perturbed systems with or without delays commonly appear in mathematical modeling of physical and chemical processes, engineering applications, and increasingly, in mathematical biology. There has been intensive work for singularly perturbed systems, yet most of the work so far focused on systems without delays. In this thesis, we provide a new set of tools for the stability analysis for singularly perturbed control systems with time delays.
- Date Issued
- 2015
- PURL
- http://purl.flvc.org/fau/fd/FA00004423, http://purl.flvc.org/fau/fd/FA00004423
- Subject Headings
- Biology -- Mathematical models, Biomathematics, Differentiable dynamical systems, Differential equations, Partial -- Numerical solutions, Global analysis (Mathematics), Lyapunov functions, Nonlinear theories
- Format
- Document (PDF)
- Title
- Dynamics of two-actor cooperation–competition conflict models.
- Creator
- Liebovitch, Larry S., Naudot, Vincent, Vallacher, Robin R., Nowak, Andrzej, Bui-Wrzosinska, Lan, Coleman, Peter T.
- Date Issued
- 2008-11-01
- PURL
- http://purl.flvc.org/fau/165475
- Subject Headings
- Nonlinear theories, Social systems--Mathematical models, Conflict management, Cooperativeness, Differential equations, Competition, Dynamics--Mathematical models
- Format
- Document (PDF)