Fourth Year Classes
Page
I am particularly proud of the class
work conducted
at Caltech. The classes have been challenging but rewarding.
A note about the courses: During the fourth year we are no-longer required to
take courses. However, I decided to take the course CDS 140a
introduction to dynamics to learn more about dynamical systems. As my
adviser Dr. Meiron said "you never know when these techniques may come
on handy". For the winter and spring terms I decided to take the course
on turbulence offered by Dr. Paul Dimotakis
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Spring 2005
AE 239b: Turbulence, Dr. Paul
Dimotakis
Content:
Karman-Howarth equation, velocity and scalar structure functions,
small-scale turbulence and Lundgren spiral vortex model of turbulence,
kinematics and dynamics of vorticity, stretched vortex model, turbulent
two-dimensional shear layers, Brown-Roshko experiments (1971, 1974),
large-eddy simulation of turbulent flows, vortex models, shear layer
flow, turbulent axisymmetric jet, entrainment and mixing in turbulent
jets, measurement of mixing through chemical reactions, mixing models
Books: Class notes
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Winter 2005
AE239a: Turbulence, Dr. Paul
Dimotakis
Content: Definition of
turbulence, Fourier decomposition of spatial correlations, kinetic
energy dissipation, spectra (Kolmogorov 1941), turbulence cascade,
mixing transition, scalar fluctuations and mixing, structure of flow at
small scales, scalar fluctuations spectrum, refined turbulence
hypothesis (Kolmogorov 1962)
Books: Class notes
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Fall 2004
CDS 140a: Introduction
to Dynamics, Dr. Mabuchi
Content: Linear systems: Uncoupled linear
systems, diagonalization, exponential of operators, the fundamental
theorem of linear systems, complex eigenvalues, multiple eigenvalues,
Jordan form, Stability theory.
Nonlinear systems: Local
Theory: The fundamental existence-uniqueness theorem, dflow
defined by a differential equation, linearization, the stable manifold
theorem, the Hartman-Grobman theorem, stability and Liapunov functions,
saddles, nodes, foci and centers, nonhyperbolic critical points in R2,
center manifold theory, normal form theory, gradient and hamiltonian
systems.
Nonlinear systems:
Global Theory: Dynamical systems and global existence theorems,
limit sets and attractors, periodic orbits, Poincare' map, the stable
manifold theorem for periodic orbits, Floquet Theory.
Analytical Mechanics:
Lagrangian Mechanics, virtual work, the Lagrangian, the Hamiltonian,
linear oscillators, the Hill equation, the Mathieu equation.
Books: Perko, Lawrence, "Differential
Equations and Dynamical Systems", Springer-Verlag 2000
Hand, LN and Finch, JD, "Analytical Mechanics", Cambridge 1998
Readings from: Guckenheimer, J and Holmes, P, "Nonlinear Oscillations,
Dynamical Systems, and Bifurcation of Vector fields, Springer-Verlag
1997
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Last updated: May 12, 2006
comments e-mail: mlatini@acm.caltech.edu
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