Ph.D. Mechanical and Aerospace Engineering

APC 523 Numerical Algorithms for Scientific Computing (also

AST 523

/

MAE 507

) A broad introduction to scientific computation using examples drawn from astrophysics. From computer science, practical topics including processor architecture, parallel systems, structured programming, and scientific visualization will be presented in tutorial style. Basic principles of numerical analysis, including sources of error, stability, and convergence of algorithms. The theory and implementation of techniques for linear and nonlinear systems of equations, ordinary and partial differential equations will be demonstrated with problems in stellar structure and evolution, stellar and galactic dynamics, and cosmology.

APC 524 Software Engineering for Scientific Computing (also

MAE 506

/

AST 506

) The goal of this course is to teach basic tools and principles of writing good code, in the context of scientific computing. Specific topics include an overview of relevant compiled and interpreted languages, build tools and source managers, design patterns, design of interfaces, debugging and testing, profiling and improving performance, portability, and an introduction to parallel computing in both shared memory and distributed memory environments. The focus is on writing code that is easy to maintain and share with others. Students will develop these skills through a series of programming assignments and a group project.

AST 551 General Plasma Physics I (also

MAE 525

) This is an introductory course to plasma physics, with sample applications in fusion, space and astrophysics, semiconductor etching, microwave generation: characterization of the plasma state, Debye shielding, plasma and cyclotron frequencies, collision rates and mean-free paths, atomic processes, adiabatic invariance, orbit theory, magnetic confinement of single-charged particles, two-fluid description, magnetohydrodynamic waves and instabilities, heat flow, diffusion, kinetic description, and Landau damping. The course may be taken by undergraduates with permission of the instructor.

CEE 530 Continuum Mechanics and Thermodynamics (also

MSE 530

/

MAE 560

) The course covers the fundamentals of the mechanics and thermodynamics of continua. It reviews concepts of tensor analysis on manifolds and tensor calculus. It then proceeds by developing the fundamental concepts of the kinematics of a deforming continuum. The notion of stress is then introduced and measures of stresses are discussed. Conservation of mass, balance of momentum and moment of momentum, conservation of energy in thermodynamic are discussed. Constitutive theories and the restriction of the second law are presented. The Euler-Lagrange equations are re-connected with balance laws.

ELE 521 Linear System Theory (also

MAE 547

) This course covers the fundamentals of linear system theory. Various topics important for further study in dynamic systems, control and communication and signal processing are presented.

ELE 523 Nonlinear System Theory (also

MAE 548

) A study of the mathematical techniques found useful in the analysis and design of nonlinear systems. Topics include stability and qualitative behavior of differential equations, functional analysis and input/output behavior of systems, and "modern'' nonlinear system theory, which uses both geometric and algebraic techniques. Prerequisite: 521.

ENE 506 Synchrotron and Neutron Techniques for Energy Materials (also

MSE 586

/

MAE 536

/

CEE 506

/

CBE 566

) Topics include an introduction to radiation generation at synchrotron and neutron facilities, elastic scattering techniques, inelastic scattering techniques, imaging and spectroscopy. Specific techniques include X-ray and neutron diffraction, small-angle scattering, inelastic neutron scattering, reflectometry, tomography, microscopy, fluorescence and infrared imaging, and photoemission spectroscopy. Emphasis is placed on application of the techniques for uncovering the material structure-property relationship, including energy storage devices, sustainable concrete, CO2 storage, magnetic materials, mesostructured materials and nanoparticles.

MAE 501 Mathematical Methods of Engineering Analysis I (also

APC 501

/

CBE 509

) Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, Sturm-Liouville theory, Green's functions for the solution of ordinary differential equations and Poisson's equation, and the calculus of variations.

MAE 502 Independent Research Project Directed study for Master of Engineering students. This course requires the student to have identified a faculty adviser and to have received approval for the research project from the MAE Graduate Committee.

MAE 502 Mathematical Methods of Engineering Analysis II (also

APC 506

) A complementary presentation of theory, analytical methods, and numerical methods. The objective is to impart a set of capabilities commonly used in the research areas represented in the Department. Standard computational packages will be made available in the courses, and assignments will be designed to use them. An extension of MAE 501.

MAE 503 Directed Research Under the direction of a faculty member, the student carries out a one-semester research project chosen jointly by the student and the faculty. Directed is normally taken during the first year of study. The project culminates in a written paper, in the style of a journal article, and presentation to at least one faculty member from the department who was involved in the research project. Students need to enroll at the beginning of the semester and must obtain permission from the instructor and the department.

MAE 509 Advanced Topics in Engineering Mathematics I Selected topics in mathematical methods, with an emphasis on advances relevant to research activities represented in the department. Possible topics include analytical methods for differential equations, numerical solution of hyperbolic equations, and statistical methods.

MAE 510 Advanced Topics in Engineering Mathematics II Selected topics in mathematical methods, with an emphasis on advances relevant to research activities represented in the department. Possible topics include analytical methods for differential equations, numerical solution of hyperbolic equations, and statistical methods.

MAE 511 Experimental Methods I A laboratory course that focuses on basic electronics techniques, digital electronics, and data acquisition and analysis. Topics include introduction to digital and analog electronics, digital-to-analog and analog-to-digital conversion, microcomputer sampling, and data analysis. There are four laboratory hours and two lecture hours per week. There is one project.

MAE 513 Independent Project I Directed study for Master of Engineering students. The topic is proposed by the student and must be approved by the student's research advisor and have received approval from the MAE Graduate Committee.

MAE 514 Master of Engineering Independent Project II Continuation of MAE 513. Directed study for Master of Engineering students. The topic is proposed by the student and must be approved by the student's research advisor and have received approval from the MAE Graduate Committee.

MAE 515 Extramural Summer Project A summer research project designed in conjunction with the student's advisor and an industrial, NGO, or government sponsor that will provide practical experience relevant to the student's thesis topic.

MAE 520 Advanced Topics in Experimental Methods II Selected topics in experimental methods, with an emphasis on advances relevant to research activities represented in the department. Possible topics include dynamic data analysis; instrumentation and systems analysis, scanning probe techniques, and nanoscale materials property measurements.

MAE 521 Optics and Lasers (also

MSE 561

) An introduction to principles of lasers. Topics include a review of propagation theory, interaction of light and matter, Fourier optics, a survey and description of operational characteristics of lasers, light scattering, and nonlinear optics. Some introductory quantum mechanics will be covered to give students an appreciation of the basic tools for the interaction of light with matter and nonlinear optical phenomena.

MAE 522 Applications of Quantum Mechanics to Spectroscopy and Lasers (also

AST 564

) An intermediate-level course in applications of quantum mechanics to modern spectroscopy. The course begins with an introduction to quantum mechanics as a "tool" for atomic and molecular spectroscopy, followed by a study of atomic and molecular spectra, radiative, and collisional transitions, with the final chapters dedicated to plasma and flame spectroscopic and laser diagnostics. Prerequisite: one semester of quantum mechanics.

MAE 527 Physics of Gases Physical and chemical topics of basic importance in modern fluid mechanics, plasma dynamics, and combustion science: statistical calculations of thermodynamic properties of gases; chemical and physical equilibria; adiabatic temperatures of complex reacting systems; quantum mechanical analysis of atomic and molecular structure and atomic-scale collision phenomena; transport properties; reaction kinetics, including chemical, vibrational, and ionization phenomena; and propagation, emission, and absorption of radiation.

MAE 528 Physics of Plasma Propulsion (also

AST 566

) Focus of this course is on fundamental processes in plasma thrusters for spacecraft propulsion with emphasis on recent research findings. Start with a review of the fundamentals of mass, momentum & energy transport in collisional plasmas, wall effects, & collective (wave) effects, & derive a generalized Ohm's law useful for discussing various plasma thruster concepts. Move to detailed discussions of the acceleration & dissipation mechanisms in Hall thrusters, magnetoplasmadynamic thrusters, pulsed plasma thrusters, & inductive plasma thrusters, & derive expressions for the propulsive efficiencies of each of these concepts.

MAE 529 Advanced Topics in Applied Physics I Selected topics in applied physics, with an emphasis on advances relevant to research activities represented in the department. Possible topics include advanced plasma propulsion, linear and nonlinear wave phenomena, and x-ray lasers in biological investigations.

MAE 531 Combustion (also

ENE 531

) Fundamentals of combustion: thermodynamics; chemical kinetics; explosive and general oxidative characteristics of fuels; premixed and diffusion flames; laminar and turbulent flame phenomena; ignition and flame stabilization; detonation, environmental combustion considerations; and coal combustion.

MAE 532 Combustion Theory Theoretical aspects of combustion: the conservation equations of chemically-reacting flows; activation energy asymptotics; chemical and dynamic structures of laminar premixed and nonpremixed flames; aerodynamics and stabilization of flames; pattern formation and geometry of flame surfaces; ignition, extinction, and flammability phenomena; turbulent combustion; boundary layer combustion; droplet, particle, and spray combustion; and detonation and flame stabilization in supersonic flows.

MAE 539 Advanced Topics in Combustion I Selected topics in theoretical and experimental combustion, with an emphasis on advances relevant to research activities represented in the department. Possible topics include turbulent combustion, theoretical calculations of rate constants, plasma fuels and natural resources, and nuclear propulsion and power plants.

MAE 540 Advanced Topics in Combustion II Selected topics in theoretical and experimental combustion, with an emphasis on advances relevant to research activities represented in the department. Possible topics include turbulent combustion, theoretical calculations of rate constants, plasma fuels and natural resources, and nuclear propulsion and power plants.

MAE 541 Applied Dynamical Systems (also

APC 571

) Phase-plane methods and single-degree-of-freedom nonlinear oscillators; invariant manifolds, local and global analysis, structural stability and bifurcation, center manifolds, and normal forms; averaging and perturbation methods, forced oscillations, homoclinic orbits, and chaos; and Melnikov's method, the Smale horseshoe, symbolic dynamics, and strange attractors. Offered in alternate years.

MAE 542 Advanced Dynamics Principles and methods for formulating and analyzing mathematical models of physical systems; Newtonian, Lagrangian, and Hamiltonian formulations of particle and rigid and elastic body dynamics; canonical transformations, Hamilton-Jacob-Jacobi; Theory; and integrable and nonintegrable systems. Additional topics are explored at the discretion of the instructor.

MAE 543 Advanced Orbital Mechanics An advanced course in orbital motion of earth satellites, interplanetary probes, and celestial mechanics. Topics include orbit specification, orbit determination, Lambert's problem, Hill's equations, intercept and rendezvous, air-drag and radiation pressure, lagrange points, numerical methods, general perturbations and variation of parameters, earth-shape effects on orbits, Hamiltonian treatment of orbits, Lagrange's planetary equations, orbit resonances, and higher-order perturbation effects.

MAE 544 Nonlinear Control Nonlinear control of dynamical systems, with an emphasis on the geometric approach. The course gives an introduction to differential geometry, nonlinear controllability and constructive controllability, nonlinear observability, state-space transformations and stability, followed by study of a selection of nonlinear control design methods, including techniques motivated by geometric mechanics.

MAE 545 Special Topics in Mechanical & Aerospace Engineering Topics vary according to the interests of the class but are drawn from emerging numerical discretization methods (finite elements, finite volume, spectral, boundary element and vortex methods), boundary condition treatment, complex geometry modeling and grid generation, solution algorithms (direct solvers, conjugate gradient, multigrid, Fourier and wavelet transforms), and parallel software and computer architectures.

MAE 546 Optimal Control and Estimation An introduction to stochastic optimal control theory and application. It reviews mathematical foundations and explores parametric optimization, conditions for optimality, constraints and singular control, numerical optimization, and neighboring-optimal solutions. Least-squares estimates, propagation of state estimates and uncertainty, and optimal filters and predictors; optimal control in the presence of uncertainty; certainty equivalence and the linear-quadratic-Gaussian regulator problem; frequency-domain solutions for linear multivariable systems; and robustness of closed-loop control are all studied.

MAE 551 Fluid Mechanics. An introduction to fluid mechanics