Department of Mechanical and Aerospace Engineering

Chair

Philip J. Holmes

Associate Chair

Michael G. Littman

Director of Graduate Studies

Luigi Martinelli

Professor

Garry L. Brown

Emily A. Carter

Frederick L. Dryer

Philip J. Holmes

Chung K. Law

Naomi Leonard

Michael G. Littman

Richard B. Miles

Alexander J. Smits

Winston O. Soboyejo

Robert H. Socolow

Robert F. Stengel

Szymon Suckewer

 

Associate Professor

Edgar Y. Choueiri

N. Jeremy Kasdin

Luigi Martinelli

Daniel M. Nosenchuck

Assistant Professor

Craig B. Arnold

Mikko P. Haataja

Yiguang Ju

Maria P. Martin-Aguirre

Clarence W. Rowley

Lecturer with Rank of Professor

Marlan O. Scully

Associated Faculty

Ilhan Aksay, Chemical Engineering

Nathaniel Fisch, Astrophysical Sciences

Jean-Hervé Prévost, Civil and Environmental Engineering

George W. Scherer, Civil and Environmental Engineering

David N. Spergel, Astrophysical Sciences

Salvatore Torquato, Chemistry

 

The Department of Mechanical and Aerospace Engineering offers three programs of graduate study and research. The degree of Doctor of Philosophy (Ph.D.) is a five-year program designed for a career in basic research and teaching. A Ph.D. candidate is expected to demonstrate strong scholarly abilities and the capacity for independent thought. The Master of Science in Engineering (M.S.E.) is designed for a career in industrial or government research and development. Typically, the program takes two years and requires an original thesis. The Master of Engineering (M.Eng.) is designed for those students seeking to meet the rigorous and advanced training needed in the applied aspects of modern technology. The program can be completed in one year of full-time study and does not require a thesis.

Prior Preparation

Normally, a student accepted for the graduate program is expected to have met the requirements for a bachelor’s degree in engineering, science, or mathematics. The degree does not need to be in mechanical or aerospace engineering. Students with a bachelor’s degree in materials science, mathematics, physics, engineering physics or applied physics, electrical engineering, or chemical engineering are well-prepared to succeed at the graduate level in the department, and applicants with these backgrounds are encouraged to apply.

Areas of Study

Coordinated programs of course work and graduate research are available in a wide range of topics. A student develops a plan of study and research in conjunction with a faculty adviser. Normally, a Ph.D. student completes eight graduate courses during the first three terms, and these may be drawn from offerings in both this and other departments. Ph.D. and M.S.E. students also begin a research project during this period. M.Eng. students complete eight courses in their year of study, two of which may be independent research projects. Major departmental areas are listed below.

Combustion, Propulsion, and Energy Conversion. The combustion of gaseous, liquid, and solid fuels; homogeneous and heterogeneous chemical kinetics; laminar and turbulent flames; spray combustion, high-pressure combustion; supersonic combustion and detonation, combustion synthesis, micro-scale power generation, catalytic combustion; plasma-asisted combustion; combustion-generated pollutants, alternate and high-energy density fuels; combustion processes in furnaces, gas turbines, and reciprocating engines; waste incineration; micro-gravity combustion and fire safety; combustion theory and computational combustion; and laser diagnostics of combustion phenomena. Technology assessment of energy efficiency and renewable energy; fuel-cell vehicles and the hydrogen economy; studies of pollution prevention in industry; and pollution migration in the environment.

Dynamics and Control Systems. Primary areas of research include nonlinear dynamical systems, optimal control and estimation, multiscale modeling, nonlinear control, and geometric mechanics. Applications and current research projects include dynamics and neuromechanics of insect locomotion; underwater locomotion, including fish, eels, and underwater gliders; cooperative control, mobile sensor networks, and adaptive ocean sampling; collective motion in nature; modeling and control of fluids; geometric integrators; orbital mechanics and space mission design; adaptive optics and the Terrestrial Planet Finder; Joint University Program for air transportation research; modeling cognitive processes; methods for cancer detection; and optimal control of disease processes.

Fluid Mechanics and Computational Methods. Two- and three-dimensional supersonic and hypersonic flows of varying complexity; boundary layers, particularly turbulent boundary layers at high Reynolds number; active control of boundary-layer transition turbulence; drag reduction; new optical flow diagnostics, performance enhancement, and control of hypersonic vehicles with air plasmas, radiatively driven hypersonic wind tunnel technologies; new methods in non-intrusive flow measurements; numerical techniques for solving equations describing fluid flow, especially transonic flows over aircraft and turbulent flows; multidisciplinary optimization; and fast iterative solutions and mesh generation, including mesh embedding techniques, improved difference formulas, and finite-element methods.

Lasers, Plasmas, and Applied Physics. Laser development, optical diagnostics, processes driven by radiation, and materials processing. X-ray laser design and applications to lithography, holography, and microscopy. Very-high-power, laser-driven phenomena. Laser, electron beam, and microwave-sustained and compelled plasmas. Magnetohydrodynamic propulsion and power generation. New short-wavelength sources and narrow-line-width tunable lasers. Laser applications to measurement of unsteady phenomena in gasses. Non-linear optics, spectroscopy, molecular dynamics, plasma dynamics, plasma propulsion for spacecraft, space plasma physics, and micropropulsion.

Materials and Solid Mechanics: Experiment and Theory. Magnetic nanoparticles for cancer detection and treatment; bioinspired materials design; surface texture and chemical modification of BioMEMS and orthopedic/dental structures; tissue engineering and the design of porous scaffolds for dentistry and medicine; reliability of MEMS structures and electronic textiles; laser processing of materials and laser-materials interactions; nanostructured materials for energy storage and power generation; adaptive optics and micromanipulation with light; surface and interface modifications. Quantum mechanical simulations of ion-surface scattering, chemical degradation of materials, and protective coating design. Computer simulation and theory of thin-film growth in micro- and opto-electronics, microstructural evolution during phase transformations and thin-film growth, thin-film and nanotube mechanics, nanoscale contact mechanics, self-assembly of nanostructures, dislocation dynamics in thin films and bulk materials, grain-boundary migration, and liquid-metal embrittlement. Multiscale modeling of stress-corrosion cracking, shock-induced microstructure, ductile fracture, radiation damage, grain growth, and deformation at the nanoscale.

Multidisciplinary Programs. Students may combine departmental courses and research with offerings by other departments or programs. The departmental Graduate Committee must approve such plans of study. Opportunities exist with the Program in Applied and Computational Mathematics, the Program in Atmospheric and Oceanic Sciences (AOS), the Program in Transportation, the Princeton Environmental Institute (PEI), and the Princeton Institute for the Science and Technology of Materials (PRISM).

Degree Programs

Admitted students are directly enrolled in their program of choice. Although these programs draw on the same set of courses and require the same level of academic performance, they are tailored to suit different career objectives. To remain in good standing, students must maintain a “B” average or better in their courses and demonstrate research proficiency. Once all degree requirements have been met, the student is recommended to the trustees of the University for the awarding of the degree.

Doctor of Philosophy. The Ph.D. program is typically of five years’ duration. Formally, a Ph.D. student must complete all graduate school requirements, pass the general examination, and submit an acceptable dissertation to the department. The Ph.D. program is designed to prepare a student for a career in basic research and teaching, and candidates are expected to demonstrate strong scholarly abilities and the capacity for independent thought.

In consultation with a faculty adviser, a Ph.D. candidate develops an integrated program of courses and research in preparation for the general examination. Although there are no formal course requirements for the degree, each candidate is expected to demonstrate competence in certain core subjects to the satisfaction of the department as a whole. The basic topics vary for individual programs, but they must include applied mathematics and at least two areas of concentration. Approved courses from other departments may be taken, and members of these departments may be invited to participate in the general examination. The first three terms are typically spent taking courses (at least eight) and performing preliminary research in preparation for the general examination, which is normally taken in January and May of the second year. The balance of the program is spent on dissertation research, teaching obligations, and additional courses. All Ph.D. candidates are normally required to serve as AIs for the equivalent of three term courses.

The culmination of the Ph.D. program is the writing of a thesis on a research topic explored by the student and a presentation of this work in a final public oral examination. The thesis must contain significant and original contributions to the advancement of a field of knowledge. Upon acceptance of the dissertation by the departmental faculty, candidates are admitted to the final public oral examination.

Master of Science in Engineering. The M.S.E. program is designed for a career in industrial or government research and development. M.S.E. candidates are required to take at least seven courses in addition to writing a thesis that demonstrates their mastery of selected technical areas. Typically, an M.S.E. program takes two years.

To qualify for the M.S.E degree, each student must complete all graduate school requirements, take a minimum of seven courses selected in consultation with the faculty adviser, and submit an acceptable thesis. If only seven courses are taken, then they are to be completed in the first year. The MAE Graduate Committee must approve all programs. A thesis is required of all master’s candidates and is the culmination of the student’s program of research conducted under the supervision of a faculty adviser. The M.S.E. thesis must be judged to contain material of publishable quality, presented in correct scholarly form, and written using good English.

Doctoral students who do not want to go on for the Ph.D. degree can, with the departmental approval, switch to the M.S.E. degree track.

Master of Engineering. The M.Eng. program is particularly suited to those students interested in either obtaining a more fundamental understanding of their field or in broadening their experiences to include disciplines outside their particular technical focus areas. Eight courses are required, six of which must be in technical areas, with no more than two being independent projects. The balance of the courses should be selected to provide a coherent exploration of a support area. Students are encouraged to develop a curriculum together with their faculty adviser. The degree does not require a thesis. Typically, the M.Eng. program requires completion of all graduate school requirements, and is awarded on the basis of course performance. Part-time study is an option.

The degree can be taken with technical courses concentrated in one of the “Areas of Study” of departmental research. Princeton University is world-renowned not only in engineering, but also in other areas related to engineering practice. Students entering this program will have the opportunity to take advantage of these Princeton strengths.

A special option for Princeton students, “The Princeton Option,” permits enrolled undergraduates to follow a five-year program leading to the awarding of both a B.S.E. and the M.Eng. Interest in this option should be indicated in the junior year.

Fellowships and Assistantships

All first-year Ph.D. candidates receive support through a first-year engineering fellowship provided through the Graduate School or through one of the other competitive fellowships available through the department. Through the financial support of the Daniel and Florence Guggenheim Foundation, the department is able to offer first-year Guggenheim Fellowships for entering Ph.D. and M.S.E. students. Other fellowships include the H.C. Phillips fellowship. These fellowships provide an academic-year stipend and tuition. Normally, financial support is not available for the M.Eng. program.

The School of Engineering and Applied Science (SEAS) offers the highly competitive Wu and Upton fellowships (the school’s most prestigious awards for graduate study in engineering), which provides first-year full support, including tuition and stipend. In the second, third, and fourth years, the fellowship offers an additional stipend to a student’s assistantship-in-research stipend. This fellowship still requires teaching and research assignments, but it augments the stipend associated with these activities. In addition, the student has a research expense account that covers items such as participation in professional society meetings. The Princeton Institute for the Science and Technology of Materials Fellowship provide a similar support arrangement, including the research expense account.

Additional fellowships may be available to qualified students, and applicants are encouraged to apply for external fellowships prior to their enrollment. Top candidates for admission may be nominated for a Hertz Foundation/Princeton Technology Centers Fellowship, which gives full support for up to five years of graduate study.

M.S.E. and Ph.D. students associate with a research project during their first year of study. In general, M.S.E. and Ph.D. theses evolve from such research experience, and the faculty member directing the research program becomes the student’s thesis adviser. For Ph.D. students, teaching experience is required and partial support derives from teaching assistantships during that period. Summer support is normally available to augment both fellowship and assistantship awards.

Laboratories

The research and graduate laboratories of the department are housed at the Engineering Quadrangle (E-Quad), the Energy Research Wing, and the von Neumann Building on the main campus, and at the James Forrestal Campus two miles away. The engineering library, machine shops, and computer facilities are described earlier under the general information section for the SEAS.

Three laboratories are associated with the activities in lasers and applied physics (LAP). The laser laboratory is dedicated to the development of new ways of imaging important properties of fluids, plasmas, and materials and to the use of lasers, microwaves, and electron beams to control and drive gas and plasma phenomena. Two versatile high-speed air/nitrogen-flow facilities are part of the laboratory and provide test beds for the development of new flow diagnostic concepts and energy addition and control methodologies. The Electric Propulsion and Plasma Dynamics Laboratory (EPPDyL) houses several pulsed and steady-state plasma accelerators, numerous basic research benches, a variety of diagnostic probes and optical instruments for plasma analysis, three thrust stands, and several large-vacuum facilities.

The Thermostructural Materials Laboratory contains more than 4,000 square feet of state-of-the-art equipment for materials characterization and the measurement of thermal and technical properties. These include special microtesters for the tensile and fatigue testing of MEMS structures; a two-beam focused-ion beam system; scanning and transmission electron microscopes with in-situ loading stages; an atomic-force microscope; a cathodo-luminescence system; an orientation imaging microscope; a thermal imaging system; high-resolution Questar telescopes; computer-controlled electromechanical and servohydraulic testing machines; a strain mapping system; creep frames; laser interferometers; a thermal cycling unit; an acoustic emission unit; a fiber push-out unit; a diffusion bonding unit; an electroplating unit; furnaces for high-temperature testing in air and controlled environments (up to 2400f C); optical microscopes; and a highly equipped metallography facility. The laboratory also has numerous workstations, commercial finite-element packages in a complementary effort on computational materials at different length scales (from atomistic to microstructural and mesoscale). Also available are parallel computers at the Computational Materials Center at PRISM.

Combustion, propulsion, and energy conversion laboratories are located in the E-Quad. The facilities of these laboratories, which are often unique, include atmospheric and high-pressure turbulent flow reactors for gas-phase chemical kinetics studies; a continuous-flow combustor for the investigation of catalytic, spray, and turbulent combustion; several high-pressure, high-temperature chambers to study atomization and spray processes; laboratory-scale gas turbine and rocket combustors; speed-controlled dynamometers and reciprocating and rotary engines with transparent heads; and a variety of unique burners for the study of droplet combustion and flame structures. These facilities are supported by advanced instrumentation and data processing systems, including various workstations for computational studies; thermobalances, differential scanning calorimenters, gas chromatographs, mass spectrometers, and gas analyzers for chemical analysis; high-speed cameras, laser-Doppler velocimeters, and many laser systems for the nonintrusive measurement of the dynamic, thermal, and composition fields in combustion environments.

Experimental research in the field of fluid mechanics is conducted in two major laboratories. At the Forrestal campus, there are extensive low- and high-speed research facilities. A water channel is used for studies of flapping membranes (“eels”) for power generation through the piezoelectric effect. Two Taylor-Couette set-ups are used in studies of quasiperiodic flow and transition control and turbulent boundary layers. A unique pipe flow experiment allows turbulence studies at Reynolds numbers from 5,000 to 40,000,000, and a new ultra-high Reynolds number wind tunnel can produce vehicle Reynolds numbers. Smoke tunnels are available for flow visualization. Five blow-down wind tunnels cover Mach numbers up to 8 over a wide range of flight conditions (Reynolds numbers up to full scale). They are used in studies of boundary layers, shock wave/boundary layer interactions, separated flows, turbulence, flow over wings and bodies, and reacting flows. The instrumentation includes multichannel hot-wire anemometers and PIV systems data acquisition and analysis systems; image processing equipment; and several sophisticated laser units for flow visualization and advanced nonintrusive measurements. At the E-Quad, a boundary-layer channel is available for fundamental studies and active control of the structure of wakes and boundary-layer transition phenomena.

Research in systems and control is supported by new microprocessor control laboratories for hardware and software development, plus extensive facilities for interactive computer graphics, data acquisition, and signal analysis. The Laboratory for Control and Automation is engaged in research projects dealing with flight bioinformatics dynamics, nonlinear control theory, stochastic robustness of linear control systems, and applications of artificial intelligence and neural networks. The Dynamical Control Systems Laboratory supports research in nonlinear dynamics and control of robotic systems, autonomous vehicles, and coordinated groups of vehicles. Two microprocessor-controlled, internally actuated underwater vehicles have been designed and built in this laboratory, and an experimental platform for testing control and coordination of a school of autonomous underwater vehicles is under development. Other facilities in the laboratory include a whirling inverted pendulum experiment, two testing tanks, and several SGI’s for 3-D graphic simulation and visualization. Another new laboratory supports research in system identification, structural control, and learning control. The laboratory for space systems supports research in advanced space missions, astrodynamic spacecraft formation flying tethered satellites, space astronomy, and space optics. The Princeton TPF laboratory is a state-of-the-art optics research laboratory studying technologies for imaging extrasolar Earth-like planets from space in support of NASA’s terrestrial planet-finder mission.

Colloquium in Mechanical and Aerospace Engineering

The Edwin G. Baetjer II and Luigi Crocco Colloquia as well as the MAE Weekly Seminar Series bring outstanding engineers and scientists from other research centers to Princeton throughout the year, and they are considered an important feature of the department’s graduate program. In addition, the major research divisions within the department hold seminars in which students and faculty members meet to discuss their research and to which outside speakers are invited. Student participation in these colloquia is mandatory.

Courses

MAE 501 Mathematical Methods of Engineering Analysis I (also APC 501)

Clancy W. Rowley

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 Mathematical Methods of Engineering Analysis II (also APC 502, CHE 502)

Philip J. Holmes

An extension of MAE 501. 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 are made available in the courses, and assignments are designed to use them.

MAE 503 Basic Numerical Methods for Ordinary and Partial Differential Equations (see APC 507)

MAE 509, 510 Advanced Topics in Engineering Mathematics I and II

Staff

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

Szymon Suckewer

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 each week. There is one project. Enrollment is limited.

MAE 512 Experimental Methods II

Richard B. Miles

An exploration of experimental techniques in fluid mechanics and combustion. Introduces experimentation, error analysis, and technical communication. Methods covered include pressure and temperature probes, flow visualization, hot-wire and laser anemometry, line reversal, Raman techniques, fluorescence, absorption, gas chromatography, and mass spectroscopy. There are three lecture hours and laboratory time each week.

MAE 513, 514 Master of Engineering Independent Project I and II

Staff

Directed study for Master of Engineering students. The topic is proposed by the student, must be approved by the student’s research adviser, and have received approval from the MAE Graduate Committee.

MAE 515 Extramural Summer Project

Staff

A summer research project designed in conjunction with the student’s adviser and an industrial, NGO, or government sponsor that will provide practical experience relevant to the student’s thesis topic. Students considering applying for this course should review the recommended guidelines before consulting their adviser and director of graduate studies.

MAE 518 Extramural Research Internship

Luigi Martinelli

Full-time research internship at a host institution, to perform scholarly research relevant to students dissertation work. Research objectives will be determined by the advisor in conjunction with outside host. A mid-term progress review and final paper are required. Enrollment limited to post-generals students for up two terms. Students may register by application only. Students considering applying for this course should review the recommended guidelines before consulting their adviser and director of graduate studies.

MAE 519, 520 Advanced Topics in Experimental Methods I and II

Staff

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

Richard B. Miles

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 is 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)

Szymon Suckewer

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. Offered in alternate years.

MAE 523 Electric Propulsion

Staff

Based on a review of pertinent atomic physics and electromagnetic theory, the particle and continuum representations of ionized gas dynamics are developed and applied to various electro-thermal, electrostatic, and electromagnetic acceleration mechanisms, each illustrated by various thruster designs, contemporary applications, and performances.

MAE 524 Plasma Engineering

Staff

The purpose of this course is to expose interested graduate and undergraduate students in engineering and the natural sciences to basic aspects of plasma physics and chemistry applicable to a variety of technologies, such as plasma propulsion, lasers, and materials processing. It involves an extension of classical fluid mechanics, kinetic theory, statistical thermodynamics, and reaction engineering methods to relatively low-temperature plasmas in electric and magnetic fields. Offered in alternate years.

MAE 525 General Plasma Physics I (see AST 551)

MAE 527 Physics of Gases

Szymon Suckewer

Understanding and prediction of engineering properties of gases, based on physical and chemical properties of atomic and molecular constituents: statistical calculations of thermodynamic properties of gases; chemical and physical equilibria; 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 529, 530 Advanced Topics in Applied Physics I and II

Staff

Selected topics in applied physics, with an emphasis on advances relevant to research activities represented in the department. Recent topics have included advanced plasma propulsion, linear and nonlinear wave phenomena, and X-ray lasers in biological investigations.

MAE 531 Combustion

Chung K. Law

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

Chung K. Law

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 533 Rocket and Air-Breathing Propulsion Technology

Yiguang Ju

Characteristics and fundamentals of aircraft and spacecraft chemical-propulsion systems are studied. The characteristics explain their optimal operating ranges. The fundamentals elucidate their limitations and potentials. The organization and extent of the material are similar to those of standard textbooks. Important details are pursued with the help of specialized reference.

MAE 539, 540 Advanced Topics in Combustion I and II

Staff

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 power plants.

MAE 541 Applied Dynamical Systems (also APC 571)

Philip J. Holmes

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

Naomi E. Leonard

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

N. Jeremy Kasdin

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, and orbit resonances.

MAE 544 Aircraft Dynamics

Robert F. Stengel

Linear and nonlinear models of aircraft dynamic characteristics; stability and control analysis, using state-space and classical formats; longitudinal and lateral-directional motion, including aerodynamic and inertial coupling effects; handling qualities criteria; applications of catastrophic theory and bifurcation analysis in flight dynamics; and problems related to density gradient, aeroelasticity, wind shear, and turbulence. Offered in alternate years.

MAE 545 Nonlinear Control

Naomi E. Leonard

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 the study of a selection of nonlinear control design methods, including techniques motivated by geometric mechanics. Offered in alternate years.

MAE 546 Optimal Control and Estimation

Robert F. Stengel

An introduction to stochastic optimal control theory and application. 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 547 Linear System Theory (see ELE 521)

MAE 548 Nonlinear System Theory (also ELE 523)

Naomi E. Leonard

Mathematical techniques 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: MAE 547.

MAE 549, 550 Advanced Topics in Dynamics and Control I and II

Staff

Selected topics in dynamics and control, with an emphasis on advances relevant to research activities represented in the department. Possible topics include bifurcation theory, nonlinear mechanics, system identification, intelligent control, learning control, and applied aerodynamics.

MAE 551 Fluid Mechanics

Luigi Martinelli

An introduction to fluid mechanics. Explores the development of basic conservation laws in integral and differential forms: one-dimensional compressible flows, shocks and expansion waves; effects of energy addition and friction; unsteady and two-dimensional flows and the method of characteristics. Reviews classical incompressible flow concepts, including vorticity, circulation, and potential flows. Introduces viscous and diffusive phenomena.

MAE 552 Viscous Flows and Boundary Layers

Garry L. Brown

The mechanics of viscous flows. Explores the kinematics and dynamics of viscous flows; solution of the Navier Stokes equations; the behavior of vorticity; the boundary-layer approximation; laminar boundary layer with and without pressure gradient; separation; integral relations and approximate methods; compressible laminar boundary layers; instability and transition; and turbulent boundary layers and self-preserving turbulent shear flows.

MAE 553 Turbulent Flow

Alexander J. Smits

Physical and statistical descriptions of turbulence; and a critical review of phenomenological theories for turbulent flows. Examines scales of motion; correlations and spectra; homogeneous turbulent flows; inhomogeneous shear flows; turbulent flows in pipes and channels; turbulent boundary layers; calculation methods for turbulent flows (Reynolds stress equations, LES, DNS); and current directions in turbulence research.

MAE 554/APC 538 Stability and Turbulence

Staff

Hydrodynamic stability: inviscid theory; viscous theory; complex physics; and numerical analysis. Examines nonlinear stability theory: nonlinear theory; secondary and elliptic instability; theories of transition; dynamics of defects; and numerical simulations. Introduction to the mathematical theory of chaos; turbulence: qualitative properties of turbulence; and introduction to turbulence transport modeling.

MAE 555 Nonequilibrium Gas Dynamics

Yiguang Ju

Noncontinuum description of fluid flow and Liouville and Boltzmann equations. Examines molecular collisions; detailed balancing; Chapman-Enskog expansion for near-equilibrium flows; transport phenomena; flows with translational, vibrational, and chemical non-equilibrium; shock structure; and shear and mixing layers with chemical reactions.

MAE 557 Simulation and Modeling of Fluid Flows

Maria P. Martin

Numerical methods are applied to solve the equations that govern fluid motion. Finite-difference and finite-volume methods are considered, together with concepts of accuracy, consistency, stability, convergence, conservation, and shock capturing. A range of current methods is reviewed, with an emphasis on multidimensional steady and unsteady compressible flows. Homework topics include writing codes to solve the conservation equation for a scalar, boundary-layer flow, shock-tube flow, and application to curvilinear coordinates.

MAE 558 Simulation and Modeling of Turbulent Fluid Flows

Maria P. Martin

The foundation of CFD as applied to turbulent flows. Concepts of numerical accuracy and bandwidth are introduced. Aliasing and Nyquist criteria are discussed. Solutions in differential form and wave space are studied. The numerical representation of turbulent transport, production, and dissipation are discussed. Techniques for the simulation and modeling of turbulent flows are described, including direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds-averaged Navier-Stokes (RANS). Homework topics include writing codes to solve isotropic turbulence using DNS, LES, and RANS methodologies.

MAE 559, 560 Advanced Topics in Fluid Mechanics I and II

Staff

Selected topics in fluid mechanics, with an emphasis on advances relevant to research activities represented in the department. Possible topics include advanced computational fluid dynamics, turbulence in fluids and plasmas, hydrodynamic stability, and turbulence.

MAE 561 Introduction to Materials (see MSE 501)

MAE 562 Fracture Mechanics (also MSE 540)

Staff

Fracture involves processes at multiple time and length scales. Covers the basic topics, including energy balance, crack tip fields, toughness, dissipative processes, and subcritical cracking. Fracture processes are then examined as they occur in some modern technologies, such as advanced ceramics, coatings, composites, and integrated circuits. Also explores fracture at high temperatures and crack nucleation processes.

MAE 563 Modeling and Simulation in Materials Science (see MSE 504)

MAE 564 Structural Materials (also MSE 512)

Winston O. Soboyejo

Stress/strain behavior of materials; dislocation theory and strengthening mechanisms; yield strength; materials selection. Fundamentals of plasticity, Tresca and Von Mises yield criteria. Case study on forging: upper and lower bounds. Basic elements of fracture. Fracture mechanics. Mechanisms of fracture. The fracture toughness. Case studies and design. Fatigue mechanisms and life-prediction methodologies.

MAE 566 Thermodynamics and Kinetics of Materials (see MSE 502)

MAE 569, 570 Advanced Topics in Materials and Mechanical Systems I and II

Staff

Selected topics in materials and mechanical systems, with an emphasis on advances relevant to research activities represented in the department. Possible topics include high-temperature protective coatings, multifunctional materials, MEMS, advanced computational methods in materials engineering, and fatigue and fracture of materials.

MAE 571 Introduction to Energy and Environmental Problems

Robert H. Socolow

Industrial ecology, which conceptualizes human activity as embedded in and constrained by the Earth’s natural systems. Many of the specific topics studied relate to energy supply and use, including the global greenhouse effect, energy and economic development, energy efficiency, reserves of fossil fuels, vehicles and urban air quality, nuclear power, and renewable energy.

MAE 579, 580 Advanced Topics in Energy and Environment I and II

Staff

Selected topics in energy and the environment, with an emphasis on advances relevant to research activities represented in the department. Possible topics include combustion control and emissions, economic development and energy resources, and energy efficiency.