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The mission of the Department of Mechanical and Aerospace Engineering is to educate leaders in engineering and applied sciences through a rigorous graduate program that defines the frontiers of knowledge in our field, and prepare them for careers in academia, industry, and government. Our program emphasizes achieving fundamental understanding in a broad range of topics, a deep understanding in a particular area, and excellent communications skills. The majority of outstanding technical problems in today’s science and engineering require a multi-disciplinary approach, and our department has a strong tradition in defining and pursuing new research areas at the intersection of engineering, physics, chemistry, biological sciences, and applied mathematics.
We offer exciting opportunities for graduate study in areas as diverse as thermal sciences and energy conversion, fluid mechanics, materials science, biomechanics, dynamics and control, underwater vehicles, flight sciences, astronomical instrumentation and space optics, computational and experimental fluid mechanics, lasers and applied physics, propulsion, and environmental technology. In addition, Princeton University is at the forefront of interdisciplinary research, and students are encouraged to sample the opportunities provided by other departments within the School of Engineering and Applied Sciences, as well as allied departments and programs outside the Engineering School.
There are normally about 100 students in residence selected from a diverse pool of applicants from around the world. The size of the student population ensures a close association between each student and a faculty adviser that continues from arrival to the completion of the degree program.
Three separate degree programs are offered by the department, Ph.D., M.S.E. and M.Eng. (industry-sponsored, part-time only). Course performance requirements are the same for all three programs, only the emphasis of the overall plan of study (courses and thesis research) is different. With the permission of the Departmental Graduate Committee and the approval of the Graduate School, students in good standing may transfer between these programs to satisfy newly realized goals. It is not possible, however, to transfer into the M.Eng. program from either the M.S.E. or Ph.D. options. It is also not necessary to obtain an M.S.E. before entering our Ph.D. program.
In addition to joining a strong department, you will be coming to a relatively small research oriented University with excellent science and liberal arts faculties. The overall graduate student body is about 2,600 people and living, social and educational encounters will put you in touch with many interesting and motivated people. We believe that this climate will enable students to:
As a candidate for the doctoral program, the student, in consultation with a faculty adviser and his or her Ph.D. committee, develops an integrated program of study in preparation for a comprehensive general examination. After passing the general examination, the student prepares a dissertation displaying technical mastery of the field and the contributions to the advancement of knowledge, followed by a public presentation of the material to the technical community. Candidates in this program are required to take a minimum of 10 courses throughout their enrollment, with eight of the courses being taken in the first three semesters. Candidates are also required to be an assistant in teaching for a minimum of three semesters after passing the general examination. The Ph.D. program typically lasts five years and includes full financial support.
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 students are expected to take eight courses for a grade and perform preliminary research during the first three semesters prior to standing for the general exam. Two of the courses must be in mathematics and four must be in the student’s primary area of research. Students must achieve a GPA of 3.0 or higher. A student may receive one C in a graduate course and remain in the Ph.D. program. Approved courses from other departments may be taken, and members of these departments may be invited to participate in the general examination.
Students will be given a single oral interview in the fall of their second year by a faculty member chosen by the major group. In case of an interdisciplinary program of study spanning two major areas, separate interviews in both areas are required. A student who is taking the math exam must also have a separate math interview. A list of available interviewers and their subjects is available online and in the graduate office. These interviews are intended to explore, in-depth, the student's knowledge of a subject area, to prepare the student for the General Examination, and to identify areas where further study may be necessary.
There is no requirement to pass or fail an interview; interviews are for the benefit of the student to ensure adequate preparation for the subject component of the general exam and to inform the graduate committee of the student’s readiness for the general exam. In some cases of weaker performance, interviewers may request additional time from the student after further studying.
The Ph.D. in Mechanical and Aerospace Engineering is a certification that the graduating student is well versed in the fundamentals of his or her chosen field, is capable of performing creative, independent research, and has the ability to effectively communicate his or her ideas to a broad audience. The general examination procedure exercises the department’s responsibility for determining a student’s potential to satisfactorily complete a Ph.D. and simultaneously encourages the student to review and consolidate material from various courses and research activities. The general examination process consists of two components: i) the subject component, an oral examination in the student’s major disciplinary area of study, taken in January of the second year, ii) the research component, a 45 minute presentation followed by questions on a topic related to the student’s planned Ph.D. program, taken in May of the second year.
The Master of Arts (M.A.) degree is normally an incidental degree on the way to full Ph.D. candidacy and is earned after a student successfully passes the general examination.
It is a requirement for students to teach a minimum of three (3) half-time assistant in instruction assignments in order to qualify for their Ph.D.
After successful completion of the general exam, the balance of the program is spent on dissertation research, teaching obligations, and additional courses. Candidates meet with their Ph.D. committee each year to review their research progress.
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.
The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted and the final public oral examination sustained.
Candidates for the M.S.E. program complete seven courses and write an acceptable thesis. The thesis is central to the program and is considered an integral aspect of graduate education in the field. It is the culmination of prior training and research and is expected to address a realistic and important problem. The thesis must be presented in good literary form and be written in good English. The technical quality is also expected to be high and differs from that expected for the Ph.D. only in the quantity of material presented. The M.S.E. program typically covers two years. The number of master’s students admitted each year is limited.
Candidates for this program generally provide their own financial support.
To qualify for the M.S.E., 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. Students must achieve a GPA of 3.0 or higher. A student may receive a single C grade and continue in the M.S.E. track.
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.
The M.Eng. degree program is a non-thesis, coursework-only degree program. This degree is an industry sponsored part time option only, offered to individuals who are working in local industry. It is particularly suited to those interested in either obtaining a more fundamental understanding of their fields or in broadening their experiences to include disciplines outside of their particular technical focus areas.
Two semesters of independent study are allowed with the approval of the girector of graduate studies. 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.
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.
Candidates for this program must provide their own financial support.
The degree requires eight courses and an average grade of B or higher. At least one of those courses must be taken as an independent study project course under the guidance of a specific faculty member. Sixof the courses 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.
There is no teaching in this program.
Howard A. Stone
Michael G. Littman
Mikko P. Haataja
Daniel M. Nosenchuck
Marlan O. Scully
Courses for Spring 2015
Courses listed below show only regular graduate-level courses for the term; undergraduate courses and graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students, are not listed.
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 and more broadly in engineering and the physical and biological sciences. Analytical methods will be emphasized, but standard computational packages will be made available and some assignments will be designed to use them. Topics will include Complex variables, PDE, Fourier and Laplace Transforms, and a brief introduction to numerical methods for ODE and PDE.
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.
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.
Chemical thermodynamics and kinetics, oxidation of hydrogen, hydrocarbons and alternate fuels, pollutant chemistry and control, transport phenomena, laminar premixed and nonpremixed flames, turbulent flames, ignition, extinction, and flammability phenomena, flame stabilization and blowoff, detonation and blast waves, droplet, spray and coal particle combustion, principles of engine operation.
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.
An introduction to the mechanics of viscous flows. The kinematics and dynamics of viscous flows. Exact solutions to the Navier-Stokes equations. Lubrication theory. The behavior of vorticity. The boundary layer approximation. Laminar boundary layers with and without pressure gradients. Introduction to stability. Introduction to turbulence.
Physical and statistical descriptions of turbulence, and a critical review of phenomenological theories for turbulent flows. The course 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. This course is offered in alternate years.
Focus is on advanced concepts in turbulence, especially relating to turbulence at different scales of motion and in both statistically stationary and non-stationary situations. Emphasis is on homogeneous turbulent flows, with particular attention to the spectral equations of motion. Classical theories of turbulence, especially similarity laws, receive considerable attention and critiqued in light of recent research. Statistical methods are discussed in some detail with particular attention to POD and spectral analysis.
This course covers the science and technology underlying existing and emerging nuclear security issues. Part I introduces the principles of nuclear fission, nuclear radiation, and nuclear weapons (and their effects). Part II develops the concepts required to model and analyze nuclear systems, including the production of fissile materials and the detection and characterization of these materials with radiation measurement techniques. Relevant applications are explored in Part III and include nuclear forensic analysis, nuclear archaeology, and nuclear warhead verification. Such case studies will also be part of the final projects.
A seminar of graduate students and staff presenting the results of their research and recent advances in flight, space, and surface transportation; fluid mechanics; energy conversion; propulsion; combustion; environmental studies; applied physics; and materials sciences. There is one seminar per week and participation at presentations by distinguished outside speakers.
A broad introduction to numerical algorithms used in scientific computing. The course will begin with a review of the 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, and ordinary and partial differential equations will be covered in detail. Examples of the application of these methods to problems in physics, astrophysics and other disciplines will be given. Issues related to the implementation of efficient algorithms on modern high-performance computing systems will be discussed.