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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
Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, linear analysis & eigenvalue problems for matrices & linear operators, Sturm-Liouville theory, Green's functions for the solution of linear ordinary differential equations and Poisson's equation, and the calculus of variations, and the inverse and implicit function theorems.
Introduction to numerical methods for the solution of problems relevant to engineering. Topics include numerical interpolation, differentiation, and integration and solution methods for initial value ordinary differential equations (explicit/implicit, stiff/non-stiff), boundary value ordinary differential equations (direct/shooting), and partial differential equations (hyperbolic/parabolic/elliptic). Emphasis is on the analysis of these methods for their accuracy, stability, and convergence.
An introduction to principles of lasers. Topics include propagation theory, interaction of light and matter, Fourier optics, and a description of operational characteristics of lasers, light scattering, and nonlinear optics.
An intermediate-level course in applications of quantum mechanics to modern spectroscopy and lasers. The course begins with quite elementary introduction to quantum mechanics as a "tool" for atomic and molecular spectroscopy, followed by a higher level of study of atomic and molecular spectra, radiative, and collisional transitions using intensily QM 'tools". The final chapters are dedicated to plasma and flame spectroscopic and laser diagnostics.
Physical and chemical topics of basic importance in modern fluid mechanics, plasma dynamics, and combustion science: statistical calculations of thermodynamic properties of gases; physical equilibria; quantum mechanical analysis of atomic and molecular structure including rotational and vibrational transitions; atomic-scale collision phenomena and excitation and ionization; emission, absorption, and propagation of radiation. Analyses of major greenhouse gases from point of view of molecular absorption and emission properties; discussion of effect of greenhouse gases concentration and disribution on climate equilibria.
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.
Detailed treatment of the physics and subsequent modeling of turbulent combustion. Turbulent premixed, nonpremixed, and partially premixed combustion will all be discussed. Emphasis in the course will be placed on understanding relevant physical and chemical phenomena that lead to various modeling approaches (derived from both experiment and computation), the implicit and explicit assumptions in the various modeling approaches, and the relative strengths and weaknesses of the various modeling approaches.
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-Jacobi theory; and integrable and nonintegrable systems. Additional topics are explored at the discretion of the instructor.
An introduction to fluid mechanics. The course explores the development of basic conservation laws in integral and differential form; one-dimensional compressible flows, shocks and expansion waves; effects of energy addition and friction; unsteady and two-dimensional flows and method of characteristics. Reviews classical incompressible flow concepts, including vorticity, circulation, and potential flows. Introduces viscous and diffusive phenomena.
Stress/strain behavior of materials; dislocation theory and strengthening mechanisms; yield strength; materials selection. Fundamentals of plasticity, Tresca and Von Mieses 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.
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.
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.
An introductory course to plasma physics, with sample applications in fusion, space and astrophysics, semiconductor etching, microwave generation, plasma propulsion, high power laser propagation in plasma; 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.
This course covers the fundamentals of linear models for data generation and analysis. The topics covered are important for further study in signal processing, machine learning, communications and feedback control. The focus is on fundamental results but these are illustrated with applications of current interest.
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.
Emphasizes the connection between microstructural features of materials and their properties, and how processing conditions control structure. Topics include atomic bonding, crystal structure, thermodynamics, phase diagrams, defects, microstructure, diffusion, phase transformations, nucleation, coarsening, glasses, elastic and plastic deformation, fracture, sol-gel processing, sintering, and composites.
This course will thus cover a broad range of subjects, with particular emphasis on characterization and control of materials at the nanoscale. The focus is on both the techniques necessary for scientific investigations at small dimensions, and the very latest research developments in this rapidly evolving area. Specific topics covered will include fundamentals of nanoscience, processing of nanomaterials, self-assembled nanostructures, bionanotechnology, graphene, nanoelectronics, size-scaling of properties, and nanodevice fabrication and testing. The course will also provide critical practice in scientific writing and presentation.