Princeton University - The Graduate School

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. Worldwide energy and emissions concerns demand extensive and detailed studies of fuel-conversion processes. Combustion is critical to power generation, propulsion, air and ground transportation, and the environment. This area of study includes combustion of conventional, alternate, and high-energy-density fuels; pyrolysis of coal and organic materials; practical combustion for application in furnaces, gas turbines, and reciprocating engines; pollutant generation and control; combustion synthesis of materials; waste incineration; supercritical combustion; supersonic propulsion; turbulent combustion; spray and dust combustion; microgravity combustion; gas and condensed-phase chemical kinetics; heat and mass transfer; combustion theory; computational combustion; and laser diagnostics of combustion phenomena.

Computational Engineering. Computation is a key tool that helps translate the growing understanding of the physics of fluids and solids to the design of the next generation of vehicles and manufacturing systems. In the materials arena, computational research is centered around theoretical and computational aspects of materials science, establishing protocols for modeling structural evolution and thermomechanical behavior across multiple-length scales. Computational fluid mechanics is concerned with the simulation of viscous flow past complex configurations with application to aircraft and ship design. Once the flow characteristics are well understood, the techniques may be applied to optimize the shape of a structure over which the fluid is flowing.

Dynamics and Control Systems. The analysis of nonlinear dynamic systems, and techniques for controlling complex systems using feedback, play important roles in many aspects of engineering. Ongoing research at Princeton in this area includes nonlinear dynamical systems, bifurcation theory, low order modeling, 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 of animal groups; modeling and control of fluids; control of unsteady aerodynamics for micro-air vehicles; geometric integrators; orbital mechanics and space mission design; adaptive optics for ground and space telescopes; modeling cognitive and other neurobiological processes; methods for cancer detection; and optimal control of disease processes.

Energy and Climate. The mechanical and aerospace engineering department is deeply involved in the University-wide Carbon Mitigation Initiative, an interdepartmental program studying the challenge of reducing the rate of global emissions of carbon dioxide. One of the department’s faculty members is the co-director of the program, and several graduate students are involved as well. Work based in mechanical engineering addresses the modifications of power plants and synthetic fuels plants necessary to capture carbon dioxide, alternative fuels with lower carbon content for mobile and stationary applications, and wind and biomass energy conversion. Across the University, other programs investigate the science of the global carbon cycle, the integrity of carbon dioxide storage in deep saline aquifers, and climate change policy.

Vehicle Sciences and Applications. Vehicle design is central to the study of aerospace engineering. Mechanical and aerospace engineering faculty explore a variety of vehicle technologies and applications. These include underwater gliders for adaptive ocean sampling, autonomous micro-air vehicles, optimal aircraft and ship design using adjoint-based methods, the Joint University Program for Air Transportation Research, satellite technology and orbital mechanics for astronomical and Earth science applications, hypersonic vehicles, advanced launch vehicles, and advanced propulsion technologies.

Bioengineering. Bioengineering is a growing, multidisciplinary area that applies methods and tools from engineering and the sciences to problems in biology and medicine. The research spans multiple length and time scales, ranging from molecules through cells to individual organisms and animal group dynamics. Current research activities include neuromechanics and hydrodynamics of swimming and legged locomotion; nanoparticles for cancer detection and treatment; cell mechanical properties and adhesion; the application of lasers for research in biomaterials and medical devices; biophysical and mechanical properties of lipid bilayers; modeling cognitive and neural mechanisms of decision and control; decision making and collective motion in animal groups; numerical simulation of steady and unsteady fluid flows in biological environments; and bioinformatic and biostatistical analysis of cancer.

Fluid Mechanics and Computational Methods. Experimental, analytical, and numerical studies of fluid flow underlie many areas of technological innovation. Turbulent flows, flow control, stability and transition, and the coupling with electromagnetic fields are areas of current interest. This area includes experimental studies of two- and three-dimensional supersonic and subsonic flows of varying complexity; boundary layer studies, especially turbulent boundary layers at subsonic, supersonic, and hypersonic speeds, over a wide range of Reynolds numbers; low-dimensional models and bifurcation analyses of turbulent and transition flows; active control of boundary layer turbulence and transition; new techniques in nonintrusive flow measurement; numerical techniques for solving the equations describing fluid flow, especially methods for calculating transonic flows over aircraft and reacting gasdynamics, and methods for calculating turbulent flows; fast iterative solutions; parallel algorithms; mesh generation; improved difference formulas; finite element and spectral methods; and aerodynamic shape optimization.

Lasers, Plasmas, and Applied Physics. Lasers are important as diagnostic tools and in instruments whose use spans a spectrum from materials fabrication to medical applications. The underlying physics is applied to diverse areas such as advanced propulsion systems, X-ray generation, and understanding the properties of complex materials and fluids. This area includes laser technology and applications; X-ray lasers; flow field and combustion diagnostics; multiphoton processes and nonlinear optics; high-energy lasers; atomic and molecular spectroscopy; molecular dynamics; plasma dynamics; high field phenomena; controlled laser-driven molecular and acoustic processes; picosecond and subpicosecond sources; high-energy incoherent source development; advanced spacecraft propulsion; space plasma physics; active space experiments; electric discharge; and radiation studies.

Materials and Mechanical Systems. Modern materials science seeks to understand and influence the behavior of materials at a variety of length scales, ranging from the atomic to the macroscopic, utilizing experimental and theoretical/computational tools as probes. Faculty are engaged in research that includes nanoscience, biomaterials, high-temperature materials, and laser-induced processing with diverse applications from medicine to alternative energy. For instance, magnetic nanoparticles are being designed for cancer detection and treatment; BioMEMS, artificial tissue, and orthopedic/dental structures are being constructed and explored; and bioinspired materials design is under way. Lasers are used to construct nanostructured materials for energy storage and power generation and are exploited in the field of adaptive optics and micromanipulation of materials with light. Quantum mechanics-based simulation tools are developed and used to explore and find ways to prevent oxidation, embrittlement, deformation, phase transitions, fracture, and mechanical wear of stressed and degraded metal alloys and ceramics at the macro and nano scale. Microstructural evolution in metals and in biophysical systems and biology are being examined with phase field approaches.

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, the Program in Transportation, the Princeton Environmental Institute, and the Princeton Institute for the Science and Technology of Materials.

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.

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., 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 department’s 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 departmental approval, switch to the M.S.E. 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.

Master of Arts Degree. A student who passes the general examination is automatically eligible to receive the Master of Arts (M.A.). Application for this degree can be made any time after the student passes the general examination.

The General Examination
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 and is capable of performing creative, independent research and of effectively communicating that work to both a technically sophisticated and a lay 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 three components: i) three pre-general interviews completed during the fall of second year, at least one of which is in mathematics, ii) an oral examination taken in January of the second year (the “subject component”) in four areas chosen by the student (one of which must be mathematics, two in a major area, and one in a minor area), and iii) a 45-minute presentation (the “research component”) followed by questions, normally in May of the second year, on a topic related to the student’s planned Ph.D. program.

English Language Requirement
Non-native English speakers who are accepted to the mechanical and aerospace engineering Ph.D. program are required to demonstrate their English language proficiency. This can be done before enrolling at Princeton University by taking and passing the Test of Spoken English (TSE) with a score of 50 or higher. Alternatively, in the entering year, the student can take the Speaking Proficiency English Assessment Kit (SPEAK) test and pass with a score of 50 or higher. The SPEAK test is administered by the English Language Program (ELP) in September after academic classes have begun. Students who do not pass the TSE or SPEAK test are required to enroll in ELP classes and successfully pass the Princeton Oral Proficiency Test (POPT). Any student who does not pass TSE, SPEAK, or POPT before the end of their first year of study cannot stand for their general exam or serve as an assistant-in-instruction, and therefore will not be reenrolled as a Ph.D. student. A student in this category who is recommended for reenrollment for his/her second year will be reenrolled as an M.S.E. candidate. Ph.D. candidacy may be reconsidered upon successful completion of the POPT.

Teaching Requirements
It is a requirement for students to teach three (3) half-time assistant-in-instruction assignments in order to qualify for their Ph.D.

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 offers the highly competitive Wu and Upton fellowships (the school’s most prestigious awards for graduate study in engineering), which provide 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 provides 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.

Colloquium in Mechanical and Aerospace Engineering
The Edwin G. Baetjer II and Luigi Crocco Colloquia as well as the department’s 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.

Mechanical and Aerospace Engineering

MAE 501/APC 501    Mathematical Methods of Engineering Analysis I
      Clarence W. Rowley