Mechanical and Aerospace Engineering

Academic Year: 
2019-20
Address: 
Engineering Quadrangle
Phone: 
609-258-4683
Website: 
Department of Mechanical and Aerospace Engineering
Program offerings: 
Ph.D.
M.S.E.
Director of Graduate Studies
Alexander Glaser
Graduate Program Administrator
Jill Ray

Academic department detail

Overview

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 propulsion and energy sciences, fluid mechanics, materials science, biomechanics and biomaterials, dynamics and control, robotics, 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.

The department offers two separate degree programs: Master of Science in Engineering (M.S.E) and Doctor of Philosophy (Ph.D.). Applicants interested in the Ph.D. program may apply directly to that program; a master’s degree is not required.

Courses

Permanent Courses

Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.

APC 523 Numerical Algorithms for Scientific Computing (also
AST 523
/
MAE 507
) A broad introduction to scientific computation using examples drawn from astrophysics. From computer science, practical topics including processor architecture, parallel systems, structured programming, and scientific visualization will be presented in tutorial style. Basic principles of numerical analysis, including sources of error, stability, and convergence of algorithms. The theory and implementation of techniques for linear and nonlinear systems of equations, ordinary and partial differential equations will be demonstrated with problems in stellar structure and evolution, stellar and galactic dynamics, and cosmology.
APC 524 Software Engineering for Scientific Computing (also
MAE 506
/
AST 506
) The goal of this course is to teach basic tools and principles of writing good code, in the context of scientific computing. Specific topics include an overview of relevant compiled and interpreted languages, build tools and source managers, design patterns, design of interfaces, debugging and testing, profiling and improving performance, portability, and an introduction to parallel computing in both shared memory and distributed memory environments. The focus is on writing code that is easy to maintain and share with others. Students will develop these skills through a series of programming assignments and a group project.
AST 551 General Plasma Physics I (also
MAE 525
) This is an introductory course to plasma physics, with sample applications in fusion, space and astrophysics, semiconductor etching, microwave generation: characterization of the plasma state, Debye shielding, plasma and cyclotron frequencies, collision rates and mean-free paths, atomic processes, adiabatic invariance, orbit theory, magnetic confinement of single-charged particles, two-fluid description, magnetohydrodynamic waves and instabilities, heat flow, diffusion, kinetic description, and Landau damping. The course may be taken by undergraduates with permission of the instructor.
CEE 530 Continuum Mechanics and Thermodynamics (also
MSE 530
/
MAE 560
) The course covers the fundamentals of the mechanics and thermodynamics of continua. It reviews concepts of tensor analysis on manifolds and tensor calculus. It then proceeds by developing the fundamental concepts of the kinematics of a deforming continuum. The notion of stress is then introduced and measures of stresses are discussed. Conservation of mass, balance of momentum and moment of momentum, conservation of energy in thermodynamic are discussed. Constitutive theories and the restriction of the second law are presented. The Euler-Lagrange equations are re-connected with balance laws.
ELE 521 Linear System Theory (also
MAE 547
) This course covers the fundamentals of linear system theory. Various topics important for further study in dynamic systems, control and communication and signal processing are presented.
ELE 523 Nonlinear System Theory (also
MAE 548
) A study of the mathematical techniques found useful in the analysis and design of nonlinear systems. Topics include stability and qualitative behavior of differential equations, functional analysis and input/output behavior of systems, and "modern'' nonlinear system theory, which uses both geometric and algebraic techniques. Prerequisite: 521.
ENE 506 Synchrotron and Neutron Techniques for Energy Materials (also
MSE 586
/
MAE 536
/
CEE 506
/
CBE 566
) Topics include an introduction to radiation generation at synchrotron and neutron facilities, elastic scattering techniques, inelastic scattering techniques, imaging and spectroscopy. Specific techniques include X-ray and neutron diffraction, small-angle scattering, inelastic neutron scattering, reflectometry, tomography, microscopy, fluorescence and infrared imaging, and photoemission spectroscopy. Emphasis is placed on application of the techniques for uncovering the material structure-property relationship, including energy storage devices, sustainable concrete, CO2 storage, magnetic materials, mesostructured materials and nanoparticles.
MAE 501 Mathematical Methods of Engineering Analysis I (also
APC 501
/
CBE 509
) Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, Sturm-Liouville theory, Green's functions for the solution of ordinary differential equations and Poisson's equation, and the calculus of variations.
MAE 502 Independent Research Project Directed study for Master of Engineering students. This course requires the student to have identified a faculty adviser and to have received approval for the research project from the MAE Graduate Committee.
MAE 502 Mathematical Methods of Engineering Analysis II (also
APC 506
) A complementary presentation of theory, analytical methods, and numerical methods. The objective is to impart a set of capabilities commonly used in the research areas represented in the Department. Standard computational packages will be made available in the courses, and assignments will be designed to use them. An extension of MAE 501.
MAE 503 Directed Research Under the direction of a faculty member, the student carries out a one-semester research project chosen jointly by the student and the faculty. Directed is normally taken during the first year of study. The project culminates in a written paper, in the style of a journal article, and presentation to at least one faculty member from the department who was involved in the research project. Students need to enroll at the beginning of the semester and must obtain permission from the instructor and the department.
MAE 509 Advanced Topics in Engineering Mathematics I Selected topics in mathematical methods, with an emphasis on advances relevant to research activities represented in the department. Possible topics include analytical methods for differential equations, numerical solution of hyperbolic equations, and statistical methods.
MAE 510 Advanced Topics in Engineering Mathematics II Selected topics in mathematical methods, with an emphasis on advances relevant to research activities represented in the department. Possible topics include analytical methods for differential equations, numerical solution of hyperbolic equations, and statistical methods.
MAE 511 Experimental Methods I A laboratory course that focuses on basic electronics techniques, digital electronics, and data acquisition and analysis. Topics include introduction to digital and analog electronics, digital-to-analog and analog-to-digital conversion, microcomputer sampling, and data analysis. There are four laboratory hours and two lecture hours per week. There is one project.
MAE 513 Independent Project I Directed study for Master of Engineering students. The topic is proposed by the student and must be approved by the student's research advisor and have received approval from the MAE Graduate Committee.
MAE 514 Master of Engineering Independent Project II Continuation of MAE 513. Directed study for Master of Engineering students. The topic is proposed by the student and must be approved by the student's research advisor and have received approval from the MAE Graduate Committee.
MAE 515 Extramural Summer Project A summer research project designed in conjunction with the student's advisor and an industrial, NGO, or government sponsor that will provide practical experience relevant to the student's thesis topic.
MAE 520 Advanced Topics in Experimental Methods II Selected topics in experimental methods, with an emphasis on advances relevant to research activities represented in the department. Possible topics include dynamic data analysis; instrumentation and systems analysis, scanning probe techniques, and nanoscale materials property measurements.
MAE 521 Optics and Lasers (also
MSE 561
) An introduction to principles of lasers. Topics include a review of propagation theory, interaction of light and matter, Fourier optics, a survey and description of operational characteristics of lasers, light scattering, and nonlinear optics. Some introductory quantum mechanics will be covered to give students an appreciation of the basic tools for the interaction of light with matter and nonlinear optical phenomena.
MAE 522 Applications of Quantum Mechanics to Spectroscopy and Lasers (also
AST 564
) An intermediate-level course in applications of quantum mechanics to modern spectroscopy. The course begins with an introduction to quantum mechanics as a "tool" for atomic and molecular spectroscopy, followed by a study of atomic and molecular spectra, radiative, and collisional transitions, with the final chapters dedicated to plasma and flame spectroscopic and laser diagnostics. Prerequisite: one semester of quantum mechanics.
MAE 527 Physics of Gases Physical and chemical topics of basic importance in modern fluid mechanics, plasma dynamics, and combustion science: statistical calculations of thermodynamic properties of gases; chemical and physical equilibria; adiabatic temperatures of complex reacting systems; quantum mechanical analysis of atomic and molecular structure and atomic-scale collision phenomena; transport properties; reaction kinetics, including chemical, vibrational, and ionization phenomena; and propagation, emission, and absorption of radiation.
MAE 528 Physics of Plasma Propulsion (also
AST 566
) Focus of this course is on fundamental processes in plasma thrusters for spacecraft propulsion with emphasis on recent research findings. Start with a review of the fundamentals of mass, momentum & energy transport in collisional plasmas, wall effects, & collective (wave) effects, & derive a generalized Ohm's law useful for discussing various plasma thruster concepts. Move to detailed discussions of the acceleration & dissipation mechanisms in Hall thrusters, magnetoplasmadynamic thrusters, pulsed plasma thrusters, & inductive plasma thrusters, & derive expressions for the propulsive efficiencies of each of these concepts.
MAE 529 Advanced Topics in Applied Physics I Selected topics in applied physics, with an emphasis on advances relevant to research activities represented in the department. Possible topics include advanced plasma propulsion, linear and nonlinear wave phenomena, and x-ray lasers in biological investigations.
MAE 531 Combustion (also
ENE 531
) Fundamentals of combustion: thermodynamics; chemical kinetics; explosive and general oxidative characteristics of fuels; premixed and diffusion flames; laminar and turbulent flame phenomena; ignition and flame stabilization; detonation, environmental combustion considerations; and coal combustion.
MAE 532 Combustion Theory Theoretical aspects of combustion: the conservation equations of chemically-reacting flows; activation energy asymptotics; chemical and dynamic structures of laminar premixed and nonpremixed flames; aerodynamics and stabilization of flames; pattern formation and geometry of flame surfaces; ignition, extinction, and flammability phenomena; turbulent combustion; boundary layer combustion; droplet, particle, and spray combustion; and detonation and flame stabilization in supersonic flows.
MAE 539 Advanced Topics in Combustion I Selected topics in theoretical and experimental combustion, with an emphasis on advances relevant to research activities represented in the department. Possible topics include turbulent combustion, theoretical calculations of rate constants, plasma fuels and natural resources, and nuclear propulsion and power plants.
MAE 540 Advanced Topics in Combustion II Selected topics in theoretical and experimental combustion, with an emphasis on advances relevant to research activities represented in the department. Possible topics include turbulent combustion, theoretical calculations of rate constants, plasma fuels and natural resources, and nuclear propulsion and power plants.
MAE 541 Applied Dynamical Systems (also
APC 571
) Phase-plane methods and single-degree-of-freedom nonlinear oscillators; invariant manifolds, local and global analysis, structural stability and bifurcation, center manifolds, and normal forms; averaging and perturbation methods, forced oscillations, homoclinic orbits, and chaos; and Melnikov's method, the Smale horseshoe, symbolic dynamics, and strange attractors. Offered in alternate years.
MAE 542 Advanced Dynamics Principles and methods for formulating and analyzing mathematical models of physical systems; Newtonian, Lagrangian, and Hamiltonian formulations of particle and rigid and elastic body dynamics; canonical transformations, Hamilton-Jacob-Jacobi; Theory; and integrable and nonintegrable systems. Additional topics are explored at the discretion of the instructor.
MAE 543 Advanced Orbital Mechanics An advanced course in orbital motion of earth satellites, interplanetary probes, and celestial mechanics. Topics include orbit specification, orbit determination, Lambert's problem, Hill's equations, intercept and rendezvous, air-drag and radiation pressure, lagrange points, numerical methods, general perturbations and variation of parameters, earth-shape effects on orbits, Hamiltonian treatment of orbits, Lagrange's planetary equations, orbit resonances, and higher-order perturbation effects.
MAE 544 Nonlinear Control Nonlinear control of dynamical systems, with an emphasis on the geometric approach. The course gives an introduction to differential geometry, nonlinear controllability and constructive controllability, nonlinear observability, state-space transformations and stability, followed by study of a selection of nonlinear control design methods, including techniques motivated by geometric mechanics.
MAE 545 Special Topics in Mechanical & Aerospace Engineering Topics vary according to the interests of the class but are drawn from emerging numerical discretization methods (finite elements, finite volume, spectral, boundary element and vortex methods), boundary condition treatment, complex geometry modeling and grid generation, solution algorithms (direct solvers, conjugate gradient, multigrid, Fourier and wavelet transforms), and parallel software and computer architectures.
MAE 546 Optimal Control and Estimation An introduction to stochastic optimal control theory and application. It reviews mathematical foundations and explores parametric optimization, conditions for optimality, constraints and singular control, numerical optimization, and neighboring-optimal solutions. Least-squares estimates, propagation of state estimates and uncertainty, and optimal filters and predictors; optimal control in the presence of uncertainty; certainty equivalence and the linear-quadratic-Gaussian regulator problem; frequency-domain solutions for linear multivariable systems; and robustness of closed-loop control are all studied.
MAE 551 Fluid Mechanics An introduction to fluid mechanics. 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.
MAE 552 Viscous Flows and Boundary Layers (also
CBE 557
) The mechanics of viscous flows. The course 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 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.
MAE 555 Non-Equilibrium Gas Dynamics Noncontinuum description of fluid flow and Liouville and Boltzmann equations. The course examines molecular collisions; detailed balancing; Chapman-Enskog expansion for near-equilibrium flows; transport phenomena; flows with transnational, vibrational and chemical non-equilibrium; shock structure; and shear and mixing layers with chemical reactions.
MAE 557 Simulation and Modeling of Fluid Flows Numerical methods are applied to solve the equations that govern fluid motion. Fluid flow problems involve convection, diffusion, and source terms. The governing equations are non-linear and coupled. 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 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, application to curvilinear coordinates.
MAE 558 Simulation and Modeling of Turbulent Fluid Flows 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 Advanced Topics in Fluid Mechanics I 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 562 Fracture Mechanics (also
MSE 540
) Fracture involves processes at multiple time and length scales. This course 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. The course also explores fracture at high temperatures and crack nucleation processes.
MAE 563 Instabilities in Fluids: Linear and Non-Linear Analysis of Waves and Patterns in the Environment (also
AOS 563
) This course describes natural patterns arising from instabilities in nature, and discusses their importance in the environment. We analyze phenomena at various scales, as diverse as wave breaking at the ocean surface, internal mixing in the atmosphere and the ocean, volcanic plumes, convection cells in the atmosphere, the break-up of fluid ligaments or bubble bursting at an interface. The course details mathematical tools (linear and non-linear stability analysis, symmetry arguments, solitons to non-linear equations such as shocks and solitions), as well as present laboratory and numerical demonstration of the instabilities.
MAE 564 Structural Materials (also
MSE 564
) 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.
MAE 566 Biomechanics and Biomaterials: From Cells to Organisms (also
CBE 561
) Bioengineering is proof that exciting developments happen at the interfaces between fields. This course introduces students to approaches spanning biomechanics and biophysics, biomaterials and tissue engineering, and biomedical device design. These approaches are explored in the context of single cells, tissues, and whole organisms. Sample topics include: mechanobiology, surface chemistry and the cell:material interface, the biomechanics of locomotion, and "lab on a chip"technologies. Special emphasis is placed on introducing practical biomedical examples from the bench to the operating room.
MAE 569 Advanced Topics in Materials and Mechanical Systems I 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.
MAE 574 Unmaking the Bomb:The Science &Technology of Nuclear Nonproliferation, Disarmament, and Verification Nuclear weapons have re-emerged as one of the main global security challenges of our time. Reducing the dangers posed by these weapons will require new verification technologies, and this course covers the relevant science and technology. Part I examines the fundamental principles of nuclear fission, nuclear radiation, and radiation detection. Hands-on prototyping team projects in Part II explore possible new inspection systems. These projects can involve autonomous robots, machine learning techniques, IoT devices, and new detector types. In a virtual-reality exercise at the end of the semester, we examine the viability of these systems.
MAE 580 Advanced Topics in Energy and Environment II 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.
MAE 597 Graduate Seminar in Mechanical and Aerospace Engineering 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. Participation is required by first year graduate students.
MAE 598 Graduate Seminar in Mechanical & Aerospace Engineering 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. Partipcation by first year graduate students is required.
MSE 501 Introduction to Materials (also
MAE 561
/
CEE 561
) Emphasizes the connection between microstructural features of materials (e.g., grain size, boundary regions between grains, defects) and their properties, and how processing conditions control structure. Topics include thermodynamics and phase equilibria, microstructure, diffusion, kinetics of phase transitions, nucleation and crystal growth, phase separation, spinodal decomposition, glass formation, and the glass transition.
MSE 513 Introduction to Nanotechnology (also
CHM 511
/
MAE 516
) The first part of the course contains fundamental chemical concepts and basic ideas needed to calculate the difference between the bulk properties of matter and the properties of aggregates. The second part describes the tools needed to probe matter at the nanoscale level. The third part discusses examples of nanoscale materials (clusters, monolayers, fullerenes, biomolecules) and their applications.