# Courses tagged with "Graduate" (73)

Each term, the class selects a new set of professional journal articles on bioengineering topics of current research interest. Some papers are chosen because of particular content, others are selected because they illustrate important points of methodology. Each week, one student leads the discussion, evaluating the strengths, weaknesses, and importance of each paper. Subject may be repeated for credit a maximum of four terms. Letter grade given in the last term applies to all accumulated units of 16.459.

This course covers examination of the state of knowledge of planetary formation, beginning with planetary nebulas and continuing through accretion (from gas, to dust, to planetesimals, to planetary embryos, to planets). It also includes processes of planetary differentiation, crust formation, atmospheric degassing, and surface water condensation. This course has integrated discussions of compositional and physical processes, based upon observations from our solar system and from exoplanets. Focus on terrestrial (rocky and metallic) planets, though more volatile-rich bodies are also examined.

We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.

We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overlap and transition to chaos; properties of chaotic motion.

Ideas will be illustrated and supported with physical examples. We will make extensive use of computing to capture methods, for simulation, and for symbolic analysis.

Cognitive robotics addresses the emerging field of autonomous systems possessing artificial reasoning skills. Successfully-applied algorithms and autonomy models form the basis for study, and provide students an opportunity to design such a system as part of their class project. Theory and application are linked through discussion of real systems such as the Mars Exploration Rover.

The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course includes: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms include: variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There is a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. The application to real engineering applications and problems in engineering science is stressed throughout the course.

The theoretical frameworks of Hartree-Fock theory and density functional theory are presented in this course as approximate methods to solve the many-electron problem. A variety of ways to incorporate electron correlation are discussed. The application of these techniques to calculate the reactivity and spectroscopic properties of chemical systems, in addition to the thermodynamics and kinetics of chemical processes, is emphasized. This course also focuses on cutting edge methods to sample complex hypersurfaces, for reactions in liquids, catalysts and biological systems.

This course provides an overview of astrophysical cosmology with emphasis on the Cosmic Microwave Background (CMB) radiation, galaxies and related phenomena at high redshift, and cosmic structure formation. Additional topics include cosmic inflation, nucleosynthesis and baryosynthesis, quasar (QSO) absorption lines, and gamma-ray bursts. Some background in general relativity is assumed.

This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.

This course begins with a study of the role of dynamics in the general physics of the atmosphere, the consideration of the differences between modeling and approximation, and the observed large-scale phenomenology of the atmosphere. Only then are the basic equations derived in rigorous manner. The equations are then applied to important problems and methodologies in meteorology and climate, with discussions of the history of the topics where appropriate. Problems include the Hadley circulation and its role in the general circulation, atmospheric waves including gravity and Rossby waves and their interaction with the mean flow, with specific applications to the stratospheric quasi-biennial oscillation, tides, the super-rotation of Venus' atmosphere, the generation of atmospheric turbulence, and stationary waves among other problems. The quasi-geostrophic approximation is derived, and the resulting equations are used to examine the hydrodynamic stability of the circulation with applications ranging from convective adjustment to climate.

This course is a graduate level subject on electromagnetic theory with particular emphasis on basics and applications to Nuclear Science and Engineering. The basic topics covered include electrostatics, magnetostatics, and electromagnetic radiation. The applications include transmission lines, waveguides, antennas, scattering, shielding, charged particle collisions, Bremsstrahlung radiation, and Cerenkov radiation.

## Acknowledgments

Professor Freidberg would like to acknowledge the immense contributions made to this course by its previous instructors, Ian Hutchinson and Ron Parker.

Electromagnetic Theory covers the basic principles of electromagnetism: experimental basis, electrostatics, magnetic fields of steady currents, motional e.m.f. and electromagnetic induction, Maxwell's equations, propagation and radiation of electromagnetic waves, electric and magnetic properties of matter, and conservation laws. This is a graduate level subject which uses appropriate mathematics but whose emphasis is on physical phenomena and principles.

Engineering principles of nuclear reactors, emphasizing power reactors. Topics include power plant thermodynamics, reactor heat generation and removal (single-phase as well as two-phase coolant flow and heat transfer), structural mechanics, and engineering considerations in reactor design.

General introduction to systems engineering using both the classical V-model and the new *Meta* approach. Topics include stakeholder analysis, requirements definition, system architecture and concept generation, trade-space exploration and concept selection, design definition and optimization, system integration and interface management, system safety, verification and validation, and commissioning and operations. Discusses the trade-offs between performance, lifecycle cost and system operability. Readings based on systems engineering standards and papers. Students apply the concepts of systems engineering to a cyber-electro-mechanical system, which is subsequently entered into a design competition.

Students will prepare a PDR (Preliminary Design Review)-level design intended for the *Cansat Competition*.This year's class will be taught in the form of a Small-Private-Online-Course (SPOC) and offered simultaneously to students at MIT under number 16.842 and Ecole Polytechnique Fédérale de Lausanne (EPFL) as ENG-421.

Human Supervisory Control of Automated Systems discusses elements of the interactions between humans and machines. These elements include: assignment of roles and authority; tradeoffs between human control and human monitoring; and human intervention in automatic processes. Further topics comprise: performance, optimization and social implications of the system; enhanced human interfaces; decision aiding; and automated alterting systems. Topics refer to applications in aerospace, industrial and transportation systems.

This class addresses some of the important issues involved with the planning, development, and implementation of lean enterprises. People, technology, process, and management dimensions of an effective lean manufacturing company are considered in a unified framework. Particular emphasis is placed on the integration of these dimensions across the entire enterprise, including product development, production, and the extended supply chain. Analysis tools as well as future trends and directions are explored. A team project is a key component of this subject.

This course integrates studies of engineering sciences, reactor physics and safety assessment into nuclear power plant design. Topics include materials issues in plant design and operations, aspects of thermal design, fuel depletion and fission-product poisoning, and temperature effects on reactivity, safety considerations in regulations and operations, such as the evolution of the regulatory process, the concept of defense in depth, General Design Criteria, accident analysis, probabilistic risk assessment, and risk-informed regulations.

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