# Courses tagged with "Graduate" (73)

In 16.540 we address fluid dynamic phenomena of interest in internal flow situations. The emphasis tends to be on problems that arise in air breathing propulsion, but the application of the concepts covered is more general, and the course is wider in scope, than turbomachines (in spite of the title). Stated more directly, the focus is on the fluid mechanic principles that determine the behavior of a broad class of industrial devices. The material can therefore be characterized, only partly tongue in cheek, as "industrial strength fluid mechanics done in a rigorous manner".

The plasma state dominates the visible universe, and is important in fields as diverse as Astrophysics and Controlled Fusion. Plasma is often referred to as "the fourth state of matter." This course introduces the study of the nature and behavior of plasma. A variety of models to describe plasma behavior are presented.

This class assesses current and potential future energy systems, covering resources, extraction, conversion, and end-use technologies, with emphasis on meeting regional and global energy needs in the 21st century in a sustainable manner. Instructors and guest lecturers will examine various renewable and conventional energy production technologies, energy end-use practices and alternatives, and consumption practices in different countries. Students will learn a quantitative framework to aid in evaluation and analysis of energy technology system proposals in the context of engineering, political, social, economic, and environmental goals. Students taking the graduate version, *Sustainable Energy*, complete additional assignments.

5.73 covers fundamental concepts of quantum mechanics: wave properties, uncertainty principles, SchrÃ¶dinger equation, and operator and matrix methods. Basic applications of the following are discussed: one-dimensional potentials (harmonic oscillator), three-dimensional centrosymmetric potentials (hydrogen atom), and angular momentum and spin. The course also examines approximation methods: variational principle and perturbation theory.

An examination of current economic and policy issues in the electric power industry, focusing on nuclear power and its fuel cycle. Introduces techniques for analyzing private and public policy alternatives, including discounted cash flow methods and other techniques in engineering economics. Application to specific problem areas, including nuclear waste management and weapons proliferation. Other topics include deregulation and restructuring in the electric power industry.

This course discusses MHD equilibria in cylindrical, toroidal, and noncircular tokamaks. It covers derivation of the basic MHD model from the Boltzmann equation, use of MHD equilibrium theory in poloidal field design, MHD stability theory including the Energy Principle, interchange instability, ballooning modes, second region of stability, and external kink modes. Emphasis is on discovering configurations capable of achieving good confinement at high beta.

This course is intended to introduce the student to the concepts and methods of transport theory needed in neutron science applications. This course is a foundational study of the effects of multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department. Stochastic and deterministic simulation techniques will be introduced to the students.

22.56J aims to give graduate students and advanced undergraduates background in the theory and application of noninvasive imaging methods to biology and medicine, with emphasis on neuroimaging. The course focuses on the modalities most frequently used in scientific research (X-ray CT, PET/SPECT, MRI, and optical imaging), and includes discussion of molecular imaging approaches used in conjunction with these scanning methods. Lectures by the professor will be supplemented by in-class discussions of problems in research, and hands-on demonstrations of imaging systems.

This short course provides an introduction to reactor dynamics including subcritical multiplication, critical operation in absence of thermal feedback effects and effects of Xenon, fuel and moderator temperature, etc. Topics include the derivation of point kinetics and dynamic period equations; techniques for reactor control including signal validation, supervisory algorithms, model-based trajectory tracking, and rule-based control; and an overview of light-water reactor startup. Lectures and demonstrations employ computer simulation and the use of the MIT Research Reactor.

This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.

This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).

The purpose of this course is to discuss modern techniques of generation of x-ray photons and neutrons and then follow with selected applications of newly developed photon and neutron scattering spectroscopic techniques to investigations of properties of condensed matter which are of interest to nuclear engineers.

This course describes the processes by which mass, momentum, and energy are transported in plasmas, with special reference to magnetic confinement fusion applications.

The Fokker-Planck collision operator and its limiting forms, as well as collisional relaxation and equilibrium, are considered in detail. Special applications include a Lorentz gas, Brownian motion, alpha particles, and runaway electrons.

The Braginskii formulation of classical collisional transport in general geometry based on the Fokker-Planck equation is presented.

Neoclassical transport in tokamaks, which is sensitive to the details of the magnetic geometry, is considered in the high (Pfirsch-Schluter), low (banana) and intermediate (plateau) regimes of collisionality.

This course studies basic optimization and the principles of optimal control. It considers deterministic and stochastic problems for both discrete and continuous systems. The course covers solution methods including numerical search algorithms, model predictive control, dynamic programming, variational calculus, and approaches based on Pontryagin's maximum principle, and it includes many examples and applications of the theory.

The central theme of this course is the interaction of radiation with biological material. The course is intended to provide a broad understanding of how different types of radiation deposit energy, including the creation and behavior of secondary radiations; of how radiation affects cells and why the different types of radiation have very different biological effects. Topics will include: the effects of radiation on biological systems including DNA damage; in vitro cell survival models; and in vivo mammalian systems. The course covers radiation therapy, radiation syndromes in humans and carcinogenesis. Environmental radiation sources on earth and in space, and aspects of radiation protection are also discussed. Examples from the current literature will be used to supplement lecture material.

This course covers interpretations of the concept of probability. Topics include basic probability rules; random variables and distribution functions; functions of random variables; and applications to quality control and the reliability assessment of mechanical/electrical components, as well as simple structures and redundant systems. The course also considers elements of statistics; Bayesian methods in engineering; methods for reliability and risk assessment of complex systems (event-tree and fault-tree analysis, common-cause failures, human reliability models); uncertainty propagation in complex systems (Monte Carlo methods, Latin Hypercube Sampling); and an introduction to Markov models. Examples and applications are drawn from nuclear and other industries, waste repositories, and mechanical systems.

This subject introduces the key concepts and formalism of quantum mechanics and their relevance to topics in current research and to practical applications. Starting from the foundation of quantum mechanics and its applications in simple discrete systems, it develops the basic principles of interaction of electromagnetic radiation with matter.

Topics covered are composite systems and entanglement, open system dynamics and decoherence, quantum theory of radiation, time-dependent perturbation theory, scattering and cross sections. Examples are drawn from active research topics and applications, such as quantum information processing, coherent control of radiation-matter interactions, neutron interferometry and magnetic resonance.

This course was created for the "product development" track of MIT's System Design and Management Program (SDM) in conjunction with the Center for Innovation in Product Development. After taking this course, a student should be able to:

- Formulate measures of performance of a system or quality characteristics. These quality characteristics are to be made robust to noise affecting the system.
- Sythesize and select design concepts for robustness.
- Identify noise factors whose variation may affect the quality characteristics.
- Estimate the robustness of any given design (experimentally and analytically).
- Formulate and implement methods to reduce the effects of noise (parameter design, active control, adjustment).
- Select rational tolerances for a design.
- Explain the role of robust design techniques within the wider context of the product development process.
- Lead product development activities that include robust design techniques.