Graduate Programs and Preliminary Exams

**Major Fields of Study**

- Design, Robotics, and Manufacturing (syllabus – Fall 2017 or earlier) (syllabus – Fall 2018 or later) (preliminary exams)
- Fluid Mechanics (syllabus) (preliminary exams)
- Micro-Nano Engineering (syllabus) (preliminary exams)
- Structural and Solid Mechanics (syllabus) (preliminary exams)
- Systems and Control (syllabus) (preliminary exams)
- Thermal Science and Engineering (TSE) (syllabus) (preliminary exams)

**Minor Fields of Study**

##### Applied Mathematics (syllabus)

A student who elects Applied Mathematics as a minor field wm be held responsible for the body of knowledge contained in a coherent croup or courses to be approved in advance by the Field Committee. The program must comprise at least 12 quarter units in J1ldulte work. Committee approval or any proposed course work group will depend on such factors as the student’s major field interests, and the breadth of his or her prior mathematical course work record.

A student may satisfy the filed requirements by examination or achieving satisfactory grades in a group of courses selected as follows:

1. One course from the following list (offered by SEAS):

EE M208A/MAE M291A, EE

M208B/MAE M291B, EE 208C, MAE 291C

2. Any two additional courses from 1, or Graduate courses offered by the Mathematics Department

Students formally enrolled in an approved program of courses u outlined above, and who achieve grades or B or better in all courses, and at least one A, will be deemed to have completed the minor field requirement.

A transfer student may petition the Field Committee for permission to list *one *course taken at another institution in his or her approved

course group, provided the course was taken by the student in graduate status.

**Examination for the Minor Field**

See General Information Bulletin. EGS.32.

**Syllabus for the Minor Field**

I.

Prerequisite Material

(see “Outline of Normal Prerequisite Coverage” below).

II.

Topics in Applied Mathematics

corresponding to approved selections u described

in “Minimum Preparation” above.

**Outline of Normal Prerequisite Coverage**

I.

Linear Algebra

Fundamentals or linear

algebra (including finite-dimensional vector space, linear transformations,

matrices) as covered in contemporary Sophomore level calculus

sequences (Mathematics 12A or 13BC).

II.

Differential Equations

Ordinary differential equations

and applications (vibrations, circuits, etc.), including transform methods

of solutions for linear systems; some basic partial differential equations

of engineering interest and simple boundary value problems, as covered

in Junior and Senior level courses in Mathematics (presently 140 series

of courses and in Engineering Mathematics 191A, 192 series).

III.

Vector Calculus

Scalar and vector fields,

gradient, divergence, curl, line integrals, surface integrals, integral

theorems (as covered in Sophomore-level calculus sequences and undergraduate

core-curriculum Engineering& courses, including E81ineerin&

1008).

IV.

Functions of a Complex

Variable

Analytic functions, series

expansions, contour integrals, conformal mapping covered in part in

Mathematics and Engineering courses in the undergraduate core-curriculum,

and in Mathematics 132 (Introduction to Complex Analysis), and Engineering

191A.

V.

Advanced Calculus (Introductory

Real Analysis)

Functions, limits, derivatives,

integrals, etc., emphasizing the axiomatic approach with complete proofs

of theorems; e.g. Mathematics 131 (Analysis) or the equivalent.

**References**

Textbooks

currently used in pertinent undergraduate Engineering and Mathematics

courses.

##### Applied Plasma Physics (syllabus)

**Applied Plasma Physics and Fusion Engineering**

The field of Applied Plasma Physics and Fusion Engineering, as partial preparation for the degree of Doctor of Philosophy in Engineering, covers the subject matter described below.

**Minimum Preparation for Major Field Students Examination**

The Major Field Examination is an eight hour examination covering material from the syllabus. Part of the examination will cover material in the core; all students are responsible for this pan. The remainder of the examination will cover material from the elective sections of the syllabus.

In advance of the examination, each student shall inform his adviser of the core elective topics on which he wishes to be tested.

**Syllabus for the Major Field Core Topics**

I.

Fundamentals of plasma

physics (MAE M185)

A.

Particle motion in

electromagnetic field; adiabatic invariants

B.

Fluid equations and

diamagnetic drifts

C.

Debye shielding; plasma

sheaths

D.

Maxwell’s equations

in the plasma; the equivalent dielectric tensor

E.

Electrostatic and electromagnetic

plasma waves at principal angles to a magnetic field; cutoffs and resonances

F.

Diffusion in partially

ionized gases

G.

Resistivity and diffusion

in fully ionized gases; In A. factor; magnetic viscosity

H.

Magnetohydrodynamic

{MHD) theory

1.

Single-fluid equations

2.

Hydromagnetic equilibrium

in confinement geometries

3.

Basic types of instabilities

I.

Kinetic theory; Vlasov

equation and Landau damping

J.

Anomalous transport

processes K. Basic diagnostic techniques

II.

Fundamentals of fusion

engineering (MAE 137)

A.

Fusion reactions and

fuel cycles; thermonuclear conditions; Lawson and ignition criteria

B.

Magnetic mirror confinement:

tandem mirrors, energy and particle flows, power balance

C.

Toroidal magnetic confinement:

tokamak, stellarator, reversed-field pinch

D.

Start-up and burning-plasma

analysis

E.

Inertial confinement

laser and particle beam drivers; concepts of compression, central ignition,

and burn-wave propagation

F.

Fusion blanket design

and nuclear analysis; tritium breeding: induced radioactivity

G.

Fission-fusion hybrids

H.

Tritium: inventor,

methods of recovery

I.

Magnets: superconductivity;

structural design

J.

Radiation damage to

materials: influence on design

K.

Designs of fusion reactors

**Elective Topics**

III.

Linear waves in uniform

plasmas (EE28SA)

A.

Waves in cold and warm

plasmas: CMA diagram; phase velocity surfaces; polarization and particle

orbits; Fredericks and Stringer diagrams for low-frequency

waves

B.

Electromagnetic waves:

ordinary and extraordinary waves, Appleton-Hartree formula, microwave

diagnostics. Alfven waves whistlers, e.m., cyclotron waves

C.

Electrostatic waves:

Bohm-Gross waves, ion acoustic waves. two-ion hybrid waves, e.g. cyclotron

waves

D.

Wave packets and group

velocity in anisotropic media; resonance cones

E.

Waves in hot plasmas:

Bernstein modes. cyclotron harmonics, Landau and cyclotron damping

F.

Damping and excitation

of waves: resistivity. viscosity, neutral collisions, resonant particles;

grids, coils

G.

Waves in bounded plasmas;

Trivelpiece-Gould modes

H.

Accessibility and tunneling

I.

R. F. heating of plasmas

J.

Tonks-Dattner resonances

IV.

Waves and instabilities

in non-uniform plasmas (EE28SB)

A.

Beam-plasma interactions;

convective and absolute instabilities

B.

Streaming instabilities;

Penrose criterion; current-driven instabilities

C.

Energy and momentum

of waves; positive and negative energy waves

D.

Drift waves and universal

instabilities

E.

Kelvin-Helmholtz instabilities

F.

Instabilities in partially

ionized gases (Simon-Hoh. Kadomtsev-Nedospasov)

G.

Wave propagation in

inhomogeneous plasmas: Budden tunneling, resonance absorption

H.

Ponderomotive force.

optical mixing, parametric decay and OTS, stimulated Brillouin and Raman

scattering, filamentation, two-plasmon decay; saturation mechanisms

I.

Nonlinear waves; Kortweg-deVries

and nonlinear Schrödinger equations; shock waves, solitons

J.

Quasilinear diffusion

V.

Magnetic confinement

of plasmas (EE286’MAE237 A)

A.

MHD equilibrium: simple

axisymmetric configurations, virial theorem, force-free fields, rotational

transform and toroidal equilibrium; Grad-Shafranov equation

B.

MHD stability: energy

principle. interchange and kink instabilities, Suydam criterion, Kroskal

limit, shear, and min-B stabilization. finite Larmor radius stabilization

C.

Microinstabilities:

drift, ballooning, tearing, and trapped particle modes

D.

Toroidal confinement

1.

Tokamaks: banana orbits,

q and Q, islands, sawteeth, Mirnov oscillations, disruptions, impurity

diffusion, runaway electrons, Alcator and Murakami scaling, elongated

cross sections, flux conservation, profile consistency

2.

Neoclassical and Pfirsch-Schlüter

diffusion

3.

Convective and poloidal

Bohm diffusion

4.

Minimum-B devices:

multipoles, spherators, levitrons

E.

Mirror confinement

1.

Ioffe bars, min-K principle

2.

Velocity space diffusion

and electron drag

3.

The DCLC instability

and its control

4.

Tandem mirrors, axisymmetric

plugs, thermal barriers

5.

Field reversal; compact

torus

F.

Plasma heating; ohmic

heating, neutral beam injection, rf heating and current drive, magnetic

pumping

VI.

Plasma diagnostics

(Phys. 180E. EE282B. EE289S)

A.

Faraday rotation, microwave

interferometry and scattering

B.

Langmuir probes

C.

Neutral and ion beam

probes

D.

Magnetic probes, Rogowski

coils. diamagnetic loops

E.

Optical and uv spectroscopy

F.

Soft x-ray diagnostics

G.

Synchrotron radiation

H.

Particle detectors

and velocity analyzers

I.

Laser diagnostics:

Thomson scattering and holography in the far-IR, IR, and visible

VII.

Fusion plasma physics

and analysis (MAE237B/EE287)

A.

Plasma energy and particle

balance

B.

Radiation processes:

bremsstrahlung, synchrotron and recombination radiation

C.

Atomic processes in

plasmas; impurities

D.

Fokker-Planck equation;

equilibrium and slowing down rates

E.

Plasma heating; neutral

beam injection

F.

Plasma burn modes;

burn kinetics and thermal stability; Q calculation of driven plama reactors

G.

Mirror reactor physics;

tandem mirror burn dynamics

H.

Tokamak reactor physics;

β limits, transport, start-up and burn dynamics

VIII.

Plasma engineering and technology (MAE237B/EE287,

MAE237C/EE288)

A.

Plasma-surface interactions

B.

Physics and technology

of limiters, divertors, and direct converters

C.

Plasma fueling

D.

Technology of plasma

heating: neutral beams. rf. lasers, pulsed power, heavy ion accelerators

IX.

Fusion engineering and reactor design (MAE237C/EE288)

A.

Fusion reactor concepts

and designs)

B.

Neutronics: nuclear

responses, nuclear heating, radioactivity

C.

Fuel cycle: function,

description, analysis

D.

Blanket function and

design

E.

Self-cooled liquid

metal blankets

F.

Solid breeder blankets

G.

In-vessel components;

first wall, limiter, divertor

H.

Radiation shielding:

design and analysis

I.

Magnet systems: normal

and superconducting magnet design, cryogenic stability, radiation effects

X.

Nuclear fuel element

behavior (MAE236A)

A.

Fuel swelling due to

fission gases

B.

Pore migration and

fuel restructuring kinetics

C.

Fission gas release

D.

Mechanical properties

of fuel materials

E.

Structural behavior

of fuel elements and assemblies

XI.

Radiation damage in

reactor materials (MAE236B)

A.

Ion transport in solids

B.

Theory of collision

cascades

C.

Ion ranges

D.

Damage and ion distributions

E.

Backscattering and

reflection

F.

Sputtering and blistering

G.

Displacement damage

H.

Microstructure evolution

and kinetic behavior

I.

Relationship to mechanical

properties

J.

Embrittlement, swelling,

irradiation creep

XII.

Nuclear reactor theory

(MAE235A)

A.

Physics and mathematics

of fission reactor core design

B.

Diffusion theory

C.

Reactor kinetics

D.

Slowing down and thermalization

E.

Multigroup method

F.

Cell calculations for

heterogeneous core lattices

XIII.

Kinetic theory of plasmas and particle

transport (MAE235B)

A.

Transport phenomena

B.

Liouville equation,

Boltzmann collision integral and H-theorem

C.

Fokker-Planck, neutron

and radiation transport equations

D.

Fluid moment equations

E.

Dispersion relations

F.

Space and time relaxation

phenomena

XIV.

Reactor thermal hydraulic design (MAE136)

A.

Thermal hydraulic design

of various nuclear power reactor concepts

B.

Power cycles

C.

Power generation and

heat removal

D.

Thermal and hydraulic

and component design

E.

Overall plant design

F.

Startup, steady-state,

and transient operation

XV.

Convective heat transfer

(MAE231A)

A.

Conservation equations

for mass, momentum, and energy

B.

Similarity in forced

and free convection

C.

Laminar boundary layer

equations

D.

Similarity solutions

for constant property two-dimensional boundary layer

E.

Laminar flow in ducts

F.

Transport in turbulent

flows

G.

Turbulent forced convection

external boundary layers

H.

Turbulent flow in ducts

I.

Laminar and turbulent

free convection boundary layers

XVI.

Numerical methods for engineering applications

(MAE192C)

A.

Matrix algebra

B.

Lagrange interpolation

and quadrature methods

C.

Numerical solutions

for ordinary differential equations

1.

Initial value problems

2.

Boundary value problems

D.

Numerical solutions

for partial differential equations

1.

Parabolic

2.

Elliptic

3.

Hyperbolic

E.

Integral equations

**Minimum Preparation for Major FieldStudents**

The body of knowledge in Sections I and II, in two of Sections

III through XIII, and in two others of Sections III through XVI.

**Recommended Course Preparation**

**Major Field**

Students

selecting Applied Plasma Physics and Fusion Engineering as their major

field are responsible for the core sections I and II comprising material

contained in EE185 and MAE137. In addition to this core material, students

are to choose four elective sections from those numbered ill through

XVI. The material described in sections ill through XVI is contained

in one or more appropriate courses, as indicated in the syllabus for

each section. Those students who wish to emphasize applied plasma physics

in the Ph.D. dissertation research should select the majority of their

four electives from sections III-IX. Students wishing to emphasize fusion

engineering in their PhD. dissertation research should select the majority

of their four electives from Sections VIII-XVI. Thesis students should

be familiar with the current literature in their chosen field of research

and become acquainted with recent developments in plasma physics and

fusion engineering by attending the various seminars, colloquia. and

tutorials offered by the faculty, staff, and visitors working in the

field.

**Minor Field**

Students

electing Applied Plasma Physics and Fusion Engineering as a minor field

can satisfy the minor requirement by taking EE185 or MAE135D and two

courses from the following list:

EE285A, 2858, 286 (MAE237A),

Phys. 180E, 222A, MAE2378 (EE287), M237C (EE288), 236B, 235B

**References**

The following books can be helpful to students emphasizing applied plasma physics:

1.

F. Chen, “Introduction

to Plasma Physics,” 2nd ed., Plenum, 1983. (EE185)

2.

Schmidt, “Physics

of High Temperature Plasmas,” Academic Press, 1979. (EE286/MAE237A, Phys. 222)

3.

N. Krall and A. W.

Trivelpiece, “Principles of Plasma Physics,” McGraw-Hill, 1973. (Phys. 222)

4.

T. H. Stix, “Theory

of Plasma Waves,’. McGraw-Hill, 1962. (EE285AB)

5.

L. Spitzer, Jr., “Physics

of Fully Ionized Gases,” 2nd ed., Wiley, 1962. (EE185, 285A, EE2861MAE237A)

6.

V. L. Ginzburg, “The

Propagation of Electromagnetic Waves in Plasmas,” Pergamon Press, 1964. (EE2858)

7.

R. Huddlestone and

S. Leonard, e&., “Plasma Diagnostic

Techniques,” Academic Press, 1965. (MAE2378/EE287)

8.

K. Nishikawa and C.

S. Liu, “Parametric Instabilities in Plasma” in Advances

in Plasma Physics, Vol. 6, ed. by A. Simon and W. B. Thompson,

Wiley-Interscience, 1976. (EE2858)

9.

B. Milhailovsky, “Theory

of Plasma Instabilities,” Vols. 1 and 2, Consultants Bureau, 1974.

10.

E. Keen, ed., “Plasma

Physics,” Institute of Physics, London, 1974.

11.

E. Sindoni and C. Wharton,

eds., “Diagnostics for Fusion Experiments,” Pergamon Press, 1979.

12.

W. Lochte-Holtgreven,

ed., “Plasma Diagnostics,” North Holland, 1968.

13.

N. C. Luhmann, Jr.,

“Instrumentation and Techniques for Plasma Diagnostics: An Overview,”

in Infrared and Millimeter Waves, ed. by K. J. Button, Vol. II,

Academic Press, 1979.

14.

“Review Modem

Fusion Diagnostics,” to be published in Review of Scientific Instruments

(a)

N. C. Luhmann and W.

A. Peebles -Magnetic Confinement Diagnostics

(b)

M. Campbell -Inertial

Confinement Diagnostics

15.

“Nonlinear Wave

Effects in Laboratory Plasmas: A Comparison Between Theory and Experiment,”

M. Porkolab and R. P. H. Chang, Review of Mod. Phys. ~ 745 (1978).

16.

“Waves and Microinstabilities

in Plasmas,”

(a)

Linear Effects: J.E.

Allen and A. D. R. Phelps, Rep. Prog. Phys. 40, 1305

(b)

Nonlinear Effects:

R. N. Franklin, Rep. Prog. Phys. 40 1369 (1977).

The

following books can be helpful to students emphasizing fusion physics

and engineering:

1.

R. A. Gross, “Fusion

Energy,” Wiley & Sons, 1982. (MAE137)

2.

R. W. Conn, “Magnetic

Fusion Reactors,” in ~ ed. by E. Teller, Vol. IB, pp. 193-410,

Academic Press, 1981. (MAE137)

3.

T. J. Dolan, “Fusion

Research,” Vols. 1-3, Pergamon Press, 1982. (MAEI37)

4.

W. M. Stacey, Jr.,

“Fusion Plasma Analysis,” Wiley, 1981. (EE286/MAE237A, MAE237B/EE287)

5.

P. Shkarofsky, T. W.

Johnston and M. P. Bachynski, “The Particle Kinetics of Plasmas,”

Addison- Wesley, 1966. (EE287/MAE237B)

6.

J. Duderstadt and G.

A. Moses, “Inertial Confinement Fusion,” Wiley 1982. (MAE237B/EE287)

7.

J. Rose and M. Clark,

“Plasmas and Controlled Fusion,” M.I.T. Press, 1961. (EE286’MAE237

A, MAE237B/EE287, MAE237C/EE288)

8.

B. Davison, “Neutron

Transport Theory,” Oxford University Press, 1958. (MAE235A)

9.

Bell and S. Glasstone, “Nuclear Reactor

Theory,” Van Nostrand, 1970. (MAE235A)

10.

J. J. Duderstadt and

W. R. Martin, “Transport Theory,” Wiley, 1979. (MAE235A)

11.

Clark and K. Hans en,

“Numerical Methods of Reactor Analysis,” Academic Press, 1964.

(MAE235C)

12.

Greenspan, C. N. Kleber,

and D. Okrent, “Computing Methods in Reactor Physics,” Gordon

and Breach, 1968. (MAE235C)

13.

R. W. Varga, “Matrix

Interactive Analysis,” Prentice-Hall, 1962). (MAE235C)

14.

R. D. Richtmyer and

K. W. Morton, “Difference Methods for Initial-Value Problems,”

2J1d Ed., Wiley-Interscience, 1967. (MAE235C)

15.

D. R. Orlander, “Fundamental

Aspects of Nuclear Reactor Fuel Elements,’” Technical Information Center, Dept of Energy, 1976. (MAE136C, 236B)

16.

Y. Y. Hsu and R. W.

Graham, “Transport Processes in Boiling and Two-Phase Systems,”

McGraw- Hill, 1976. (MAE231C)

17.

R. T. Lahey and F.

J. Moody, “Thermal Hydraulics of Boiling Water Reactors,”

American Nuclear Society, 1977. (MAE231C)

18.

M. EI-Wakil, “Nuclear

Power Engineering,” McGraw-Hill, 1962 (MAE136B)

19.

W. Thompson, “Defects

and Radiation Damage in Metals,” Cambridge University Press, 1969. (MAE236B )

20.

L. T. Chadderton, “Radiation

Damage in Crystals,” Methaen and Co., 1965. (MAE236B)

**Literature: Pertinent Journals andSerial Publications**

Nuclear

Fusion

Physical

Review Letters

Applied

Physics Letters

Physics

of Fluids

Plasma

Physics and Controlled Fusion

Soviet

Journal of Plasma Physics

IEEE

Trans. on Plasma Science Journal of Fusion Energy

Nuclear

Technology

Fusion

Technology

Nuclear

Science and Engineering

Nuclear

Engineering and Design/Fusion

Journal

of Nuclear Materials

Journal

of Heat Transfer

Comments

on Plasma Physics and Controlled Fusion

Transactions

of the American Nuclear Society

Plasma

Physics and Controlled Nuclear Fusion Research:

1961, 1965, 1968, 1971,

1974, 1976, 1978, 1980, 1982, 1984

Published every other year

by the International Atomic Energy Agency, Vienna

SIAM J. of Computational Physics

J.

of Vacuum Science and Technology

Inter.

Journal of Infrared and Millimeter Waves

Review

of Scientific Instruments

## MAJORS

**DESIGN, ROBOTICS, AND MANUFACTURING****Mohamed Abdou, Tyler Clites, Rajit Gadh, Greg Carman, Dennis Hong, Jonathan Hopkins, Xiaochun Li, Jacob Rosen (Chair), Veronica Santos, Tsu-Chin Tsao**

The program is developed around an integrated approach to manufacturing and mechanical product design. It includes research on material behavior (physical and mechanical) in manufacturing processes and design; design of mechanical systems (for example, power, micro-electro-mechanical systems and transportation); design methodology; automation, robotics and unmanned machinery; manufacturing and mechanical systems(reliability, safety, and optimization); CAD/CAM theory and applications; computational geometry and geometrical modeling, composite structure; beam and plasma assisted manufacturing.

**FLUID MECHANICS****Jeff Eldredge, Ann Karagozian, Pirouz Kavehpour, Neil Lin, Mitchell Spearrin, Sam Taira, Richard Wirz (Chair), Xiaolin Zhong**

This program includes experimental, numerical, and theoretical studies related to topics on fluid mechanics such as stratified and rotating flows, thermal convection, interfacial phenomena, acoustically driven combustion flows, high-speed combustion, hazardous waste incineration, laser diagnostics, aerodynamic noise production, unsteady aerodynamics of fixed and rotary wings, flow instabilities and transition, turbulence, flow control, and micro-scale fluid mechanics.

**MICRO-NANO ENGINEERING****Greg Carman, Yong Chen, Pei-Yu Chiou, Artur Davoyan, Tim Fisher, Vijay Gupta, Yongjie Hu, Lihua Jin, Y. Sungtaek Ju, Pirouz Kavehpour, Chang-Jin Kim (Chair), Xiaochun Li, Neil Lin, Laurent Pilon**

The Micro-Nano Engineering program focuses on the integration of science, engineering, and technology in the length scale of micrometers and nanometers. The study topics include science, fabrication technologies, devices, systems, material processing, intelligent material systems, flow phenomena, heat transfer, and biotechnologies at the micron/nano scales. The program is highly interdisciplinary in nature.

**STRUCTURAL AND SOLID MECHANICS****Greg Carman, Vijay Gupta (Chair), Jonathan Hopkins, M. Khalid Jawed, Lihua Jin, Xiaochun Li, Ajit Mal**

The solid mechanics program features theoretical, numerical and experimental studies, including fracture mechanics and damage tolerance, micromechanics with emphasis on technical applications, wave propagation and nondestructive evaluation, mechanics of composite materials, mechanics of thin films and interfaces, and investigation into coupled electro-magneto-thermo-mechanical material systems. The structural mechanics program includes structural dynamics with applications to aircraft and spacecraft, fixed-wing and rotary-wing aeroelasticity, fluid structure interaction, computational transonic aeroelasticity, structural optimization, finite element methods and related computational techniques, structural mechanics of composite material components, and analysis of adaptive structures.

**SYSTEMS AND CONTROL****Elisa Franco (Chair), Jonathan Hopkins, Tetsuya Iwasaki, Neil Lin, Robert M’Closkey, Jacob Rosen, Veronica Santos, Jason Speyer, Tsu-Chin Tsao**

This program features systems engineering principles and applied mathematical methods of modeling, analysis, and design of continuous and discrete-time control systems. Emphasis is on computational methods, simulation, and modern applications in engineering, system concepts, applied optimal control, differential games, and computer process control. This field covers a broad spectrum of topics, emphasizing primarily aerospace and mechanical engineering applications.

**THERMAL SCIENCE AND ENGINEERING (TSE)****Mohamed Abdou, Vijay Dhir, Tim Fisher, Yongjie Hu (Chair), Y. Sungtaek Ju, Pirouz Kavehpour, Adrienne Lavine, Jayathi Murthy, Laurent Pilon**

This program includes studies of convection, radiation, conduction, evaporation, condensation, boiling, two-phase flow, chemically reacting and radiating flow, instability and turbulent flow, and reactive flows in porous media.

## MINORS

**APPLIED MATHEMATICS****Jason Speyer, Chair**

Students opting for Applied Mathematics as a minor field are responsible for the body of knowledge contained in a coherent group of courses offered by the School of Engineering and/or the Mathematics Department. The program must consist of at least twelve quarter units of graduate study. In addition to the graduate course work, students in this minor field are expected to be familiar with the basic material in linear algebra, differential equations, vector calculus, functions of complex variables, and advanced calculus.

**APPLIED PLASMA PHYSICS****Mohamed Abdou, Chair**

Research in Applied Plasma Physics and Fusion Engineering is an appropriate advanced extension of traditional research and multi-disciplinary graduate-oriented field. The program emphasizes fusion as an important future option for energy production, conversion, and utilization. Research explores challenging applications of structural and solid mechanics, fluid mechanics, heat transfer, plasma-material interactions, and particle transport. The minor field offers education and training in plasma and fusion engineering to supplement the education received via one of the traditional major fields offered by the Department.