Course Descriptions
Courses offered in our department for Applied Mechanics, Civil Engineering and Mechanical Engineering are listed below. Be aware that some courses are not offered every year; see the course schedule page to check if the class is offered this year.
Applied Mechanics Courses

Ae/AM/CE/ME 102 abc. Mechanics of Structures and Solids. 9 units (306); first, second, third terms. Prerequisites: ME 12 abc. Introduction to continuum mechanics: kinematics, balance laws, constitutive laws with an emphasis on solids. Static and dynamic stress analysis. Two and threedimensional theory of stressed elastic solids. Wave propagation. Analysis of rods, plates and shells with applications in a variety of fields. Variational theorems and approximate solutions. Elastic stability. Instructors: Lapusta, Bhattacharya, Pellegrino.

CE/Ae/AM 108 ab. Computational Mechanics. 9 units (351); first, second terms. Prerequisites: Ae/AM/ME/CE 102 abc or Ae/GE/ME 160 ab, or instructor's permission. Numerical methods and techniques for solving initial boundary value problems in continuum mechanics (from heat conduction to statics and dynamics of solids and structures). Finite difference methods, direct methods, variational methods, finite elements in small strains and at finite deformation for applications in structural mechanics and solid mechanics. Solution of the partial differential equations of heat transfer, solid and structural mechanics, and fluid mechanics. Transient and nonlinear problems. Computational aspects and development and use of finite element code. Not offered 201920.

AM/ACM 127. Calculus of Variations. 9 units (306); third term. Prerequisites: ACM 95/100. First and second variations; EulerLagrange equation; Hamiltonian formalism; action principle; HamiltonJacobi theory; stability; local and global minima; direct methods and relaxation; isoperimetric inequality; asymptotic methods and gamma convergence; selected applications to mechanics, materials science, control theory and numerical methods. Not offered 201920.

AM/CE/ME 150 abc. Graduate Engineering Seminar. 1 unit; first, second, third terms. Students attend a graduate seminar each week of each term and submit a report about the attended seminars. At least four of the attended seminars each term should be from the Mechanical and Civil Engineering seminar series. Students not registered for the M.S. and Ph.D. degrees must receive the instructor's permission. Graded pass/fail. Instructor: Staff.

AM/CE 151. Dynamics and Vibration. 9 units (306); first term. Equilibrium concepts, conservative and dissipative systems, Lagrange's equations, differential equations of motion for discrete single and multi degreeoffreedom systems, natural frequencies and mode shapes of these systems (Eigenvalue problem associated with the governing equations), phase plane analysis of vibrating systems, forms of damping and energy dissipated in damped systems, response to simple force pulses, harmonic and earthquake excitation, response spectrum concepts, vibration isolation, seismic instruments, dynamics of continuous systems, Hamilton's principle, axial vibration of rods and membranes, transverse vibration of strings, beams (BernoulliEuler and Timoshenko beam theory), and plates, traveling and standing wave solutions to motion of continuous systems, Rayleigh quotient and the RayleighRitz method to approximate natural frequencies and mode shapes of discrete and continuous systems, frequency domain solutions to dynamical systems, stability criteria for dynamical systems, and introduction to nonlinear systems and random vibration theory. Instructor: Asimaki.

AM/ME 165. Finite Elasticity. 9 units (306); third term. Prerequisites: Ae/Ge/ME 160 a. Finite theory of elasticity: constitutive theory, semiinverse methods. Variational methods. Applications to problems of current interest. Not offered 201920.

AM 200. Advanced Work in Applied Mechanics. Hours and units by arrangement. A faculty mentor will oversee a student proposed, independent research or study project to meet the needs of graduate students. Graded pass/fail. The consent of a faculty mentor and a written report is required for each term of work.

AM 201. Advanced Topics in Applied Mechanics. 9 units (306). The faculty will prepare courses on advanced topics to meet the needs of graduate students.

Ae/AM/MS/ME 213. Mechanics and Materials Aspects of Fracture. 9 units (306); first term. Prerequisites: Ae/AM/CE/ME 102 abc (concurrently) or equivalent and instructor's permission. Analytical and experimental techniques in the study of fracture in metallic and nonmetallic solids. Mechanics of brittle and ductile fracture; connections between the continuum descriptions of fracture and micromechanisms. Discussion of elasticplastic fracture analysis and fracture criteria. Special topics include fracture by cleavage, void growth, rate sensitivity, crack deflection and toughening mechanisms, as well as fracture of nontraditional materials. Fatigue crack growth and life prediction techniques will also be discussed. In addition, "dynamic" stress wave dominated, failure initiation growth and arrest phenomena will be covered. This will include traditional dynamic fracture considerations as well as discussions of failure by adiabatic shear localization. Not offered 201920.

Ae/AM/CE/ME 214 ab. Computational Solid Mechanics. 9 units (351); second, third terms. Prerequisites: ACM 100 ab or equivalent; CE/AM/Ae 108 ab or equivalent or instructor's permission; Ae/AM/CE/ME 102 abc or Ae/Ge/ME 160 ab or instructor's permission. Introduction to the use of numerical methods in the solution of solid mechanics and multiscale mechanics problems. First term: Variational principles. Finite element analysis. Variational problems in linear and finite kinematics. Time integration, initial boundary value problems. Elasticity and inelasticity. Constitutive modeling. Error estimation. Accuracy, stability and convergence. Iterative solution methods. Adaptive strategies. Second term: Multiscale modeling strategies. Computational homogenization in linear and finite kinematics. Spectral methods. Atomistic modeling and atomistictocontinuum coupling techniques. Not offered 201920.

Ae/AM/ME 215. Dynamic Behavior of Materials. 9 units (306); third term. Prerequisites: ACM 100 abc or AM 125 abc; Ae/AM/CE/ME 102 abc. Fundamentals of theory of wave propagation; plane waves, wave guides, dispersion relations; dynamic plasticity, adiabatic shear banding; dynamic fracture; shock waves, equation of state. Instructor: Ravichandran.

Ae/AM/ME 223. Plasticity. 9 units (306); second term. Prerequisites: Ae/AM/CE/ME 102 abc or instructor's permission. Theory of dislocations in crystalline media. Characteristics of dislocations and their influence on the mechanical behavior in various crystal structures. Application of dislocation theory to single and polycrystal plasticity. Theory of the inelastic behavior of materials with negligible time effects. Experimental background for metals and fundamental postulates for plastic stressstrain relations. Variational principles for incremental elasticplastic problems, uniqueness. Upper and lower bound theorems of limit analysis and shakedown. Slip line theory and applications. Additional topics may include soils, creep and ratesensitive effects in metals, the thermodynamics of plastic deformation, and experimental methods in plasticity. Instructor: Andrade.

Ae/AM/ME/Ge 225. Special Topics in Solid Mechanics. Units to be arranged; first, second, third terms. Subject matter changes depending on staff and student interest.

AM/CE/ME 252. Linear and Nonlinear Waves in Structured Media. 9 units (216); second term. The course will cover the basic principles of wave propagation in solid media. It will discuss the fundamental principles used to describe linear and nonlinear wave propagation in continuum and discrete media. Selected recent scientific advancements in the dynamics of periodic media will also be discussed. Students learn the basic principles governing the propagation of waves in discrete and continuum solid media. These methods can be used to engineer materials with predefined properties and to design dynamical systems for a variety of engineering applications (e.g., vibration mitigation, impact absorption and sound insulation). The course will include an experimental component, to test wave phenomena in structured media. Instructor: Daraio.

Ae/AM/CE/ME 265 ab. Static and Dynamic Failure of Brittle Solids and Interfaces, from the Micro to the Mega. 9 units (306); first, second terms. Prerequisites: Ae/AM/CE/ME 102 abc (concurrently) or equivalent and/or instructor's permission. Linear elastic fracture mechanics of homogeneous brittle solids (e.g. geomaterials, ceramics, metallic glasses); small scale yielding concepts; experimental methods in fracture, fracture of bimaterial interfaces with applications to composites as well as bonded and layered engineering and geological structures; thinfilm and microelectronic components and systems; dynamic fracture mechanics of homogeneous engineering materials; dynamic shear dominated failure of coherent and incoherent interfaces at all length scales; dynamic rupture of frictional interfaces with application to earthquake source mechanics; allowable rupture speeds regimes and connections to earthquake seismology and the generation of Tsunamis. Instructor: Rosakis.

AM 300. Research in Applied Mechanics. Hours and units by arrangement. Research in the field of applied mechanics. By arrangement with members of the staff, properly qualified graduate students are directed in research.
Civil Engineering Courses

CE 90 abc. Structural Analysics and Design. 9 units (306); first, second, third terms. Prerequisites: ME 35 abc. Structural loads; influence lines for statically determinate beams and trusses; deflection of beams; moment area and conjugate beam theorems; approximate methods of analysis of indeterminate structures; slope deflection and moment distribution techniques. Generalized stiffness and flexibility analyses of indeterminate structures. Design of selected structures in timber, steel, and reinforced concrete providing an introduction to working stress, load and resistance factor, and ultimate strength approaches. In each of the second and third terms a design project will be undertaken involving consideration of initial conception, costbenefit, and optimization aspects of a constructed facility. Not offered 201920.

CE 100. Special Topics in Civil Engineering. Units to be based upon work done, any term. Special problems or courses arranged to meet the needs of firstyear graduate students or qualified undergraduate students. Graded pass/fail.

Ae/APh/CE/ME 101 abc. Fluid Mechanics. 9 units (306); first, second, third terms. Prerequisites: APh 17 or ME 11 abc, and ME 12 or equivalent, ACM 95/100 or equivalent (may be taken concurrently). Fundamentals of fluid mechanics. Microscopic and macroscopic properties of liquids and gases; the continuum hypothesis; review of thermodynamics; general equations of motion; kinematics; stresses; constitutive relations; vorticity, circulation; Bernoulli's equation; potential flow; thinairfoil theory; surface gravity waves; buoyancydriven flows; rotating flows; viscous creeping flow; viscous boundary layers; introduction to stability and turbulence; quasi onedimensional compressible flow; shock waves; unsteady compressible flow; and acoustics. Instructors: Austin, Colonius.

Ae/AM/CE/ME 102 abc. Mechanics of Structures and Solids. 9 units (306); first, second, third terms. Prerequisites: ME 12 abc. Introduction to continuum mechanics: kinematics, balance laws, constitutive laws with an emphasis on solids. Static and dynamic stress analysis. Two and threedimensional theory of stressed elastic solids. Wave propagation. Analysis of rods, plates and shells with applications in a variety of fields. Variational theorems and approximate solutions. Elastic stability. Instructors: Lapusta, Bhattacharya, Pellegrino.

CE/Ae/AM 108 ab. Computational Mechanics. 9 units (351); first, second terms. Prerequisites: Ae/AM/ME/CE 102 abc or Ae/GE/ME 160 ab, or instructor's permission. Numerical methods and techniques for solving initial boundary value problems in continuum mechanics (from heat conduction to statics and dynamics of solids and structures). Finite difference methods, direct methods, variational methods, finite elements in small strains and at finite deformation for applications in structural mechanics and solid mechanics. Solution of the partial differential equations of heat transfer, solid and structural mechanics, and fluid mechanics. Transient and nonlinear problems. Computational aspects and development and use of finite element code. Not offered 201920.

CE/ME 112 ab. Hydraulic Engineering. 9 units (306); second, third terms. Prerequisites: ME 11 abc, ME 12 abc; ACM 95/100 or equivalent (may be taken concurrently). A survey of topics in hydraulic engineering: open channel and pipe flow, subcritical/critical flow and the hydraulic jump, hydraulic structures (weirs, inlet and outlet works, dams), hydraulic machinery, hydrology, river and flood modeling, solute transport, sediment mechanics, groundwater flow. Not offered 201920.

AM/CE/ME 150 abc. Graduate Engineering Seminar. 1 unit; first, second, third terms. Students attend a graduate seminar each week of each term and submit a report about the attended seminars. At least four of the attended seminars each term should be from the Mechanical and Civil Engineering seminar series. Students not registered for the M.S. and Ph.D. degrees must receive the instructor's permission. Graded pass/fail. Instructor: Staff.

AM/CE 151. Dynamics and Vibration. 9 units (306); first term. Equilibrium concepts, conservative and dissipative systems, Lagrange's equations, differential equations of motion for discrete single and multi degreeoffreedom systems, natural frequencies and mode shapes of these systems (Eigenvalue problem associated with the governing equations), phase plane analysis of vibrating systems, forms of damping and energy dissipated in damped systems, response to simple force pulses, harmonic and earthquake excitation, response spectrum concepts, vibration isolation, seismic instruments, dynamics of continuous systems, Hamilton's principle, axial vibration of rods and membranes, transverse vibration of strings, beams (BernoulliEuler and Timoshenko beam theory), and plates, traveling and standing wave solutions to motion of continuous systems, Rayleigh quotient and the RayleighRitz method to approximate natural frequencies and mode shapes of discrete and continuous systems, frequency domain solutions to dynamical systems, stability criteria for dynamical systems, and introduction to nonlinear systems and random vibration theory. Instructor: Asimaki.

CE 160 ab. Structural and Earthquake Engineering. 9 units (306); second, third terms. Matrix structural analysis of the static and dynamic response of structural systems, Newmark time integration, NewtonRaphson iteration methodology for the response of nonlinear systems, stability of iteration schemes, static and dynamic numerical analysis of planar beam structures (topics include the development of stiffness, mass, and damping matrices, material and geometric nonlinearity effects, formulation of a nonlinear 2D beam element, uniform and nonuniform earthquake loading, soilstructure interaction, 3D beam element formulation, shear deformations, and panel zone deformations in steel frames, and large deformation analysis), seismic design and analysis of steel moment frame and braced frame systems, steel member behavior (topics include bending, buckling, torsion, warping, and lateral torsional buckling, and the effects of residual stresses), reinforced concrete member behavior (topics include bending, shear, torsion, and PMM interaction), and seismic design requirements for reinforced concrete structures. Not offered 201920.

ME/CE 163. Mechanics and Rheology of FluidInfiltrated Porous Media. 9 units (306); third term. Prerequisites: Continuum MechanicsAe/Ge/ME 160 ab. This course will focus on the physics of porous materials (e.g., geomaterials, biological tissue) and their intimate interaction with interstitial fluids (e.g., water, oil, blood). The course will be split into two parts: Part 1 will focus on the continuum mechanics (balance laws) of multiphase solids, with particular attention to fluid diffusionsolid deformation coupling. Part 2 will introduce the concept of effective stresses and state of the art rheology available in modeling the constitutive response of representative porous materials. Emphasis will be placed on poroelasticity and poroplasticity. Not offered 201920.

Ae/CE 165 ab. Mechanics of Composite Materials and Structures. 9 units (225); first, second terms. Prerequisites: Ae/AM/CE/ME 102 a. Introduction and fabrication technology, elastic deformation of composites, stiffness bounds, on and offaxis elastic constants for a lamina, elastic deformation of multidirectional laminates (lamination theory, ABD matrix), effective hygrothermal properties, mechanisms of yield and failure for a laminate, strength of a single ply, failure models, splitting and delamination. Experimental methods for characterization and testing of composite materials. Design criteria, application of design methods to select a suitable laminate using composite design software, hand layup of a simple laminate and measurement of its stiffness and thermoelastic coefficients. Not offered 201920.

CE/ME/Ge 173. Mechanics of Soils. 9 units (306); second term. Prerequisites: Continuum MechanicsAe/Ge/ME 160 a. Basic principles of stiffness, deformation, effective stress and strength of soils, including sands, clays and silts. Elements of soil behavior such as stressstrainstrength behavior of clays, effects of sample disturbance, anisotropy, and strain rate; strength and compression of granular soils; consolidation theory and settlement analysis; and critical state soil mechanics. Not offered 201920.

ME/CE/Ge 174. Mechanics of Rocks. 9 units (306); third term. Prerequisites: Ae/Ge/ME 160 a. Basic principles of deformation, strength, and stressing of rocks. Elastic behavior, plasticity, viscoelasticity, viscoplasticity, creep, damage, friction, failure mechanisms, shear localization, and interaction of deformation processes with fluids. Engineering and geological applications. Not offered 201920.

CE 180. Experimental Methods in Earthquake Engineering. 9 units (153); first term. Prerequisites: AM/CE 151 abc or equivalent. Laboratory work involving calibration and performance of basic transducers suitable for the measurement of strong earthquake ground motion, and of structural response to such motion. Study of principal methods of dynamic tests of structures, including generation of forces and measurement of structural response. Not offered 201920.

CE 181 ab. Engineering Seismology. 9 units (306); second, third terms. Characteristics of potentially destructive earthquakes from the engineering point of view. Theory of seismometers, seismic waves in a continuum, plane waves in layered media, surface waves, basin waves, site effects, dynamic deformation of buildings, seismic sources, earthquake size scaling, earthquake hazard calculations, rupture dynamics. Not offered 201920.

CE 200. Advanced Work in Civil Engineering. 6 or more units as arranged; any term. A faculty mentor will oversee a student proposed, independent research or study project to meet the needs of graduate students. Graded pass/fail. The consent of a faculty mentor and a written report is required for each term.

CE 201. Advanced Topics in Civil Engineering. 9 units (306). The faculty will prepare courses on advanced topics to meet the needs of graduate students.

Ae/AM/CE/ME 214 ab. Computational Solid Mechanics. 9 units (351); second, third terms. Prerequisites: ACM 100 ab or equivalent; CE/AM/Ae 108 ab or equivalent or instructor's permission; Ae/AM/CE/ME 102 abc or Ae/Ge/ME 160 ab or instructor's permission. Introduction to the use of numerical methods in the solution of solid mechanics and multiscale mechanics problems. First term: Variational principles. Finite element analysis. Variational problems in linear and finite kinematics. Time integration, initial boundary value problems. Elasticity and inelasticity. Constitutive modeling. Error estimation. Accuracy, stability and convergence. Iterative solution methods. Adaptive strategies. Second term: Multiscale modeling strategies. Computational homogenization in linear and finite kinematics. Spectral methods. Atomistic modeling and atomistictocontinuum coupling techniques. Not offered 201920.

Ae/CE 221. Space Structures. 9 units (306); first term. This course examines the links between form, geometric shape, and structural performance. It deals with different ways of breaking up a continuum, and how this affects global structural properties; structural concepts and preliminary design methods that are used in tension structures and deployable structures. Geometric foundations, polyhedra and tessellations, surfaces; space frames, examples of space frames, stiffness and structural efficiency of frames with different repeating units; sandwich plates; cable and membrane structures, formfinding, wrinklefree pneumatic domes, balloons, tensionstabilized struts, tensegrity domes; deployable and adaptive structures, coiled rods and their applications, flexible shells, membranes, structural mechanisms, actuators, concepts for adaptive trusses and manipulators. Not offered 201920.

CE/Ge/ME 222. Earthquake Source Processes, Debris Flows, and Soil Liquefaction: Physicsbased Modeling of Failure in Granular Media. 6 units (204); third term. A seminarstyle course focusing on granular dynamics and instabilities as they relate to geophysical hazards such as fault mechanics, debris flows, and liquefaction. The course will consist of studentled presentations of active research at Caltech and discussions of recent literature. Not offered 201920.

AM/CE/ME 252. Linear and Nonlinear Waves in Structured Media. 9 units (216); second term. The course will cover the basic principles of wave propagation in solid media. It will discuss the fundamental principles used to describe linear and nonlinear wave propagation in continuum and discrete media. Selected recent scientific advancements in the dynamics of periodic media will also be discussed. Students learn the basic principles governing the propagation of waves in discrete and continuum solid media. These methods can be used to engineer materials with predefined properties and to design dynamical systems for a variety of engineering applications (e.g., vibration mitigation, impact absorption and sound insulation). The course will include an experimental component, to test wave phenomena in structured media. Instructor: Daraio.

Ae/AM/CE/ME 265 ab. Static and Dynamic Failure of Brittle Solids and Interfaces, from the Micro to the Mega. 9 units (306); first, second terms. Prerequisites: Ae/AM/CE/ME 102 abc (concurrently) or equivalent and/or instructor's permission. Linear elastic fracture mechanics of homogeneous brittle solids (e.g. geomaterials, ceramics, metallic glasses); small scale yielding concepts; experimental methods in fracture, fracture of bimaterial interfaces with applications to composites as well as bonded and layered engineering and geological structures; thinfilm and microelectronic components and systems; dynamic fracture mechanics of homogeneous engineering materials; dynamic shear dominated failure of coherent and incoherent interfaces at all length scales; dynamic rupture of frictional interfaces with application to earthquake source mechanics; allowable rupture speeds regimes and connections to earthquake seismology and the generation of Tsunamis. Instructor: Rosakis.

CE 300. Research in Civil Engineering. Hours and units by arrangement. Research in the field of civil engineering. By arrangements with members of the staff, properly qualified graduate students are directed in research.
Mechanical Engineering Courses

EE/ME 7. Introduction to Mechatronics. 6 units (231); first term. Mechatronics is the multidisciplinary design of electromechanical systems. This course is intended to give the student a basic introduction to such systems. The course will focus on the implementations of sensor and actuator systems, the mechanical devices involved and the electrical circuits needed to interface with them. The class will consist of lectures and short labs where the student will be able to investigate the concepts discussed in lecture. Topics covered include motors, piezoelectric devices, light sensors, ultrasonic transducers, and navigational sensors such as accelerometers and gyroscopes. Graded pass/fail. Instructor: George.

ME 10. Thinking Like an Engineer. 1 unit; first term. A series of weekly seminars by practicing engineers in industry and academia to introduce students to principles and techniques useful for Mechanical Engineering. The course can be used to learn more about the different areas of study within mechanical engineering. Topics will be presented at an informal, introductory level. Required for ME undergraduates. Graded pass/fail. Instructor: Andrade.

ME 11 abc. Thermal Science. 9 units (306); first, second, third terms. Prerequisites: Sophomore standing required; ME 12 abc, may be taken concurrently. An introduction to classical thermodynamics and transport with engineering applications. First and second laws; closed and open systems; properties of a pure substance; availability and irreversibility; generalized thermodynamic relations; gas and vapor power cycles; propulsion; mixtures; combustion and thermochemistry; chemical equilibrium; momentum and heat transfer including boundary layers with applications to internal and external flows. Not offered on a pass/fail basis. Instructors: Hunt, Blanquart.

ME 12 abc. Mechanics. 9 units (306); first, second, third terms. Prerequisites: Sophomore standing required; ME 11 abc, may be taken concurrently. An introduction to statics and dynamics of rigid bodies, deformable bodies, and fluids. Equilibrium of force systems, principle of virtual work, distributed force systems, friction, static analysis of rigid and deformable structures, hydrostatics, kinematics, particle dynamics, rigidbody dynamics, Euler's equations, ideal flow, vorticity, viscous stresses in fluids, dynamics of deformable systems, waves in fluids and solids. Not offered on a pass/fail basis. Instructors: Mello, Daraio, Asimaki.

ME 13/113. Mechanical Prototyping. 4 units (040); first, second, summer terms. Enrollment is limited and is based on responses to a questionnaire available in the Registrar's Office. Introduction to the technologies and practices needed to fabricate mechanical prototypes. Students will acquire the fundamental skills necessary to begin using 3D ComputerAided Design (CAD) software. Students will learn how to build parametric models of parts and assemblies and learn how to generate detailed drawings of their designs. Students will also be introduced to manual machining techniques, as well as computercontrolled prototyping technologies, such as threedimensional printing, laser cutting, and water jet cutting. Students will receive safetytraining, instruction on the theories underlying different machining methods, and handson demonstrations of machining and mechanical assembly methods. Several prototypes will be constructed using the various technologies available in the mechanical engineering machine shop. Instructor: Van Deusen.

ME 14. Design and Fabrication. 9 units (351); third term. Prerequisites: ME 12 ab, ME 13. Enrollment is limited and is based on responses to a questionnaire available in the Registrar's office. Introduction to mechanical engineering design, fabrication, and visual communication. Concepts are taught through a series of short design projects and design competitions emphasizing physical concepts. Many class projects will involve substantial use of the shop facilities, and construction of working prototypes. Not offered on a pass/fail basis. Instructors: Mello, Van Deusen.

ME 23/123. CNC Machining. 4 units (040); third, summer terms. Prerequisites: ME 13/113. Enrollment is limited and is based on responses to a questionnaire available in the Registrar's office. Introduction to computer numerical control machining. Students will learn to create Gcode and Mcode using ComputerAided Manufacturing (CAM) software; they will be instructed on how to safely prepare and operate the machine's functions; and will be taught how to implement programmed data into several different types of CNC equipment. The class will cover the parts and terminology of the equipment, fixturing materials, setting workpiece, and tool offsets. Weekly assignments will include the use of CAM software, machine operation demonstrations, and machining projects. Instructor: Staff.

ME 40. Dimensional and Data Analyses in Engineering. 9 units (306); first term. Prerequisites: Ma 1 abc. The first part of this course covers the application of symmetry and dimensional homogeneity (Buckingham Pi theorem) to engineering analysis of systems. The important role of dimensional analysis in developing empirical theories, designing experiments and computer models, and analyzing data are stressed. The second part of the course focuses on quantitative data analysis including linear regression, leastsquares, principle components, Fourier analysis, and Bayesian methods. The underlying theory is briefly covered, but the focus is on application to realworld problems encountered by mechanical engineers. Applications to uncertainty analysis and quantification are discussed. Homework will include implementation of techniques in Matlab. First offered 202021. Instructor: Colonius.

ME 50 ab. Experiments and Modeling in Mechanical Engineering. 9 units (063); second, third terms. Prerequisites: ME 11 abc, ME 12 abc, ME 13, ME 14, and programming skills at the level of ACM 11. Twoquarter course sequence covers the general theory and methods of computational fluid dynamics (CFD) and finite element analysis (FEA) with experimental laboratory methods applied to complementary engineering problems in solid, structural, and fluid mechanics. Computational procedures are discussed and applied to the analysis of steadystate, transient, and dynamic problems using a commercial software. CFD and FEA topics covered include meshing, types of elements, steady and unsteady solvers, inviscid and viscous flow, internal and external flow, drag and lift, static and dynamic mechanical loading, elastic and plastic behavior, and vibrational (modal) analysis. Fluid mechanics laboratory experiments introduce students to the operation of a water tunnel combined with laser particle image velocimetry (PIV) for quantified flow field visualization of velocity and vorticity. Solid mechanics experiments introduce students to the operation of a mechanical (axial/torsional) load frame combined with digital image correlation (DIC) and strain gage transducers for quantification and full field visualization of displacement and strain. Technical writing skills are emphasized through the generation of detailed fulllength lab reports using a scientific journal format. Instructor: Mello.

ME 72 ab. Engineering Design Laboratory. 9 units (342) first term; (180) second term. Prerequisites: ME 14. Enrollment is limited. A projectbased course in which teams of students design, fabricate, analyze, test, and operate an electromechanical device to compete against devices designed by other student teams. The class lectures and the projects stress the integration of mechanical design, sensing, engineering analysis, and computation to solve problems in engineering system design. The laboratory units of ME 72 can be used to fulfill a portion of the laboratory requirement for the EAS option. Not offered on a pass/fail basis. Instructors: Mello, Van Deusen.

CS/EE/ME 75 abc. Multidisciplinary Systems Engineering. 3 units (201), 6 units (204), or 9 units (207) first term; 6 units (231), 9 units (261), or 12 units (291) second and third terms; first, second, third terms. This course presents the fundamentals of modern multidisciplinary systems engineering in the context of a substantial design project. Students from a variety of disciplines will conceive, design, implement, and operate a system involving electrical, information, and mechanical engineering components. Specific tools will be provided for setting project goals and objectives, managing interfaces between component subsystems, working in design teams, and tracking progress against tasks. Students will be expected to apply knowledge from other courses at Caltech in designing and implementing specific subsystems. During the first two terms of the course, students will attend project meetings and learn some basic tools for project design, while taking courses in CS, EE, and ME that are related to the course project. During the third term, the entire team will build, document, and demonstrate the course design project, which will differ from year to year. Freshmen must receive permission from the lead instructor to enroll. Instructor: Burdick.

ME 90 abc. Senior Thesis, Experimental. 9 units (009); first term. Prerequisites: senior status; instructor's permission. Experimental research supervised by an engineering faculty member. The topic selection is determined by the adviser and the student and is subject to approval by the Mechanical Engineering Undergraduate Committee. First and second terms: midterm progress report and oral presentation during finals week. Third term: completion of thesis and final presentation. The second and third terms may be used to fulfill laboratory credit for EAS. Not offered on a pass/fail basis. Instructor: Minnich.

ME 100. Independent Studies in Mechanical Engineering. Units are assigned in accordance with work accomplished. A faculty mentor will oversee a student proposed, independent research or study project to meet the needs of undergraduate students. Graded pass/fail. The consent of a faculty mentor and a written report is required for each term of work.

Ae/APh/CE/ME 101 abc. Fluid Mechanics. 9 units (306); first, second, third terms. Prerequisites: APh 17 or ME 11 abc, and ME 12 or equivalent, ACM 95/100 or equivalent (may be taken concurrently). Fundamentals of fluid mechanics. Microscopic and macroscopic properties of liquids and gases; the continuum hypothesis; review of thermodynamics; general equations of motion; kinematics; stresses; constitutive relations; vorticity, circulation; Bernoulli's equation; potential flow; thinairfoil theory; surface gravity waves; buoyancydriven flows; rotating flows; viscous creeping flow; viscous boundary layers; introduction to stability and turbulence; quasi onedimensional compressible flow; shock waves; unsteady compressible flow; and acoustics. Instructors: Austin, Colonius.

Ae/AM/CE/ME 102 abc. Mechanics of Structures and Solids. 9 units (306); first, second, third terms. Prerequisites: ME 12 abc. Introduction to continuum mechanics: kinematics, balance laws, constitutive laws with an emphasis on solids. Static and dynamic stress analysis. Two and threedimensional theory of stressed elastic solids. Wave propagation. Analysis of rods, plates and shells with applications in a variety of fields. Variational theorems and approximate solutions. Elastic stability. Instructors: Lapusta, Bhattacharya, Pellegrino.

E/ME/MedE 105 ab. Design for Freedom from Disability. 9 units (306); terms to be arranged. This Product Design class focuses on people with Disabilities and is done in collaboration with Rancho Los Amigos National Rehabilitation Center. Students visit the Center to define products based upon actual stated and observed needs. Designs and testing are done in collaboration with Rancho associates. Speakers include people with assistive needs, therapists and researchers. Classes teach normative design methodologies as adapted for this special area. Instructor: TBD.

ME/EE/EST 109. Energy Technology and Policy. 9 units (306); first term. Prerequisites: Ph 1 abc, Ch 1 ab and Ma 1 abc. Energy technologies and the impact of government policy. Fossil fuels, nuclear power, and renewables for electricity production and transportation. Resource models and climate change policies. New and emerging technologies. Instructor: Blanquart.

ME 110. Special Laboratory Work in Mechanical Engineering. 39 units per term; maximum two terms. Special laboratory work or experimental research projects may be arranged by members of the faculty to meet the needs of individual students as appropriate. A written report is required for each term of work. Instructor: Staff.

CE/ME 112 ab. Hydraulic Engineering. 9 units (306); second, third terms. Prerequisites: ME 11 abc, ME 12 abc; ACM 95/100 or equivalent (may be taken concurrently). A survey of topics in hydraulic engineering: open channel and pipe flow, subcritical/critical flow and the hydraulic jump, hydraulic structures (weirs, inlet and outlet works, dams), hydraulic machinery, hydrology, river and flood modeling, solute transport, sediment mechanics, groundwater flow. Not offered 201920.

ME 115 ab. Introduction to Kinematics and Robotics. 9 units (306); second, third terms. Prerequisites: Ma 2, ACM 95/100 ab recommended. Introduction to the study of planar, rotational, and spatial motions with applications to robotics, computers, computer graphics, and mechanics. Topics in kinematic analysis will include screw theory, rotational representations, matrix groups, and Lie algebras. Applications include robot kinematics, mobility in mechanisms, and kinematics of open and closed chain mechanisms. Additional topics in robotics include path planning for robot manipulators, dynamics and control, and assembly. Course work will include laboratory demonstrations using simple robot manipulators. Not offered 201920.

MS/ME/MedE 116. Mechanical Behavior of Materials. 9 units (306); second term. Introduction to the mechanical behavior of solids, emphasizing the relationships between microstructure, architecture, defects, and mechanical properties. Elastic, inelastic, and plastic properties of crystalline and amorphous materials. Relations between stress and strains for different types of materials. Introduction to dislocation theory, motion and forces on dislocations, strengthening mechanisms in crystalline solids. Nanomaterials: properties, fabrication, and mechanics. Architected solids: fabrication, deformation, failure, and energy absorption. Biomaterials: mechanical properties of composites, multiscale microstructure, biological vs. synthetic, shear lag model. Fracture in brittle solids and linear elastic fracture mechanics. Instructor: Greer.

Ae/ME 118. Classical Thermodynamics. 9 units (306); first term. Prerequisites: ME 11 abc, ME 12, or equivalent. Fundamentals of classical thermodynamics. Basic postulates and laws of thermodynamics, work and heat, entropy and available work, and thermal systems. Equations of state, compressibility functions, and the Law of Corresponding States. Thermodynamic potentials, chemical and phase equilibrium, phase transitions, and thermodynamic properties of solids, liquids, and gases. Examples will be drawn from fluid dynamics, solid mechanics, and thermal science applications. Instructor: Dimotaki.

ME 119 ab. Heat and Mass Transfer. 9 units (306); second, third terms. Prerequisites: ME 11 abc, ME 12 abc, ACM 95/100 (may be taken concurrently). Transport properties, conservation equations, conduction heat transfer, convective heat and mass transport in laminar and turbulent flows, phase change processes, thermal radiation. Not offered 201920.

Ae/ME 120 ab. Combustion Fundamentals. 9 units (306); second, third terms. Prerequisites: ME 119 a or equivalent. The course will cover thermodynamics of pure substances and mixtures, equations of state, chemical equilibrium, chemical kinetics, combustion chemistry, transport phenomena, and the governing equations for multicomponent gas mixtures. Topics will be chosen from nonpremixed and premixed flames, the fluid mechanics of laminar flames, flame mechanisms of combustiongenerated pollutants, and numerical simulations of multicomponent reacting flows. Not offered 201920.

ME/CS/EE 129. Experimental Robotics. 9 units (360); first term. This course covers the foundations of experimental realization on robotic systems. This includes software infrastructures, e.g., robotic operating systems (ROS), sensor integration, and implementation on hardware platforms. The ideas developed will be integrated onto robotic systems and tested experimentally in the context of class projects. Instructor: Staff.

ME/CS/EE 133 abc. Robotics. 9 units (333); first, second, third terms. Prerequisites: ME/CS/EE 129, may be taken concurrently, or with permission of instructor. The course focuses on current topics in robotics research in the area of robotic manipulation and sensing. Past topics have included advanced manipulator kinematics, grasping and dexterous manipulation using multifingered hands, and advanced obstacle avoidance and motion planning algorithms. Additional topics include robotics research in the area of autonomous navigation and vision. Including mobile robots, multilegged walking machines, use of vision in navigation systems. The lectures will be divided between a review of the appropriate analytical techniques and a survey of the current research literature. Course work will focus on an independent research project chosen by the student. Not offered 201920.

ME/CS/EE 134. Robotic Systems. 9 units (360); second term. Prerequisites: ME/CS/EE 129, may be taken concurrently, or with permission of instructor. This course covers the basics of robotic systems at the intersection of computer vision, machine learning and control. It includes selected topics from each of these domains, and their integration points. The lectures will be accompanied by a project that will integrate these ideas on hardware, including building a custom robotic, with the end result being a final demonstration of the concepts studied in the course. Instructor: Staff.

AM/CE/ME 150 abc. Graduate Engineering Seminar. 1 unit; first, second, third terms. Students attend a graduate seminar each week of each term and submit a report about the attended seminars. At least four of the attended seminars each term should be from the Mechanical and Civil Engineering seminar series. Students not registered for the M.S. and Ph.D. degrees must receive the instructor's permission. Graded pass/fail. Instructor: Staff.

Ae/Ge/ME 160 ab. Continuum Mechanics of Fluids and Solids. 9 units (306); first, second terms. Elements of Cartesian tensors. Configurations and motions of a body. Kinematicsstudy of deformations, rotations and stretches, polar decomposition. Lagrangian and Eulerian strain velocity and spin tensor fields. Irrotational motions, rigid motions. Kineticsbalance laws. Linear and angular momentum, force, traction stress. Cauchy's theorem, properties of Cauchy's stress. Equations of motion, equilibrium equations. Power theorem, nominal (PiolaKirchoff) stress. Thermodynamics of bodies. Internal energy, heat flux, heat supply. Laws of thermodynamics, notions of entropy, absolute temperature. Entropy inequality (ClausiusDuhem). Examples of special classes of constitutive laws for materials without memory. Objective rates, corotational, convected rates. Principles of materials frame indifference. Examples: the isotropic NavierStokes fluid, the isotropic thermoelastic solid. Basics of finite differences, finite elements, and boundary integral methods, and their applications to continuum mechanics problems illustrating a variety of classes of constitutive laws. Instructors: Lapusta, Ortiz.

MS/ME 161. Imperfections in Crystals. 9 units (306); third term. Prerequisites: graduate standing or MS 115. The relation of lattice defects to the physical and mechanical properties of crystalline solids. Introduction to point imperfections and their relationships to transport properties in metallic, covalent, and ionic crystals. KroegerVink notation. Introduction to dislocations: geometric, crystallographic, elastic, and energetic properties of dislocations. Dislocation reactions and interactions including formation of locks, stacking faults, and surface effects. Relations between collective dislocation behavior and mechanical properties of crystals. Introduction to computer simulations of dislocations. Grain boundaries. The structure and properties of interfaces in solids. Emphasis on materials science aspects of role of defects in electrical, morphological, optical, and mechanical properties of solids. Not offered 201920.

ME/CE 163. Mechanics and Rheology of FluidInfiltrated Porous Media. 9 units (306); third term. Prerequisites: Continuum MechanicsAe/Ge/ME 160 ab. This course will focus on the physics of porous materials (e.g., geomaterials, biological tissue) and their intimate interaction with interstitial fluids (e.g., water, oil, blood). The course will be split into two parts: Part 1 will focus on the continuum mechanics (balance laws) of multiphase solids, with particular attention to fluid diffusionsolid deformation coupling. Part 2 will introduce the concept of effective stresses and state of the art rheology available in modeling the constitutive response of representative porous materials. Emphasis will be placed on poroelasticity and poroplasticity. Not offered 201920.

AM/ME 165. Finite Elasticity. 9 units (306); third term. Prerequisites: Ae/Ge/ME 160 a. Finite theory of elasticity: constitutive theory, semiinverse methods. Variational methods. Applications to problems of current interest. Not offered 201920.

MS/ME 166. Fracture of Brittle Solids. 9 units (306); third term. Prerequisites: MS 115 a (or equivalent). The mechanical response of brittle materials (ceramics, glasses and some network polymers) will be treated using classical elasticity, energy criteria, and fracture mechanics. The influence of environment and microstructure on mechanical behavior will be explored. Transformation toughened systems, largegrain crackbridging systems, nanostructured ceramics, porous ceramics, anomolous glasses, and the role of residual stresses will be highlighted. Strength, flaw statistics and reliability will be discussed. Instructor: Faber.

CE/ME/Ge 173. Mechanics of Soils. 9 units (306); second term. Prerequisites: Continuum MechanicsAe/Ge/ME 160 a. Basic principles of stiffness, deformation, effective stress and strength of soils, including sands, clays and silts. Elements of soil behavior such as stressstrainstrength behavior of clays, effects of sample disturbance, anisotropy, and strain rate; strength and compression of granular soils; consolidation theory and settlement analysis; and critical state soil mechanics. Not offered 201920.

ME/CE/Ge 174. Mechanics of Rocks. 9 units (306); third term. Prerequisites: Ae/Ge/ME 160 a. Basic principles of deformation, strength, and stressing of rocks. Elastic behavior, plasticity, viscoelasticity, viscoplasticity, creep, damage, friction, failure mechanisms, shear localization, and interaction of deformation processes with fluids. Engineering and geological applications. Not offered 201920.

ME 200. Advanced Work in Mechanical Engineering. A faculty mentor will oversee a student proposed, independent research or study project to meet the needs of graduate students Graded pass/fail. The consent of a faculty mentor and a written report is required for each term of work.

ME 201. Advanced Topics in Mechanical Engineering. 9 units (306); first, third terms. The faculty will prepare courses on advanced topics to meet the needs of graduate students. Instructor: Minnich.

ME 202 abc. Engineering TwoPhase Flows. 9 units (306). Prerequisites: ACM 95/100 ab, Ae/APh/CE/ME 101 abc, or equivalents. Selected topics in engineering twophase flows with emphasis on practical problems in modern hydrosystems. Fundamental fluid mechanics and heat, mass, and energy transport in multiphase flows. Liquid/vapor/gas (LVG) flows, nucleation, bubble dynamics, cavitating and boiling flows, models of LVG flows; instabilities, dynamics, and wave propagation; fluid/structure interactions. Discussion of twophase flow problems in conventional, nuclear, and geothermal power plants, marine hydrofoils, and other hydraulic systems. Not offered 201920.

Ae/AM/MS/ME 213. Mechanics and Materials Aspects of Fracture. 9 units (306); first term. Prerequisites: Ae/AM/CE/ME 102 abc (concurrently) or equivalent and instructor's permission. Analytical and experimental techniques in the study of fracture in metallic and nonmetallic solids. Mechanics of brittle and ductile fracture; connections between the continuum descriptions of fracture and micromechanisms. Discussion of elasticplastic fracture analysis and fracture criteria. Special topics include fracture by cleavage, void growth, rate sensitivity, crack deflection and toughening mechanisms, as well as fracture of nontraditional materials. Fatigue crack growth and life prediction techniques will also be discussed. In addition, "dynamic" stress wave dominated, failure initiation growth and arrest phenomena will be covered. This will include traditional dynamic fracture considerations as well as discussions of failure by adiabatic shear localization. Not offered 201920.

Ae/AM/CE/ME 214 ab. Computational Solid Mechanics. 9 units (351); second, third terms. Prerequisites: ACM 100 ab or equivalent; CE/AM/Ae 108 ab or equivalent or instructor's permission; Ae/AM/CE/ME 102 abc or Ae/Ge/ME 160 ab or instructor's permission. Introduction to the use of numerical methods in the solution of solid mechanics and multiscale mechanics problems. First term: Variational principles. Finite element analysis. Variational problems in linear and finite kinematics. Time integration, initial boundary value problems. Elasticity and inelasticity. Constitutive modeling. Error estimation. Accuracy, stability and convergence. Iterative solution methods. Adaptive strategies. Second term: Multiscale modeling strategies. Computational homogenization in linear and finite kinematics. Spectral methods. Atomistic modeling and atomistictocontinuum coupling techniques. Not offered 201920.

Ae/AM/ME 215. Dynamic Behavior of Materials. 9 units (306); third term. Prerequisites: ACM 100 abc or AM 125 abc; Ae/AM/CE/ME 102 abc. Fundamentals of theory of wave propagation; plane waves, wave guides, dispersion relations; dynamic plasticity, adiabatic shear banding; dynamic fracture; shock waves, equation of state. Instructor: Ravichandran.

Ae/ME 218. Statistical Mechanics. 9 units (306); third term. Prerequisites: Ae/ME 118, or equivalent. Overview of probability and statistics, and the MaxwellBoltzmann distribution. Overview and elements of Quantum Mechanics, degenerate energy states, particles in a box, and energystate phase space. Statistics of indistinguishable elementary particles, FermiDirac and BoseEinstein statistics, partition functions, connections with classical thermodynamics, and the Law of Equipartition. Examples from equilibrium in fluids, solidstate physics, and others. Instructor: Dimotakis.

CE/Ge/ME 222. Earthquake Source Processes, Debris Flows, and Soil Liquefaction: Physicsbased Modeling of Failure in Granular Media. 6 units (204); third term. A seminarstyle course focusing on granular dynamics and instabilities as they relate to geophysical hazards such as fault mechanics, debris flows, and liquefaction. The course will consist of studentled presentations of active research at Caltech and discussions of recent literature. Not offered 201920.

Ae/AM/ME 223. Plasticity. 9 units (306); second term. Prerequisites: Ae/AM/CE/ME 102 abc or instructor's permission. Theory of dislocations in crystalline media. Characteristics of dislocations and their influence on the mechanical behavior in various crystal structures. Application of dislocation theory to single and polycrystal plasticity. Theory of the inelastic behavior of materials with negligible time effects. Experimental background for metals and fundamental postulates for plastic stressstrain relations. Variational principles for incremental elasticplastic problems, uniqueness. Upper and lower bound theorems of limit analysis and shakedown. Slip line theory and applications. Additional topics may include soils, creep and ratesensitive effects in metals, the thermodynamics of plastic deformation, and experimental methods in plasticity. Instructor: Andrade.

Ae/AM/ME/Ge 225. Special Topics in Solid Mechanics. Units to be arranged; first, second, third terms. Subject matter changes depending on staff and student interest.

Ae/ACM/ME 232 ab. Computational Fluid Dynamics. 9 units (306); first, second terms. Prerequisites: Ae/APh/CE/ME 101 abc or equivalent; ACM 100 abc or equivalent. Development and analysis of algorithms used in the solution of fluid mechanics problems. Numerical analysis of discretization schemes for partial differential equations including interpolation, integration, spatial discretization, systems of ordinary differential equations; stability, accuracy, aliasing, Gibbs and Runge phenomena, numerical dissipation and dispersion; boundary conditions. Survey of finite difference, finite element, finite volume and spectral approximations for the numerical solution of the incompressible and compressible Euler and NavierStokes equations, including shockcapturing methods. Instructors: Colonius, Meiron.

Ae/CDS/ME 251 ab. Closed Loop Flow Control. 9 units (306 a, 161 b); second, third term. Prerequisites: ACM 100 abc, Ae/APh/CE/ME 101 abc or equivalent. This course seeks to introduce students to recent developments in theoretical and practical aspects of applying control to flow phenomena and fluid systems. Lecture topics in the second term drawn from: the objectives of flow control; a review of relevant concepts from classical and modern control theory; highfidelity and reducedorder modeling; principles and design of actuators and sensors. Third term: laboratory work in open and closedloop control of boundary layers, turbulence, aerodynamic forces, bluff body drag, combustion oscillations and flowacoustic oscillations. Not offered 201920.

AM/CE/ME 252. Linear and Nonlinear Waves in Structured Media. 9 units (216); second term. The course will cover the basic principles of wave propagation in solid media. It will discuss the fundamental principles used to describe linear and nonlinear wave propagation in continuum and discrete media. Selected recent scientific advancements in the dynamics of periodic media will also be discussed. Students learn the basic principles governing the propagation of waves in discrete and continuum solid media. These methods can be used to engineer materials with predefined properties and to design dynamical systems for a variety of engineering applications (e.g., vibration mitigation, impact absorption and sound insulation). The course will include an experimental component, to test wave phenomena in structured media. Instructor: Daraio.

ME/MS 260. Micromechanics. 9 units (306); third term. Prerequisites: ACM 95/100 or equivalent, and Ae/AM/CE/ME 102 abc or Ae 160 abc or instructor's permission. The course gives a broad overview of micromechanics, emphasizing the microstructure of materials, its connection to molecular structure, and its consequences on macroscopic properties. Topics include phase transformations in crystalline solids, including martensitic, ferroelectric, and diffusional phase transformations, twinning and domain patterns, active materials; effective properties of composites and polycrystals, linear and nonlinear homogenization; defects, including dislocations, surface steps, and domain walls; thin films, asymptotic methods, morphological instabilities, selforganization; selected applications to microactuation, thinfilm processing, composite materials, mechanical properties, and materials design. Open to undergraduates with instructor's permission. Not offered 201920.

Ae/AM/CE/ME 265 ab. Static and Dynamic Failure of Brittle Solids and Interfaces, from the Micro to the Mega. 9 units (306); first, second terms. Prerequisites: Ae/AM/CE/ME 102 abc (concurrently) or equivalent and/or instructor's permission. Linear elastic fracture mechanics of homogeneous brittle solids (e.g. geomaterials, ceramics, metallic glasses); small scale yielding concepts; experimental methods in fracture, fracture of bimaterial interfaces with applications to composites as well as bonded and layered engineering and geological structures; thinfilm and microelectronic components and systems; dynamic fracture mechanics of homogeneous engineering materials; dynamic shear dominated failure of coherent and incoherent interfaces at all length scales; dynamic rupture of frictional interfaces with application to earthquake source mechanics; allowable rupture speeds regimes and connections to earthquake seismology and the generation of Tsunamis. Instructor: Rosakis.

ME/Ge/Ae 266 ab. Dynamic Fracture and Frictional Faulting. 9 units (306); third term. Prerequisites: Ae/AM/CE/ME 102 abc or Ae/Ge/ME 160 ab or instructor's permission. Introduction to elastodynamics and waves in solids. Dynamic fracture theory, energy concepts, cohesive zone models. Friction laws, nucleation of frictional instabilities, dynamic rupture of frictional interfaces. Radiation from moving cracks. Thermal effects during dynamic fracture and faulting. Crack branching and faulting along nonplanar interfaces. Related dynamic phenomena, such as adiabatic shear localization. Applications to engineering phenomena and physics and mechanics of earthquakes. Instructor: Lapusta.

ME 300. Research in Mechanical Engineering. Hours and units by arrangement. Research in the field of mechanical engineering. By arrangement with members of the faculty, properly qualified graduate students are directed in research.