The online version of the Caltech Catalog is provided as a convenience; however, the printed version is the only authoritative source of information about course offerings, option requirements, graduation requirements, and other important topics. AEROSPACEAe 100. Research in Aerospace. Units to be arranged in accordance with work accomplished. Open to suitably qualified undergraduates and firstyear graduate students under the direction of the staff. Credit is based on the satisfactory completion of a substantive research report, which must be approved by the Ae 100 adviser and by the option representative. 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. Instructor: Pullin, Austin. Ae/AM/CE/ME 102 abc. Mechanics of Structures and Solids. 9 units (306); first, second, third terms. Prerequisite: ME 35 abc or equivalent. Static and dynamic stress analysis. Two and threedimensional theory of stressed elastic solids. Analysis of structural elements with applications in a variety of fields. Variational theorems and approximate solutions, finite elements. A variety of special topics will be discussed in the third term such as, but not limited to, elastic stability, wave propagation, and introductory fracture mechanics. Instructors: Kochmann, Ravichandran, Bhattacharya. Ae/APh 104 abc. Experimental Methods. 9 units (306) first term; (063) second, third terms. Prerequisites: ACM 95/100 ab or equivalent (may be taken concurrently), Ae/APh/CE/ME 101 abc or equivalent (may be taken concurrently). Lectures on experiment design and implementation. Measurement methods, transducer fundamentals, instrumentation, optical systems, signal processing, noise theory, analog and digital electronic fundamentals, with data acquisition and processing systems. Experiments (second and third terms) in solid and fluid mechanics with emphasis on current research methods. Instructor: McKeon. Ae 105 abc. Aerospace Engineering. 9 units (306); first, second, third terms. Prerequisites: ME 11 abc and ME 12 abc or equivalent. Part a: Introduction to spacecraft systems and subsystems, mission design, fundamentals of orbital and rocket mechanics, launch vehicles and space environments; JPLassisted design exercise; spacecraft mechanical, structural, and thermal design; numerical modeling, test validation. Part b: Introduction to guidance, navigation, and control (GNC), measurement systems, Kalman filtering, system analysis, simulation, statistical error analysis, case studies of GNC applications; preliminary discussion and setup for team project leading to system requirements review. Part c: Team project leading to preliminary design review and critical design review. Instructors: Davis, Freeman, Scharf. CE/Ae/AM 108 ab. Computational Mechanics. 9 units (306). For course description, see Civil Engineering. Ae 115 ab. Spacecraft Navigation. 9 units (306); first, second terms. Prerequisite: CDS 110 a. This course will survey all aspects of modern spacecraft navigation, including astrodynamics, tracking systems for both lowEarth and deepspace applications (including the Global Positioning System and the Deep Space Network observables), and the statistical orbit determination problem (in both the batch and sequential Kalman filter implementations). The course will describe some of the scientific applications directly derived from precision orbital knowledge, such as planetary gravity field and topography modeling. Numerous examples drawn from actual missions as navigated at JPL will be discussed. Not offered 2015–16. APh/Ph/Ae 116. Physics of Thermal and Mass Transport in Hydrodynamic Systems. 12 units (309), second term. For course description, see Applied Physics. 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. Not offered 2015–2016. Ae/ME 120 ab. Combustion Fundamentals. 9 units (306); second, third terms. Prerequisite: 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 2015–2016. Ae 121 abc. Space Propulsion. 9 units (306); each term. Open to all graduate students and to seniors with instructor’s permission. Ae 121 is designed to introduce the fundamentals of chemical, electric and advanced propulsion technologies. The course focuses on the thermochemistry and aerodynamics of chemical and electrothermal propulsion systems, the physics of ionized gases and electrostatic and electromagnetic processes in electric thrusters. These analyses provide the opportunity to introduce the basic concepts of nonequilibrium gas dynamics and kinetic theory. Specific technologies such as launch vehicle rocket engines, monopropellant engines, arcjets, ion thrusters, magnetoplasmadynamic engines and Hall thrusters will be discussed. Ae 121 also provides an introduction to advanced propulsion concepts such as solar sails and antimatter rockets. Instructor: Polk. Ae 150 abc. Aerospace Engineering Seminar. 1 unit; first, second, third terms. Speakers from campus and outside research and manufacturing organizations discuss current problems and advances in aerospace engineering. Graded pass/fail. Instructor: McKeon. EE/Ae 157 ab. Introduction to the Physics of Remote Sensing. 9 units (306); first, second terms. For course description, see Electrical Engineering. Ae 159. Space Optical System Engineering. 9 units (306); third term. Prerequisites: Ph 2, EE/Ae 157, or equivalent; APh 23 desirable. Introduction to optical system engineering for remote sensing from space will be presented. Endtoend optical systems are discussed within the framework of the 10 scientific/technical disciplines required to build a successful system: optical engineering, physical optics of materials, solidstate physics/detectors, mechanics and mechanisms engineering, wavefront sensing and control, structures and dynamics, thermal engineering, spacecraft engineering, psychology of vision and software processing of images, and endtoend system validation and calibration. Emphasis will be on the development of optical engineering tools. Instructor: Breckinridge. 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. Kinematics—study of deformations, rotations and stretches, polar decomposition. Lagrangian and Eulerian strain velocity and spin tensor fields. Irrotational motions, rigid motions. Kinetics—balance 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. Instructor: Kochmann. Ae/CE 165 ab. Mechanics of Composite Materials and Structures. 9 units (225); first, second terms. Prerequisite: Ae/AM/CE/ME 102 a or ME 65. 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. Pellegrino. Ae 200. Advanced Research in Aerospace. Units to be arranged. Ae.E. or Ph.D. thesis level research under the direction of the staff. A written research report must be submitted during finals week each term. Ae 201 ab. Advanced Fluid Mechanics. 9 units (306); first, second terms. Prerequisites: Ae/APh/CE/ME 101 abc or equivalent; AM 125 abc or ACM 101 (may be taken concurrently). Foundations of the mechanics of real fluids. Basic concepts will be emphasized. Subjects covered will include a selection from the following topics: physical properties of real gases; the equations of motion of viscous and inviscid fluids; the dynamical significance of vorticity; vortex dynamics; exact solutions; motion at high Reynolds numbers; hydrodynamic stability; boundary layers; flow past bodies; compressible flow; subsonic, transonic, and supersonic flow; shock waves. Instructors: Pullin, Meiron. Ae 204. Technical Fluid Mechanics. 9 units (306); first term. Prerequisite: Ae/APh/CE/ME 101 abc or equivalent. External and internal flow problems encountered in engineering, for which only empirical methods exist. Turbulent shear flow, separation, transition, threedimensional and nonsteady effects. Basis of engineering practice in the design of devices such as mixers, ejectors, diffusers, and control valves. Studies of flowinduced oscillations, wind effects on structures, vehicle aerodynamics. Not offered 2015–16. Ae 205 ab. Advanced Space Project. 9 units (243); second, third terms. Prerequisites: Ae105 abc. This is an advanced course on the design and implementation of space projects and it is currently focused on the flight project Autonomous Assembly of a Reconfigurable Space Telescope (AAReST). The objective is to be ready for launch and operation in 2015. Each student will be responsible for a specific activity, chosen from the following: optimization of telescope system architecture; design, assembly and testing of telescope optics; telescope calibration procedure and algorithms for wavefront control; thermal analysis; boom design and deployment test methods; effects of spacecraft dynamics on telescope performance; environmental testing of telescope system. Each student will prepare a survey of the state of the art for the selected activity, and then develop a design/implementation plan, execute the plan and present the results in a final report. Instructor: Pellegrino. Ae 208 abc. GALCIT Colloquium. 1 unit; first, second, third terms. A seminar course in fluid, solid, space, and bio mechanics. Weekly lectures on current developments are presented by staff members, graduate students, and visiting scientists and engineers. Graded pass/fail. Instructors: Kochmann, Austin. Note: The following courses, with numbers greater than 209, are one, two, or threeterm courses offered to interested students. Depending on conditions, some of the courses may be taught as tutorials or reading courses, while others may be conducted more formally. Ae/AM/MS/ME 213. Mechanics and Materials Aspects of Fracture. 9 units (306); second 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. Instructor: Ortiz. Ae/AM/CE/ME 214 abc. Computational Solid Mechanics. 9 units (306); first, second, third terms. Prerequisites: AM 125 abc or equivalent; ACM 100 abc or equivalent; CE/AM/Ae 108 abc or equivalent or instructor’s permission; Ae/AM/CE/ME 102 abc or equivalent; Ae/Ge/ME 160 ab desirable or taken concurrently. Introduction to the use of numerical methods in the solution of solid mechanics and materials problems. First term: geometrical representation of solids. Automatic meshing. Approximation theory. Interpolation error estimation. Optimal and adaptive meshing. Second term: variational principles in linear elasticity. Finite element analysis. Error estimation. Convergence. Singularities. Adaptive strategies. Constrained problems. Mixed methods. Stability and convergence. Variational problems in nonlinear elasticity. Consistent linearization. The NewtonRahpson method. Bifurcation analysis. Adaptive strategies in nonlinear elasticity. Constrained finite deformation problems. Contact and friction. Third term: time integration. Algorithm analysis. Accuracy, stability, and convergence. Operator splitting and product formulas. Coupled problems. Impact and friction. Subcycling. Spacetime methods. Inelastic solids. Constitutive updates. Stability and convergence. Consistent linearization. Applications to finite deformation viscoplasticity, viscoelasticity, and Lagrangian modeling of fluid flows. Not offered 2015–16. Ae/AM/ME 215. Dynamic Behavior of Materials. 9 units (306); second 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. Not offered 2015–16. Ae/ME 218. Statistical Mechanics. 306; second term. Prerequisites: Ae/ME118, 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. Not offered 2015–2016. Ae 220. Theory of Structures. 9 units (306); first term. Prerequisite: Ae/AM/CE/ME 102 abc. Fundamentals of buckling and stability, total potential energy and direct equilibrium approaches; classification of instabilities into snapthrough type and bifurcation type; rigidelastic structures, eigenvalues, and eigenvectors of stiffness matrix; elastic structures; approximate estimates of buckling load; Rayleigh quotient; lateral buckling of columns: Euler strut, imperfections, Southwell plot, beamcolumns, stability coefficients, buckling of frames; elastoplastic buckling: tangentmodulus, doublemodulus, Shanley’s analysis; lateraltorsional buckling of beams; buckling of plates; buckling of cylindrical shells. Not offered 2015–16. 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 2015–2016. Ae/AM/ME 223. Plasticity. 9 units (306); third term. Prerequisite: 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: Ortiz. Ae/AM/ME 225. Special Topics in Solid Mechanics. Units to be arranged; first, second, third terms. Subject matter changes depending upon staff and student interest. (1) Stress Waves in Solids. 9 units (306); second term. Stress waves will be introduced by considering plane waves which allow the principal features of stress wave propagation to be explored without introducing the geometric complexities of waves in 3D. Formulation will include elastic materials and dissipative materials that are modeled as viscoelastic or viscoplastic. For elastic materials, we will consider waves in unbounded anisotropic media, refraction at plane boundaries, surface waves, wave guides, phase velocity and group velocity, waves in periodic media, energy transport, and diffraction. For dissipative materials, we will consider frequency dependent attenuation, elastic precursor decay, and nonlinear waves in 1D. Examples, and opportunities to explore more advanced topics, will be chosen to try to respond to student interests. Not offered 2015–2016. Ae 228. Computational Mechanics Simulations Using Particles. 9 units (306); second term. Prerequisites: Ae/AM/CE/ME 214 or equivalent or Ae/ACM/ME 232 or equivalent, ACM 104, ACM 105, or equivalent.Particle simulations of continuum and discrete systems. Advances in molecular, mesoscopic, and macroscale simulations using particles, identification of common computing paradigms and challenges across disciplines, discretizations and representations using particles, fast summation algorithms, time integrators, constraints, and multiresolution. Exercises will draw on problems simulated using particles from diverse areas such as fluid and solid mechanics, computer graphics, and nanotechnology. Not offered 2015–16. 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. Not offered 2015–2016. Ae 233. Hydrodynamic Stability. 9 units (306); third term. Prerequisite: Ae/APh/CE/ME 101 abc or equivalent. Laminarstability theory as a guide to laminarturbulent transition. Rayleigh equation, instability criteria, and response to small inviscid disturbances. Discussion of KelvinHelmholtz, RayleighTaylor, RichtmyerMeshkov, and other instabilities, for example, in geophysical flows. The OrrSommerfeld equation, the dual role of viscosity, and boundarylayer stability. Modern concepts such as pseudomomentum conservation laws and nonlinear stability theorems for 2D and geophysical flows. Weakly nonlinear stability theory and phenomenological theories of turbulence. Not offered 2015–2016. Ae 234. Hypersonic Aerodynamics. 9 units (306); first term. Prerequisites: Ae/APh/CE/ME 101 abc or equivalent, AM 125 abc, or instructor’s permission. An advanced course dealing with aerodynamic problems of flight at hypersonic speeds. Topics are selected from hypersonic smalldisturbance theory, bluntbody theory, boundary layers and shock waves in real gases, heat and mass transfer, testing facilities and experiment. Not offered 2015–16. Ae 235. Rarefied Gasdynamics. 9 units (306); third term. Molecular description of matter; distribution functions; discretevelocity gases. Kinetic theory: freepath theory, internal degrees of freedom. Boltzmann equation: BBGKY hierarchy and closure, H theorem, Euler equations, ChapmanEnskog procedure, freemolecule flows. Collisionless and transitional flows. Direct simulation Monte Carlo methods. Applications. Not offered 2015–16. Ae 237 a. Nonsteady Gasdynamics. 9 units (306); second term. Part a: dynamics of shock waves, expansion waves, and related discontinuities in gases. Adiabatic phasetransformation waves. Interaction of waves in one and twodimensional flows. Boundary layers and shock structure. Applications and shock tube techniques. Part b: shock and detonation waves in solids and liquids. Equations of state for hydrodynamic computations in solids, liquids, and explosive reaction products. CJ and ZND models of detonation in solids and liquids. Propagation of shock waves and initiation of reaction in explosives. Interactions of detonation waves with water and metals. Not offered 2015–16. Ae 239 ab. Turbulence. 9 units (306); second, third terms. Prerequisites: Ae/APh/CE/ME 101 abc; AM 125 abc or ACM 101. Reynolds averaged equations and the problem of closure. Statistical description of turbulence. Homogeneous isotropic turbulence and structure of fine scales. Turbulent shear flows. Physical and spectral models. Subgridscale modeling. Turbulent mixing. Structure of low and high Reynolds number wall turbulence. Instructor: Dimotakis. Ae 240. Special Topics in Fluid Mechanics. Units to be arranged; first, second, third terms. Subject matter changes depending upon staff and student interest. (1) Educational exchange at Ecole Polytechnique. Students participating in the Ecole Polytechnique educational exchange must register for 36 units while they are on detached duty at Ecole Polytechnique. For further information refer to the graduate option information for Aerospace. Instructor: McKeon. Ae 241. Special Topics in Experimental Fluid and Solid Mechanics. Prerequisite: Ae/APh 104 or equivalent or instructor’s permission. Units to be arranged; first, second, third terms. Subject matter changes depending upon staff and student interest. Ae/BE 242. Biological Flows: Propulsion. 9 units (306); third term. Prerequisite: Ae/APh/CE/ME 101 abc or equivalent or ChE 103 a. Physical principles of unsteady fluid momentum transport: equations of motion, dimensional analysis, conservation laws. Unsteady vortex dynamics: vorticity generation and dynamics, vortex dipoles/rings, wake structure in unsteady flows. Life in moving fluids: unsteady drag, addedmass effects, virtual buoyancy, bounding and schooling, wake capture. Thrust generation by flapping, undulating, rowing, jetting. Low Reynolds number propulsion. Bioinspired design of propulsion devices. Not offered 2015–2016. MedE/BE/Ae 243. Biological Flows: Transport and Circulatory Systems. 9 units (306); second term. For course description, see Medical Engineering. Ae 244. Mechanics of Nanomaterials. 9 units (306); second term. Basics of the mechanics of nanomaterials, including the physical and chemical synthesis/processing techniques for creating nanostructures and their relation with mechanical and other structural properties.Overview of the properties of various types of nanomaterials including nanostructured metals/ceramics/composites, nanowires, carbon nanotubes, quantum dots, nanopatterns, selfassembled colloidal crystals, magnetic nanomaterials, and biorelated nanomaterials. Innovative experimental methods and microstructural characterization developed for studying the mechanics at the nanoscale will be described. Recent advances in the application of nanomaterials in engineering systems and patentrelated aspects of nanomaterials will also be covered. Open to undergraduates with instructor’s permission. Not offered 2015–16. Ae/CDS/ME 251 ab. Closed Loop Flow Control. 9 units; (306 a, 161 b); second, third term. Prerequisites: ACM 100abc, Ae/APh/CE/ME 101abc 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 2015–16. ME/Ge/Ae 266 ab. Dynamic Fracture and Frictional Faulting. 9 units (306). For course description, see Mechanical Engineering.
