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ENG ME 707: Finite Element Analysis
Undergraduate Prerequisites: ENG ME 512; and ENGME580 or ENGME542
An introduction to the finite element method with emphasis on fundamental concepts. Variational equations, Galerkin's method. Finite element applications to linear elliptic boundary value problems in structures, solid and fluid mechanics, and heat transfer. Optimality, convergence, function spaces and energy norms. Isoparametric elements. Mixed methods, penalty methods, selective reduced integration; applications may include Kirchoff plate theory, incompressible elasticity, Stokes flow. Thick and thin beams, plates, and shells. Implementation: element data structures, numerical integration, assembly of equations, element routines, solvers. Advanced topics may include dynamic analysis, stabilized methods, eigenvalue problems, and hybrid analytical methods.
ENG ME 709: Turbulent Flows
Undergraduate Prerequisites: ENG ME 421; or equivalent
Introduction to turbulence. Deterministic versus statistical descriptions of fluids; kinematics; correlations and spectra; closure of the fluid equations of turbulence. Reynolds stresses; spectral evolution; analysis of scales. Analysis of isotropic turbulence and modeling of turbulent flows. Current topics.
ENG ME 710: Dynamic Programming and Stochastic Control
Undergraduate Prerequisites: CAS MA 381 or ENG EK 500 or ENG ME 308; and ENGEC402, ENGEC501 or ENGME510
Introduction to sequential decision making via dynamic programming. The principle of optimality as a unified approach to optimal control of dynamic systems and Markovian decision problems. Applications from control theory and operations research include linear-quadratic problems, the discrete Kalman Filter, inventory control, network, investment, and resource allocation models. Adaptive control and numerical solutions through successive approximation and policy iteration, suboptimal control, and neural network applications involving functional approximations and learning. Meets with ENGEC710 and ENGSE710. Students may not receive credit for both.
ENG ME 711: Multiscale Methods in Computational Mechanics
Undergraduate Prerequisites: ENG ME 707 or CAS MA 539 or CAS MA 556.
This course will cover the state-of-the-art in analytical and (especially) computational techniques for solving problems with multiple spatial and temporal scales. Such problems are now at the forefront of computational mechanics with applications ranging from turbulence and its modeling to the coupling of atomistic and continuum scales in solid mechanics. We will begin with the more traditional methods including multi-scale perturbation techniques and renormalization group theory. Thereafter we will focus on more recent developments with distinct computational focus including: the Optimal Prediction Method of Chorin et al., the Equation Free Method of Kevrekidis et al, the Variational Multiscale Method of Hughes et al. and the Heterogeneous Multiscale Method of Weinan et al. We will also cover an approach to determine unknown parameters in the models derived from these methods. The differences and similarities between these methods will also be discussed and highlighted.
ENG ME 713: Viscous Flow
Undergraduate Prerequisites: ENG ME 542.
Brief review of the fundamental conservation and constitutive equations, exact solutions of the viscous Navier-Stokes equations, similarity solutions, boundary layer theory; creeping flows, flow in Hele-Shaw cells, lubrication theory, thin shear layer approximations, jets and wakes, hydrodynamic instability and transition to turbulence, Reynolds-averaged Navier-Stokes equations.
ENG ME 714: Advanced Stochastic Modeling and Simulation
Undergraduate Prerequisites: ENG EK 500; or equivalent, knowledge of stochastic processes, or consent of the instructor.
Graduate Prerequisites: .
Introduction to Markov chains, point processes, diffusion processes as models of stochastic systems of practical interest. The course focuses on numerical and simulation methods for performance evaluation, optimization, and control of such systems. Meets with ENGSE714. Students may not receive credit for both.
ENG ME 715: Waves in Fluids
Analytical methods are developed for studying the propagation and diffraction of waves in uniform and in homogeneous fluid media. Illustrative applications are made to sound waves, gravity waves, waves in random media, evanescent waves.
ENG ME 718: Advanced Topics in Nanotechnology
Undergraduate Prerequisites: Undergraduate solid-state physics and quantum mechanics courses or instructor's consent.
Nanotechnology is emerging as the technology of the 21st century. There is an ever growing effort by scientists and engineers across disciplines to envision, fabricate and integrate nanoscale devices for countless applications. This course will give a rigorous introduction to the basic concepts and experimental techniques in nanoscience and nanotechnology. The course will review relevant quantum mechanics and solid state physics as a basis for understanding the physical phenomena at the nanoscale. Then, basic issues in nanofabrication, Scanning Probe Microscopy (SPM), nanoelectronics and nanomechanics will be discussed.
ENG ME 719: Computational Problem Solving
Graduate Prerequisites: Programming experience, working knowledge of C, or consent of instructor.
Intensive course in computer problem solving using object-oriented programming and research paradigms. Student learns programming skills required to use computer as a research tool and develops ability to design algorithms and data structures for efficient computation. Problems selected from areas including modeling, simulation, optimization, and computer-aided design. Topics include programming techniques, data representation, data management, searching and sorting, recursion, graph theory, formal language theory, and combinatorial analysis.
ENG ME 720: Acoustics II
Undergraduate Prerequisites: ENG ME 520.
Wave equation in cylindrical and spherical co-ordinate systems. Propagation in waveguides. Diffraction: the Rayleigh integral and the Helmholtz-Kirchhoff integral. Green's function and angular spectrum methods. Diffraction of sound beams: Guassian beams, unfocused and focused sources, and arrays. Diffraction by apertures, discs and wedges. Scattering of sound; Rayleigh scattering, scattering cross-section, elastic scatters. Propagation in inhomogeneous media: rays, the eikonal equation, the Blokhintzev invariant and the acoustic field near caustics. Absorption and dispersion of acoustic waves. Transmission and reflection at a fluid-solid interface.
ENG ME 721: Acoustic Bubble Dynamics
Undergraduate Prerequisites: ENG ME 520 and ENG ME 542; or equivalent
Bubbles and acoustic cavitation play an important role in many aspects of application of sonic and ultrasonic energy in fluids and biological tissue. This course will introduce the study of bubble phenomena in sound fields. The fundamental physical acoustics of bubbles (and the fundamental physics which can be illustrated by the study of bubble dynamics) will be stressed. The family of Rayleigh-Plesset equations for time-dependent bubble behavior will be derived from the Navier-Stokes equations. Analytical approximations to the Rayleigh-Plesset equations in limiting cases will be derived and studied. Approximations to the thermodynamic behavior of oscillating bubbles will be considered in detail. Thermal, acoustic and viscous contributions to dissipation will be treated. Numerical solutions will also be studied, specifically in the context of highly nonlinear behavior during acoustically-forced oscillations. Specific experiments, and experimental techniques for measuring bubble dynamics will be studied in detail. Topics covered will contrast agent microbubbles, acoustics of bubbly liquids, bubble-mediated bioeffects, shape instabilities, acoustic levitation, sonoluminescence, heat and mass transfer during bubble oscillations, sonochemistry and cavitation detection and monitoring.
ENG ME 723: Waves in Random Media
Undergraduate Prerequisites: At least one graduate-level course in either acoustics or fluid dynamics.
Systematic development of wave phenomena in weakly inhomogeneous and moving media. Emphasis is on acoustic waves, with selected examples from other branches of wave physics. Both ray-tracing and full-wave methods are discussed. Introduction to the statistical description of random media and of turbulent media. Formulations for relating statistical properties of wave phenomena to the statistical properties of the medium.
ENG ME 724: Advanced Optimization Theory and Methods
Undergraduate Prerequisites: ENGEC524 or consent of instructor.
Graduate Prerequisites: ENG EC 524 or consent of instructor.
Complements ENGEC524 by introducing advanced optimization techniques. Emphasis on nonlinear optimization and recent developments in the field. Topics include: unconstrained optimization methods such as gradient and incremental gradient, conjugate direction, Newton and quasi-Newton methods; constrained optimization methods such as projection, feasible directions, barrier and interior point methods; duality; and stochastic approximation algorithms. Introduction to modern convex optimization including semi-definite programming, conic programming, and robust optimization. Applications drawn from control, production and capacity planning, resource allocation, communication and sensor networks, and bioinformatics. Meets with ENGEC724 and ENGSE724. Students may not receive credit for both.
ENG ME 725: Queueing Systems
Undergraduate Prerequisites: ENG EK 500 or ENG EC 505; or consent of instructor.
Graduate Prerequisites: ENG EK 500 or ENG EC 505; or consent of instructor.
Performance modeling using queueing networks, analysis of product form and non-product form networks, numerical methods for performance evaluation, approximate models of queueing systems, optimal design and control of queueing networks. Applications from manufacturing systems, computer systems and communication networks. Meets with ENGEC725 and ENGSE725. Students may not receive credit for both.
ENG ME 726: Fundamentals of Biomaterials
Undergraduate Prerequisites: ENG EK 301 ; ENG EK 424 ; CAS CH 101 ; CAS CH 102 ; ENG BE 209.
Provides the chemistry and engineering skills needed to solve challenges in the biomaterials and tissue engineering area, concentrating on the fundamental principles in biomedical engineering, material science, and chemistry. Covers the structure and properties of hard materials (ceramics and metals) and soft materials (polymers and hydro-gels). Same as ENG BE 726 and ENG MS 726. Students may not receive credit for both.
ENG ME 727: Principles and Applications of Tissues
Undergraduate Prerequisites: ENG EK 301 ; ENG EK 424 ; CAS CH 101 ; CAS CH 102 ; ENG BE 209.
Provides the chemistry and engineering skills needed to solve challenges in the biomaterials and tissue engineering area, concentrating on cell-biomaterial interactions, soft tissue mechanics and specific research topics. Students will write a NIH-style grant proposal on a specific research topic. Note that the laboratory portion is not offered in ENG ME 727. Same as ENG BE 727/ENG MS 727. Students may not receive credit for both.
ENG ME 728: Special Topics in Wave Propagation
Undergraduate Prerequisites: Consent of instructor.
Format is similar to that of regular classroom courses, with in-depth coverage of an announced topic of current interest in wave propagation. Subject matter varies from year to year.
ENG ME 729: Non-linear Acoustics and Sonic Booms
Undergraduate Prerequisites: Understanding of fluid mechanics at a depth consistent with what is covered in an undergraduate curriculum in aerospace or mechanical engineering.
Propagation of finite amplitude sound, principles of one-dimensional unsteady compressible flow. Discussion of non-linear distortion, generation of harmonics, weak shocks, N-waves, and of shock profiles. Supersonic aerodynamics, flow around bodies in supersonic flight, generation of sonic booms, non-linear acoustics theory of boom propagation through the atmosphere. Selected additional topics in non-linear acoustics.
ENG ME 732: Combinatorial Optimization and Graph Algorithms
Undergraduate Prerequisites: ENG ME 411 or CAS CS 330; or equivalent course on optimization or algorithms.
Design data structures and efficient algorithms for priority queues, minimum spanning trees, searching in graphs, strongly connected components, shortest paths, maximum matching, and maximum network flow. Some discussion of intractable problems and distributed network algorithms.
ENG ME 733: Discrete Event and Hybrid Systems
Undergraduate Prerequisites: ENG EK 500; or equivalent or consent of instructor.
Graduate Prerequisites: ENG EK 500; or equivalent or consent of instructor.
Review of system theory fundamentals distinguishing between time-driven and event-driven dynamics. Modeling of Discrete Event and Hybrid Systems; Automata, Hybrid Automata, Petri Nets, basic queueing models, and stochastic flow models. Monte Carlo computer simulation: basic structure and output analysis. Analysis, control, and optimization techniques based on Markov Decision Process theory with applications to scheduling, resource allocation, and games of chance. Perturbation Analysis and Rapid Learning methods with applications to communication networks, manufacturing systems, and command-control. Meets with ENGEC733 and ENGSE733. Students may not receive credit for both.