Chemical and Biological Engineering

Academic Year 2022 – 2023

General Information

Address
Engineering Quadrangle
Phone

Program Offerings:

  • Ph.D.
  • M.S.E.
  • M.Eng.

Director of Graduate Studies:

Graduate Program Administrator:

Overview

The Department of Chemical and Biological Engineering’s mission is to educate the leaders in chemical and biological engineering by conducting research that defines the frontiers of knowledge in our field. We prepare chemical and biological engineers for careers in teaching, research and development, entrepreneurship, and management in academia, government, and industry. Building on world-class research and scholarship, Princeton’s Department of Chemical and Biological Engineering has particular strengths, including our small student-to-faculty ratio, ensuring true mentorship during graduate study; a diverse graduate student body producing outstanding scholarship; uniformly strong academic departments throughout Princeton University; a diversity of mutually beneficial research collaborations; and our location, amidst the greatest concentration of chemical and pharmaceutical industrial research laboratories in the United States.

The Department of Chemical and Biological Engineering’s graduate programs are centered on the Doctor of Philosophy (Ph.D.) degree, and the majority of our students are doctoral candidates. Our department also offers two masters degree programs (Master of Science in Engineering, Master of Engineering) geared toward practicing engineers interested in expanding their knowledge, who generally come with financial support from their employers or an external fellowship. All three graduate programs are based on the principles of chemical engineering, chemistry, biochemistry, biology, mathematics, physics, and related science and engineering disciplines.

Apply

Application deadline
December 1, 11:59 p.m. Eastern Standard Time (This deadline is for applications for enrollment beginning in fall 2023)
Program length
Ph.D. 5 years, M.S.E. 1.5 or 2 years, M.Eng. 1 year
Fee
$75
GRE
for M.S.E. applicants only

Additional departmental requirements

Please briefly describe how your academic interests, background, or life experiences would promote Princeton’s commitment to diversity and inclusion within the Graduate School and to training individuals in an increasingly diverse society. Please submit a succinct statement of no more than 250 words.

M.S.E. and M.Eng. applicants typically have support from their employers or from external fellowships.

Program Offerings

Program description

The Ph.D. program aims to prepare students for positions as independent researchers, whether in industry or academia. We believe that our program's close mentorship and strong emphasis on written and oral communication benefit students who follow such career paths. The central feature of the program is original research leading to the student’s Ph.D. dissertation. In addition, students must exhibit a firm and broad grasp of modern chemical engineering and allied fields through coursework, and demonstrate the ability to conceive and plan original research.  Every admitted Ph.D. student is given financial support in the form of a first-year fellowship. In addition, all admitted Ph.D. students are automatically considered for the prestigious Wu and Upton Fellowships.

Courses

Satisfactory completion of ten courses for the core course requirement is required for this degree, including five departmental core courses (CBE 503; CBE 504; CBE 507; MAE 501/CBE 509; CBE 510 or MAE 552/CBE 557) and a research ethics course (EGR 501). Among the remaining four courses, at least three must be technical courses at the graduate level (500-level) or senior level (400-level). Exemptions from certain core courses may be granted for students who have completed a similar course at another institution; exemptions should be sought in writing from the director of graduate studies.

General exam

The general examination has two components. The first component is mastery of graduate-level chemical engineering material, demonstrated by satisfactory grades in the departmental core courses. The second component is the first proposition, which is a written document defended orally.  The written document outlines plans for dissertation research, including progress already made. This document is submitted in the late fall of the second year of residence and is defended orally in January, before a committee of faculty members. Satisfactory completion of the core course requirements and the first proposition defense is required to achieve post-generals degree candidacy. Students must pass both components before May of the second year. Deficiencies noted at either the end of the first year of study or at the first proposition defense may result in a student being required to retake one of the core courses (not for credit), possibly after auditing a relevant undergraduate course.

Qualifying for the M.A.

The Master of Arts (M.A.) degree is normally an incidental degree on the way to Ph.D. candidacy and is earned after a student successfully passes the general examination.  It may also be awarded to students who, for various reasons, leave the Ph.D. program, provided that these requirements have been met.

Please note, students admitted to the Ph.D. program who do not wish to complete the program may be considered for an M.S.E. degree with approval from the department and the Graduate School.  Ph.D. students who have already been awarded the incidental M.A. are not eligible to earn an M.S.E.

Teaching

All Ph.D. students must serve a minimum of one semester as an assistant in instruction (teaching assistant) to broaden their experience and expose them to the other side of the instructional process.  For students who secure certain competitive fellowships that do not allow teaching, this requirement can be lifted with approval from the DGS.  Students are expected to serve six AI (assistant in instruction) hours, which equates to approximately twenty hours/week for the semester.  Six AI hours is based on the number of contact hours each week with undergraduates.   Students generally serve as AIs in their second year of graduate study, never in their first. Some students may serve more than once if the student so desires; if AI service is needed to ensure a student’s continued financial support; or if the department cannot fill the AI position otherwise. In addition, some “half” (three-hour) AI positions may be available, which should require approximately 10 hours/week; these would normally be filled by students who have already completed their term of “full” AI service.

Dissertation and FPO

The doctoral dissertation must demonstrate the student’s independent research and mastery of the field and extend existing knowledge or present a significant new interpretation of known phenomena. The dissertation must be approved by the student’s research adviser and a knowledgeable second reader.

The final public oral examination culminates the student’s graduate studies. A faculty committee examines the student’s technical mastery of the material in the dissertation.

Program description

The Master of Science in Engineering (M.S.E.) is a research-based master’s degree, culminating in an M.S.E. thesis describing the student’s original research. Each candidate’s experience is broadened through satisfactory completion of six graduate courses in chemical and biological engineering. The typical duration of M.S.E. study is 18 to 22 months (three to four academic terms with summer in between); students admitted in candidacy for the M.S.E. degree typically have support from their employers or external fellowships.

Courses

M.S.E. students must successfully complete a minimum of six graduate-level courses from either the chemical and biological engineering curriculum or approved technical electives.

Thesis

The M.S.E. program has a strong research focus, reflected in a master’s thesis requirement, which the student’s research adviser must approve.

Program description

The Master of Engineering (M.Eng.) is a coursework-based master’s degree offered to practicing engineers.  Candidates for the M.Eng. degree, if enrolled full time, will normally satisfy that requirement in one 10-month academic year.  Students admitted in candidacy for the M.Eng. degree will always have external support, typically from their employers or external fellowship; financial support is not offered. The M.Eng. degree may also be pursued part-time by staff from the many nearby industrial laboratories.  No research nor thesis is required.

Courses

Candidates for the M.Eng. degree must successfully complete at least eight courses, all taken for a letter grade. A minimum of six of these eight courses must be technical, having their primary listing in a department or a program within the natural sciences or engineering. A minimum of four of these courses must be chosen from graduate offerings (500-level) in the Department of Chemical and Biological Engineering (primary or cross-listed); options include any of the four core courses for the Ph.D. degree (CBE 503; CBE 504; MAE 501/CBE 509; CBE 510), as well as graduate-level CBE electives (primary or cross-listed) chosen according to the student’s area of interest. Of the remaining four courses, a minimum of two must be at the graduate level (500-level). Up to two courses at the senior level (400-level) will be counted towards the degree requirement of eight total courses.  Students are encouraged, although not required, to focus their course choices to develop significant expertise in a particular area.  Students must have a “B” (3.00) average or better when they complete the program requirements to receive the degree.

Please note, CBE 507 cannot be counted towards the course requirement for M.Eng. candidates. It is designed for entering Ph.D. students and is graded P/D/F only.

Faculty

  • Chair

    • Christos Maravelias
  • Director of Graduate Studies

    • Sujit S. Datta
  • Director of Undergraduate Studies

    • José L. Avalos (fall)
    • Mark P. Brynildsen (spring)
  • Professor

    • Clifford P. Brangwynne
    • Mark P. Brynildsen
    • Pablo G. Debenedetti
    • David B. Graves
    • Bruce E. Koel
    • A. James Link
    • Lynn Loo
    • Christos Maravelias
    • Celeste M. Nelson
    • Athanassios Z. Panagiotopoulos
    • Rodney D. Priestley
    • Robert K. Prud'homme
    • Richard A. Register
    • Sankaran Sundaresan
  • Associate Professor

    • José L. Avalos
  • Assistant Professor

    • Pierre-Thomas Brun
    • Jonathan M. Conway
    • Sujit S. Datta
    • Emily C. Davidson
    • Marcella Lusardi
    • Michele L. Sarazen
    • Michael A. Webb
  • Associated Faculty

    • Mohamed S. Abou Donia, Molecular Biology
    • Ian C. Bourg, Civil and Environmental Eng
    • Daniel J. Cohen, Mechanical & Aerospace Eng
    • Kelsey B. Hatzell, Mechanical & Aerospace Eng
    • William M. Jacobs, Chemistry
    • Cameron A. Myhrvold, Molecular Biology
    • Sabine Petry, Molecular Biology
    • Stanislav Y. Shvartsman, Molecular Biology
    • Howard A. Stone, Mechanical & Aerospace Eng
    • Jared E. Toettcher, Molecular Biology
    • Claire E. White, Civil and Environmental Eng
    • Martin Helmut Wühr, Molecular Biology
  • Lecturer

    • Charles M. Smith

For a full list of faculty members and fellows please visit the department or program website.

Permanent Courses

Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.

CBE 501 - Incompressible Fluid Mechanics

Elements of fluid mechanics relevant to liquids and gases at subsonic conditions are studied, beginning with unidirectional flows and macroscopic balances; flows without inertia treated via lubrication approximation and Stokes' equations; and effects of inertia in inviscid and boundary layer flows. The course introduces hydrodynamic stability theory and turbulent flows.

CBE 502 - Mathematical Methods of Engineering Analysis II (also APC 502)

Linear ordinary differential equations (systems of first-order equations, method of Frobenius, two-point boundary-value problems); spectrum and Green's function; matched asymptotic expansions; partial differential equations (classification, characteristics, uniqueness, separation of variables, transform methods, similarity); and Green's function for the Poisson, heat, and wave equations, with applications to selected problems in chemical, civil, and mechanical engineering.

CBE 503 - Advanced Thermodynamics (also MSE 521)

A systematic treatment of chemical thermodynamics from an advanced point of view. It explores the equilibrium properties of chemical systems under a wide range of conditions and applications to problems of a chemical engineering nature, with an emphasis on multicomponent mixtures and reactive systems.

CBE 504 - Chemical Reactor Engineering

The elements of chemical rate processes; reactor properties in continuous flow; staged, steady-state, and transient operations; optimal distribution of properties; and stability. The effect of physical transport rates when coupled with chemical rates on reactor design and characteristics is examined.

CBE 506 - Application of Statistical Methods

A study of the principles involved in the control of chemical processes and dynamic analysis and modeling of lumped, distributed, and delay processes; stability; design strategies for scalar and multidimensional systems; and optimal control.

CBE 507 - Research Topics in Chemical & Biological Engineering

A seminar course designed to acquaint first-year graduate students with the different research areas represented by the CBE department, as well as to train these students in the methodologies and practices used in chemical engineering research. Students learn how to read and evaluate the literature, and the techniques for formulating and developing an original research problem in the field. Each lecture is given by a different member of the CBE faculty (or associated faculty), who will review his or her field of research and discuss open questions for future investigation.

CBE 508 - Numerical Methods for Engineers

Applications of numerical methods to problems of engineering and scientific significance.

CBE 510 - Transport Phenomena

A survey of modeling and solutions methods for problems involving heat, mass and momentum transport. Topics include conservation equations, conductive heat transfer, species diffusion, kinematics and dynamics of viscous flows, the Navier-Stokes equations, scaling principles and approximation techniques, boundary layer theory, convective heat and mass transfer, multi-component energy and mass transfer, buoyancy-driven convection, transport in ionic solutions, introduction to instability and turbulence.

CBE 517 - Soft Matter Mechanics: Fundamentals & Applications

We cover fundamental aspects of the mechanics of soft matter and see how they provide useful insights about novel engineering designs and materials (3D printing, soft robotics, metamaterials). Particular attention is given to interfacial effects, which dominate the physics of small objects. Topics include, drops, bubbles, wetting, coatings, instabilities. We also cover the mechanics of thin elastic objects whose deformability characterizes many biological systems. Students learn how to build quantitative physical models, combining experimental observations, scaling analysis and formal approaches.

CBE 521 - Advanced Chemical Reactor Engineering

Dynamic behavior of chemical reactors; steady-state multiplicity and oscillations; phase-plane characteristics; and bifurcation theory, singularity theory, and their computational aspects are studied. Software packages for automatic bifurcation analysis in multiparameter space are examined. Coupled and periodically forced reactor dynamics are explored as are nonlinear dynamics of reactors under control.

CBE 522 - Colloidal Dispersions I

An overview of the behavior of small particles dispersed in liquids. Assessment is made of the hydrodynamic, Brownian, electrostatic, and dispersion forces acting among particles. Electrokinetic phenomena generated by an applied electric field; stabilization and flocculation of aqueous dispersions; and collection of particles in deep-bed filters are studied.

CBE 523 - Colloidal Dispersions II

An exploration of the connection between macroscopic behavior of dispersions and microscopic forces; forces induced by grafted, adsorbing, and nonadsorbing polymer; equilibrium phase behavior; hindered sedimentation and transient settling processes; diffusion and photon correlation spectroscopy; and rheology of concentrated dispersions.

CBE 526 - Surface Science: Processes and Probes (also CHM 527/MSE 526)

An introduction to processes at surfaces and interfaces. Experimental methods of surface science. Electron spectroscopy, ion scattering, and scanning probe microscopy. Atomic structure of surfaces and adsorbed layers. Thermodynamics of surface processes. Adsorption and molecular dynamics of gas-surface reactions. Kinetics of adsorption, desorption, diffusion, and reactions. Liquid interfaces. Heterogeneous catalysts. Etching. Film growth and epitaxy. Applications to energy and environmental science and technology.

CBE 528 - Advanced Process Flowsheeting and Process Control

Sequential modular, simultaneous modular, and equation-oriented approaches; sparse systems of linear equations; algorithms of nonlinear equations; decomposition approach in systems of nonlinear equations; control of lumped parameter systems; linear and nonlinear multivariable control; controllability; generic rank; connectability; structural controllability; observability; and plant-wide control strategies.

CBE 529 - Hydrodynamic Stability

Instability phenomena at fluid interfaces; and effects of surface tension, adsorbed layers, effects due to heat and mass transfer, flows in porous mediums, Rayleigh-Taylor and Kelvin-Hemholtz instabilities, and electrohydrodynamic effects. Convective instabilities in stratified fluids and rotating systems; shear flow instability and stability of thin films; and nonlinear phenomena are examined.

CBE 530 - Systems Engineering

Introduction to steady-state and dynamic simulation, process synthesis, and process operations. Topics include mathematical modelling techniques; advanced linear algebra; non-linear systems of equations; dynamic simulation; optimization; and case studies.

CBE 532 - Interfacial Science and Engineering

A study of the structure and property of interfaces and associated interfacial materials, such as membranes. Thermodynamics and mechanics as applied to interfacial systems. Interfacial phenomena such as wetting, adhesion, and membrane fusion. Experimental methods in interface science.

CBE 535 - Computational Biology of Cell Signaling Networks

Computational tools for analyzing dynamics, control, and signal processing capabilities of cell signaling and gene expression networks. Analysis of reaction and diffusion processes in receptor-mediated cellular processes. Foundations of the quantitative assays of cell signaling systems. Pattern formation in development. Models of the eukaryotic cell cycle. Deterministic and stochastic models of gene regulatory networks; Monte Carlo simulations. Model robustness and parameter estimation. Mathematical background at the level of undergraduate ODE course is desirable.

CBE 536 - Glasses and Supercooled Liquids

Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscious liquid fast enough to avoid crystallization. Although this route to the vitreous state - supercooling - has been known for millenia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. The course will address both the theory and applications of supercooled liquids and glasses.

CBE 541 - Polymer Synthesis (also MSE 534)

Fundamentals and practice of polymer synthesis, both at the laboratory and industrial scales. Mechanism, kinetics, and range of application of important polymerization methods: condensation, free-radical, anionic, cationic, coordination; polymerization thermodynamics; chemical reactions on polymers; selected industrial processes (e.g., polyesterification, emulsion polymerization, high- and low-pressure routes to polyethylene).

CBE 542 - Polymer Viscoelasticity (also MSE 524)

An examination of equilibrium and dynamic properties from dilute solutions to the melt state. Explores scaling concepts; Flory-Huggins theory; polymer blends; network structure and elasticity; diffusion and viscoelasticity; influence of chain architecture and temperature; and molecular theory.

CBE 543 - Structure and Properties of Complex Fluids

Equilibrium and dynamic properties of polymers in dilute solution. The emphasis is on experimental measurements used to characterize polymer size, molecular weight, and interactions and the theories of equilibrium chain statistics and dynamics. Concepts covered include random-walk chain statistics, excluded volume interactions, polyelectrolyte effects, diffusion, sedimentation, viscosity, osmotic pressure, and light scattering.

CBE 544 - Solid-State Properties of Polymers (also MSE 522)

Amorphous polymers, including modulus-temperature behavior, mechanical and dielectric measurements, the glass transition, and yielding and fracture in glassy polymers; semicrystalline polymers, including crystal structure by X-ray diffraction; rheo-optical techniques and birefringence, dichroism, and fluorescence; small-angle scattering techniques, including light, X-ray, and neutron; and other multiphase and multicomponent polymers, including block and segmented copolymers, blends, ionomers, and interpenetrating networks.

CBE 545 - Science and Technology of Fibrous Materials

The chemical structure, morphological characteristics, and physical properties of organic polymer fibers; chemistry and chemical technology of synthetic polymers (polyamide, polyester, acrylic, polyolefin), cellulose, and proteins; the physical processes of fiber production; structure-property relationships; and high-performance fibers.

CBE 546 - Aerosol Physics and Chemistry

An introduction to the dynamics of suspended liquid and solid particles in gas media. Processes of particle nucleation, coagulation, condensation, deposition, and transport are examined. Atmospheric aerosols and particle activation in the supersaturated environment of clouds are considered in addition to combustion, ceramic, and pharmaceutical aerosol applications. Theoretical modeling approaches and experimental methods are reviewed.

CBE 547 - Mechanics of Granular Materials and Gas-Particle Flows

Regimes of granular rheology. Plasticity theory for quasi-static flow. Kinetic theory for rapid flow. Examples of granular statics and quasi-static flow. Stability of rapid flow. Locally averaged equations of motion for gas-particle flows. Examples on the role of interstitial gas. Stability of fluidized suspensions. Hierarchical structures in gas-particle flows.

CBE 548 - Dynamics of Films, Jets and Drops

The development of electronic and biomedical devices for actuating flow and mixing in micro- and nanofluidic systems requires a solid understanding of the static and dynamic behavior of ultrasmall liquid volumes. Since small liquid structures maintain a large surface to volume ratio, their fluidic behavior is dominated by interfacial forces. This course surveys current research in micro- and nanofluidic phenomena with special emphasis on free surface flows. Students will evaluate technologies, concepts and theoretical models involving transport phenomena in small scale systems by reading and critiquing recently published work in the field.

CBE 550 - Physics of Polymeric Glasses

Formation of glasses represents an important transition in soft matter physics and is of enormous importance in a wide variety of commercial applications. The phys. of glass formation and glassy-state, while highly investigated, are rich in phenomena not fully understood. This will give an overview of the current understanding of this properties of polymeric glasses and the viscous liquids from which they are commonly formed. Experimental, theoretical and computational contributions to our understanding of amorphous polymers will be covered. Viscoelasticity will be discussed within the context of the glass transition and glassy state.

CBE 552 - Topics in Chemical Engineering

Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state - supercooling - has been known for millenia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. The course will address current theoretical knowledge of the manner in which intermolecular forces give rise to complex behavior in supercooled liquids and glasses.

CBE 553 - Topics in Interfacial Chemistry

Chemical reactions at fluid-solid interfaces. Thermodynamics of surfaces; electronic structure; adsorption bonding; adsorption isotherms; heterogeneous catalysis; electrochemical reactions; interactions of electrons with surfaces; interaction of light with surfaces; energy transfer at surfaces; thin-film deposition; and tribology are studied.

CBE 554 - Topics in Computational Nonlinear Dynamics (also APC 544)

The numerical solution of partial differential equations (finite element and spectral methods); computational linear algebra; direct and interactive solutions and continuation methods; and stability of the steady states and eigen problems. Time-dependent solutions for large systems of ODEs; computation and stability analysis of limit cycles; Lyapunov exponents of chaotic solutions are explored. Vectorization and FORTRAN code optimization for supercomputers as well as elements of symbolic computation are studied.

CBE 555 - Introduction to Polymer Materials

An introduction to the relationship between molecular structure and properties of bulk matter. Atomic bonding, elements of statistical mechanics, polymer physics, and biophysical chemistry are studied.

CBE 556 - Topics in Chemical Engineering

Presentation of the basic principles of quantum theory and statistical mechanics, with an emphasis on their applications to high-technology engineering and science. One of the main purposes of the course is to discuss what can and cannot be done with quantum theory.

CBE 556A - Topics in Chemical Engineering

Presentation of the basic principles of quantum theory and statistical mechanics, with an emphasis on their applications to high-technology engineering and science. One of the main purposes of the course is to discuss what can and cannot be done with quantum theory.

CBE 556C - Special Topics in Chemical Engineering

Presentation of the basic principles of quantum theory and statistical mechanics, with an emphasis on their applications to high-technology engineering and science. One of the main purposes of the course is to discuss what can and cannot be done with quantum theory.

CBE 567 - Metabolic Engineering

Introduction to engineering metabolism. The objective of this course is to introduce students to current techniques and challenges within the field of metabolic engineering. Specific topics include introduction to metabolism, transcriptional regulation, signal transduction, flux balance analysis, and metabolic flux analysis.

CEE 535 - Statistical Mechanics II: Methods (also CBE 525)

Statistical mechanics provides a microscopic basis for calculating the equilibrium and nonequilibrium properties of matter. The course aims to provide engineers, physicists, chemists, biologists, and geologists with working knowledge of the fundamentals and applications of statistical mechanics. Part two covers modern theoretical and computational techniques.

CHM 503 - Introduction to Statistical Mechanics (also CBE 524/MSE 514)

Statistical mechanics provides the basis for understanding the equilibrium and nonequilibrium properties of matter in terms of the microscopic details of molecular interactions and structure. The course aims to provide students with working knowledge of the fundamentals and applications of statistical mechanics.

ENE 506 - Synchrotron and Neutron Techniques for Energy Materials (also CBE 566/CEE 506/MAE 536/MSE 586)

Topics include an introduction to radiation generation at synchrotron and neutron facilities, elastic scattering techniques, inelastic scattering techniques, imaging and spectroscopy. Specific techniques include X-ray and neutron diffraction, small-angle scattering, inelastic neutron scattering, reflectometry, tomography, microscopy, fluorescence and infrared imaging, and photoemission spectroscopy. Emphasis is placed on application of the techniques for uncovering the material structure-property relationship, including energy storage devices, sustainable concrete, CO2 storage, magnetic materials, mesostructured materials and nanoparticles.

ENE 570 - Advanced Optimization Methods for Energy Systems Engineering (also CBE 570/MAE 570)

The course covers (1) basic theory, (2) modeling techniques, (3) basic algorithms and solution methods, and (4) software tools for optimization. We also discuss how optimization methods can be used to design, analyze, and operate energy systems.

MAE 501 - Mathematical Methods of Engineering Analysis I (also APC 501/CBE 509)

Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, Sturm-Liouville theory, Green's functions for the solution of ordinary differential equations and Poisson's equation, and the calculus of variations.

MAE 552 - Viscous Flows and Boundary Layers (also CBE 557)

The mechanics of viscous flows. The course explores the kinematics and dynamics of viscous flows; solution of the Navier Stokes equations; the behavior of vorticity; the boundary layer approximation; laminar boundary layer with and without pressure gradient; separation; integral relations and approximate methods; compressible laminar boundary layers; instability and transition; and turbulent boundary layers and self-preserving turbulent shear flows.

MAE 566 - Biomechanics and Biomaterials: From Cells to Organisms (also CBE 561)

Bioengineering is proof that exciting developments happen at the interfaces between fields. This course introduces students to approaches spanning biomechanics and biophysics, biomaterials and tissue engineering, and biomedical device design. These approaches are explored in the context of single cells, tissues, and whole organisms. Sample topics include: mechanobiology, surface chemistry and the cell:material interface, the biomechanics of locomotion, and "lab on a chip"technologies. Special emphasis is placed on introducing practical biomedical examples from the bench to the operating room.

MSE 501 - Introduction to Materials (also CBE 514/CEE 561/MAE 561)

Emphasizes the connection between microstructural features of materials (e.g., grain size, boundary regions between grains, defects) and their properties, and how processing conditions control structure. Topics include thermodynamics and phase equilibria, microstructure, diffusion, kinetics of phase transitions, nucleation and crystal growth, phase separation, spinodal decomposition, glass formation, and the glass transition.

MSE 504 - Monte Carlo and Molecular Dynamics Simulation in Statistical Physics & Materials Science (also CBE 520/CHM 560/PHY 512)

This course examines methods for simulating matter at the molecular and electronic scale. Molecular dynamics, Monte Carlo and electronic structure methods will be covered with emphasis on hands-on experience in writing and/or exercising simulation codes for atomistic and electronic structure simulation.

QCB 511 - Modeling Tools for Cell and Developmental Biology (also CBE 511)

Using a number of real biological systems, course demonstrates how mathematical models of complex natural systems can organize large amounts of data, provide access to properties that are difficult or impossible to measure experimentally, and suggest new experimental tests of proposed regulatory mechanisms. Participants will demonstrate these ideas in the context of cell and developmental biology. For QCB program students, quantitatively inclined molecular biology students, and physics, chemistry and engineering students interested in quantitative biology. An extension of MOL 510.