Chemical and Biological Engineering

Academic Year:

2018-19

Address:

Engineering Quadrangle

Phone:

609-258-4619

Website:

Chemical and Biological Engineering

Program offerings:

Ph.D.

M.S.E.

M.Eng.

Director of Graduate Studies

Rodney Priestley

Graduate Program Administrator

Karen Oliver

Academic department detail

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, 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; our ability to ensure true mentorship during graduate study; the uniformly strong departments throughout the rest of 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 master's 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.

Applying

Application Deadline:

December 1 - 11:59PM Eastern Standard Time

Program Length:

Ph.D. 5 years, M.S.E. 1.5 or 2 years, M.Eng. 1 year

Application Fee:

$90

Application Requirements:

Statement of Academic Purpose

Resume/Curriculum Vitae

Recommendation Letters

Transcripts

Fall Semester Grades

Required Tests

English Language Tests

Statement of Financial Resources:

for M.S.E. and M.Eng. applicants only

GRE :

General Test required

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.

Ph.D.

Ph.D. Requirements:

Program Description:

The Ph.D. program aims to prepare students for positions as independent researchers, whether in industry or in academia. We believe that the close mentorship characterized by our program and our 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 eleven courses for the core course requirement is required for this degree, including six departmental core courses (CBE 501/MAE 552, CBE 502/MAE 501, 503, 504, 505, and 507) and a research ethics course (EGR 501). Among the remaining four courses, at least three are required to be technical graduate-level courses. 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, which will be considered to have been demonstrated by a passing grade in the departmental core courses. The second component is the first proposition defense, which is a written document outlining plans for dissertation research, including progress already made. This document is submitted in the fall of the second year of residence and is defended orally 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. Both must be passed no later than May of the second year of residence. 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 full Ph.D. candidacy and is earned after a student successfully: (a) passed the first proposition and successfully defended it orally before a committee of faculty members.. 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:

Every Ph.D. student is required to serve a minimum of one semester as an assistant in instruction (teaching assistant), to broaden the student’s experience and expose him or her to the other side of the instructional process. Under special circumstances, to be discussed with the director of graduate studies, this requirement can be lifted. Students are expected to serve six AI hours, which equates to twenty hours/week for the semester. Six AI hours is based on the number of contact hours each week with undergraduates. Students generally serve 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 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 must 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 and the second proposition.

M.S.E.

M.S.E. Requirements:

Program Description:

The 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 24 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 from 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 the requirement of a master’s thesis. Candidates must prepare and submit an acceptable thesis as well as present an open seminar on their research.

M.Eng.

M.Eng. Requirements:

Program Description:

The 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. The M.Eng. degree may also be pursued part-time by staff from the many nearby industrial laboratories. No research or thesis is required, and financial support is normally not offered.

Courses:

Candidates for the M.Eng. degree must successfully complete at least eight graduate-level courses. 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 six courses must be chosen from graduate offerings in the Department of Chemical and Biological Engineering; options include any of the following five core courses for the Ph.D. degree (CBE 501/MAE 552, CBE 502/MAE 501, 503, 504, 505), as well as several graduate-level chemical engineering electives chosen according to the student’s area of interest. To complete the set of eight courses, students with an interest in economics, entrepreneurship, finance, or public policy may choose up to two graduate-level courses from the Department of Economics or the Woodrow Wilson School of Public and International Affairs. Students must have a “B” (3.0) average or better at the time they complete the program requirements in order to receive the degree.

Students are encouraged, although not required, to focus their course choices so as to develop significant expertise in a particular area. Possible specializations, and some courses that fall within each area, include: (1) materials, CBE 522, 531, 532, 541, 543, 544; MSE 501, 502, 503, 504, 505, 515, 519, 531; MAE 562, 563, 564; ELE 541, 549, 551; CHM 507, 511, 522; PHY 525, 526; GEO 501; (2) environmental engineering, CBE 522, 546; CEE 571, 576, 581, 582, 586, 587; MAE 571; GEO 524, 526, 537; WWS 582b, 584, 585b, 586c; (3) systems engineering, CHE 521, 527, 528, 530, 554; MAE 541, 545, 546, 548; ELE 521; ORF 522, 526, 562; COS 525; and (4) bioengineering, APC 514; CBE 532, 533, 538, 539, 540; CHM 515, 516, 543, 544, 550; MOL 504, 505, 506, 507, 551, 558; WWS 586a. Any of the core chemical engineering courses (CHB 501/MAE 552, 502, 503, 504, and 505) can be used to complement selections from any of these areas.

Certificate

Certificate Requirements:

Program Description:

The Graduate Certificate in Bioengineering is designed to formalize the training of students specializing in the engineering analysis of living systems. Over the past decade, Princeton faculty have developed new courses that address the design and control of living systems at multiple scales, from single molecules, to cells, tissues, and organisms. Taken together, these classes provide a coherent educational framework that can take the place of a missing graduate program in bioengineering. The graduate certificate program in bioengineering is intended to recognize the efforts and accomplishments of Ph.D. students in engineering and the natural sciences who have gone beyond the requirements of their own degree programs to acquire training in bioengineering.

The certificate is based on core graduate courses, a research seminar, and graduate research. The bioengineering core classes can be taken as graduate electives, in partial fulfillment of the course requirements in home departments.

Please note, students cannot be admitted to Princeton University through the Bioengineering Interdepartmental Graduate Certificate Program since it is not a degree program.

Courses:

The core curriculum provides rigorous training in the engineering analysis of biological molecules and networks, cells, tissues, organs, and organisms. Students are required to take for credit and pass with a grade, one course in each of the thematic areas (“molecules”, “cells”, “tissues and organs”) for a total of three courses. This requirement is designed to guarantee that all students, regardless of their thesis area, have a solid foundation in the engineering analysis of living systems at multiple scales.

Molecules:

CBE 538 / MOL 538: Biomolecular Engineering
CBE 567: Metabolic Engineering
MOL 515 / PHY 570 / EEB 517 / CHM 517: Method and Logic in Quantitative Biology
CBE 518 / ENE 518: Fundamentals of Biofuels

Cells:

CBE 533: Introduction to the Mechanics and Dynamics of Soft Living Matter
PHY 412: Biological Physics

Tissues and Organs:

CBE 540: Physical Basis of Human Disease
QCB 511 / CBE 511: Modeling Tools for Cell and Developmental Biology
CBE 539 / MOL 539: Quantitative Physiology
ELE / NEU / PSY 480: fMRI Decoding: Reading Minds Using Brain Scans
NEU / MOL / PSY 404: Cellular and Systems Neuroscience

Dissertation and FPO:

Graduate research should be conducted under the supervision of one of the participating faculty. The main requirements are quantitative experiments, rigorous data analysis, and/or mathematical and computational modeling of biological processes. The research topic should be approved by the program director.

Additional Requirements:

Students are required to attend the biweekly BioEngineering Colloquium, which serves as a venue for reporting current results and discussing the integration of different research approaches to the analysis and design of living systems. Students will be required to give a research presentation at this colloquium before completing their FPO. This requirement will teach students how to communicate their research to a broad audience of bioengineers, as well as interact with students, postdoctoral fellows, and faculty investigating problems at multiple scales.

Faculty

Chair

Athanassios Z. Panagiotopoulos

Director of Graduate Studies

Rodney D. Priestley

Professor

Ilhan A. Aksay
Jay B. Benziger
Pablo G. Debenedetti
Bruce E. Koel
A. James Link
Lynn Loo
Celeste M. Nelson
Athanassios Z. Panagiotopoulos
Robert K. Prud'homme
Richard A. Register
Stanislav Y. Shvartsman, also Lewis-Sigler Institute for Integrative Genomics
Sankaran Sundaresan

Visiting Professor

Nancy Lape, William R. Kenan, Jr., Visiting Professor for Distinguished Teaching

Associate Professor

Clifford P. Brangwynne
Mark P. Brynildsen
Rodney D. Priestley

Assistant Professor

Jose L. Avalos, also Andlinger Center for Energy and the Environment
Pierre-Thomas Brun
Sujit S. Datta
Michele L. Sarazen

Associated Faculty

Ian C. Bourg, Civil and Environmental Engineering, Princeton Environmental Institute
Emily A. Carter, Mechanical and Aerospace Engineering, Applied and Computational Mathematics
David Cohen, Mechanical and Aerospace Engineering
Sabine Petry, Molecular Biology
Daniel A. Steingart, Mechanical and Aerospace Engineering, Andlinger Center for Energy and the Environment
Howard A. Stone, Mechanical and Aerospace Engineering
Jared E. Toettcher, Molecular Biology
Claire E. White, Civil and Environmental Engineering
Martin Wühr, Molecular Biology, Lewis-Sigler Institute for Integrative Genomics

Courses

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 505 Advanced Heat and Mass Transfer A survey of modeling and solutions methods for processes involving heat and mass transfer. Topics will include convective and difffusive transport, conservation equations, scaling principles and approximation techniques, forced convection, multi-component energy and mass transfer as well as buoyancy and turbulent driven transport.

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 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 539 Quantitative Physiology A treatment of the quantitative tools to understand the human body. Course reviews cell biology and anatomy, then examines cells, tissues, and organs using principles from engineering kinetics and transport processes. Topics include: cell physiology; organ system physiology (including the cardiovascular, renal, and respiratory systems); pathophysiology. Clinical treatments for human disease will also be analyzed.

CBE 540 Physical Basis of Human Disease Course views disease from the perspective of mass transport and the biophysical limitations of the human body (as opposed to the genetic and biochemical basis of disease progression). Cancer, diabetes, cardiovascular and infectious diseases will be covered from a physical point of view. The etiology, physical causes of morbidity and mortality, and design constraints for treatment will be covered.

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

MSE 586

MAE 536

CEE 506

CBE 566

) 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.

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 504 Monte Carlo and Molecular Dynamics Simulation in Statistical Physics & Materials Science (also

CHM 560

PHY 512

CBE 520

) 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.