Commonly-Taken Core and Elective Courses in the Chemical Engineering MS Program

CHEN E4001x and E4002x Essentials A and B Course Syllabus

Welcome to CHEN E4001 and CHEN E4002, Essentials of Chemical Engineering A & B. These two courses will cover essential material from the undergraduate chemical engineering curriculum in a program especially designed for students with a BS in chemistry or a related field, such as biochemistry, polymer science, or mathematics.

Each course consists of four modules, with each module taught by a different member of the Chemical Engineering faculty, and covering essential elements of one undergraduate course.

Here is a list of the modules to be covered, including the faculty members who will teach the modules:

CHEN E4001x

1. Math – Prof. West
2. Thermodynamics I – Prof. Moment
3. Thermodynamics II – Prof. Kumar
4. Reaction Kinetics & Reactor Design – Prof. McNeill

CHEN E4002x

1. Introduction to Chemical Engineering and Process Contro1 – Prof. Bozic
2. Transport Phenomena I – Prof. Durinng
3. Transport Phenomena II – Prof. Bishop
4. Chemical & Biochemical Separations – Prof. Banta

Each module will consist of lectures, recitation classes, and homework assignments, all within approximately a three-week period. These courses assume you have a working knowledge of multivariable calculus and ordinary differential equations. You will need to purchase a total of 5 textbooks for the two courses. While that may appear excessive, these books will be useful to you throughout your chemical engineering career.

The required textbooks are as follows:

CHEN E4001x

• Koretsky, M.D. Engineering and Chemical Thermodynamics, 2nd Edition Wiley, New York 2012. ISBN-13: 978-0470259610
• Folger, H.S. Elements of Chemical Reaction Engineering 5th Edition, Prentice Hall, Upper Saddle River, N.J. 2016 . ISBN-9780133887518

CHEN E4002x

• Seborg, D.E. Mellichamp, D.A, Edgar, T. F., and Doyle III, F.J. Process Dynamics and Control, 3rd Edition, Wiley, New York 201. ISBN-13: 978-0470128671
• Bird, R.B. Stewart, W.E. and Lightfoot, E. N., Transport Phenomena, 2nd edition, Wiley, New York, 2007. ISBN-13: 978-0-470-11539-8
• Seader, J.D., Henley, E.J, and Roper, D.K., Separation Process Principles, 3rd Edition, Wiley, New York, 2010. ISBN-13: 978-0470481837

While not required, a nice reference for “Intro to ChE” (i.e. Mass and Energy Balances) is Felder, R. M., Rousseau, R.W. and Lisa G. Bullard Elementary Principles of Chemical Processes, 4th Edition, Wiley, New York, 2015. ISBN-13: 978-0470616291

CHEN E 4112 Y TRANSPORT PHENOMENA IN FLUIDS AND MIXTURES

Spring 2021

PREREQUISITES: A working knowledge of vector calculus, linear algebra and ordinary differential equations is needed. An undergraduate course in transport, and some exposure to methods in partial differential equations, are also needed.

DESCRIPTION: The course develops and applies a framework for continuum-level modeling of transport phenomena in fluids and their mixtures. The first part of the course considers simple fluids. Continuum balances of mass, energy and momentum (linear and angular momentum) are combined with linearized constitutive equations for the conductive fluxes of momentum and energy (Newton’s law of viscosity and Fourier’s law), the latter being consistent with the constraints demanded by the second law. Applications of the framework to classes of problems important in chemical engineering technologies are reviewed (conduction dominated energy transport, forced and free convection transport). In the second part of the course, a treatment of mixtures is given. Importantly, constitutive laws for species conductive fluxes are developed (e.g. Fick’s law for binary, isothermal systems). Applications to modeling important classes of mass transport problems are reviewed, with empahsis on isothermal systems (e.g diffusion-reaction problems, analogy between energy and mass transport processes, transport in electrolyte solutions, sedimentation).

INSTRUCTOR: INSTRUCTOR C.J. Durning, 811A Mudd, [email protected],

Office hour TBD.

CLASS MEETING: M/W 11:40 AM - 12:55 PM.

REQUIREMENTS: Homework, Take Home Midterm (tentatively the week of March 15), Take Home Final exam (finals week).

OPTIONAL EXTRA CREDIT: Submit class notes during finals week.

HOMEWORKS: Readings and problems assigned approximately biweekly; Homeworks checked for submission/completeness/integrity, but not graded in detail; Solutions will be posted.

GRADES: Based on exams, homeworks.

REFERENCES:

1. D.C. Venerus, H.C. Ottinger, A Modern Course in Transport Phenomena, Cambridge University Press, NY (2018) (VO)
2. W.M. Deen, Analysis of Transport Phenomena, 2nd. (US) Ed., Oxford University Press, NY (2012) (De)
3. R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd Edition, J. Wiley, NY (2002) (BSL)

SUPPLEMENTAL READINGS: To appear on CANVAS website.2

CHEN E 4112 Y - Spring 2021 COURSE OUTLINE

1. OVERVIEW / PRIMER (1 week):
   1. Continuum description of matter locally averaged microstate frames of reference; kinematics; Eulerian and Lagrangian descriptions
2. NON-EQUIL THERMODYNAMICS (NET) OF SIMPLE FLUIDS (3 weeks):
   1. Eulerian balances and the second law balances of mass, momentum, energy second law, entropy inequality, non-equilibrium temperature, T assessment of closure
   2. Development of constitutive laws for the conductive fluxes frame-indifferent, linearized constitutive representations second law )local equilibrium relations, Newton’s law of viscosity; Fourier’s law T explicit form of the energy equation
   3. Limiting cases isotropic, rigid media; incompressible fluids; Boussinesq approximation
3. APPLICATIONS OF NET FOR SIMPLE FLUIDS (4 weeks):
   1. Energy conduction in "rigid media"
   2. Laminar forced convection energy transport in incompressible fluids Graetz/Leveque problems at high Peclet number forced convection energy transport from submerged, heated bodies and localized sources
   3. Laminar free convection energy transport free convection in slots, from submerged, heated bodies; thermal plumes
4. FRAMEWORK FOR ANALYSIS OF MIXTURES (2 weeks):
   1. Framework for isothermal binary mixtures minimal set of Eulerian balances: species mass balances and mixture momentum balance assessment of closure ad-hoc assignment of mixture conductive momentum flux NET development for species diffusive fluxes (Fick’s law)
5. APPLICATIONS FOR ISOTHERMAL MIXTURES (4 weeks)
   1. analogy between energy and mass transport
   2. mass transport under body fields sedimentation transport in electrolyte solutions and electrokinetic phenomena3 Department of Chemical Engineering

Course Calendar

WEEK DATES REMARKS

1. Jan. 11/13 Overview, Math Review, Kinematics
2. Jan. 18/20 Balance Laws: Mass, Momentum, Energy
3. Jan. 25/27 NET of Simple Fluids: Constitutive Laws
4. Feb. 1/3 NET of Simple Fluids: Limiting Cases
5. Feb. 8/10 Energy Conduction in Rigid Media
6. Feb. 15/17 Forced Convection ET
7. Feb. 22/24 Forced/Free Convection ET
8. March 8/10 Free Convection ET
9. March 15/17 Midterm/Balances for Mixtures
10. March 22/24 Constitutive Laws for Mixtures
11. Mar 29/31 Diffusion Dominated MT
12. April 5/7 Trace Limit, ET/MT Analogy, Forced Convection MT
13. April 12/14 MT Under Body Fields
14. April 16-23 Reading Days/ Final

CHEN E 4110 X

MECHANISMS OF TRANSPORT IN FLUIDS

Fall 2020

PREREQUISITES: A working knowledge of vector calculus, linear algebra any ordinary differential equations is needed. An undergraduate course in transport, and some exposure to methods in partial differential equations, are also needed.

DESCRIPTION: The course develops and applies a continuum framework for modeling non-equilibrium phenomena in fluids with clear connections to the molecular/microscopic mechanisms for "conductive" transport. The first part of the course reviews and extends beyond undergraduate level the common continuum approach to transport analysis in fluids. Continuum balances of mass and momentum (linear and angular momentum) are developed. Closure through the continuum-level development of frame indifferent constitutive laws for the conductive momentum flux (stress tensor) is considered for simple fluids in the incompressible limit. Applications of this common framework to several classes of flow problems important in chemical engineering technologies are reviewed (lubrication flows, creeping flows). In the second part of the course, a microscopic development of the conductive fluxes for simple and/or complex fluids is developed along with select applications. Options for this part include (i) kinetic theory of gases by an ad-hoc mechanical treatment or via the Boltzman equation to predict transport coefficients, (ii) review of liquid state "free-volume" and activated state models for predicting transport coefficients in simple liquids (iii) development and application of Langevin/Fokker-Plank/Smoluchowskibframework for modeling the conductive momentum flux in complex fluids and (iv) introduction to active matter.

INSTRUCTOR: INSTRUCTOR C.J. Durning, 811A Mudd, [email protected], office hour Tue: 2:30-3:30 PM via Zoom invitation

CLASS MEETING: Tue/Th 11:40 AM - 12:55 via Zoom Invitation (on CANVAS).

REQUIREMENTS: Homeworks, Midterm (tentatively the week of October 19), Final (during finals week 12/17-23). Exam format TBD.

HOMEWORKS: Readings and problems assigned approximately biweekly; Homeworks checked for submission/completeness/integrity, but not graded in detail; HW solutions will be posted.

EXTRA CREDIT: Course notes

GRADES: Based on exams, homeworks.and extra credit.

REFERENCES:

1. Required Text: D.C. Venerus, H.C. Ottinger, A Modern Course in Transport Phenomena, Cambridge University Press, NY (2018) (VO)

2. Supplemental Texts: W.M. Deen, Analysis of Transport Phenomena, 2nd. (US) Ed., Oxford University Press, NY (2012) (De); R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd Edition, J. Wiley, NY (2002) (BSL).

3. SELECTED READINGS: To appear on CANVAS website.²

CHEN E 4110 X - Fall 2020 COURSE OUTLINE

1. OVERVIEW / PRIMER (1 week):

   1. Continuum description of matter local averagingframes of referencekinematics; Eulerian and Lagrangian descriptions

2. CONTINUUM FRAMEWORK FOR FLUIDS (2 weeks):

   1. Eulerian balance laws mass, linear and angular momentum assessment of closure

   2. Continuum level development of constitutive laws for the conductive momentum flux (stress tensor) continuum definition of simple fluids consequences of material frame-indifference Euler, Newtonian and non-Newtonian models

   3. Incompressiblility dynamic pressure Navier-Stokes (NS) eqns

3. APPLICATIONS OF CONTINUUM FRAMEWORK (4 weeks):

   1. Incompressible Laminar Channel and Couette flows steady/psuedo-steady lubrication flows for incompressible Newtonian fluids

   2. Creeping flows Stokes equation; general features of creeping flow: psuedo-steady description, kinematic reversibility, superpostion stream function and its use for select 2-d creeping flows point source solutions and their applications creeping flows of non-Newtonian fluids

4. MICROSCOPIC FRAMEWORK AND APPLICATIONS (6 weeks)

   1. Langevin/Smoluchowski model modeling Brownian motion in "simple" suspensions including complex particles, external fields, and particle interactions in suspensions

   2. Applications of Langevin/Smoluchowski framework barrier crossing and first passage time problems stress tensor in elastic dumbell suspensions modeling active media³

Course Calender

WEEK DATES REMARKS

1. Sept. 8/10 Objectives/Continuum description

2. Sept. 15/17 Eulerian balance laws

3. Sept. 17/19 Constitutive laws for stress

4. Sept. 22/24 Constitutive laws/Lubricatiom flows

5. Sept. 29/Oct. 1 Lubrication flows

6. Oct. 6/8 Creeping flows

7. Oct. 13/15 Creeping flows

8. Oct. 20/22 Creeping flows/Midterm

9. Oct. 27/29 Brownian motion in "simple" suspensions

10. Nov. 5 Election Day/Langevin-Smoluchowski model

11. Nov. 10/12 BM: complex particles, external fields

12. Nov. 17/19 Dumbell suspensions

13. Nov. 24 Dumbell suspensions/Thanksgiving

14. Dec. 1/3 Dumbell suspensions/Active media

15. Dec. 8/10 Active media

16. Dec. 17-23 Finals Week

CHENE4235: Surface Reactions and Kinetics

Instructor: Jingguang Chen ([email protected])

Textbook: Principles of Adsorption and Reaction on Solid Surfaces, Richard I Masel,Wiley

Series in Chemical Engineering, 1996, Wiley and Sons; & Class Handouts

• Jan. 12, 14: Nomenclature and definition of surface structures. Mathematical methods for converting surface structures between real and reciprocal spaces.
• Jan. 19, 21: Principles of experimental techniques in characterizing surface structures.
• Jan. 26, 28: Kinetics and thermodynamics of adsorption on surfaces.
• Feb. 2, 4, 9: Kinetics and thermodynamics of chemical reactions on surfaces; principles and application of experimental techniques in characterizing surface reactions and intermediates.
• Feb. 11: Midterm 1
• Feb. 16: Guest lecture: density functional theory (DFT).
• Feb. 18, 23, 25: Kinetics and thermodynamics of desorption from surfaces. Temperature programmed desorption.
• Mar. 2, 4: No class; Spring Break
• Mar. 9, 11: Surface kinetic modeling of adsorption, reaction, and desorption processes.
• Mar. 16: Midterm 2
• Mar. 18: Correlating kinetics and thermodynamics.
• Mar. 23, 25, 30: Effect of surface electronic structures on kinetics.
• Apr. 1, 6, 8, 13: Transport effects on kinetics.
• Apr. 15: Class overview.
• Apr. 20: Final Exam

Overall Course Grade

HW: 10%; Midterm 1: 30%; Midterm 2: 30%; Final: 30%

CHEN E4330 Advanced Chemical Kinetics 

Time: TBD 

Location: TBD 

Course Description: Reaction kinetics, molecular view of reaction kinetics, reactions in liquid, reactions at surfaces, diffusion-reaction systems. Applications to the design of batch and continuous reactors. Special topics in kinetics and reactor design. 

Prerequisites: Undergraduate Chemical Kinetics, Mass transport, or Kinetics S2E Module. 

Course Objectives: 

1. Understand kinetic rate expressions and how to design experiments to determine them.
2. Develop computer skills for mathematical modeling of reactive systems, with the understanding that these skills can be broadly applied to a wide range of real-world problems.
3. Develop problem-solving methodologies and creative thinking skills for the design and optimization of continuous and batch reactors.
4. Gain exposure to advanced topics in kinetics and reactor design relevant to graduate-level research and industry, with an emphasis on opportunities to engineer more sustainable chemical and energy conversion systems. 

Required Textbook: 

S. Fogler, Elements of Chemical Reaction Engineering, 5th Ed., Prentice Hall, 2016. ****Unless you are very strong in programming (Matlab, Python, etc) or another package with numerical solvers (e.g. Mathematica) you are strongly encouraged to purchase a version of Fogler that includes Polymath software. Polymath contains simple-to-learn ODE and non-linear equation solvers, and educational versions of Polymath are available $20 (4 mo. license), $30 (12 mo. license), or $39 (perpetual-use license. You can purchase and download this software from: http://www.polymath-software.com/fogler/ (Note: unfortunately Polymath is only available for Windows, and not Mac) 

Fogler’s 5th Ed. website: http://umich.edu/~elements/5e/ (additional resources found here) 

Highly recommended Textbook: 

P.L. Houston, "Chemical Kinetics and Reaction Dynamics," 2nd Ed., Dover Publishing, 2006. Note: the paperback and e-book versions of Houston are available online for around $20. 

Other potentially helpful references: 

• Sandler, S., “Chemical, Biochemical, and Engineering Thermodynamics,” Wiley, 2006. (for chemical equilibrium)
• Atkins and de Paula, “Physical Chemistry” (for molecular kinetics)
• Steinfeld, Francisco, and Hase, “Chemical Kinetics and Dynamics,” Prentice Hall, 1998.
• Rawlings and Ekerdt, “Chemical Reactor Analysis and Design Fundamentals, “Nob Hill Publishing, 2002.
• “Matlab Guide,” Higham and Higham, SIAM: Philadelphia, 2005, ISBN 0-89871-578-4. 
   

Exams: These dates are tentative and subject to change 

Midterm 1: TBD Midterm 2: TBD 

Final: TBD. 

Course Grades (*may be adjusted slightly depending on attendance app) 

Final grade will be determined by: Attendance (3%), Class participation (5%), Homework assignments (20%), Midterm #1 (17%), Midterm #2 (25%), Final exam (30%). Class participation is based on active participation in discussions, Q&A, and Canvas discussion board. 

Other Information: 

Course Website: Canvas will be used for course maintenance and information dissemination: https://courseworks2.columbia.edu/ 

Computational software: Certain homework problems will require Matlab, Polymath, Python, Mathematica, or other comparable software to be used. If you do not know how to program (i.e. for Matlab or Python), then students are recommended to learn Polymath, which contains canned solvers and is relatively easy to learn. Videos of tutorials of Polymath and Matlab solvers that will be useful for this course can be found in the “Video Library” tab on the course page on Canvas. The demo files used in those videos are located under Files → Helpful Resources & Handouts → Matlab_Polymath Session Materials 

Matlab and Mathematica are available for free download by Columbia students here.

STATISTICAL MECHANICS AND COMPUTATIONAL METHODS 

CHAP E4120 

Professor Ben O’Shaughnessy 

3 Points 

Prerequisites: Thermodynamics, elementary probability theory and statistical processes, calculus. 

STATISTICAL MECHANICS AND COMPUTATIONAL METHODS 

Microscopic to Macroscopic. Statistical Mechanics is the science of gases, liquids, solids and any other system comprising huge numbers of molecules. Thus, statistical mechanics is an extremely broad and general subject. The laws and methods of statistical mechanics are powerful: they enable us to determine all the thermodynamic (macroscopic) properties from knowledge of the molecules. In fact statistical mechanics explains the very laws of thermodynamics microscopically. 

A powerful tool. Statistical Mechanics is a powerful tool for engineers and applied scientists since it provides a means of calculating material properties from the basic molecular constituents and thus understanding the behavior mechanistically and rationally. Thermodynamics does not provide this possibility. This predictive power is invaluable in the design of products and processes. 

Computational Methods. The methods of statistical mechanics include a host of computational and statistical techniques. Statistical Mechanics is the science of statistical analysis, and its concepts and tools are designed to analyze complex stochastic processes involving vast numbers of variables. The arsenal of computational methods that exist today to attack statistical problems with huge numbers of variables were primarily born in statistical mechanics. Today, these methods find usage not only for study of molecular systems, but in diverse applications from neural brain circuits to artificial intelligence to data science. 

Aims of course. The assumptions, principles and methods of statistical mechanics will be introduced. The basic underlying concepts will be explained, whose firm understanding is a prerequisite for successfully applying the techniques to real problems. Applications cover a broad range of phenomena, many of technological importance. Modern computational techniques of statistical mechanics will be introduced, explained and applied to molecular statistical problems to illustrate the techniques and their usage. Students will discover how to code statistical mechanical computational simulations, and will see basic results derived earlier in the course vividly demonstrated in these simulations. 

Course Topics: Fundamentals and Applications. Boltzmann’s entropy hypothesis and its restatement in terms of Helmholtz and Gibbs free energies and for open systems. Correlation times, lengths and functions. Exploration of phase space and observation timescale. Calculating free energies from molecules. Applications to ideal gases, interfaces, liquid crystal displays, polymeric materials, crystalline solids, heat capacity of solids, electrical conductivity, fuel cell solid electrolytes , rubbers, surfactants, molecular self-assembly, ferroelectricity. 

Course Topics: Computational Methods: Monte Carlo (MC) and molecular dynamics (MD) computer simulation methods and their usage to calculate statistical properties of systems with large numbers of stochastic variables. MC computational method applied to phase transitions and other thermodynamic properties of liquids and gases. Deterministic MD simulations of isolated gases and liquids: hard core and general molecular interactions. Stochastic MD simulation methods (non-isolated systems): viscosity, random force and the fluctuation-dissipation theorem. Applications: 2nd law, Maxwell velocity distribution, equations of state. 

BACKGROUND TO THE COURSE 

Statistical Mechanics Explains Thermodynamics, and Enables Calculation of Material Properties from the Molecules. When thermodynamics was developed, it was not known that matter consists of molecules! Thus, the origins of the laws of thermodynamics were unknown. (1) Thermodynamics does NOT tell us what the functions of state are that define a material, E(S,V,N) or F(T,V,N) or G(T,P,N) or H(S,P,N), etc. These functions are input data to the laws of thermo, and they must be measured for each material. We cannot use thermodynamics to compute these functions. (2) Neither does thermodynamics have a fundamental microscopic basis – it is based on empirical postulates. The 2nd law and the existence of the entropy property are based on an empirical postulate, typically that “heat doesn’t spontaneously flow from one body to another hotter body.” Why is this true? Thermodynamics cannot answer this. 

Statistical mechanics provides the answers, with beautiful simplicity. In 1874 the famous entropy hypothesis of the Austrian physicist Ludwig Boltzmann provided the connection between the macroscopic (thermodynamic) and microscopic worlds: 𝑆=_𝑘𝐵 _𝑙𝑛 _Γ _. Here Γ _is the number of possible states (consistent with the constraints) and 𝑘𝐵 _is Boltzmann’s constant. Thus, all we have to do is calculate how many possible states the molecules can be in, and this yields the entropy (from which one can obtain all the other thermodynamic functions like F, G, H, Ω). Hence, if the molecules are known (so their interactions are known, etc.), then all thermodynamic functions can be obtained and all material properties and behaviors in different processes predicted. The 2nd law, ^ΔSuniverse>0, emerges instantly and logically from Boltzmann’s hypothesis. It becomes very clear that this law is entirely a consequence of the molecular nature of materials. It explains the arrow of time, an arrow missing from the basic Newtonian and quantum mechanical laws of nature that exhibit t→-t invariance (consider a collision of 2 balls on a pool table – if you played the movie backwards you wouldn’t know, because Newton’s laws are still obeyed). 

Molecularly Based Engineering Design. Thus, statistical mechanics provides the link between the microscopic and the macroscopic, the world of molecules and the world of materials. It has therefore opened the door to a modern era of molecularly based engineering, central to the present and the future of chemical engineering. Statistical mechanics enables us to design molecules (even to build entirely new ones, like polymers) that will constitute new materials with desired properties, to build nanoscale devices that harness molecules for applications in sensing and other new technologies, or to understand molecular mechanisms in living cells and thereby guide the treatment and prevention of disease. 

Computational Techniques of Statistical Analysis. Statistical mechanics is, of course, about statistics. It is the science of statistical analysis, and its concepts and tools are designed to analyze and understand complex stochastic processes involving vast numbers of variables. The arsenal of computational methods that exist today to attack statistical problems involving huge numbers of variables were primarily born in the field of statistical mechanics. Today, these methods find usage not only in the study of molecular systems, but in diverse applications from neural circuits in the brain to artificial intelligence to data science. 

Syllabus 

Topic 1. Aims of Statistical Mechanics. Liquid crystal displays. Mathematical preliminaries (delta functions, integrals, etc.). Statistical concepts, fluctuations, Gaussian distributions. Probability distributions, multiple sums and integrals. 

Topic 2. Counting possible realizations: random walks, model of polymer chain. Toy problems with balls, balls in a box. Equal probability postulate. Stirling’s approximation. Law of large numbers, central limit theorem. Balls in a box: Gaussian distributions, √𝑁 _fluctuations. Phase space and state vector. Gases, liquids and solids: labeling and counting states. Macroscopic properties. 

Topic 3. Basic assumption of statistical mechanics: Boltzmann’s entropy hypothesis. Equal probability postulate to calculate time averages. Equilibrium. Calculating average values of macroscopic properties of isolated systems: the procedure. 

Topic 4. Ideal gas law. Entropy is extensive. Second Law of Thermodynamics. Temperature. Probability distributions of macroscopic properties. 

Topic 5. The crystalline state. Defects in crystals. Electrical conductivity of ionic solids, fuel cell electrolytes. 

Topic 6. Rubbers (elastomers). Industrial and commercial importance. Natural elastomers in living tissue. Using statistical mechanics to calculate rubber modulus. Why rubbers are much softer than metals.

Topic 7. Rephrasing Boltzmann’s entropy hypothesis for non-isolated systems: formulae for Helmholtz and Gibbs free energies and Grand Potential. Applications to ideal gases, elastic waves in solids and specific heat of solids (Debye theory). 

Topic 8. Insulators, polarization, and ferroelectricity. Technologies using ferroelectricity. Surfactant self assembly. Applications involving micelles. Surfactant aggregation and the critical micelle concentration, CMC. 

Topic 9. Computational methods in statistical mechanics: introduction. Monte Carlo (MC) computational methods. The Metropolis algorithm. Applications of MC methods: thermodynamics of gases and liquids, gas-liquid phase equilibrium, ferromagnetism and the Ising model. 

Topic 10. Molecular dynamics (MD) computational methods. Deterministic MD simulations for isolated systems. Coding up an isolated hard core gas MD simulation. Introduction to Jupyter Notebook (web-based interactive computational environment). Jupyter Notebook documents for live code, numerical simulation and data visualization. 

Topic 11. Hard core MD simulations to test predictions of statistical mechanics: 2nd law, reversibility and irreversibility; emergence of temperature property; spatial distributions, fluctuations; velocity distributions. 

Topic 12. Deterministic MD simulations of general gases/liquids (Lennard-Jones, arbitrary intermolecular potentials). Coding up and running the simulation using Jupyter Notebook. 

Topic 13. Stochastic MD simulations (non-isolated systems). Drag forces, random forces to impose temperature. Fluctuation-dissipation theorem. Coding up and running a stochastic MD simulation using Jupyter Notebook. 

COURSE WEBSITE 

https://courseworks.columbia.edu/

• Access Zoom links for classes and office hours
• Downloadable homeworks and solutions
• Downloadable practice exams plus solutions from past years
• Selected Topics and Applications: Slide shows illustrating applications of statistical mechanics in technology, biology and materials fundamentals
• Course info: office hours, TA contact, etc.
• Bibliography 

BIBLIOGRAPHY 

Course textbook 

Course pack containing all lecture notes that Prof. O’Shaughnessy will present in class, plus Reif extracts. 

This year, all lecture notes will be available for download from the course website. 

Recommended reading :

• Statistical Mechanics,  S. K. Ma (World Scientific, Philadelphia, 1985)
• Fundamentals of Statistical and Thermal Physics, F. Reif (McGraw-Hill, New York, 1965
• Understanding Molecular Simulation: From Algorithms to Applications, Daan Frenkel and Berend Smit (Academic Press, 2002)
• The Fokker-Planck Equation: Methods of Solution and Applications, H. Risken (Springer, 1996) 

GENERAL INFORMATION 

Instructor: Prof. Ben O’Shaughnessy, [email protected]

REQUIREMENTS 

• Weekly homeworks.
• (i) Midterm exam (ii) Final exam 

ADVANCED CHEMICAL ENGINEERING THERMODYNAMICS 

Instructor: Sanat Kumar 

Electronic mail: [email protected] 

Assigned Textbook: Aydil & Arora Lectures in Thermodynamics 

Recommended Texts: 

• Koretsky
• Panagiotopoulos Essential Thermodynamics
• Smith, Van Ness, Abott Introduction to Chemical Engineering Thermodynamics 7th edition, McGraw-Hill, 2005 

Classroom Etiquette: Class notes will be posted on line. Please come to class on time – no more than 10 min late if you have to. You do not need to be in class if you don't want. 

Teaching Philosophy: You will be expected to do a lot of “self-learning”. This means that material assigned to you will not be covered completely in class. Also, I will not cover details of calculation procedures. Expect the class to be very interactive. I will set up break outs so that you can solve problems. The whole focus of the lectures will be problem solving 

Quizzes/Homework: Homeworks will be assigned but no homework will be collected. 

Exams: There will be one midterm test and a final exam. The midterm and final exams will be open book and notes.

Grades: The final course grade will be based on the following percentages. Test 50%; Final: 50%. I will not grade on a curve. Past experience teaches that there is a rough correspondence between unscaled scores and grades. Over the last few years this is the pattern that has emerged: A (>70%), A- (65-70%), B+(60-65), B(55-60), B-(50-55), C(40-50), C-(38-40), D(<38). Even with the addition of the project you can assume that this will continue to apply. 

Personal Pronouns: I would like to use the personal pronouns of your choice. Please let me know – and please remind me as necessary. 

HONOR CODE: Each of you is expected to follow an honor code. You will not copy from each other or the literature without proper attribution. You will not talk to other groups about specific solutions – general discussions are fine. In each case, if you have any doubt at all, ASK me or the TAs - don't presume. 

TENTATIVE SCHEDULE 

Date(s) Comment Section* Pages* Subject 

Oct 26 Ch 1,2 1-18 Definitions, First law 

Oct 28 Ch 2 18-24 Energy 

Nov 2 Ch 2 24-39 Open systems 

Nov 4 Ch 2 39-58 Differential balances 

Nov 9 Ch 3 59-64 Entropy, Second law 

Nov 11 Ch 3 64-70 Second law open systems 

Nov 16 Ch 4 71-82 Legendre tranforms 

Nov 18 Ch 4 82-99 Maxwell relationships, calculus of thermodynamics 

Nov 23 Midterm 

Nov 25 No class 

Nov 30 Ch 5 99-107 Thermodynamics of pure materials 

Dec 2 Ch 7 129-139 Equilibrium 

Dec 7 Ch 7 139-155 One component materials, nucleation 

Dec 9 Ch 8 155-163 Phase equilibria in one component systems

Dec 14 Ch 9 163- Thermodynamics of mixtures

CHEN E4010 Mathematical Methods in Chemical Engineering 

Syllabus and Lectures Schedule – Spring 2020 

Welcome! 

CHEN E4010 Mathematical Methods in Chemical Engineering is a rigorous course that is an important component of the foundations of your graduate education in chemical engineering. I love math for its inherent beauty and awesome power in solving practical problems in almost any field. In this course, you will have an opportunity to appreciate this in the context of chemical engineering problems. 

1. CHEN E4010 Math Methods in Chemical Engineering - 3.0 pts 
   Prerequisites: CHEN E3120 and E4230, or equivalent, or instructor's permission. Mathematical description of chemical engineering problems and the application of selected methods for their solution. General modeling principles, including model hierarchies. Linear and nonlinear ordinary differential equations and their systems, including those with variable coefficients. Partial differential equations in Cartesian and curvilinear coordinates for the solution of chemical engineering problems. (http://www.columbia.edu/cu/bulletin/uwb/ ) 
    
2. Instructor: 

Professor Venkat Venkatasubramanian 

Mudd 819 

212-854-4453, [email protected] 

Teaching Assistant, Mr. Jagan Mohan Sanghishetty email: [email protected] 

3. Class Hours/Office Hours:
   1. Class Hours: Tue and Thu - 10:10 AM – 11:25 AM
   2. Office Hours: Thursday 4 – 5 PM in Mudd 233. Otherwise by appointment. Email contact is the preferred method of contact for ease of recording information.
   3. TA Office Hours: TBA
4. Classroom: Mudd 233
5. Textbook and Materials (required and supplemental):
   1. Textbook (Required): Rice, Richard G. and Duong D. Do Applied Mathematics and Modeling for Chemical Engineers 2nd Edition, New York, Wiley 2012. ISBN-13: 978-1118024720. ISBN-10: 1118024729 2 

(Suggested): 

Francis B. Hildebrand, Advanced Calculus for Applications, 2nd Edition, Prentice-Hall (1976). ISBN-13: 978-0130111890, ISBN-10: 0130111899 

Materials(required): 

CHEN E4010 – CourseWork's web site https://courseworks2.columbia.edu/welcome/

Materials (supplemental) 

Reference books and internet sites 

Abramowitz, Milton and Irene A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover, 1965 9th printing. 

Billo, E. Joseph, Excel for Scientists and Engineers, Numerical Methods, Hoboken, NJ: Wiley, 2007 

Fogler, H. Scott, Elements of Chemical Reaction Engineering 4th Edition (3rd Printing), New York: Prentice Hall, 2006 

Fong, C.F. Chan Man, D. De Kee and P.N. Kaloni, Advanced Mathematics for Applied and Pure Sciences, Canada: Gordon Breach Science Publishers, 1997. 

(http://cuit.columbia.edu/mathematica-students accessed Jan 5, 2017) 

(http://www.mathworksheetsgo.com/trigonometry-calculators/inverse-cosine-calculator.php accessed Jan 5, 2017) 

(http:// http://integrals.wolfram.com/index.jsp accessed Jan 5, 2017) 

Aris, Rutherford, Vectors, Tensors, and the Basic Equations of Fluid Mechanics. New York: Dover Publications Inc. 1962. 

Stewart, James, Calculus Concepts and Contexts, New York: Brooks/Cole Publishing. 1998, P402 -408, Section 5.6 Integration by parts 

Strang, Gilbert, Introduction to Linear Algebra, Wellesley-Cambridge Press and SIAM, Fifth Edition (2016). Excellent introduction to the subject. 

Zill, Dennis G. and Warren S. Wright, Advanced Engineering Mathematics, Burlington, MA: Jones and Bartlett Learning LLC, 2014. Engineering mathematics textbook. 

Other supplemental material, notes, and problems will be posted on the CourseWorks web page, which will be updated throughout the course. 

6. Course Objectives: 

a. Be able to mathematically describe chemical engineering problems and the application of selected methods for their solution. 

b. Apply general modeling principles, including model hierarchies. 

c. Solve linear and nonlinear ordinary differential equations and their systems, including those with variable coefficients. 

d. Solve partial differential equations in Cartesian and curvilinear coordinates for the solution of chemical engineering problems. 

e. Hopefully, learn to love and admire mathematics for its inherent beauty and its almost magical power in solving practical problems. 

7. Classroom Procedures: 

a. What you should to bring to class: A calculator, writing implement, a notebook, textbook, computer laptop as desired. 

b. What not to bring to class: Anything that could disturb others around you. Anything that would distract you or others from the guest speaker such as but not limited to a plate of food, computer games, any device that make sounds, course work from another class, social media connecting devices, etc. 

c. Be on time for class and actively participate. Being on time for class means that you are seated, ready to take notes, solve problems, listen to lecture, and take other class room instructions prior to the start time. You are also expected not to chat and distract. This standard is adopted in order to provide the best class experience possible. Class participation is part of your grade. You are required to be in class and seated ready to go at the start time. If you are found to be a distraction, you may be asked to leave. 

d. Web Site. The web site for this class contains important administrative and scheduling information, and is located at the Columbia Course Works web site: https://courseworks.columbia.edu/welcome/ I will update the site with lecture slides and links to articles and resources as appropriate. 

8. Course Grade: The final grade in this course will be based on points awarded according to the following system: 

a. Final grade: 50 % midterms (two midterms, 25% each) + 50 % final 

b. References for In-Class Exams: The exams are closed book and closed notes. You are not allowed to use any books or notes of any sort during the exams, except for a “crib sheet” (one page for all exams) as a concise set of notes used for quick reference. Exam “Blue books” will be provided for you. You are not allowed to use any cell phones, calculators, computers, or any device that allows for storage of data during the exams. Any exceptions to this policy will be announced by the instructor prior to the specific event.

9. Homework: Homework problems will be assigned and completion dates suggested. However, homework will not be collected or graded. You are ultimately responsible for knowing all aspects of the problems. To help you learn, homework solutions will be made available through the TA. A student in the course can do the work and contact TA for assistance in order to learn the material. Copying solutions will not achieve this and is against Columbia University Policy. (http://bulletin.engineering.columbia.edu/policy-conduct-and-discipline). The re-distribution of the homework solutions in CHEN E4010 is not authorized. The TA has office hours so that you can meet and cover homework problems that you have attempted or perhaps need assistance or clarification with the solution. While the homework in the math methods course is not graded, the homework is still an assignment for a student in the course and are assigned to help your learning. 

10. Academic integrity: If a student is suspected of a breach of academic integrity, the student will be referred to the university office on matters of honor and academic integrity. As your grade is determined based on in-class examinations, it is imperative that you do your own work. Do not cheat on any exams. Students who are suspected of cheating on an exam will be reported to the School of Engineering and Applied Science for further processing, which can result in dismissal from Columbia. All students are reminded of the following information from the Columbia University Web site: 

“Academic integrity defines a university and is essential to the mission of education. At Columbia students are expected to participate in an academic community that honors intellectual work and respects its origins….As such, a violation of academic integrity is one of the most serious offenses a student can commit at Columbia and can result in dismissal.” 

(http://bulletin.engineering.columbia.edu/policy-conduct-and-discipline, accessed 23 Jan 2016) 

“Academic Integrity Policies and Expectations: Violations of policy may be intentional or unintentional and may include dishonesty in academic assignments or in dealing with University officials, including faculty and staff members. Moreover, dishonesty during the Dean’s Discipline hearing process may result in more serious consequences” 

(http://bulletin.engineering.columbia.edu/policy-conduct-and-discipline, accessed 23 Jan 2016) 

“Common types of academic integrity violations: 

-Plagiarism: the use of words, phrases, or ideas belonging to another, without properly citing or acknowledging the source 

-Self-plagiarism: the submission of one piece of work in more than one course without the explicit permission of the instructors involved 

-Falsification or misrepresentation of information in course work or lab work; on any application, petition, or forms submitted to the School 

-Fabrication of credentials in materials submitted to the University for administrative or academic review 

-Violating the limits of acceptable collaboration in course work set by a faculty member or department 

-Facilitating academic dishonesty by enabling another to engage in such behavior 

-Cheating on examinations, tests, or homework assignments 

-Unauthorized collaboration on an assignment 

-Receiving unauthorized assistance on an assignment 

-Copying computer programs 

-Unauthorized distribution of assignments and exams 

-Lying to a professor or University officer 

-Obtaining advance knowledge of exams or other assignments without permission “ 

(http://bulletin.engineering.columbia.edu/policy-conduct-and-discipline, accessed 23 Jan 2016) 

11. Lecture Schedule 

(Note: (1) 1/21 – Lecture # and Date; Pages in parentheses refer to Rice & Do; Schedule and topics might change somewhat depending on the course progress.) 

1. I. Model formulation (1) 1/21 A. General modeling principles (pp. 3-10)
   1. B. Model hierarchies (pp. 19-25)
      1. C. Typical ChE model formulation examples 
         
          
   2. II. Review of Linear Algebra A. Vectors and Matrices (pp. 10-17; Strang, Ch. 1-2) (2) 1/23
      1. B. Solving linear equations (3) 1/28
         1. C. Vector Subspaces, Orthogonality, Determinants (Strang, Ch. 3-5) (4) 1/30,(5) 2/4
            1. D. Eigenvalues and Eigenvectors, Linear transformations (Strang, Ch. 6, 8) (6) 2/6 
   3.  

III. Linear ODEs (7) 2/11 A. First order (pp. 32-33) 

B. Systems of linear first order ODEs (pp. 55-60) (8) 2/13 

C. Higher order with constant coefficients (9) 2/18 

1. Homogeneous (pp. 42-47) 

1. 2. Non-homogeneous (pp. 47-50, 54-55) 

D. Systems with constant coefficients (pp. 55-60) 

E. Higher order with variable coefficients (10) 2/25 

1. Special cases and strategies (p. 40, 41) 

2. Power series solutions (pp. 75-77) (11) 2/27 

3. Method of Frobenius (pp. 77-86) (12) 3/3 

4. Bessel and Gamma functions (pp. 86-92, 98-99) (13) 3/5 

5. Legendre polynomials (Hildebrand pp. 159-165) (14) 3/10 

F. Eigenvalue problems (15) 3/12

Midterm Exam 1 on 2/20 

Spring Recess (3/16-20) 6 

IV. Linear PDEs (pp. 229-233) (16) 3/24 

A. Separation of variables (pp. 238-248) 

1. Sturm-Liouville Problems, Cartesian Parabolic PDEs 

2. Cylindrical Parabolic PDEs (17) 3/26 

3. Parabolic PDEs with non-homogeneities (18) 3/31 

4. Elliptic PDEs (19) 4/2 

B. Finite Fourier Transforms (pp. 273-289) (20) 4/7 

C. Combination of variables/Similarity transform (pp. 233-8; 97-8) (21) 4/14 

1. Rayleigh problem and error function (22) 4/16 

Midterm Exam 2 on 4/9 

V. Nonlinear ODEs (23) 4/21 

A. First order strategies (pp. 33-37) 

B. Second order strategies (pp. 37-42) (24) 4/23 

C. Systems of nonlinear ODEs 

D. Linearization 

VI. Laplace transforms (pp. 204-215, 248-253) (25) 4/28 

A. Solving ODEs, systems of ODEs, and PDEs 

B. Inversion: practical guidelines 

VII. Numerical Solution Methods (pp. 139-156) (26) 4/30 

A. Euler’s method, Midpoint method, Trapezoidal method 

B. Runge-Kutta 

C. Stiff differential equations, Implicit Euler’s method 

D. MATLAB ODE Suite 

Exam Schedule 

Midterm Exam 1: Modeling principles, Linear Algebra, Linear ODEs with constant coefficients, Systems of linear ODEs with constant coefficients – _2/19 

Midterm Exam 2: Higher order linear ODEs with variable coefficients, Eigenvalue problems, Linear PDEs by separation of variables -- 4/9 

Final Exam: All course topics – _TBA 

12. Acknowledgements: 

This document is based on earlier versions prepared by Mr. Michael Hill and Dr. Robert Bozic, who had taught this course in previous years. I have benefited greatly from their input about the course.

Engineering Applications of Electrochemistry 

Chemical Engineering E 4201 

Fall, 2019 

Textbook: 

Alan C. West, Electrochemistry and Electrochemical Engineering. An Introduction. ISBN. 9781470076047 

Course Prerequisite: Physical chemistry and transport phenomena, or permission of instructor. 

Homework: Homework will be required on a nearly weekly basis. We anticipate 10 HW assignments. Homework will be collected but not graded. Solutions will be provided. We will record whether they were turned in or not (10% of grade). Late assignments not accepted. 

Course Grade: Depending on the year, mix of exams, design projects, homework 

Topics. 

Chapter 1-10 

Tentative Outline (Changes from year-to-year, especially towards the semester end). 

Week #1: Chapters 1 and 2 : Introduction, Background Concepts 

Week #2: Chapters 2 and 3: Background Concepts, Electrode Kinetics 

Week #3: Chapter 3: Electrode Kinetics 

Week #4: Chapter 4: Thermodynamics 

Week #5: Chapter 4: Thermodynamics 

Week #6: Chapter 5: Transport Phenomena 

Week #7: Chapter 5: Transport Phenomena 

Week #8: Chapter 6: Current Distributions 

Week #9: Chapter 6 and 7: Current Distributions and Rotating Electrodes 

Week #10: Chapter 7: Rotating Electrodes 

Week #11: Chapter 9: Porous Electrodes 

Week #12: Chapter 9: Porous Electrodes 

Week #13: Special Topics 

Week #14: Special Topics

CHEN E4231: Solar Fuels 

*Note*: this is an example syllabus that is reflective of typical content for this course. Specific subjects and assignments vary from year to year. 

Lecture Hours: 3 pts 

Prerequisites: Graduate standing or completed CHEN E4230. Open to grad and undergrads. 

Time: Varies from year to year 

Location: Varies from year to year 

Instructor: Prof. Daniel Esposito 

TA: Varies from year to year 

Course Description
Fundamentals and applications of solar energy conversion, especially technologies for conversion of sunlight into storable chemical energy, or solar fuels. Topics include fundamentals of electrochemistry, photoelectrochemistry, kinetics of solar fuels production, solar harvesting technologies, and solar reactors for production of solar fuels. Applications include solar fuels technology for grid-scale energy storage, chemical industry, manufacturing, and environmental remediation. Additionally, students will learn to perform systems-level design and analyses of solar fuels technologies, with an emphasis on the integration of different solar harvesting and (electro)chemical unit operations. The course will include group projects based on a problem-based learning (PBL) philosophy that will (i.) expose students to interdisciplinary problems, (ii.) develop strong collaborative skills, and (iii.) promote critical thinking skills that are essential for solving open-ended problems. 

Primary Course Objectives: 

1. Learn fundamental principles that underlie solar and (photo)electrochemical energy conversion processes and technologies.
2. Develop problem-solving methodologies and creative thinking skills for the design and optimization of solar and electrochemical reactors.
3. Gain exposure to advanced topics in solar- and electrochemical engineering relevant to graduate-level research and emerging technologies in the clean-tech industry. 

Required Textbook: 

1. PVCDROM, online photovoltaics textbook, Honsberg, C., Bowden, S., www.pveducation.org (Freely available) 

Recommended Textbook: 

1. West, Electrochemistry and Electrochemical Engineering, 1st Ed., 2012. 

Other helpful references: 

• PVCDROM, online photovoltaics textbook, Honsberg, C., Bowden, S., www.pveducation.org (Freely available)
• Principles of Solar Engineering, 3rd, Edition by D. Yogi Goswami, Frank Kreith, and Jan F. Kreider. Taylor & Francis, 2015.
• Handbook of Photovoltaic Science and Engineering Luque, A. and Hegedus, S., eds. 2011, 2nd ed., Wiley (Electronic version available for free through Columbia)
• J. Newman & K.E. Thomas-Alyea, Electrochemical Systems, 3rd Ed., Wiley, 2004.
• Bard and Faulkner, Electrochemical Methods, 2nd Ed., Wiley, 2001.
• M.A. Green, Solar Cells, Prentice-Hall, 1982. 

Course Grades will be based on: 

Homework and idea filter assignments (30%), Midterm (30%), Final Project (30%), Class participation (10%). 

Exams: These dates are tentative and subject to change: 

Midterm: TBD, Final Exam: TBD. 

*If you require disability-related academic accommodations for exams, see the last page of this syllabus for more details about registering for Disability Services (DS). 

Final Project: A group project will be assigned mid-way into the semester. This project is based on open-ended “solar fuels” problems that each group will get to choose from project ideas proposed by the class through an idea filter. A 4 page report and final presentation will be due by each group at the end of the semester (See course schedule next page). 

Other Information: 

• A few homework problems may require Matlab, Polymath, Python, or other comparable software to be used.
• Canvas will be used for course maintenance and information dissemination.
• Class participation may be based on attendance, active participation in discussions, Q&A, participation in Canvas discussion boards. 

Homework Policy 

• Homework is due at the beginning of class on the due date specified. No exceptions.
• Late homework will be accepted with a 50% penalty up until the date the graded assignment is returned to the class or the hw solution has been posted online.
• Select homework problems will be graded.
• You must show your work in order to receive full credit. For problems solved using software such as Matlab or Python, include your code at the end of the hw set. If excel was used to generate solution plots, be sure to write-up all equations input into excel to generate those plots and fully describe the methodology used to solve the problem.
• Collaboration with classmates on homework is encouraged, with limits.
• Acceptable collaboration includes discussing the problem statement, sharing ideas or approaches to solving the problem, and explaining concepts to one another.
• You must write the name of collaborators on the top of your HW assignment.
• Directly copying answers from ANY source is unacceptable. Turning in anything that does not represent your own work and thought process is considered plagiarism and is subject to the Columbia Policy on Academic Integrity.
• For the report sections of the final project, plagiarism or “copying” of written sections is also strictly prohibited. Cite all references for information used within your report.
• List your collaborators at the top of your homework solutions when you turn it in. 

Syllabus unavailable

Syllabus unavailable

Biochemical Engineering CHEN E4660

Generalized/Tentative Syllabus

Summary of Course:

Application of engineering principles to biological systems. The design, development, and analysis of processes using biocatalysts will be explored. Processes of interest include those that are involved in the formation of desirable compounds and products or in the transformation or destruction of unwanted or toxic substances.

Educational Objectives:

1. Understand the data requirements, analysis, and interpretation for kinetic, thermodynamic, and
2. stoichiometric calculations used for biochemical engineering
3. Assess the biological factors that are important for the design, operation, and performance of a
4. biotechnology process
5. Formulate how to apply kinetic calculations and mass balance analysis for biological reactor
6. design and operation
7. Describe some of the contributions (and potential) of biochemical engineering to society
8. Communicate biochemical engineering concepts through images, writing, and presentation

Instructor: Prof. Allie Obermeyer

Time and Location: TBD

Prerequisites: CHEN E3230 (Reaction kinetics and reactor design) or equivalent. May be taken concurrently or with permission from the instructor.

Textbook:

Shuler and Kargi Bioprocess Engineering Basic Concepts, 3rd Ed. Prentice Hall 2017

Diversity & Inclusion: I would like to create a learning environment that supports a diversity of thoughts, perspectives and experiences, and honors your identities (including race, gender, class, sexuality, religion, ability, etc.) To help accomplish this: (1) if you have a preferred name and/or set of pronouns that differs from what is presented on Courseworks, please let me know; (2) if you feel like your performance in the class is being impacted by your experiences outside of class, please do not hesitate to talk with me; (3) if something was said in class (by me or anyone) that made you feel uncomfortable, please feel like you can talk to me about it. I want to be a resource for you and want to make sure that everyone has the opportunity to succeed in the course.

Examination and Grading Policies:

In class problem solving: We will work problems together during class time. Students will work in small groups on the problems and the instructor will circulate amongst the groups. We will then come back together and you may be randomly called on to lead the discussion of the problem. But, before anyone is called on you will have had the opportunity to work in your small groups on the problem. Students will turn in scanned copies of the worked problems on Courseworks by midnight ET on the day that problems were worked in class.

Participation in online quizzes: In conjunction with the asynchronous video lectures, there will be checkin quizzes on Courseworks. These brief quizzes need to be completed prior to class to receive credit.

Paper Reflections: Over the course of the semester we will read 12 pre-selected research articles, perspectives, and reviews and then discuss them in class. To help facilitate our in-class discussions, everyone will need to fill out a reflection on the article prior to the beginning of class. These reflections are posted as quizzes on Courseworks, but are graded based on completion.

Paper Presentation: Students will take turns presenting one of the pre-selected papers to the class. Students will work in small groups to provide a brief overview of the paper prior to the class discussion. This should be in the format of a PowerPoint presentation that includes relevant background, a summary of the article, and schematics/figures from the paper. Guidance on giving a good presentation will be covered in the second lecture in addition to the Instructor’s example presentation of Paper 1.

Exams: There will be a final exam to be completed at the end of the semester. It will be open book and open note. You are strongly encouraged to make a 1-2 page cheat sheet as a study guide and exam tool as the exams will be timed. The final exam is to be completed independently without the help of your classmates, peers, or the internet. Academic dishonesty will not be tolerated on exams (or any other assignments) in the course.

Policy on late assignments: Students are allowed one unexcused late submission of an assignment (excluding the final exams). If you are concerned about turning in assignments on time reach out to the instructor prior to the assignment being late to make accommodations. Additional accommodations may be made on a case-by-case basis for students personally impacted by COVID19.

Participation: Attendance in class is strongly recommend and active participation in class may be taken in to account in your final grade, particularly if your grade falls near a letter grade cutoff.

Your overall grade in the course will be determined as follows:

In class problems: 22%

Online quizzes: 10%

Paper reflections: 11%

Paper presentation: 22%

Final exam: 35%

Academic Integrity: On each assignment, I ask you (implicitly or explicitly) to commit to Columbia’s policy on academic integrity. Any violations will be reported to proper administration officials and can result in disciplinary action as well as a zero on the assignment or a reduction in your final course grade. It is never worth it to cheat, even if the alternative is doing poorly on an assignment. 

Please review Columbia’s policy on academic integrity carefully: https://bulletin.engineering.columbia.edu/policy-conduct-and-discipline.

I look forward to facilitating your learning of biochemical engineering throughout the semester. Your comments on the course are appreciated at any point during the semester. Good luck with the course!

Tentative Schedule for CHEN E4660

Week # Topic Reading Activity

Week 1 

1 Introduction to biochemical engineering pg 1-11 -

Week 2

2 Fundamental biological concepts pg 13-58, 113-139 Paper 1

3 Enzyme kinetics pg 61-71 In-class problems

Week 3

4 Enzyme inhibition, pH and T effects pg 71-83 Paper 2

5 Immobilized enzyme kinetics pg 86-98 In-class problems

Week 4

6 Immobilized enzyme kinetics pg 86-98 Paper 3

7 Microbial growth pg 169-184 In-class problems

Week 5

8 Stoichiometry of growth pg 227-236 Paper 4

9 Microbial growth kinetics pg 191-208 In-class problems

Week 6

10 Continuous culture pg 208-219 Paper 5

11 Bioreactor design pg 275-297 In-class problems

Week 7

12 Bioreactor design pg 275-297 Paper 6

13 Bioreactor design - In-class problems

Week 8

14 Mass transfer pg 184-191, 331-337 Paper 7

15 Mass transfer pg 184-191, 331-337 In-class problems

Week 9

- Election Holiday - -

16 Sterilization of media and air pg 356-365 Paper 8

Week 10

17 Animal cell culture pg 431-449 In-class problems

18 Genetic modification of organisms pg 471-506 Paper 9

Week 11

19 Genetic modification of organisms pg 471-506 In-class problems

20 Cellular and metabolic engineering pg 506-514 Paper 10

Week 12

21 Recovery and purification pg 371-382, 395-420 In-class problems

- Thanksgiving Holiday - -

Week 13

22 Recovery and purification pg 371-382, 395-420 Paper 11

23 Recovery and purification pg 371-382, 395-420 In-class problems

Week 14

24 Catch-up - Paper 12

25 In-class Jeopardy review - -

Week 15 

26 FINAL EXAM - -

CHEN E4860 

NMR for Biological, Soft, and Energy Materials 

Syllabus

Time: Mon/Wed, 5:40–6:55pm, but subject to change 

Location: varies 

Instructor: Prof. Lauren Marbella 

Recommended (but not required) texts: “Spin Dynamics” Malcolm H. Levitt. John Wiley & Sons Ltd, 2008. (on reserve) and “Understanding NMR Spectroscopy” James Keeler. John Wiley & Sons, 2005. (available through Columbia online) 

Additional useful texts: "In vivo NMR Spectroscopy: Principles and Techniques" Robin A. De Graaf. John Wiley & Sons, 1998.

“Introduction to Solid-state NMR Spectroscopy” Melinda J. Duer. John Wiley & Sons, 2005. 

“NMR Imaging in Chemical Engineering” Seigfried Stapf and Song-I Han. John 

Prerequisites: UN1401, CHEE E3010, or instructor’s approval 

Course Description: This course is for junior/senior undergraduates and graduate (MS) students as well as PhD students interested in applying nuclear magnetic resonance (NMR). The course focuses on the fundamentals of NMR spectroscopy and imaging with applications in fields ranging from biomedical engineering to electrochemical energy storage. Course material covers basic NMR theory, instrumentation (including in situ/operando setup), data interpretation, and experimental design to couple with other materials characterization strategies. Course grade is based on problem sets, quizzes, participation, and final project presentation. 

Course Significance: The design of next generation materials is one of the global challenges facing our society. The ability to engineer solar fuels, batteries, and therapeutics that withstand degradation while simultaneously displaying optimal performance rests on our ability to understand how material structure changes during operation or dynamics in the human body. NMR spectroscopy and imaging has played a crucial role in tracking the evolution of phase transformations, ion dynamics, and interfacial phenomena in real time for these complex materials. Currently, many scientists and engineers participating in these critical research fields are not exposed to NMR in their training and likewise—many NMR experts are not active in materials science applications. This course aims to bridge this gap as the use of NMR in both academics and industry becomes increasingly important in material design, system monitoring, and device fabrication. 

Grading 

• 50% Problem sets/quizzes
• 10% Participation
• 40% Final Project 

Academic Integrity 

You are all encouraged to work together at all stages of this course, so there is no need or excuse for cheating, we are a team. “Copying” answers from ANY source is unacceptable. Turning in anything that does not represent your own (or that of your group) work and thought process is

considered plagiarism and is subject to the Columbia Policy on Academic Integrity: http://www.studentaffairs.columbia.edu/fysaac/forms/acadinteg.pdfLinks to an external site. 

Disability Accommodations 

In order to receive disability-related academic accommodations, students must first be registered with Disability Services (DS). More information on the DS registration process is available online at www.health.columbia.edu/odsLinks to an external site. Please notify Prof. Marbella of registered students’ accommodations before the exam or other accommodations will be provided. Students who have, or think they may have, a disability are invited to contact Disability Services for a confidential discussion at (212) 854-2388 (Voice/TTY) or by email at [email protected]. 

Syllabus unavailable

Biochemical Engineering

CHEN E4660

Generalized/Tentative Syllabus

Summary of Course:

Application of engineering principles to biological systems. The design, development, and analysis of processes using biocatalysts will be explored. Processes of interest include those that are involved in the formation of desirable compounds and products or in the transformation or destruction of unwanted or toxic substances.

Educational Objectives:

1. Understand the data requirements, analysis, and interpretation for kinetic, thermodynamic, and stoichiometric calculations used for biochemical engineering
2. Assess the biological factors that are important for the design, operation, and performance of a biotechnology process
3. Formulate how to apply kinetic calculations and mass balance analysis for biological reactor design and operation
4. Describe some of the contributions (and potential) of biochemical engineering to society
5. Communicate biochemical engineering concepts through images, writing, and presentation

Instructor: Prof. Allie Obermeyer

Time and Location: TBD

Prerequisites: CHEN E3230 (Reaction kinetics and reactor design) or equivalent. May be taken concurrently or with permission from the instructor.

Textbook: Shuler and Kargi Bioprocess Engineering Basic Concepts, 3rd Ed. Prentice Hall 2017

Diversity & Inclusion: I would like to create a learning environment that supports a diversity of thoughts, perspectives andexperiences, and honors your identities (including race, gender, class, sexuality, religion, ability, etc.) To help accomplish this: (1) if you have a preferred name and/or set of pronouns that differs from what is presented on Courseworks, please let me know; (2) if you feel like your performance in the class is being impacted by your experiences outside of class, please do not hesitate to talk with me; (3) if something was said in class (by me or anyone) that made you feel uncomfortable, please feel like you can talk to me about it. I want to be a resource for you and want to make sure that everyone has the opportunity to succeed in the course.

Examination and Grading Policies: In class problem solving: We will work problems together during class time. Students will work in small groups on the problems and the instructor will circulate amongst the groups. We will then come back together and you may be randomly called on to lead the discussion of the problem. But, before anyone iscalled on you will have had the opportunity to work in your small groups on the problem. Students will turn in scanned copies of the worked problems on Courseworks by midnight ET on the day that problems were worked in class.

Participation in online quizzes: In conjunction with the asynchronous video lectures, there will be check in quizzes on Courseworks. These brief quizzes need to be completed prior to class to receive credit.

Paper Reflections: Over the course of the semester we will read 12 pre-selected research articles, perspectives, and reviews and then discuss them in class. To help facilitate our in-class discussions, everyone will need to fill out a reflection on the article prior to the beginning of class. These reflections are posted as quizzes on Courseworks, but are graded based on completion.

Paper Presentation: Students will take turns presenting one of the pre-selected papers to the class. Students will work in small groups to provide a brief overview of the paper prior to the class discussion. This should be in the format of a PowerPoint presentation that includes relevant background, a summary of the article, and schematics/figures from the paper. Guidance on giving a good presentation will be covered in the second lecture in addition to the Instructor’s example presentation of Paper 1.

Exams: There will be a final exam to be completed at the end of the semester. It will be open book and open note. You are strongly encouraged to make a 1-2 page cheat sheet as a study guide and exam tool as the exams will be timed. The final exam is to be completed independently without the help of your classmates, peers, or the internet. Academic dishonesty will not be tolerated on exams (or any other assignments) in the course.

Policy on late assignments: Students are allowed one unexcused late submission of an assignment (excluding the final exams). If you are concerned about turning in assignments on time reach out to the instructor prior to the assignment being late to make accommodations. Additional accommodations may be made on a case-by-case basis for students personally impacted by COVID19.

Participation: Attendance in class is strongly recommend and active participation in class may be taken in to account in your final grade, particularly if your grade falls near a letter grade cutoff.

Your overall grade in the course will be determined as follows:

• In class problems: 22%
• Online quizzes: 10%
• Paper reflections: 11%
• Paper presentation: 22%
• Final exam: 35%

Academic Integrity: On each assignment, I ask you (implicitly or explicitly) to commit to Columbia’s policy on academic integrity. Any violations will be reported to proper administration officials and can result in disciplinary action as well as a zero on the assignment or a reduction in your final course grade. It is never worth it to cheat, even if the alternative is doing poorly on an assignment. Please review Columbia’s policy on academic integrity carefully: https://bulletin.engineering.columbia.edu/policy-conduct-and-discipline.

I look forward to facilitating your learning of biochemical engineering throughout the semester. Your comments on the course are appreciated at any point during the semester. Good luck with the course!

Tentative Schedule for CHEN E4660

Week # Topic Reading Activity

1               1 Introduction to biochemical engineering pg 1-11 -

2               2 Fundamental biological concepts pg 13-58, 113-139 Paper 1

3 Enzyme kinetics pg 61-71 In-class problems

3               4 Enzyme inhibition, pH and T effects pg 71-83 Paper 2

5 Immobilized enzyme kinetics pg 86-98 In-class problems

4               6 Immobilized enzyme kinetics pg 86-98 Paper 3

7 Microbial growth pg 169-184 In-class problems

5               8 Stoichiometry of growth pg 227-236 Paper 4

9 Microbial growth kinetics pg 191-208 In-class problems

6               10 Continuous culture pg 208-219 Paper 5

11 Bioreactor design pg 275-297 In-class problems

7               12 Bioreactor design pg 275-297 Paper 6

13 Bioreactor design - In-class problems

8               14 Mass transfer pg 184-191, 331-337 Paper 7

15 Mass transfer pg 184-191, 331-337 In-class problems

9

- Election Holiday - -

16 Sterilization of media and air pg 356-365 Paper 8

10            17 Animal cell culture pg 431-449 In-class problems

18 Genetic modification of organisms pg 471-506 Paper 9

11            19 Genetic modification of organisms pg 471-506 In-class problems

20 Cellular and metabolic engineering pg 506-514 Paper 10

12            21 Recovery and purification pg 371-382, 395-420 In-class problems

- Thanksgiving Holiday - -

13            22 Recovery and purification pg 371-382, 395-420 Paper 11

23 Recovery and purification pg 371-382, 395-420 In-class problems

14            24 Catch-up - Paper 12

25 In-class Jeopardy review - -

15            26 FINAL EXAM - -

CHEN 4700. Principles of Genomic Technologies (Points: 3) 

Course Description 

This lecture course provides a comprehensive approach to integrate chemical science, engineering and biological science to study the structure, assembly and the function of the genome. The emphasize is on the understanding of how chemistry and molecular engineering is utilized in living systems to synthesize, replicate, modify and regulate the genome, and the molecular mechanism to translate the genetic information in the genome to the functional molecule of proteins. This knowledge provides the molecular basis for using organic synthesis and biophysical methods to modify, label and dissect the components involved in the genomic process, which allows the development of new approaches to sequence the genome, detect mutation, and measure gene expression at the genomic scale. 

Outline of Course Content 

Chemical and physical aspects of genome structure and organization, genetic information flow from DNA to RNA to Protein. Nucleic acid hybridization and sequence complexity of DNA and RNA. Genome mapping and sequencing methods. The engineering of DNA polymerase for DNA sequencing and polymerase chain reaction. Fluorescent DNA sequencing and high-throughput DNA sequencer development. Construction of gene chip and microarray for gene expression analysis. Technology and biochemical approach for functional genomics analysis. Gene discovery and genetics database search method. The application of genetic database for new therapeutics discovery.

Other Points: 

• Homework will be due the week after it is assigned. Late homework will receive a 25% deduction.
• Midterm and final exams will be open book and open notes.
• Two individual protein engineering projects will be assigned. Additional information will be provided during the semester.
• Courseworks system will be used for course maintenance and information dissemination. 

Syllabus unavailable

CHEN 4900 Topics in Chemical Engineering Fall 2022

Computer Simulation in Biology: Machine Learning & Physical Methods

CHEN 4900

Instructor: Professor Ben O’Shaughnessy

3 Points

Prerequisites: Basic thermodynamics

Textbook: No required textbook

Recommended background reading

• Understanding Molecular Simulation: From Algorithms to Applications, Daan Frenkel and Berend Smit (Academic Press, 2002)
• Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems, 2nd Edition, Aurélien Géron (O’Reilly)
• Molecular Biology of the Cell, 6th Edition, Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter (Garland Press, New York).
• The Fokker-Planck Equation: Methods of Solution and Applications, Risken (Springer, 1996)

Course Requirements and Grading

Participation in class discussion. Weekly assignments: reading or coding (Jupyter Notebook). Final exam: take home, written report on an assigned course topic. Final grade based on participation in class discussion, weekly assignments and final take-home exam.

Rationale for course and course summary

A vast research effort in science, engineering, medicine and biotechnology revolves around the

machineries of life at the cellular and multicellular organism level. Computer simulation is central to these spheres of biological research, whether the goal is to unlock the secrets of life, to prevent or treat disease, to develop new drugs or to evolve novel biotechnologies with societal and commercial impact. Computational methods are needed because the machineries and systems of life have high complexity. In individual cells, vast numbers of molecules and multimolecular structures coordinate for essential functions, such as synthesis of nutrients, secretion of signaling molecules, migration, cell division, gene expression, chromosome replication, defense against pathogens and countless others. At the supracellular level, in humans and other organisms multiple cells coordinate in complex systems to execute tasks such as tissue reshaping during embryogenesis, specialized organ function and synchronized firing of neurons in complex neural circuits for brain function. Due to this complexity and increasingly sophisticated experimental methods, vast amounts of data have recently become available. A major current challenge is to integrate computer simulation with machine learning methods to extract information from big data and Prof. Ben O’Shaughnessy CHEN 4900 Computer Simulation in Biology

improve and accelerate simulations.

The subject of this course is the integration of physical and machine learning methods for computer simulation of multimolecular and multicellular living systems. We discuss how simulation can unravel mechanisms, help combat disease and aid biotechnology development. Introduction to biological principles and jargon, with cellular and multicellular examples. Introduction to principles and results of statistical mechanics. Methods of many-molecule molecular dynamics (MD) simulation, from isolated deterministic MD to non-isolated stochastic MD (temperature, fluctuation-dissipation theorem). Simulations of biological molecular, subcellular and multicellular systems at different scales: from atomistic to mildly coarse-grained MARTINI MD of protein and viral systems, to ultracoarse-grained MD of cellular and multicellular systems. Introduction to neural networks (NN) and machine learning (ML). Using ML and NN to accelerate MD simulations by enhanced sampling, to determine simulation parameters from big data, and to extract complex simulation behaviors including dimensional reduction. Using ML and NN for systematic coarse-graining. Throughout, methods will be illustrated by review and class discussion of recently published research papers. Students will gain hands-on exposure to simulation code through use of Jupyter Notebook.

Transcript title (30 char max):

Computer Simulation Biosystems

Syllabus

1. Aims of Statistical Mechanics. Liquid crystal displays. Mathematical preliminaries (delta functions, integrals, etc.). Statistical concepts, fluctuations, Gaussian distributions. Probability distributions, multiple sums and integrals.
2. Counting possible realizations: random walks, model of polymer chain. Toy problems with balls, balls in a box. Equal probability postulate. Stirling’s approximation. Law of large numbers, central limit theorem. Balls in a box: Gaussian distributions, √𝑁 _fluctuations. Phase space and state vector. Gases, liquids and solids: labeling and counting states. Macroscopic properties.
3. Basic assumption of statistical mechanics: Boltzmann’s entropy hypothesis. Equal probability postulate to calculate time averages. Equilibrium. Calculating average values of macroscopic properties of isolated systems: the procedure.
4. Ideal gas law. Entropy is extensive. Second Law of Thermodynamics. Temperature. Probability distributions of macroscopic properties.
5. The crystalline state. Defects in crystals. Electrical conductivity of ionic solids, fuel cell electrolytes.
6. Rubbers (elastomers). Industrial and commercial importance. Natural elastomers in living tissue. Using statistical mechanics to calculate rubber modulus. Why rubbers are much softer than metals.
7. Rephrasing Boltzmann’s entropy hypothesis for non-isolated systems: formulae for Helmholtz and Gibbs free energies and Grand Potential. Applications to ideal gases, elastic waves in solids and specific heat of solids (Debye theory).
8. Insulators, polarization, and ferroelectricity. Technologies using ferroelectricity. Surfactant self assembly. Applications involving micelles. Surfactant aggregation and the critical micelle concentration, CMC.
9. Computational methods in statistical mechanics: introduction. Monte Carlo (MC) computational methods. The Metropolis algorithm. Applications of MC methods: thermodynamics of gases and liquids, gas-liquid phase equilibrium, ferromagnetism and the Ising model.
10. Molecular dynamics (MD) computational methods. Deterministic MD simulations for isolated systems. Coding up an isolated hard core gas MD simulation. Introduction to Jupyter Notebook (web-based interactive computational environment). Jupyter Notebook documents for live code, numerical simulation and data visualization.
11. Hard core MD simulations to test predictions of statistical mechanics: 2nd law, reversibility and irreversibility; emergence of temperature property; spatial distributions, fluctuations; velocity distributions.
12. Deterministic MD simulations of general gases/liquids (Lennard-Jones, arbitrary intermolecular potentials). Coding up and running the simulation using Jupyter Notebook.
13. Stochastic MD simulations (non-isolated systems). Drag forces, random forces to impose temperature. Fluctuation-dissipation theorem. Coding up and running a stochastic MD simulation using Jupyter Notebook. 

Syllabus unavailable

CHEN E4920 Pharmaceutical Industry for Engineers Syllabus 

Fall 2020

Instructor: Aaron Moment, [email protected]

Prerequisites: Undergraduate General Chemistry, Organic Chemistry

Course Description: This course provides students an overview of biopharmaceutical design, development, manufacturing, and regulatory requirements from an engineering perspective. The unit operations, equipment selection, and process development associated with small molecule, biologics, and vaccine manufacturing are all illustrated through examples, and quantitative engineering approaches are applied as appropriate. Small molecules, biologics, vaccines, solid oral formulations, sterile processing, and design of experiments (DoE) are treated.

Learning Objectives: Students will learn statistical and risk-assessment approaches to product development, and develop a foundational knowledge of the regulatory and engineering requirements for developing a new biopharmaceutical product. In addition, several chemical engineering transport and thermodynamic analyses will be applied to pharmaceutical unit operations including crystallization, filtration, gas-liquid mass transfer, and industrial mixing.

Lessons by week:

1. Modalities, chemical structure, and therapy: small molecules, biologics, and vaccines
2. Mixing and Scale-up in Stirred Tanks
3. Filtration and Drying
4. Crystallization and Polymorphism
5. Powder Processing
6. Solid Oral Formulation and Controlled Release
7. Review
8. Vaccine Processes
9. Biologics Upstream Processing
10. Biologics Downstream Processing
11. Sterilization Technology
12. Design of Experiments (DoE) in process development
13. Process Validation and FDA Regulations
14. Review and project presentations

Grading:

• 33% Mid-Term
• 33% Final
• 33% Project

Texts:

Recommended:

• “Chemical Engineering in the Pharmaceutical Industry: R&D to Manufacturing” A. Am Ende, D.G., Wiley & Son, 2010

Supplemental texts provided via Courseworks.

Project:

Final projects will be assigned about ó way through the class, and are due the last week. Projects have a ~ 5 page written report to the instructor, and a recorded video presentation to the class. A typical project will encompass a literature review and a design proposal or experimental plan. You may consult with anyone you wish to provide input on your reports and projects, but please provide documentation and acknowledgement of all your sources.

Academic Integrity: Turning in anything that does not represent your own work or thought process is considered plagiarism and is subject to the Columbia policy on Academic Integrity. You are expected to cite and credit others as appropriate.

Mid-Terms and Final: The mid-term and final are administered as a quizzes via Courseworks and involve multiple choice answers as well as calculations.

CHEN 4930 Biopharmaceutical Process Laboratory

Instructor: Aaron Moment, [email protected], Mudd 803

Location: ET380 and Carleton Lab. Please go to the Carleton lab for required safety briefing, lab tours, and introductions.

Prerequisites: Organic Chemistry Lab I, Undergraduate Organic Chemistry

Course Description: This laboratory based course is intended for junior and senior undergraduates and graduate students interested in gaining hands-on experience in biopharmaceutical processing. The exercises relate directly to processes and unit operations applied widely in the biopharmaceutical industry, including tableting, dissolution, disintegration, fermentation, chromatography, tangential flow filtration, mixing, and crystallization. The connections between process parameters, chemical and molecular properties, process performance, and product attributes will be illustrated through a combination of discussions in lab, experiments, and report writing.

Course Significance: This course provides students with hands on skills and direct understanding of several important pharmaceutical production techniques from both small molecule and macromolecule biologics perspectives. ABET outcomes 1,2, 5, and 6 are directly addressed by this class, especially 5 and 6.

ABET student outcome 5: An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.

ABET student outcome 6: An ability to conduct appropriate experimentation, analyze and interpret data, and use engineering judgement to draw conclusions.

Logistics: The lab activities are scheduled in a 2.5 hr block Tuesdays from 1.10 pm to 3.40 pm. There are three students per lab group, and your group will be working in the lab in six total instances, alternating with other groups. In other words you will cycle one week on/ one week off in lab. Your lab report is due the Friday of the off week, and you group is expected to work on the lab report during the off week.

Location: The primary location of the lab activities will be in ETA380. The module in tableting and compaction will be run in the Carleton Lab utilizing the MTS Universal Testing Instrument.

Office hr: There are no formal office hr. You are welcome to come to the lab sessions in your off week to ask questions, and are encouraged to discuss the material and ask questions during lab time.

Safety: Lab safety is part of this course, and is not optional. You are required to complete the training listed below before starting your lab modules. Wear lab goggles and gloves at all times, and lab coats as necessary. Safety is first and look out for your lab mates.

1. Through Rascal (https://www.rascal.columbia.edu )
   1. Carleton Lab Site-Specific Training (TC2600)
   2. Machine Shop Safety Training (TC0600)
2. In person EH&S Laboratory Safety/Chemical Hygiene/Hazardous Waste/Laboratory Fire Safety Training provided on 21 Jan at 1.10 pm in Carleton Lab (https://research.columbia.edu/safety-trainings)
3. In person first day walkthrough on 21 Jan at 1.10 pm in Carleton, then to ET380.

Access Form: Please fill out after completing your training: https://carleton.columbia.edu/access

TAs: The TAs play a big role in this class and there are multiple. One TA will be stationed in the Carleton Lab and the other in A380. Please talk to them about your lab set ups and the lab work. We also have additional volunteer TAs who may be supporting individual activities such as protein purification or crystallization.

Quizzes: There will be a 10-minute quiz before each lab module to test if you read and understood basic elements of the module before starting.

Modules:

1. Tableting, Mechanical Properties
   1. Use of MTS Universal Testing machine to make tablets and measure their mechanical properties on student designed formulations
2. Pharmaceutical Properties of Solid Oral Dosage Forms
   1. Measurement of biopharmaceutical properties with dissolution and disintegration
3. Protein Purification with Chromatography
   1. Cation Exchange
   2. Gradient Elution
4. Tangential Flow Filtration
   1. Separation of solutes based on molecular size
   2. MWCO and membrane permeability
   3. Buffer Exchange and Concentration
5. Bioreactor kLa
   1. Measurement of kLa, the gas liquid mass transfer coefficient
6. Crystallization of alpha and beta glutamic acid from monosodium glutamate
   1. Measurement of induction time for nucleation vs. supersaturation
   2. Determination of crystal from via XRD/ DSC
   3. Particle size analysis and Optical Microscopy

Grading:

• 85%: Group lab reports are due the Friday of your “off week.”
• 10%: Quizzes are ~ 10 minutes and administered in the lab to each student before starting the session. These are generally multiple choice and involve materials to be covered in the lab that day, as well as safety questions.
• 5% participation, e.g. asking questions, being present, and engaging with the TA and the instructor.

Required Texts:

Laboratory Manuals and supplementary readings provided via Courseworks.

Schedule:

Equipment:

1. MTS Universal Testing (Carleton Lab)
2. Keyence Microscope (Carleton Lab)
3. Spinner Bioreactors (ET A380)
4. Dissolved Oxygen Probe (ET A380)
5. Conductivity Probe (ET A380)
6. UV-VIS (ET A380) for concentration determination
7. AKTA Start (ET A380) for protein purification and columns
8. Tangential Flow Filtration Membrane cartridges and pumps (ET A380)
9. Crystallization Vessels (ET A380)
10. Optical Polarizing Microscope (ET A380)
11. DSC/ XRD from shared facilities (Havermeyer 5th floor, samples run by TA)

CHEN E4860 NMR for Biological, Soft, and Energy Materials

Syllabus

Time: Mon/Wed, 5:40–6:55pm, but subject to change

Location: varies

Instructor: Prof. Lauren Marbella

Recommended (but not required) texts: “Spin Dynamics” Malcolm H. Levitt. John Wiley & Sons Ltd, 2008. (on reserve) and “Understanding NMR Spectroscopy” James Keeler. John Wiley & Sons, 2005. (available through Columbia online)

Additional useful texts:

• "In vivo NMR Spectroscopy: Principles and Techniques" Robin A. De Graaf. John Wiley & Sons, 1998.
• “Introduction to Solid-state NMR Spectroscopy” Melinda J. Duer. John Wiley & Sons, 2005.
• “NMR Imaging in Chemical Engineering” Seigfried Stapf and Song-I Han. John

Prerequisites: UN1401, CHEE E3010, or instructor’s approval

Course Description: This course is for junior/senior undergraduates and graduate (MS) students as well as PhD students interested in applying nuclear magnetic resonance (NMR). The course focuses on the fundamentals of NMR spectroscopy and imaging with applications in fields ranging from biomedical engineering to electrochemical energy storage. Course material covers basic NMR theory, instrumentation (including in situ/operando setup), data interpretation, and experimental design to couple with other materials characterization strategies. Course grade is based on problem sets, quizzes, participation, and final project presentation.

Course Significance: The design of next generation materials is one of the global challenges facing our society. The ability to engineer solar fuels, batteries, and therapeutics that withstand degradation while simultaneously displaying optimal performance rests on our ability to understand how material structure changes during operation or dynamics in the human body. NMR spectroscopy and imaging has played a crucial role in tracking the evolution of phase transformations, ion dynamics, and interfacial phenomena in real time for these complex materials. Currently, many scientists and engineers participating in these critical research fields are not exposed to NMR in their training and likewise—many NMR experts are not active in materials science applications. This course aims to bridge this gap as the use of NMR in both academics and industry becomes increasingly important in material design, system monitoring, and device fabrication.

Grading

• 50% Problem sets/quizzes
• 10% Participation
• 40% Final Project

Academic Integrity

You are all encouraged to work together at all stages of this course, so there is no need or excuse for cheating, we are a team. “Copying” answers from ANY source is unacceptable. Turning in anything that does not represent your own (or that of your group) work and thought process is considered plagiarism and is subject to the Columbia Policy on Academic Integrity: http://www.studentaffairs.columbia.edu/fysaac/forms/acadinteg.pdf (links to an external site).

Disability Accommodations

In order to receive disability-related academic accommodations, students must first be registered with Disability Services (DS). More information on the DS registration process is available online at www.health.columbia.edu/odsLinks to an external site.. Please notify Prof. Marbella of registered students’ accommodations before the exam or other accommodations will be provided. Students who have, or think they may have, a disability are invited to contact Disability Services for a confidential discussion at (212) 854-2388 (Voice/TTY) or by email at [email protected].

Syllabus unavailable

Syllabus unavailable

Syllabus unavailable

CHEN 4900 Topics in Chemical Engineering Fall 2022

Computer Simulation in Biology: Machine Learning & Physical Methods

Instructor

Professor Ben O’Shaughnessy

3 Points

Prerequisites

Basic thermodynamics

Textbook

No required textbook

Recommended background reading

• Understanding Molecular Simulation: From Algorithms to Applications
  Daan Frenkel and Berend Smit (Academic Press, 2002)
• Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems, 2nd Edition
  Aurélien Géron (O’Reilly)
• Molecular Biology of the Cell, 6th Edition
  Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter (Garland Press, New York).
• The Fokker-Planck Equation: Methods of Solution and Applications
  Risken (Springer, 1996)

Course Requirements and Grading

Participation in class discussion. Weekly assignments: reading or coding (Jupyter Notebook). Final exam: take home, written report on an assigned course topic. Final grade based on participation in class discussion, weekly assignments and final take-home exam.

Rationale for course and course summary

A vast research effort in science, engineering, medicine and biotechnology revolves around the machineries of life at the cellular and multicellular organism level. Computer simulation is central to these spheres of biological research, whether the goal is to unlock the secrets of life, to prevent or treat disease, to develop new drugs or to evolve novel biotechnologies with societal and commercial impact. Computational methods are needed because the machineries and systems of life have high complexity. In individual cells, vast numbers of molecules and multimolecular structures coordinate for essential functions, such as synthesis of nutrients, secretion of signaling molecules, migration, cell division, gene expression, chromosome replication, defense against pathogens and countless others. At the supracellular level, in humans and other organisms multiple cells coordinate in complex systems to execute tasks such as tissue reshaping during embryogenesis, specialized organ function and synchronized firing of neurons in complex neural circuits for brain function. Due to this complexity and increasingly sophisticated experimental methods, vast amounts of data have recently become available. A major current challenge is to integrate computer simulation with machine learning methods to extract information from big data and improve and accelerate simulations.

The subject of this course is the integration of physical and machine learning methods for computer simulation of multimolecular and multicellular living systems. We discuss how simulation can unravel mechanisms, help combat disease and aid biotechnology development. Introduction to biological principles and jargon, with cellular and multicellular examples. Introduction to principles and results of statistical mechanics. Methods of many-molecule molecular dynamics (MD) simulation, from isolated deterministic MD to non-isolated stochastic MD (temperature, fluctuation-dissipation theorem). Simulations of biological molecular, subcellular and multicellular systems at different scales: from atomistic to mildly coarse-grained MARTINI MD of protein and viral systems, to ultracoarse-grained MD of cellular and multicellular systems. Introduction to neural networks (NN) and machine learning (ML). Using ML and NN to accelerate MD simulations by enhanced sampling, to determine simulation parameters from big data, and to extract complex simulation behaviors including dimensional reduction. Using ML and NN for systematic coarse-graining. Throughout, methods will be illustrated by review and class discussion of recently published research papers. Students will gain hands-on exposure to simulation code through use of Jupyter Notebook.

Transcript title (30 char max):

Computer Simulation Biosystems

Topics

1. Overview of biological systems. Molecules in cells including proteins and Protein Data Bank (PDB) database for protein structures. Subcellular structures: cytoskeleton, actomyosin rings and networks for cell division and shape regulation, membrane-enclosed organelles, neurotransmitter release machinery in neurons. Exocytosis, release of insulin and other hormones. Misregulated cell division and cancer. Tissue reshaping during embryogenesis, supracellular force networks. Neurotransmission, neural circuitry in the brain. Viruses: CoV-2 spike protein cell entry mechanism, influenza. Antiviral vaccines and drugs.
2. Review of Statistical Mechanics. Entropy, molecular origin of the 2nd law. Boltzmann distribution, formulae for entropy, free energy.
3. Molecular dynamics (MD) computational methods. Deterministic MD simulations for isolated systems. Coding up isolated hard core or interacting gas/liquid MD simulations. Introduction to Jupyter Notebook (web-based interactive computational environment). Jupyter Notebook documents for live code, numerical simulation, data visualization. Emergence of temperature concept. Velocity distributions, fluctuations.
4. Stochastic MD simulations (non-isolated systems). Drag forces, random forces to impose temperature. Fluctuation-dissipation theorem. Coding and running a stochastic MD simulation using Jupyter Notebook.
5. All-atom molecular dynamics (MD) simulation methods. Using PDB files as input to MD simulations. Creating, analyzing MD simulation trajectories: GROMACS and other MD simulation packages. All-atom force fields (e.g. GROMOS-96, AMBER, CHARMM.)
6. Coarse-grained (CG) force fields: Martini. Martinizing (CG procedure for a protein). Molecular dynamics Martini simulations. All-atom and Martini simulations of viral fusion proteins. Ultra coarse-grained (UCG) force fields. HOOMD-blue MD simulation package. UCG molecular dynamics of extended membranes and cellular membrane fusion machinery.
7. Introduction to machine learning and neural networks.
8. Enhanced sampling to accelerate MD simulations. Using neural networks to identify collective coordinates and to impose enhanced sampling.
9. Using machine learning and large experimental datasets to optimize simulation parameters and to systematically coarse grain molecular representations.
10. Machine learning and neural networks to extract complex behaviors from big simulation output datasets. Neural networks to identify dimensional reduction.

CHENE 4670 Chemical Engineering Data Analysis

Instructor
Prof. Kyle Bishop, [email protected], 212.854.7260, https://bishop.cheme.columbia.edu/

Teaching Assistant
Varies from year to year

Time
Varies from year to year

Location
Varies from year to year

Course Description
The ability to understand and design chemical engineering processes relies on mathematical models, which explain existing observations and make testable predictions. This course describes how experimental and chemical-process data can be used to estimate model parameters (parameter estimation), assess the relative plausibility of competing models (model selection), and design effective experiments (experimental design). These topics are connected within a common framework of probability theory as extended logic, which provides the unique consistent rules for conducting inference of any kind. Knowledge of these fundamental concepts will be of immediate and lasting value to all chemical engineers regardless of their future pursuits. Theory is reduced to practice through example problems drawn from chemical engineering practice and implemented in Python.

Course Prerequisites
This course is aimed at senior undergraduate and graduate students in Chemical Engineering. Familiarity with mathematical models in the context of thermodynamics, chemical kinetics, and transport phenomena is assumed. Prior knowledge of Python programming will be helpful but is not required.

Required Textbook

1. Sivia, J. Skilling, Data Analysis: A Bayesian Tutorial, 2nd Edition, Oxford University Press

(2006)

Recommended Textbooks

• Gelman et al. Bayesian Data Analysis, 3rd Edition, Chapman & Hall (2013)
• C. Gregory, Bayesian Logical Data Analysis for the Physical Sciences, Cambridge University Press (2005)
• T. Jaynes, Probability Theory: The Logic of Science, Cambridge University Press (2003)
• Bishop, Pattern Recognition & Machine Learning, Springer (2006)

Exams
One Midterm Exam. The exam is open book and open notes.

Homeworks
There will be five (5) problem sets, one due every two weeks. Late assignments will not be accepted.

Final Project
The course will culminate in a team project focused on a real-world problem in chemical engineering data analysis. The final project will include both a written report and a virtual poster presentation.

Course Grade
The following table provides an approximate conversion from points to letter grades.

Points

• Midterm 30
• Homework 40
• Project 30
• Total 100

Grade Points

• -A+ 85:90:95
• -B+ 70:75:80
• -C+ 65:70:75
• -D+ 50:55:60
• F <50

Course Schedule
Subject to modification from year to year.

Topic Reading

Lecture number:

1. Introduction to Bayesian data analysis (Sivia, Ch. 1)
2. Estimation of a single parameter (Sivia, Ch. 2.1)
3. Reliabilities in parameter estimation (Sivia, Ch. 2.2)
4. Gaussian noise model (known variance) (Sivia, Ch. 2.3, 2.4)
5. Multivariate parameter estimation (Sivia, Ch. 3.1)
6. Multivariate reliabilities (Sivia, Ch. 3.2)
7. Gaussian noise model (unknown variance) (Sivia, Ch. 3.3, 3.4)
8. Least squares regression (Sivia, Ch. 3.5)
9. Error propagation and variable transformations (Sivia, Ch. 3.6)
10. Bayesian model selection (Sivia, Ch. 4.1)
11. Hypothesis testing (Gregory, Ch. 7)
12. Model criticism
13. Midterm review session
14. Markov Chain Monte Carlo (MCMC) sampling
15. Logistic regression
16. Outliers (Sivia, Ch. 8.1–8.3)
17. Correlated noise (Sivia, Ch. 8.5)
18. Spectral analysis (Gregory, Ch. 13)
19. Assigning prior probabilities (Sivia, Ch. 5)
20. Experimental design
21. Parameter estimation in systems of ODEs
22. Gaussian mixture models (Bishop, Ch. 9)
23. Variational inference (Bishop, Ch. 10)
24. Bayesian neural nets
25. More numerics: autodifferentiation

Disability-related academic accommodations
In order to receive disability-related academic accommodations for this course, students must first be registered with their school Disability Services (DS) office. Detailed information is available online for both the Columbia and Barnard registration processes. Refer to the appropriate website for information regarding deadlines, disability documentation requirements, and drop-in hours (Columbia)/intake session (Barnard).

Students registered with the Columbia DS office can refer to the Master TARF section of the DS Testing Accommodations page for more information regarding disability-related academic accommodations for this course.

CHEN E4580 Artificial Intelligence in Chemical Engineering

Instructor: Venkat Venkatasubramanian

Credits and Meeting Times: 3 credits; Mon-Wed 1:10 – 2:25 pm

Prerequisite/Co-Requisite: Background in chemical engineering and Python/MATLAB programming, or instructor permission.

Background: The practice of chemical engineering routinely involves decision-making to solve challenging problems that often arise in process/product design, fault diagnosis and control, optimization, and process operations and safety. To accomplish this, historically, chemical engineers have adapted modeling concepts and techniques from different disciplines such as applied mathematics and operations research over the decades. To this, Artificial Intelligence (AI) methods have increasingly been incorporated in the last three decades. Contrary to common impression, AI in chemical engineering is not new – it has a 35-year-long history and a body of literature comprising of a few thousand papers in chemical engineering1-2. It has become clear that AI-based approaches need to be part of the modeling arsenal of well-educated chemical engineers. This course is offered to address this important need.

Description: This course is aimed at chemical engineering students to teach them how to incorporate AI-based modeling in combination with first-principles-based models derived from the understanding of the physics and chemistry (and biology) of our products, processes, and systems. To accomplish this, this course will combine the traditional symbolic AI with the more recent data-driven AI. In this regard, this course is different from the standard data science course which typically focuses only on the data-driven aspect.

Topics would include: Chemical engineering modeling approaches, knowledge representation, symbolic reasoning and inference, knowledge-based systems, statistical data analysis, and machine learning methods such as clustering, neural networks, random forests, Bayesian networks, and directed evolution. All these will be discussed using chemical engineering case studies in process monitoring, diagnosis, and control, process/product design, scheduling, optimization, and process hazards analysis. In particular, the course will address the development of hybrid models that combine first-principles knowledge of the underlying physics & chemistry with data-driven techniques and the development of causal mechanism-based models, in contrast with typical AI courses taught in computer science departments.

Grading: Homework 40% and Project 60% (using MATLAB, Python, TensorFlow and/or Keras)

Textbook: There is no textbook. Several papers from the literature will be made accessible during the course.

1. Venkatasubramanian, V., Artificial Intelligence in Process Engineering: Experiences from a Graduate Course. Chem. Eng. Educ., Fall Issue, 188–192, 1986.
2. Venkatasubramanian, V., The promise of artificial intelligence in chemical engineering: Is it here, finally?. AIChE J., 65: 466-478, 2019.

STATISTICAL MECHANICS AND COMPUTATIONAL METHODS

CHAP E4120 

Professor Ben O’Shaughnessy

3 Points

Prerequisites:

Thermodynamics, elementary probability theory and statistical processes, calculus. 
 

STATISTICAL MECHANICS AND COMPUTATIONAL METHODS

Microscopic to Macroscopic. Statistical Mechanics is the science of gases, liquids, solids and any other system comprising huge numbers of molecules. Thus, statistical mechanics is an extremely broad and general subject. The laws and methods of statistical mechanics are powerful: they enable us to determine all the thermodynamic (macroscopic) properties from knowledge of the molecules. In fact statistical mechanics explains the very laws of thermodynamics microscopically.

A powerful tool. Statistical Mechanics is a powerful tool for engineers and applied scientists since it provides a means of calculating material properties from the basic molecular constituents and thus understanding the behavior mechanistically and rationally. Thermodynamics does not provide this possibility. This predictive power is invaluable in the design of products and processes.

Computational Methods. The methods of statistical mechanics include a host of computational and statistical techniques. Statistical Mechanics is the science of statistical analysis, and its concepts and tools are designed to analyze complex stochastic processes involving vast numbers of variables. The arsenal of computational methods that exist today to attack statistical problems with huge numbers of variables were primarily born in statistical mechanics. Today, these methods find usage not only for study of molecular systems, but in diverse applications from neural brain circuits to artificial intelligence to data science.

Aims of course. The assumptions, principles and methods of statistical mechanics will be introduced. The basic underlying concepts will be explained, whose firm understanding is a prerequisite for successfully applying the techniques to real problems. Applications cover a broad range of phenomena, many of technological importance. Modern computational techniques of statistical mechanics will be introduced, explained and applied to molecular statistical problems to illustrate the techniques and their usage. Students will discover how to code statistical mechanical computational simulations, and will see basic results derived earlier in the course vividly demonstrated in these simulations.

Course Topics: Fundamentals and Applications. Boltzmann’s entropy hypothesis and its restatement in terms of Helmholtz and Gibbs free energies and for open systems. Correlation times, lengths and functions. Exploration of phase space and observation timescale. Calculating free energies from molecules. Applications to ideal gases, interfaces, liquid crystal displays, polymeric materials, crystalline solids, heat capacity of solids, electrical conductivity, fuel cell solid electrolytes , rubbers, surfactants, molecular self-assembly, ferroelectricity.

Course Topics: Computational Methods: Monte Carlo (MC) and molecular dynamics (MD) computer simulation methods and their usage to calculate statistical properties of systems with large numbers of stochastic variables. MC computational method applied to phase transitions and other thermodynamic properties of liquids and gases. Deterministic MD simulations of isolated gases and liquids: hard core and general molecular interactions. Stochastic MD simulation methods (non-isolated systems): viscosity, random force and the fluctuation-dissipation theorem. Applications: 2nd law, Maxwell velocity distribution, equations of state.

BACKGROUND TO THE COURSE

Statistical Mechanics Explains Thermodynamics, and Enables Calculation of Material Properties from the Molecules. When thermodynamics was developed, it was not known that matter consists of molecules! Thus, the origins of the laws of thermodynamics were unknown. (1) Thermodynamics does NOT tell us what the functions of state are that define a material, E(S,V,N) or F(T,V,N) or G(T,P,N) or H(S,P,N), etc. These functions are input data to the laws of thermo, and they must be measured for each material. We cannot use thermodynamics to compute these functions. (2) Neither does thermodynamics have a fundamental microscopic basis – it is based on empirical postulates. The 2nd law and the existence of the entropy property are based on an empirical postulate, typically that “heat doesn’t spontaneously flow from one body to another hotter body.” Why is this true? Thermodynamics cannot answer this.

Statistical mechanics provides the answers, with beautiful simplicity. In 1874 the famous entropy hypothesis of the Austrian physicist Ludwig Boltzmann provided the connection between the macroscopic (thermodynamic) and microscopic worlds: 𝑆=_𝑘𝐵 _𝑙𝑛 _Γ _. Here Γ _is the number of possible states (consistent with the constraints) and 𝑘𝐵 _is Boltzmann’s constant. Thus, all we have to do is calculate how many possible states the molecules can be in, and this yields the entropy (from which one can obtain all the other thermodynamic functions like F, G, H, Ω). Hence, if the molecules are known (so their interactions are known, etc.), then all thermodynamic functions can be obtained and all material properties and behaviors in different processes predicted. The 2nd law, ΔS_u_n_i_v_e_r_s_e_>_0_ _, emerges instantly and logically from Boltzmann’s hypothesis. It becomes very clear that this law is entirely a consequence of the molecular nature of materials. It explains the arrow of time, an arrow missing from the basic Newtonian and quantum mechanical laws of nature that exhibit t→-t invariance (consider a collision of 2 balls on a pool table – if you played the movie backwards you wouldn’t know, because Newton’s laws are still obeyed).

Molecularly Based Engineering Design. Thus, statistical mechanics provides the link between the microscopic and the macroscopic, the world of molecules and the world of materials. It has therefore opened the door to a modern era of molecularly based engineering, central to the present and the future of chemical engineering. Statistical mechanics enables us to design molecules (even to build entirely new ones, like polymers) that will constitute new materials with desired properties, to build nanoscale devices that harness molecules for applications in sensing and other new technologies, or to understand molecular mechanisms in living cells and thereby guide the treatment and prevention of disease.

Computational Techniques of Statistical Analysis. Statistical mechanics is, of course, about statistics. It is the science of statistical analysis, and its concepts and tools are designed to analyze and understand complex stochastic processes involving vast numbers of variables. The arsenal of computational methods that exist today to attack statistical problems involving huge numbers of variables were primarily born in the field of statistical mechanics. Today, these methods find usage not only in the study of molecular systems, but in diverse applications from neural circuits in the brain to artificial intelligence to data science.

Topics

1. Aims of Statistical Mechanics. Liquid crystal displays. Mathematical preliminaries (delta functions, integrals, etc.). Statistical concepts, fluctuations, Gaussian distributions. Probability distributions, multiple sums and integrals.
2. Counting possible realizations: random walks, model of polymer chain. Toy problems with balls, balls in a box. Equal probability postulate. Stirling’s approximation. Law of large numbers, central limit theorem. Balls in a box: Gaussian distributions, √N fluctuations. Phase space and state vector. Gases, liquids and solids: labeling and counting states. Macroscopic properties.
3. Basic assumption of statistical mechanics: Boltzmann’s entropy hypothesis. Equal probability postulate to calculate time averages. Equilibrium. Calculating average values of macroscopic properties of isolated systems: the procedure.
4. Ideal gas law. Entropy is extensive. Second Law of Thermodynamics. Temperature. Probability distributions of macroscopic properties.
5. The crystalline state. Defects in crystals. Electrical conductivity of ionic solids, fuel cell electrolytes.
6. Rubbers (elastomers). Industrial and commercial importance. Natural elastomers in living tissue. Using statistical mechanics to calculate rubber modulus. Why rubbers are much softer than metals.
7. Rephrasing Boltzmann’s entropy hypothesis for non-isolated systems: formulae for Helmholtz and Gibbs free energies and Grand Potential. Applications to ideal gases, elastic waves in solids and specific heat of solids (Debye theory).
8. Insulators, polarization, and ferroelectricity. Technologies using ferroelectricity. Surfactant self assembly. Applications involving micelles. Surfactant aggregation and the critical micelle concentration (CMC).
9. Computational methods in statistical mechanics: introduction. Monte Carlo (MC) computational methods. The Metropolis algorithm. Applications of MC methods: thermodynamics of gases and liquids, gas-liquid phase equilibrium, ferromagnetism and the Ising model.
10. Molecular dynamics (MD) computational methods. Deterministic MD simulations for isolated systems. Coding up an isolated hard core gas MD simulation. Introduction to Jupyter Notebook (web-based interactive computational environment). Jupyter Notebook documents for live code, numerical simulation and data visualization.
11. Hard core MD simulations to test predictions of statistical mechanics: 2nd law, reversibility and irreversibility; emergence of temperature property; spatial distributions, fluctuations; velocity distributions.
12. Deterministic MD simulations of general gases/liquids (Lennard-Jones, arbitrary intermolecular potentials). Coding up and running the simulation using Jupyter Notebook.
13. Stochastic MD simulations (non-isolated systems). Drag forces, random forces to impose temperature. Fluctuation-dissipation theorem. Coding up and running a stochastic MD simulation using Jupyter Notebook.

COURSE WEBSITE

https://courseworks.columbia.edu/

• Access Zoom links for classes and office hours
• Downloadable homeworks and solutions
• Downloadable practice exams plus solutions from past years
• Selected Topics and Applications: Slide shows illustrating applications of statistical mechanics in technology, biology and materials fundamentals
• Course info: office hours, TA contact, etc.
• Bibliography

BIBLIOGRAPHY

Course textbook

Course pack containing all lecture notes that Prof. O’Shaughnessy will present in class, plus Reif extracts.

This year, all lecture notes will be available for download from the course website.

Recommended reading

• Statistical Mechanics 
  K. Ma (World Scientific, Philadelphia, 1985)
• Fundamentals of Statistical and Thermal Physics 
  Reif (McGraw-Hill, New York, 1965
• Understanding Molecular Simulation: From Algorithms to Applications 
  Daan Frenkel and Berend Smit (Academic Press, 2002)
• The Fokker-Planck Equation: Methods of Solution and Applications 
  Risken (Springer, 1996)

GENERAL INFORMATION

Instructor:

Prof. Ben O’Shaughnessy

[email protected]

REQUIREMENTS

• Weekly homeworks.
• (i) Midterm exam (ii) Final exam

CHEN E4150: Computational Fluid Dynamics

CHEN E4880 – Syllabus – Spring 2020

Alexander Urban

([email protected])

Lectures: Tue/Thu 1:10 pm – 2:25 pm, 214 Pupin Laboratories

Office Hours: Mon/Thu 2:30 pm – 3:30 pm, 812 Mudd

Course Description: This course is aimed at senior undergraduates and graduate students. The course covers atomistic simulation techniques for applications at the interface of chemical engineering and materials science. Students will learn the theoretical background of various simulation techniques ranging from empirical to first-principles approaches and will get hands-on experience in using state-of the- art (free and open source) simulation software. Practical examples will focus on inorganic materials most of which will be crystalline solids, though the methods taught are transferable to other materials classes. Course grades are based on reports for practical assignments.

Textbooks: No specific textbook is required or recommended for this course. Primary literature,

scientific reviews, and/or textbook chapters for each subject will be pointed out.

Course Outcomes:

• Working knowledge of the most common atomistic simulation techniques.
• Improved ability to understand/assess results from atomistic simulations.
• Basic knowledge of state-of-the-art simulation software.

Modules and Projects: The course consists of four modules: (1) Interatomic Potentials, (2) Density-

Functional Theory, (3) Monte Carlo Simulations, and (4) Molecular Dynamics Simulations. In each

module, the required technical background is first introduced, which is followed by a hands-on lab in which a project assignment is discussed. For each project, roughly three weeks will be available to complete the assignment.

Course Grade: 100% of the course grade will be based on the four projects/assignments. There is no exam. The report for each project will count 1/4 of the final grade.

Collaborations: All outcomes (written reports, input files, output files, scripts, etc.) must be the product of your efforts. However, you may discuss with anyone in the present class for help in solving the practical assignments. It is not permissible to speak to others (outside your classmates) about your projects. It is strongly encouraged that you work with classmates! However, if you collaborate with your peers, it must be documented. Failure to reference all who helped will be considered plagiarism. Discussions with others (including seniors) about the project, or looking at previous year solutions, if available, will be considered plagiarism.

Policy for Late Submissions: Reports are due at 11:59 pm on the due date. 10% will be deducted if late by less than 24 hours. 20% off for submissions that are late by 24-48 hours, and so on.

Lecture Schedule and Due Dates (Subject to Changes):

1. Tue, 01/21 Introduction and Overview
2. Thu, 01/23 Basic Crystallography
3. Tue, 01/28 Interatomic Potentials (Part I)
4. Thu, 01/30 Interatomic Potentials (Part II)
5. Tue, 02/04 Practical Considerations using Interatomic Potentials; Preparations for Lab 1
6. Thu, 02/06 Lab 1: Interatomic Potentials
7. Tue, 02/11 Basics of Quantum Mechanics
8. Thu, 02/13 Density-Functional Theory (DFT)
9. Tue, 02/18 Practical DFT Part I: Predicting Properties of Li-Ion Batteries
10. Thu, 02/20 Practical DFT Part II: Heterogeneous Catalysis
11. Tue, 02/25 Practical Considerations and Failures of DFT; Preparations for Lab 2; Lab 1 Due
12. Thu, 02/27 Lab 2: DFT Calculations
13. Tue, 03/03 Guest Lecture: J. A. Garrido Torres – AI-Accelerated DFT Calculations
14. Thu, 03/05 Basic Statistical Mechanics
15. Tue, 03/10 Fundamentals of Monte Carlo (MC) Simulations
16. Thu, 03/12 Advanced MC Topics

03/16-03/20 Spring Recess

17. Tue, 03/24 Lab 3: MC Simulations; Lab 2 Due
18. Thu, 03/26 Fundamentals of Molecular Dynamics (MD) Simulations
19. Tue, 03/31 Static Properties from MD: Equilibrium Structure
20. Thu, 04/02 Dynamic Properties from MD: Mass Transport (Diffusion)
21. Tue, 04/07 Ab-Initio MD Simulations
22. Thu, 04/09 Accelerated MD Simulations; Lab 3 Due
23. Tue, 04/14 Lab 4: MD Simulations
24. Thu, 04/16 Guest Lecture: N. Artrith – Machine-Learning Models for MD Simulations
25. Tue, 04/21 Computational Prediction of Atomic Structures
26. Thu, 04/23 Automated High-Throughput DFT Calculations
27. Tue, 04/28 Current Research and Future Directions in Atomistic Simulations
28. Thu, 04/30 Recap and Q&A; Lab 4 Due

Tue Thu Tue Thu Tue Thu

CHEN E4880 – Tentative Lecture Schedule (Subject to Changes)

Changes may arise and regular attendance in class is the best way to be informed.

Changes in due dates will be posted in CourseWorks.