Univercity: Massachusetts Institute of Technology
Instructors: Prof. Markus Buehler
Dr. Timo Thonhauser
Prof. Raúl Radovitzky
Course Number: 18.361J
This course explores the basic concepts of computer modeling and simulation in science and engineering. We'll use techniques and software for simulation, data analysis and visualization. Continuum, mesoscale, atomistic and quantum methods are used to study fundamental and applied problems in physics, chemistry, materials science, mechanics, engineering, and biology. Examples drawn from the disciplines above are used to understand or characterize complex structures and materials, and complement experimental observations.
Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Recitations: 1 session / week, 1 hour / session
Introduction to Modeling and Simulation (IM/S) provides an introduction into modeling and simulation approaches, covering continuum methods (e.g. finite element analysis), atomistic simulation (e.g. molecular dynamics) as well as quantum mechanics. Atomistic and molecular simulation methods are new tools that allow one to predict functional material properties such as Young's modulus, strength, thermal properties, color, and others directly from the chemical makeup of the material by solving Schroedinger's equation (quantum mechanics). This approach is an exciting new paradigm that allows to design materials and structures from the bottom up — to make materials greener, lighter, stronger, more energy efficient, less expensive; and to produce them from abundant building blocks. These tools play an increasingly important role in modern engineering! In this subject you will get hands-on training in both the fundamentals and applications of these exciting new methods to key engineering problems.
The subject will be taught by two instructors, each covering approximately one half of the subject. Each lecturer will teach a set of 13 lectures (Part I, lectures 2-13, Prof. Markus Buehler, continuum and particle methods; Part II, lectures 14-24, Prof. Jeff Grossman, quantum mechanics). The two parts will be based on one another and are integrated.
Lecture notes will be distributed for each lecture, usually covering the material discussed in class. On occasion, detailed notes on "theoretical" aspects (derivations, formulas, algorithms, concepts etc.) or research papers will be distributed. The subject content is defined by the material presented in lectures, recitations and reading assignments, so regular attendance is advisable.
Recitations will illustrate and/or expand concepts presented in lectures by working through numerical example problems, or by showing how to use the simulation codes. Material covered in recitations is often related to the problem sets and is considered part of the subject content, so regular attendance is advisable.
We will assign a total of approximately 6 problem sets, focused on simulation work and data analysis. Each problem set is designed to build upon the material covered in the preceding lectures and recitations. The homework assignments will be prepared by teams consisting of three students. In this case, each team will hand in one solution, with the names of team members who contributed as indicated on the cover page. The problem sets worked out by a team of students typically cover more complex problem that require numerical simulation.
Due dates for problem sets are firm and homework assignments will be corrected and handed back (with solutions) no later than two lectures after the due date. You may use any material to complete the solution. However, it is important that you properly reference the material used (e.g. books, website, journal articles).
There will be one in-class 1.5 hour midterm exam and a final exam during finals week. All exams are open-book, but bear in mind to develop an appropriate exam strategy. The exams typically cover theoretical material and important concepts related to the two parts, respectively.
The final grade will be based on: Homework (50%) and in-class exams (50%). Additional projects can be used to improve your overall score.
Course calendar. SES # TOPICS KEY DATES Part I: Particle and Continuum Methods 1 Introduction 2 Basic molecular dynamics HW 1 out 3 Property calculation I 4 Property calculation II 5 How to model chemical interactions I HW 1 due 6 How to model chemical interactions II HW 2 out 7 Application to modeling brittle materials 8 Reactive potentials and applications I 9 Reactive potentials and applications II HW 2 due 10 Applications to biophysics and bionanomechanics I 11 Applications to biophysics and bionanomechanics II HW 3 out 12 Review session - Preparation Quiz 1 Part II: Quantum Mechanical Methods 13 It's a quantum world: The theory of quantum mechanics 14 Quantum mechanics: Practice makes perfect 15 From many-body to single-particle; Quantum modeling of molecules HW 3 due 16 From atoms to solids HW 4 out 17 Quantum modeling of solids: Basic properties 18 Advanced properties of materials 19 Nanotechnology
HW 4 due
HW 5 out
20 Solar photovoltaics: Converting photons into electrons 21 Thermoelectrics: Converting heat into electricity
HW 5 due
HW 6 out
22 Solar fuels: Pushing electrons up a hill 23 Hydrogen storage: The strength of weak interactions 24 Review HW 6 due
Part I: Continuum methods (Raúl Radovitzky)
Part II: Atomistic and molecular methods (Markus Buehler)
Part III: Quantum mechanical methods (Timo Thonhauser)
This page contains homework assignments for Part II of this course and suggested readings for the assignments in Part I of the course. The assignments for Part I are not available.
Assignment 1 readings:
Vlachos, D., L. Schmidt, et al. "Structures of Small Metal Clusters. I. Low Temperature Behavior." Journal of Chemical Physics 96, no. 9 (1992): 6880–90.
Sanchez, J., et al. "Modeling of Y/Y' Phase Equilibrium in the Nickel-Aluminum System." Acta Metallurgica 32, no. 9 (1982): 1519–25.
Assignment 2 readings:
Sen, D., and M. Buehler. "Chemical Complexity in Mechanical Deformation of Metals." International Journal for Multiscale Computational Engineering 5, no. 3 and 4 (2007): 181–202.
Buehler, M., et al. "Multi-Paradigm Modeling of Fracture of a Silicon Single Crystal Under Mode II Shear Loading." Journal of Algorithms & Computational Technology 2, no. 2 (2008): 203–21.
Buehler, M., et al. "Multiparadigm Modeling of Dynamical Crack Propagation in Silicon Using a Reactive Force Field." Physical Review Letters 96 (2006).
Buehler, M., et al. "Threshold Crack Speed Controls Dynamical Fracture of Silicon Single Crystals." Physical Review Letters 99 (2007).
Assignment 3 readings:
Gautieri, A., et al. "Hierarchical Structure and Nanomechanics of Collagen Microfibrils from the Atomistic Scale Up." Nano Lett 11, no. 2 (2011): 757–66.
Qin, Z., et al. "Hierarchical Structure Controls Nanomechanical Properties of Vimentin Intermediate Filaments." PLoS ONE 4, no. 10 (2009).