Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session


18.03 Differential Equations or 3.016 Mathematical Methods for Materials Scientists and Engineers.

Course Description

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. Part I will be taught by Prof. Markus Buehler covering continuum and particle methods, and Part II on quantum mechanics will be taught by Prof. Jeff Grossman. The two parts will be based on one another and are integrated.


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.


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 for Quiz 1  
Part II: Quantum Mechanical Methods
13 It's a quantum world: The theory of quantum mechanics  
14 Quantum mechanics (QM): Practice makes perfect  
15 From many-body to single-particle: Quantum modeling of molecules HW 4 out
16 Application of quantum mechanics to solar thermal fuels  
17 More QM modeling for solar thermal fuels, plus a little H-storage  
18 From atoms to solids

HW 4 due

HW 5 out

19 Quantum modeling of solids: Basic properties  
20 Advanced properties of materials: What else we can do?  
21 Some review and introduction to solar photovoltaics (PV)

HW 5 due

HW 6 out

22 Quiz 2  
23 Solar photovoltaics  
24 A bit more solar PV, some verification and validation and a few concluding thoughts HW 6 due