# Syllabus

This page includes a calendar of lecture topics.

## Course Overview

### Why Modeling and Simulation (Mod/Sim)?

Modeling is a fundamental and quantitative way to understand complex systems and phenomena. Simulation is complementary to the traditional approaches of theory and experiment. Together, they (Mod/Sim) make up an approach that can deal with a wide range of physical problems, and at the same time exploit the power of large-scale computing. This paradigm is becoming increasingly widespread in a number of disciplines in science and technology, giving rise to active fields of studies such as computational physics, chemistry, mechanics, and biology, to name just a few. Through modeling and simulation one can readily cross over from one discipline to another, which is to say that the basic concepts and techniques one learns are applicable to problems seemingly very different at the surface.

### Why Teach Mod/Sim at the Undergraduate Level?

Mod/Sim studies are mostly being carried out at the graduate and postgraduate levels. But there is no reason why the undergraduates cannot participate in a meaningful way and benefit from the physical insights and technical know-how that these activities can provide. We believe that engaging the undergrads broadly across the Institute through a team of multidisciplinary faculty, as instructors and mentors, can succeed at MIT. The students would gain a broader academic exposure than what they would normally encounter within their own departments. Because this is a new way of teaching and networking among the faculty, everyone who participates can contribute to the success of this experiment, and in turn learn a great deal about studying across traditional boundaries. Intro Mod Sim is receiving considerable support from the Dean of Engineering and has the blessings of the department heads of all the participating units. In many ways, a subject like this is an experiment in educational innovation. We hope the students will get into the spirit and work with us to make it a worthwhile experience for all concerned.

### What are the aims of Mod/Sim?

We expect the students will gain a significant appreciation of the broad use of modeling in several fields of science and engineering, acquire hands-on experience with simulation, ranging from basic use of computers to advanced techniques, and develop communication skills by working with practicing professionals. Additional benefits could come from further interactions with the faculty afterwards, such as mentoring, UROPs, thesis supervision, etc.

## Prerequisites

## Textbook

There is no required textbook for the course. Class lectures and tutorial discussions will be supported by various readings that will be assigned from various books and journals.

## Grading

activities | percentages |
---|---|

Problem Sets | 40% |

Quiz 1 | 20% |

Quiz 2 | 20% |

Term Project | 20% |

## Course Structure

Lectures are grouped into 3 parts: Continuum Methods (CM), Particle Methods (PM), and Quantum Methods (QM).

CM Faculty: Beers, Powell, Radovitzky, Ulm

PM Faculty: Bazant, Buehler, Hadjiconstantinou, Mirny

QM Faculty: Yip

## Calendar

lec # | topics | instructors | key dates |
---|---|---|---|

Introduction |
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1 | Overview - Aspirations of Modeling and Simulation, Logistics | Yip | |

2 | Diffusion at the Particle Level | Yip | |

3 | From Random Walks to Continuum Diffusion | Bazant | |

Part 1: Continuum Methods (CM) |
|||

4 | Conservation Laws | Rosales | |

5 | Constitutive Relations | Rosales | |

6 | Discrete/Continuum Issues | Rosales | |

7 | Finite Difference Methods | Powell | |

8 | Weighted Residual Finite Element Methods | Powell | |

9 | Heat Conduction | Powell | |

10 | Materials Processing Applications | Powell | Problem set 1 due |

11 | Variational Finite Element Methods | Ulm | |

12 | Elasticity Concepts and Problems | Ulm | |

13 | Applications in Structural Mechanics | Ulm | Problem set 2 due |

14 | Equations of Fluids Dynamics | Beers | |

15 | Problems in Incompressible Flow | Beers | |

16 | Fluid-Structure Interactions | Radovitzky | |

17 | Multiscale Problems involving Continuum Mechanics | Radovitzky | |

18 | CM Review | Problem set 3 due | |

19 | Quiz 1 | ||

Part 2: Particle Methods (PM) |
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20 | Monte Carlo Methods I: Percolation | Bazant | |

21 | Monte Carlo Methods II: Fractal Patterns | Bazant | |

22 | Monte Carlo Methods III: Random Packings | Bazant | |

23 | Basic Monte Carlo | Mirny | |

24 | Monte Carlo Modeling of Physical Systems | Mirny | Problem set 4 due |

25 | Optimization by MC and Genetic Programming | Mirny | |

26 | Stochastic Simulations in Biology | Mirny | |

27 | Basic Classical Molecular Dynamics | Buehler | |

28 | Introduction to Interatomic Potentials | Buehler | Problem set 5 due |

29 | Modeling of Metals | Buehler | |

30 | Reactive Potentials | Buehler | |

31 | MD Simulation of Fluids | Hadjiconstantinou | |

32 | Dilute Gases and Direct Simulation Monte Carlo (DSMC) I | Hadjiconstantinou | |

33 | Dilute Gases and DSMC II | Hadjiconstantinou | Problem set 6 due |

34 | PM Review | ||

35 | Quiz 2 | ||

Part 3: Quantum Methods (QM) |
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36 | Quantum Calculations in Modeling and Simulation | Yip | |

37 | Introduction - Hartree-Fock and Density Function Theory Methods | Yip | |

Final Project Presentations | Final paper due two days after the final project presentations |