Modeling and simulation

Modeling and simulation 

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Lecture Notes:

System Concepts
Cash-flow models
Supervised Learning: Classification
Unsupervised learning: Clustering
Extrapolation, Forecasting 
General Systems Models: Inventory
General Systems Models: Exponential System
Differential Systems, stability, etc. 
Some GPSS models
More GPSS models
Discrete Markov Chains
Queuing System
Section 7
Section 8
Section 9
Section 10
Section 11
Section 12


Course Syllabus

Introduction to Modeling and Simulation

As taught in: Spring 2008

Level:

Undergraduate

Instructors:

Markus Buehler

Raúl Radovitzky

Timo Thonhauser

Course Description

Technical Requirements

Systems at different time and length scales are modeled using different simulation techniques, derived from the appropriate governing equations. (Image courtesy of Elsevier, Inc., Science Direct. Used with permission.)

Course Description

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.

Syllabus

Description

This subject provides an introduction to modeling and simulation. Scientists and engineers have long used models to better understand the system they study, for analysis and quantification, performance prediction and design. This subject will provide you with the relevant theoretical and numerical tools that are necessary to build models of complex physical phenomena and to simulate their behavior using computers. The physical system can be a collection of electrons and nuclei/core shells, atoms, molecules, structural elements, grains, or a continuum medium. The lectures will provide an exposure to areas of application, based on the scientific exploitation of the power of computation.

Instructors

The subject will be taught by three instructors, each covering approximately one third of the subject. Each lecturer will teach a consecutive set of 7 or 8 lectures (part I, Lec #2-9, Raúl Radovitzky, continuum methods; part II, Lec #10-18, Markus Buehler, atomistic and molecular methods; part III, Lec #19-27, Timo Thonhauser, quantum mechanics). The three parts are not independent. Instead, they will base on one another and are integrated.

Lectures

Detailed lecture notes will be distributed for each lecture, usually covering "theoretical" aspects (derivations, concepts etc.) in more detail or in a different manner than done during class. The subject content is defined by the material presented in lectures, recitations and reading assignments, so regular attendance is advisable.

Lecture Notes

This section contains documents that could not be made accessible to screen reader software. A "#" symbol is used to denote such documents.

Special software is required to use some of the files in this section: .nb.

LEC #	TOPICS	MATERIALS
1	Introduction: general info (PDF) Continuum methods (PDF - 1.1 MB)# Atomistic and molecular methods (PDF - 1.4 MB)# Quantum mechanical methods (PDF - 1.6 MB)#
Part I: Continuum methods (Raúl Radovitzky)		Mathematica Scripts
2	Analysis; formulation of discrete mathematical models (PDF)
3	Continuous systems (PDF)	(NB)
4	Weighted residual and weak formulations (PDF)	(NB)
5	Energy formulations and the Ritz method (PDF)	(NB)
6	The finite element method (part I) (PDF)
7	The finite element method (part II) (PDF)	(NB)
8	The finite element method (part III) (PDF)
9	The finite element method (part IV) (PDF)
10	The finite element method (part V) (PDF)
11	Quiz 1
Part II: Atomistic and molecular methods (Markus Buehler)		Concept Questions
12	Introduction to atomistic modeling (PDF - 1.0 MB)	(PDF)
13	Basic statistical mechanics (PDF)	(PDF)
14	Basic molecular dynamics (PDF)	(PDF)
15	Interatomic potential and force field (PDF - 2.2 MB)	(PDF)
16	Interatomic potential and force field (cont.) (PDF - 2.9 MB)	(PDF)
17	Application to mechanics of materials: brittle materials (PDF - 3.2 MB)	(PDF)
18	Application to mechanics of materials: ductile materials (PDF - 6.0 MB)	(PDF)
19	Review (PDF - 4.8 MB)
20	Quiz 2
Part III: Quantum mechanical methods (Timo Thonhauser)
21	The theory of quantum mechanics (PDF - 1.8 MB)
22	Practice makes perfect (PDF - 2.5 MB)
23	From many-body to single-particle: quantum modeling of molecules (PDF - 4.7 MB)
24	From atoms to solids (PDF - 2.2 MB)
25	Quantum modeling of solids: basic properties of materials (PDF - 2.0 MB)
26	Quantum modeling of solids: advanced properties of materials (PDF - 1.8 MB)
27	What else can we do?