| Instructor: | Burkhard Militzer | GSI: Zack Geballe |
| militzer@berkeley.edu | zgeballe@gmail.com | |
| Office hours: | We 11 am -1 pm | Tu 10 am-12 pm |
| 407 McCone Hall | 255 McCone Hall |
| 4 units: | Lectures: | Tu 9-10 | 325 McCone Hall | Computer lab: | We 9-11 |
| Th 9-10 | 325 McCone Hall | 212 Wheeler Hall |
 | | This course offers a general introduction to computer simulations for all science majors. Participants will use the MATLAB software to perform calculations, design 3D graphics, and build on existing computer programs. No prior programming experience is required. The course teaches fundamental skills for scientists and helps students with future homework. It covers standard numerical methods including Monte Carlo and molecular dynamics. The algorithms are illustrated with a variety of applications in earth and planetary science and astronomy. |
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| Cassini spacecraft in Saturn orbit | Choatic behabior in
dynamical systems: Lorenz attractor |
Combined gravity
field of sun and planet |
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| Fractal nature of ferns | Koch snowflake | Sierpinski gasket |
Selected examples from the 2008 computer lab exercises and homework assignments:
| Type of assignment | Description | Files |
| Lab 1 | Getting to know Matlab: vectors & matrices | lab01_Matlab_intro02.pdf |
| Homework 1 | Getting to know Matlab: loops and plots | hw01_plotting_and_loops.pdf |
| Lab 2 | Fractals in Matlab: Mandelbrot set | lab02_Mandelbrot01.pdf example.m mandelbrot14.m |
| Homework 2 | Fractals in Matlab: Julia set | hw02_Mandelbrot_and_Julia_sets.pdf |
| Lab+homework 3 | Diffusion limited aggregation | lab_hw03_DLA_html.pdf diffusion_limited_aggregation2D_exercise.m |
| Lab 4 | Keplerian orbits of planets integrated with Euler's method | lab04_kepler04.pdf run_kepler_ode_euler04.m |
| Homework 11 | Cooling of a lava dike | hw11_cooling_dike.pdf |
Additional example movies that will be discussed in this course:
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| Molecular dynamics simulations using a Lennard-Jones pair potential |
Apollonian gasket |
| Protect yourself
from lighting with a Faraday's cage by solving the Laplace equation ;=) | Dynamical simulation of the Lorenz equation from above |
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| Diffusion limited aggregation along a sticky wall | Modified aggregation to increase the fractal dimension |
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| Triangular fractal (click on image to start movie) | Aggregation in 3D (click on image to start movie) |
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| Mandelbrot fractal (click on image to start movie) | Julia set (click on image to start movie) |
 Landscape evolution model (code written by former EPS109 student Jeff Prancevic) |
| Three movies for different models are available: movie 1, movie 2, and movie 3. |
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| Click on image to start movie. |
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| Water wave traveling along a mid-ocean ridge. Numerical solution of the shallow water wave equation. Click on image to start movie. |
Syllabus:
| Date | Lecture topic | Computer lab exercises |
| Thu 8/27 |
1: Introduction of course, historical overview, interplay of experiments, theory, and simulation | Lab 1: Matlab as a pocket calculator |
| Tue 9/1 |
2: Fractals in nature, models and computer simulations, fractal dimension and examples in topography and coast line structure | Lab 2: Loops and plots in Matlab |
| Tue 9/3 |
3: Mandelbrot set and related fractals |
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| Tue 9/8 | 4: Random walks and diffusion limited aggregation (DLA), percolation theory | Lab 3: Programming the Mandelbrot and Julia set |
| Thu 9/10 |
5: Group discussion on fractals | |
| Tue 9/15 | 6: Numerical algorithms for finding roots and minima | Lab 4: DLA in 2D on a flat sheet |
| Thu 9/17 | 7: Introduction to time independent partial differential equations (PDE), algorithms and stationary state of 1D heat equation | |
| Tue 9/22 | 8: Methods to find the stationary state of 2D heat equation | Lab 5: Heat equation solver in 2D |
| Thu 9/24 | 9: Time dependent PDEs, diffusion equation (heat and chemical diffusion), solution of the 1D heat equation, cooling of a lave dike | |
| Tue 9/29 | 10: Landscape erosion models | Lab 6: Perron’s erosion model |
| Thu 10/1 | 11: Wave equations and numerical solutions | |
| Tue 10/6 | 12: Shallow water wave equation, tsunamis | Lab 7: 3D water wave simulations |
| Thu 10/8 | Midterm | |
| Tue 10/13 | 13: Introduction to ordinary differential equations, Euler’s method | Lab 8: Keplerian orbits |
| Thu 10/15 | 14: Newton’s law of motion, Keplerian orbits | |
| Tue 10/20 | 15: Planetary orbits, Hohmann transfers, spacecraft trajectories | Lab 9: Lagrange points |
| Thu 10/22 | 16: Runge-Kutta method | |
| Tue 10/27 | 17: Lagrange points, horseshoe and tadpole orbits of asteroids | Lab 10: Exercise on tadpole and horseshoe orbits |
| Thu 10/29 | 18: Strange attractors | |
| Tue 11/3 | 19: Chaotic dynamical systems and Lyaponov exponents | Lab 11: Roessler attractor |
| Thu 11/5 | 20: Simple models for climate change | |
| Tue 11/10 | 21: Molecular dynamics (MD) | Lab 12: Box model for climate change |
| Thu 11/12 | 22: Crystal structures, simulations in periodic boundary conditions | |
| Tue 11/17 | 23: Many particle simulations | Lab 13: Molecular dynamics I |
| Thu 11/19 | 24: Thermodynamic equilibrium, different states of matter | |
| Tue 11/24 | 25: Introduction to Monte Carlo (MC) simulations | Lab 14: Molecular dynamics II |
| Thu 11/26 | Holiday | |
| Tue 12/1 | 26: Applications of MC simulations | Lab 15: Comparison of MC and MD |
| Thu 12/3 | 27: Curve fitting using the least-squares method, revisions, and exam preparations | |
| Tue 12/8 | 28: Students present their movie projects, part A | Lab 16: Students present their movie projects, part B |
Grade assignment:
The final grade will be calculated using the following percentages:
15% Grades for solving problem sets in weekly computer labs,
35% Grades for homework,
25% One mid-term exam taken in class,
25% A final exam taken in class at the end of the semester.
Course description:
109. Computer simulations in Earth and Planetary Sciences (4) Two hours of lecture and two hours of computer lab exercises. Prerequisites: Math 1A or equivalent. Introduction to modern computer simulation methods and their application to selected Earth and Planetary Science problems. In hands-on computer labs, students will learn about numerical algorithms, learn to program and modify provided programs, and display the solution graphically. This is an introductory course and no programming experience is required. Examples include fractals in geophysics, properties of materials at high pressure, celestial mechanics, and diffusion processes in the Earth. Topics range from ordinary and partial differential equations to molecular dynamics and Monte Carlo simulations.
Motivation:
Computer simulations have become an integral part of earth and planetary science (EPS) but students arrive on campus with very different levels of computational skills. This course teaches the fundamental computational methods and their application in EPS. These skills are needed for later course work and research.
Proposed reading list:
(*) C. B. Moler, “Numerical Computing with Matlab”, Society for Industrial and Apllied Mathematics (SIAM) Philadelphia, 2004, QA 297 M625 2004 ENGI, pages 14, 120, 187, 203, available online: http://www.mathworks.com/moler/index.html
Fractals:
(*) H.-O. Peitgen, D. Saupe (ed), The Science of Fractal Images”, Springer Verlag 1988, QA 614 .86 S351 1998 MATH, pages 40, 44, 50, 147, 155,
(*) D. L. Turcotte, “Fractals and Chaos in Geology and Geophysics”, Cambridge, U.K. ; New York : Cambridge University Press, 1997, page 14, 22,45, 59, 69, 71, 91, 97, 149, 201, 235, 299
(*) H.-O. Peigten, H. Jurgens, D. Saupe, “Fractals for the Classroom Part II Complex Systems and Mandelbort Set”, Springer 1992, QA 614 .86 P45 1992 v.2 MATH, pages 27. 58, 127, 199, 304, 318, 381, 401, 420, 446, 453.
(*) B. B. Mandelbrot, “The Fractal Geometry of Nature”, W.H. Freeman and Co. NY 1983, QA 447 M357 1983 MATH, pages 30, 112,
D.J. Higham, N. J. Highham, “Matlab Guide”. Society for Industrial and Apllied Mathematics (SIAM) Philadelphia, 2000, QA 297 H5217 2000 ENGI, pages 14, 17, 90, , 132, 178, 221, 246.
A. Stanoyevitch, “Introduction to MATLAB with Numercial Preliminaries” Wiley 2004, TA 345 S75 2004 ENGI, pages 177.
J. Feder, “Fractals” Plenuym Press, NY, 1988, QA 447 F371 1998 MATH.
Ordinary Differential Equations, Molecular Dynamics, Solar System Dynamics:
J.H. Mathews, K.D. Fink, “Numerical Methods Using Matlab”, 4th edition, Pearson Education Inc., 2004, QA 297 M39 2004 ENGI, pgaes: 262, 418, 434, 465, 496, 505, 544, 557, 567,
(*) J. B. Marion, S. T. Thornton, “Classical Dynamics of particles and systems”, Saunders College Publishing, Fort Worth Philadelphia.
C.D. Murray, S.F Dermott, “Solar Systems Dynamics”, Cambridge University Press, 1999.
I. De Pater, J.J. Lissauer, “Planetary Science”, Cambridge University Press, 2001.
M. P. Allen, D.J. Tildesley, “Computer Simulations of Liquids”, Oxford University Press.
S. Nakamura, “Numerical Analysis and Graphic Visualization with Matlab” 2nd edition, Prentice Hall PTR 2001, T 385 N34 2002 ENGI, pages 63, 302, 385, 396, 453, 465.
W. J. Palm III, “Introduction to Matlb 6 for Engineers”, McGraw-Hill, 2001, TA 345 P35 2001 ENGI, pages 452.
H. B. Wilson, L. H Turcotte, “Advanced Mathematics and Mechanics Applications Using Matlab”, 2nd edition, CRC Press 1997, TA 354 W55 1997 ENGI, pages: 271, 352, 382.
A.H.Nayfeh, B. Balachandram, “Applied Nonlinear Dynamics, Analytical Computational, and Experimental Maethods”, Wiley, QA 845 N39 1994 ENGI.
E. A. Jackson, “Perspectives of Non-linear Dynamics”, Cambridge University Press, 1989, QA 845 J28 1989 V.1 ENGI
V.S. Anishchenko, V. Astakhov, A. Neiman, T. Vadivasova, L. Schimansky-Geier, “Nonlinear Dynamics of Chaotic and Stochastic Systems” Springer 2007, QA 845 .N667 2007 ENGI, pages 110.
Monte Carlo:
M. H. Kalos, P. A. Whitlock, “Monte Carlo Methods”, John Wiley & Sons, NY.
Partial Differential Equations:
(*) D. L. Turcotte and G. Schubert, “Geodynamics”, Cambridge ; New York : Cambridge University Press, 2002.
X.-S. Yang, “An Introduction to Computational Engineering with Matlab”, Cambridge International Science Publishing, 2006, TA 345 Y36 2006 ENGI, pages 33, 53, 57, 79, 224
W. E. Boyce, R. DiPirma, “Elementary Differential Equations and Boundary Value Problems”, Textbook, John Wiley & Sons, NY.
Climate:
K. Mcguffie, A. Henderson-Sellers, “A Climate modeling Primer”, Wiley 1997, QC 981 M482 1997 EART, page 85
(*) indicates the most relevant books.