| Lectures | Location | Computer labs |
|---|---|---|
| Tue 5–6 pm; Thu 5–6 pm | Valley Life Sciences 2060 | Most labs are on Wednesday. See UCB’s schedule of classes for times and locations. |
| Name | Contact | Office hours | |
|---|---|---|---|
| Instructor | Burkhard Militzer | militzer@berkeley.edu | Tue 6–7 pm |
| GSI | Salma Ahmed | salma_ahmed@berkeley.edu | tbd |
| GSI | Youssef Miled | youssef_miled@berkeley.edu | tbd |
This course offers a general introduction to computer simulations for all science majors. Participants will use the Jupyter notebooks 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 data processing techniques as well standard simulations methods including Monte Carlo and molecular dynamics. The algorithms are illustrated with a variety of applications in earth and planetary science as well as astronomy.
Check out our YouTube channel.
Check out the animations made by students of our fall 2008, 2009, 2011, 2012, 2013, 2014, 2015, 2016, 2018, 2019, 2020, 2021, 2022, and 2023 classes. For a quick scan, see the collection of titles from past projects.
Media gallery
Selected computer lab exercises and homework assignments form our Python class in 2018
In 2018, the class switched from using Matlab to Jupyter notebooks. While there appears to be a general trend in that direction, the real motivation was the fact that all our students' Matlab codes would stop working once they left the university and their relatively inexpensive Matlab student licenses would expire.
To do the following Jupyter exercises, we recommend:
- Install Anaconda on your Mac or PC.
- Make a new directory
Jupyterin your home directory and place any data files like ice_core_temperature_data.txt there. - Start Jupyter from a terminal:
cd ~/Jupyter jupyter lab - Start a new notebook (File → New notebook) and step-by-step paste the commands for the first lab assignment Intro_to_python_05.pdf. Press Shift + Return each time.
| Type of assignment | Description | Files |
|---|---|---|
| Lab 1 | Getting to know Jupyter notebooks |
Intro_to_python_05.pdf ice_core_temperature_data.txt |
| Homework 1 | Simple calculations with Jupyter notebooks |
hw01_course_intro13.pdf ice_core_CO2_data.txt |
| Lab 2 | Pixel graphs and filling matrices |
pixel_graphics12.pdf topography_180x360_grid.txt |
| Homework 2 | Practice making a smiley | hw02_pixel_graphics_13.pdf |
In this course, we generate a number of simple animations and store them as MP4 files. Two examples—wave1d.ipynb and wave2d.ipynb—use the FFMPEG package in combination with the screen grab function.
Computer lab exercises and homework assignments from our Matlab class in 2016
| Type of assignment | Description | Files |
|---|---|---|
| Lab 1 | Getting to know Matlab: vectors and matrices | lab01_Matlab_intro.pdf |
| Homework 1 | Getting to know Matlab: loops and plots | hw01_Matlab_intro.pdf |
| Lab 2 | Pixel graphics and ocean volume |
lab02_pixel_and_ocean_volume.pdf example.m topography_18x18_grid.txt topography_180x360_grid.txt |
| Homework 2 | Pixel graphics and ocean volume | hw02_pixel_and_ocean_volume.pdf |
| Lab and homework 3 | Logistic map |
lab_hw03_logistic_map.pdf run_sin2.m sin2.m |
| Lab 4 | Mandelbrot set |
lab04_Mandelbrot.pdf mandelbrot.m |
| Homework 4 | San Andreas fault, Mandelbrot and Newton fractals |
hw04_San_Andreas_fault_and_Mandelbrot.pdf san_andreas.m SA_fault.txt CA_coast_line.txt plate.txt CA_coast_line_no_islands.txt |
| Lab and homework 5 | Diffusion limited aggregation |
lab05_DLA.pdf hw05_DLA.pdf diffusion_limited_aggregation2D_lab01.m |
| Lab and homework 6 | Stationary state of heat equation |
lab06_heat.pdf hw06_heat.pdf |
| Lab and homework 7 | Solving the 1D heat equation in real time. Cooling of a lava dike |
lab07_heat_real_time.pdf hw07_cooling_lava.pdf |
| Lab and homework 8 | Solving the 2D heat equation and animations |
lab08_2D_heat.pdf hw08_2D_heat.pdf |
| Lab 9 | Landscape evolution model |
lab09_erosion.pdf erosion_lab_start.m calculate_collection_area2.m pool_check8.m |
| Homework 9 | Erosion of a landscape you created |
hw09_erosion.pdf erosion_ocean07.m calculate_collection_area2.m pool_check10.m initial_conditions_add_hill.m |
| Lab 10 | Shallow water waves |
lab10_water_waves.pdf waterwaves03.m |
| Homework 10 | Waves over a mid-ocean ridge |
hw10_water_waves04.pdf waterwave10.m |
| Lab and homework 11 | Tadpole and horseshoe orbits |
lab11_kepler.pdf hw11_tadpole_horseshoe_orbits.pdf run_kepler_ode.m kepler_ode.m |
| Homework 12 | Image processing |
hw12_image_processing.pdf HW12.zip |
| Lab and homework 13 | Chaos in dynamical systems: Rössler attractor | lab_hw_13_roessler_attractor08.pdf |
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
- 20% One midterm exam taken in class
- 30% A final exam taken in class at the end of the semester
Course description
Computer simulations in Earth and Planetary Sciences (4 units) 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.
Selected examples for computer simulations that may be discussed in this course
Click on the following images to start the animations. Large files (up to ~1.3 GB) may be better downloaded and played locally (with e.g. the VLC player).
Exoplanet orrery : simulations of exoplanetary orbits
Click on the images to start the animations. Here are links to additional exoplanet animations: 11, 12, 13, 14, 15, 17, 19, 20.
Animations of filled Apollonian gasket fractals
Click on the images to start the animations.
Modified diffusion limited aggregation to grow compact structures
Diffusion limited aggregation with two species
Series of Newton fractals and animations
Animations: one, two, three, four, and five.
2D Monte Carlo simulations of Ising spin magnets
Additional examples discussed in this course
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 |
| Thu 9/3 | 3: Mandelbrot set and related fractals | |
| 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 lava 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 Lyapunov exponents | Lab 11: Rössler 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 |
Reading physical books appears to be a thing of the past. Still here is a lists of books that we found useful:
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.htmlFractals:
(*) 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