Computational Methods in Physics
1
Important Questions
ž  Who knows computer programming?
—  Which language(s)?
—  How much experience?
ž  Who does *not* have access to a laptop?
—  Have it with you today? If not, partner up
ž  What
operating system is on it?
ž  Which plotting software do you use?
ž  How many of you got both my e-mails?
ž  Next,
let us all go over the syllabus…
2
3 Steps to Projects in This Course
ž  Something
you use write your code
ž  Something to compile your code into an
executable
—  “Computer program” can refer to either your
raw source code or the executable
ž  In
many cases, you want to make a
graph of your results: something vs.
something or a histogram, et al.
—  Creating a simple plot of your data
—  Occasionally a table or just one number
3
Word Processors
ž
Linux/Unix: emacs, vi/vim, pico, nano
—
—
—
—
ž
http://www.gnu.org/software/emacs/tour/
http://www.openvim.com
https://www.cs.colostate.edu/helpdocs/pico.html
http://www.howtogeek.com/howto/42980/the-beginnersguide-to-nano-the-linux-command-line-text-editor/
Mac: Xcode graphically or same as above in
Terminal (Unix)
—  https://developer.apple.com/xcode/ (free!)
ž
Windows: Microsoft Visual C++, Borland C++,
OR install a Unix shell wrapper like Cygwin,
VirtualBox, or Gow and use Unix
—  https://cygwin.com/install.html (free!)
4
Compilers (Your Biggest Hurdle?)
ž  Linux/Unix:
can use gcc or g++ natively
(*best* option is a rare laptop OS)
ž  Mac: Xcode graphically or clang or gcc
or g++ in Terminal (very close 2nd place)
—  https://developer.apple.com/xcode/ (free!!)
ž  Windows:
Microsoft Visual C++, Borland
C++, OR install a Unix shell wrapper like
Cygwin, VirtualBox, or Gow and use gcc
or g++ (Windows is most work…)
—  https://cygwin.com/install.html (free!!)
5
Plotters
ž  Excel
of course (not very good) for PC, Mac
ž  gnuplot (free!) for any operating system
—  http://www.gnuplot.info
—  Warning -- command-line-based, not GUI
ž  KaleidaGraph for PC, Mac (student license)
—  http://www.synergy.com/wordpress_650164087/
—  Excel on steroids (custom functions for example)
—  A free, 30-day (?) student demo/trial available
ž  ROOT (for Windows you must get
—  https://root.cern.ch (partially GUI)
Cygwin...)
6
Help Getting Set Up
ž
For users of Windows machines (PCs):
ž
Code Blocks (word processing AND compiling
in one; Sean can help you)-http://www.codeblocks.org/
Install https://www3.ntu.edu.sg/home/ehchua/
programming/howto/CodeBlocks_HowTo.html
ž
ž
Another option: FREE latest version of MS
Visual C++ potentially, https://
www.dreamspark.com/Support/FAQ/
7
Unix and emacs Commands
ž  Quick
reference “Cheat sheets” for both
Linux and Mac (Terminal)
ž  unix
https://ubuntudanmark.dk/filer/
fwunixref.pdf
ž  emacs https://www.gnu.org/software/emacs/
refcards/pdf/refcard.pdf
8
Your Very First Program
ž  Live
demo on my machine, Apple laptop
—  10.8.5 (old version of OS X)
—  I will use emacs, gcc, and Excel
9
Resources for Learning C & C++
ž  http://www.sphoorthyengg.com/wp-
content/uploads/2015/07/Teach-YourselfC-in-24-Hours-2nd-Edition.pdf
ž  http://www.angelfire.com/art2/ebooks/
teachyourselfcplusplusin21days.pdf
ž  Just
use Google for even more help!
—  Including searching the exact phrase of any
error messages you get as you are working
10
Time Permitting
ž  http://plotdigitizer.sourceforge.net
(all systems)
—  Automatic version
11
Your First Homework Assignment
ž  Write
a program about special relativity
ž  You input a velocity, a time, a length, and a
mass
ž  The program spits out beta, gamma, the time
dilation amount (seconds per second), the
new, contracted length, and the new larger
mass, plus the kinetic and the total energies
ž  Will be due on Friday Jan. 29 at 11:59 p.m.
—  No extensions. You would get too far behind
ž  Bonus:
Handle faster than light situations
12
Note: changing rooms to 225
13
Homework #2
ž  Study
the random number generator in C++
vs. another one I will provide you
ž  Make histograms of value frequencies (0 to
0.1, 0.1 to 0.2, etc.) and the digit frequencies
(1st through 6th decimal places)
ž  Which generator (if either) is the better one?
ž  BONUS:
Make 3D plot of random triplets
(Excel can do this) and re-judge which better
14
More Links of Use
ž
How to make a histogram
—  https://support.microsoft.com/en-us/kb/214269 (for
multiple different versions of Excel)
—  http://www.life.illinois.edu/biochem/455/Lab
%20exercises/2Photometry/KaleidaGraph
%20Manual.pdf (search the word histogram; you can
also just take note of example in class)
—  http://gnuplot.sourceforge.net/demo/histograms.html
—  ftp://root.cern.ch/root/doc/ROOTUsersGuideHTML/
ch03s08.html
ž
https://en.wikipedia.org/wiki/
Random_number_generation
15
Homework #3
ž
Create a Monte Carlo simulation of electrons traversing the
element xenon, used as a detector
—  Make the density a user input, but your default can be 3 grams per
cm^3 (liquid xenon). Energy also an input
—  Use the “total stopping power” tables from this website:
http://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html but
convert values into MeV per cm OR spline the results
ž
ž
ž
ž
Optimize the step size in distance until you get the right
answer on average for the total track length (using the CSDA
range from site above, converting into length units using the
default density above)
Allow for 15% variation on each mean dE/dx from the table as
a function of the energy (Gaussian)
Have your code do argon and water as well (also detectors)
Output is histogram of track lengths for >=10,000 elec’s
—  For several example energies: 1,2,5,10,20,50,100,200,500,1000 keV
ž
BONUS: Imagine electrons decay. New result=?
—  Also, separate the radiative and collisional dE/dx losses
16
Links for HW #4,+ Plot Digitization
ž  http://tutorial.math.lamar.edu/Classes/DE/
EulersMethod.aspx
—  Study the many examples on this webpage!
ž  For
later/future: Java-based Plot Digitizer
for Windows, Apple Mac, and Linux / Unix
(at least some flavors) -http://plotdigitizer.sourceforge.net/
—  If for any reason this fails to work for your
machine, Googling “digitizing plots” as an exact
phrase should provide alternative programs
17
Homework #4, due Friday, Feb. 19
ž
Solve the pendulum equation for both the small
angle approximation and not, under conditions
of damping and (sinusoid) driving too
—  Damped: nothing, under, critically, over
—  Driven: damped with all four cases above
—  Angles: 15, 30, 45, 60, 90, 120, 180 deg.
That’s 112 plots! I don’t want that many:
combine things. Don’t plot for sake of plots. In email: analyze, draw conclusions on behavior!
ž  First things first: you have to make sure h is
small enough that your program is accurate
ž
—  2 ways to do this: analytical solutions or asymptoting
ž
EC: Euler vs. Euler-Cromer method. Optimize!
18
web links for HW # 4
ž
Full analytical solution with sin(theta) which you can
compare to:
—  http://sbfisica.org.br/rbef/pdf/070707.pdf
ž
Damped oscillation
—  http://farside.ph.utexas.edu/teaching/315/Waves/node10.html
—  Different types:
http://homepages.abdn.ac.uk/nph120/vpl/pendulum/
Equations.html
—  http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html
ž
Driven aka forced
—  http://hyperphysics.phy-astr.gsu.edu/hbase/oscdr.html
19
If you ever have problems with
getting random numbers
ž  You
can always get them from
https://www.random.org (best on web)
20
Homework #5: Cosmology, GR
ž
Compare Euler (or Euler-Cromer) to the “RK4”
approach to differential equations that you’ll code up
yourselves, for the ΛCDM model
—  Use Runge-Kutta (RK4) exclusively for the rest of HW5
—  Determine in default scenario age of the universe plus the
dark-energy inflection point (the correct answers are 13.82
billion years old and a = 0.57). Get it right
—  Plot first and second derivatives of the scale factor a
—  Plot all the omegas as a function of time, z, and scale factor
ž
Plot a(t) with z and “absolute” size for cases of
—  Phantom dark energy (Big Rip, and find time scale)
—  Decreasing dark energy (Big Crunch, and find out when)
—  Matter-dominated cosmos: flat, open, closed (combined)
ž
ž
Verify code working for 4 simple cases; show
Bonus: *early* universe including inflation done well
—  Was going to do adaptive step size but you’ll need it
21
What you need
ž
ž
ž
Cosmological parameter values (latest, final):
http://arxiv.org/pdf/1502.01589v2.pdf
Hyperphysics discussion of Friedmann equation with Hubble
parameter:
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/fried.html
Wikipedia
—  Scale factor with redshift definition:
https://en.wikipedia.org/wiki/Scale_factor_%28cosmology%29
—  Equation of state in cosmology:
https://en.wikipedia.org/wiki/Equation_of_state_%28cosmology%29
—  How to code up the Runge-Kutta formulae:
https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
ž
For your further edification and knowledge
—  http://www-com.physik.hu-berlin.de/~fjeger/Cosmolect1-7.pdf
(Friedmann equations hard-core full solutions and explanations)
ž
Cutting edge research on scale factor (also, gives you the
inflection point)
—  http://www.ringermacher.com/images/stories/downloadable_pdfs/
aj_148_5_94o_scalefactorplot.pdf
22
Example Plot
23
Next topic
ž  BBN
24