Genetic Algorithms for Spiral Galaxy Rotation Department of Natural Sciences: Physics Project Adviser: Dr. Scott Schneider Presented by: Ceré L. Rettig 1 http://tinyurl.com/ p7flm6e
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Genetic Algorithms for Spiral Galaxy Rotation
Department of Natural Sciences: Physics
Project Adviser: Dr. Scott Schneider
Presented by: Ceré L. Rettig
1
http://tinyurl.com/p7flm6e
Genetic Algorithms for Spiral Galaxy Rotation
Department of Natural Sciences: Physics
Project Adviser: Dr. Scott Schneider
Presented by: Ceré L. Rettig
2
http://tinyurl.com/p7flm6e
Genetic Algorithms for Spiral Galaxy Rotation Finding the Period of
Single Exoplanet Orbit
Department of Natural Sciences: Physics
Project Adviser: Dr. Scott Schneider
Presented by: Ceré L. Rettig
3
http://tinyurl.com/p7flm6e
Vera Rubin
“Science Progresses best when observations force us to alter our perceptions.”
http://41.media.tumblr.com/0151bf79098f8ee356809cd7c2a8f734/tumblr_mq4axmCj0Q1svt1dio1_1280.jpg 4
Original Objectives• Research galaxy rotation curves for spiral galaxies.
• Investigate models for dark matter to generate rotationcurves.
• Research Vera Rubin’s work on Galaxy Rotation Curves.
• Research genetic algorithms.
• Adapt existing genetic algorithm programs.
• Modify the software, to fit galaxy rotation.
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Proposal Timeline• July 8 – September 8 2014
• Investigate current theories on rotation curves with ordinary and dark matter.
• September 8 – November 8, 2014• Modify GA programs to search for desired parameters.
• November 8 – January 8, 2015• Gather data sets for rotation curves.
• January 8 – March 8, 2015• Run GA programs to search for parameters to find best fit.
• March 8 – May 8, 2015• Ideally present project at conferences
• Switched to planetary orbits.6
Why Genetic Algorithms?
•Genetic algorithms.
•Random walks through “parameter space”.
•Computationally faster than brute force.
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• How big a number do you think you have (needs to be 2n).
• Magnitude of the range = 100 (variable)
• How many divisions = 100 (variable)
• (Magnitude of the Range)*(Number of Divisions) =(100)*(100) = 10,000• Look for the next highest factor of 2.• 214 = 16384
• Possible variable ranges = 0 to 99.99 or 0 to 9.999 or 0 to 999.9, etc.
Encoding/Decoding the Genetic Strings
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Encoding/Decoding the Genetic Strings• 50 individuals in the population.
• Each individual is a string of 14 1’s or 0’s multiplied by how many variables you want: 3x14 = 42
• Each character in the string is a gene (1 or a 0).
• Each string is evaluated to a number.
• Binary decimal function …• Result = decimal (string) * (range)/(2n-1) [round to sig
place]
•We want fitness of the fittest to be the same X times in a row.• Sum of least squares – low = good.
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Genetic Algorithm (GA) ProcessInitialization
Evolution (Selection, Crossover, Mutation)
Evaluation (decode)
Good fit with data?
NO
Yes
Print out final answers 10
GA – Galaxy Rotation Curves
•Galaxy model requires 3 variables.• Code adjusted for 3 variables.
•Model/Data Sets-Houston we have a problem!
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What is a Galaxy Rotation Curve?
http://milkyway.cs.rpi.edu/download/images/gal_rotation_curve.png12
What About One Planet Around a Star?
http://upload.wikimedia.org/wikipedia/commons/3/33/ESO_-_The_Radial_Velocity_Method_(by).jpg13
51 Pegasus Radial Velocity – Phase Curve
http://www.astrosurf.com/buil/exoplanet2/fig/51peg_phase.png
Phase
Period
Amplitude
𝐴 sin2𝜋𝑡
𝐵+ 𝐶
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NASA Exoplanet Database
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NASA Exoplanet Database Sorted
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Data
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51 Pegasus
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Tau Boo
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HD195019 (“Mary Poppins Star”)
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Future Work•Getting data sets and model equations for Galaxy
Rotation.
•Multiple planet systems with circular orbits.
•Planets with elliptical orbits.
• Looking at data sets where this couldn’t find a period
• Future students here at LTU can use the code for astronomy and astrophysics or modify for something new.
• I can continue this on my own at graduate school.22
References• J.Q. Feng and C.F. Gallo, Res. Astron. Astrophys. 11 1429-1449, 1 (2011).
• P. Charbonneau, Astrophys. J. Suppl. Ser. 101 309-334, 1 (1995).
• L. Jacobson, theProjectSpot, http://www.theprojectspot.com/tutorial-post/creating-a-genetic-algorithm-for-beginners/3 (2012).
• A. Rebelo, GitHubGist, https://gist.github.com/arthurrebelo/6689655 (2013).
• L. Doyle, SETI Institute, http://archive.seti.org/seti/seti-science/detecting_new/wobble_method.php (2015).
• R.L. Akeson et al, NASA Exoplanet Science Institute, http://exoplanetarchive.ipac.caltech.edu/cgi-bin/TblView/nph-tblView?app=ExoTbls&config=planets (2015).
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Acknowledgements
• Lawrence Technological University
• The Department of Natural Sciences
• Dr. Tim McKay at the University of Michigan
• Dr. Scott Schneider
• Friends and Family
• Chet
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CUWiP
https://plus.google.com/photos/104574436595725911903/albums/6130616175941374209/6130616457291780658?banner=pwa&pid=6130616457291780658&oid=104574436595725911903
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Ceré L. Rettig
Dr. Scott Schneider
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http://tinyurl.com/p7flm6e
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