University of Arizona |
Department of Mathematics |
Ildar Gabitov |
MATH 485
MATH 485
Mathematical Modeling
Section , Spring 2020
Education 337,
TR, 2:00–3:15pm
Office Hours:
Tuesday 4:00–5:00pm, Wednesday 2:00–3:00pm, Thursday 4:00–5:00pm (subject to change) and by appointment.
Homework: Will be assigned
regularly.
Syllabus
Math 485/585 modeling projects:
1. Field: Ecology and Enviromental Science. Title: Optimization of the thermodynamic balance control between the atmosphere and carbon mixture during
its transformation into soil on the facilities of the Biosphere 2.
2. Field: Ecology and Enviromental Science. Title: Ocean - atmosphere heat exchange: analysis of data obtained on
the facilities of the Biosphere 2.
- Mentor: Sam McLaren ( smclaren@math.arizona.edu )
- Team members : Sasha Sepulveda, Carl Solway, Lyra Troy
- Literature:
1) Data will be provoded from Biosphere 2 facilities;
- Midterm presentation: Education 337, 2:00 - 3:15pm, March 5, 2020
- Midterm report: Apr 07, 2020
- Final presentation: April 28, 2020
- Final report: May 12, 2020
- Poster 1. May 7, 2020
- Poster 2. May 7, 2020
3. Field: Classical Mechanics.
Title: Unexpected around us: the mysteries of the evolution of the moon-earth system
- Mentor: Tiffany Jones (tnjones@math.arizona.edu )
- Team members : Michael Inouye, Zack Wellington, and Kian Milani
- Literature:
1) Peter Goldreich, History of the Lunar Orbit, Geophysics Vol. 4(4), pp. 411 - 439, (1966);
2) Jihad Touma, Jack Wisdom, Evolution of the Earth-Moon System, Astronomical Journal Vol. 108(5), pp. 1943 - 1961 (1994);
3) Stephen R. Meyersa, and Alberto Malinvernob, Proterozoic Milankovitch cycles and the history of the solar system, PNAS, Vol. 115(25), pp. 6363-6368, (2018);
- Midterm presentation: Education 337, 2:00 - 3:15pm, March 5, 2020
- Midterm report: Apr 07, 2020
- Final presentation: April 28, 2020
- Final report: May 12, 2020
- Poster: May 7, 2020
4. Field: Classical Mechanics. Title: Stability of inverted pendulum with vibrating base.
- Mentor: Kevin Luna ( kevinluna@email.arizona.edu )
- Team members : Devin Johnson, Zach Kirch, Phillip Shelton
- Literature:
1) Landau L. D. & Lifshitz E. M., Mechanics, Second Edition: Volume 1, (Course of Theoretical Physics), (Oxford ; New York : Pergamon Press, 1976), pp 665-70. Oscillations of systems with more than one degree of freedom;
2) Mark Levi 1998 Nonlinearity 11 1365;
3) Shew, Woody, Inverted Equilibrium of a Vertically Driven Pendulum, wooster.edu, College of Wooster. 24 Apr, 1997. Web. 23 Mar, 2013;
4) VanDalen J., Gordon, The driven pendulum at arbitrary drive angles, arvix.org, Department of Physics at University of California and Embry-Riddle Aeronautical University. 2 Feb, 2008. Web. 24 Mar, 2013;
5) Mark Levi, (1988), Stability of the Inverted Pendulum, A Topological Explanation, Siam Review - SIAM REV. 30. 10.1137/1030140.
6) Ivan Demidov, and Vladislav Sorokin, AIP Conference Proceedings 1959, 080013 (2018); https://doi.org/10.1063/1.5034730
Published Online: 02 May 2018;
7) T. Zh. Esirkepov and S. V. Bulanov, Paradoxical Stabilization of Forced Oscillations by Strong Nonlinear Friction, Physics Letters A
Volume 381, Issue 32, 28 August 2017, Pages 2559-2564;
8) Arthur V. Straube, Dmitry V. Lyubimov, and Sergey V. Shklyaev, Averaged dynamics of two-phase media in a vibration field, Physics of Fluids. 18. 10.1063/1.2204057, (2006).
9) Jon Juel Thomsen and Dmitri M. Tcherniak, Chelomei's pendulum explained, Proceedings Royal Society London A (2001) 457, 1889 - 1913;
10) Yevhen Lapshyn1, Robert Molchanov, and Oleksandr Khaminich, Method for determining the rational parameters of dynamic dampers of low-frequency
vibrations, E3S Web of Conferences 109, 00049 (2019) https://doi.org/10.1051/e3sconf/201910900049
Essays of Mining Science and Practice 2019;
11) V.G. Shironosov, RESONANCE in Physics, Chemistry and Biology, "IIS-RT"-2001 Collection ?22 http://eng.ikar.udm.ru/mis-rt.htm;
- Midterm presentation: Education 337, 2:00 - 3:15pm, March 3, 2020
- Midterm report: Apr 07, 2020
- Final presentation: April 28, 2020
- Final report: May 12, 2020
- Poster: May 07, 2020
5. Field: Biology. Title: Evolution future and genealogical trees
- Mentor: Nicole Fider ( nfider@math.arizona.edu )
- Team members : Dominique Hughes , Nur Izzati Johari and Ling Yang
- Literature:
1) Richard A Neher, Colin A Russell, Boris I Shraiman, Predicting evolution from the shape of genealogical trees, eLife vol. 3 e03568, (2014), doi:10.7554/eLife.03568;
- Midterm presentation: Education 337, 2:00 - 3:15pm, March 5, 2020
- Midterm report: Apr 07, 2020
- Final presentation: April 28, 2020
- Final report: May 12, 2020
- Poster May 7, 2020
6. Field: Biology. Title: DNA repair models
- Mentor: Ruby Abrams ( rabrams12@math.arizona.edu> )
- Team members : Jericho Lawson, Steven Fried, and Andrew Alamban
- Literature:
1) Maryam Rouhani, Modeling the interplay between DNA-PK, Artemis, and ATM
in non-homologous end-joining repair in G1 phase of the cell cycle, Journal of Biological Physics, vol. 45, (2019),
https://doi.org/10.1007/s10867-018-9519-2;
2) Philip S. Crooke1 and Fritz F. Parl, A Mathematical Model for DNA Damage and Repair, Journal of Nucleic Acids
Vol. 2010, Article ID 352603, 7 pages, (2010), doi:10.4061/2010/352603;
3) Stephen J. McMahon, Jan Schuemann, Harald Paganetti, and Kevin M. Prise, Mechanistic Modelling of DNA Repair and Cellular Survival Following Radiation-Induced DNA Damage,
Scientific Reports, vol. 6(33290) (2016), https://doi.org/10.1038/srep33290;
- Midterm presentation: Education 337, 2:00 - 3:15pm, March 3, 2020
- Midterm report: Apr 07, 2020
- Final presentation April 28, 2020
- Final report: May 12, 2020
- Poster May 12, 2020
7. Field: Neurobiology. Title: Brain - eye connection.
- Mentor: Ildar Gabitov (gabitov@math.arizona.edu )
- Team members : Rasheed Alshahrani, Ibraheem Al-Abdulelah, Yifan Li, and Tiancheng Xu
- Literature:
1) Catherine E. Graves, Ryan G. McAllister, William J. Rosoff, and Jeffrey S. Urbach, Optical neuronal guidance in three-dimensional matrices, J. Neurosci Methods,
vol. 179(2), pp. 1-16 ,(2009), doi:10.1016/j.jneumeth.2009.02.004;
2) Oster, S F, and D W Sretavan, Connecting the eye to the brain: the molecular basis of ganglion cell axon guidance, the British journal of ophthalmology,
vol. (87)5, pp. 639-45, (2003), doi:10.1136/bjo.87.5.639;
3) Alexei Koulakov, Formation of connectome: nature versus nurture, Cold Spring Harbor Labhttps://www.poncelet.ru/sites/default/files/files/slides/koulakov.pdf;
- Midterm presentation: Education 337, 2:00 - 3:15pm, March 3, 2020
- Midterm report: Apr 07, 2020
- Final presentation: April 30, 2020
- Final report: May 12, 2020
- Poster: May 7, 2020
8. Field: Financial Mathematics. Title: Stock Trend Evolution.
- Mentor: Melinda Lanius (lanius@math.arizona.edu )
- Team members : Taylor Agarwal, Henk Quelle, Cooper Ryan.
- Literature:
1) Muhammad Waqar, Hassan Dawood,Muhammad Bilal Shahnawaz, Mustansar Ali Ghazanfar, and Ping Guo,
Prediction of Stock Market by Principal Component Analysis, Proceedings of the 2017 13th International Conference on Computational
Intelligence and Security, 0-7695-6341-4/17/31.00 © 2017 IEEE, pp. 599-601, DOI 10.1109/CIS.2017.00139, CPS Conference Publishing Services;
2) Carol Anne Hargreaves, and Chandrika Kadirvel Mani, The Selection of Winning Stocks Using Principal
Component Analysis, American Journal of Marketing Research, Vol. 1, No. 3, pp. 183-188, (2015);
3) Stock database: https://www.kaggle.com/borismarjanovic/price-volume-data-for-all-us-stocks-etfs/data,
- Midterm presentation: Education 337, 2:00 - 3:15pm, March 5, 2020
- Midterm report: Apr 07, 2020
- Final presentation: April 28, 2020
- Final report: May 12, 2020
- Poster May 7, 2020
9. Field: Optics and Astronomy. Title: Olbers' paradox: the darkness of the night sky filled with myriad of stars
- Mentor: Ildar Gabitov (gabitov@math.arizona.edu )
- Team members : Juan Angel Bravo, Scott Harrison LaFerriere, Ariel Lamdan, Kaiqi Shangguan
- Literature:
1) Olbers, H.W. Ueber die Durchsichtigkeit des Weltraums, von Hrn. Dr. Olbers in Bremen, unterm
7. Mai 1823. eingesandt. In Astronomisches Jahrbuch für das Jahr 1826; Bode, J.E., Ed.; Ferd.
Dümmler: Berlin, Germany, 1823; pp. 110-121. (In German);
2) E. R. Harrison, The Dark Night-Sky Riddle: A ``Paradox'' that Resisted Solution, Science
New Series, Vol. 226, No. 4677, pp. 941-945 (5 pages), (Nov. 23, 1984);
3) Paul S. Wesson, The Real Reason the Night Sky is Dark: Correcting a Myth in Astronomy Teaching,
Journal of the British Astronomical Association, vol.99, no.1, p.10-13, (1989)
4) E. R. Harrison,The Dark Night Sky Riddle, "Olbers's Paradox", The Galactic and Extragalactic Background Radiation.
Proceedings of the 139th. Symposium of the International Astronomical Union, June 12-16, 1989.
Editors, Stuart Bowyer, Christoph Leinert; Publishers, Kluwer Academic Publishers, Dordrecht, Boston, 1990.
ISBN # 0-7923-0841-7. LC # QB991.C64 I57 1989;
5) Lorenzo Iorio, Editorial for the Special Issue 100 Years of
Chronogeometrodynamics: The Status of the Einstein's
Theory of Gravitation in Its Centennial Year, Universe,I, pp 38-82, (2015); doi:10.3390/universe1010038
6) Albrecht Unsöld, Bodo Baschek, The New Cosmos: An Introduction to Astronomy and Astrophysics, Publisher
Springer Science & Business Media, 2013, ISBN 3662043564, 9783662043561;
7) Harrison, E. Cosmology. The Science of the Universe, 2nd ed.; Cambridge University Press:
Cambridge, UK, 2000; pp. 491-514;
8) Riess, A.G.; Filippenko, A.V.; Challis, P.; Clocchiatti, A.; Diercks, A.; Garnavich, P.M.;
Gilliland, R.L.; Hogan, C.J.; Jha, S.; Kirshner, R.P.; et al. Observational Evidence from
Supernovae for an Accelerating Universe and a Cosmological Constant. Astron. J. 1998, 116,
1009-1038;
- Midterm presentation: Education 337, 2:00 - 3:15pm, March 3, 2020
- Midterm report: Apr 07, 2020
- Final presentation: April 28, 2020
- Final report: May 12, 2020
- Poster May 7, 2020