University of Arizona | Department of Mathematics | Ildar Gabitov |

Section ,

Classroom:	, ,
Instructor:	Ildar Gabitov office:   249C e-mail:  gabitov@math.arizona.edu phone:  (520) 626-8853
Office Hours:	Tue 4–5pm, Wed 2–3pm, Thu 11:00am–12:00pm (subject to change) and by appointment
Text:	J. Lega, Mathematical Modeling, Class Notes, MATH 485/585, (University of Arizona, 2013) available at UA Bookstore

Grades: The total number of points available on tests and homework is . Midterm presentations will be at Tue, Mar 26 and Thu, Mar 28. Poster session is scheduled on May 2th. More points — higher grade. Learn more at “how grades work” page about points↔grade correspondence, about withdrawing from the course, and about incomplete grade.

Math 485/585 modeling projects :

Biology: Olfactory search in turbulent flows
• Mentor: Steven Rosenthal (wsrosenthal@gmail.com )
• Team members: Burns, Andrew; Kroc Jonathan Fleming; Pearson, Antony; Tatem, Alexia Rae
• Literature: Balkovsky E. and Shraiman, B.I. “Olfactory search at high Reynolds number”, Proc Natl Acad Sci USA.99,12589-93 (2002).
• Midterm presentation: March 26, 2013 (first presentation)
• Midterm report: April 5, 2013
• Final presentation April 30, 2013.
• Final report May 7, 2013
• Poster May 2, 2013
• Epidemics: Sensitivity analyses of a mathematical model of smallpox transmission
  • Mentor: Jeffrey D. Hyman (jhyman@math.arizona.edu )
  • Team members: Jardini, Michael Anthony; Ma, Xiaosi; Mohty, Ralph Mohammad; O'Ketch, Marvin
  • Literature: Nakul Chitnisa, James M. Hymanb, Jim M. Cushing, Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model, Bulletin of Mathematical Biology (2008) 70: 1272–1296 DOI 10.1007/s11538-008-9299-0.
  • Midterm presentation: March 26, 2013 (first presentation)
  • Midterm report: April 5, 2013
  • Final presentation April 25, 2013.
  • Final report May 7, 2013
  • Poster May 2, 2013
• Physics: Sinking bubbles in oscilating fluid
  • Mentor: Matthew Pennybacker ( pennybacker@math.arizona.edu )
  • Team members: Gentry, Christian Dane; Greenberg, James; Kearns, Nicholas; Matthew, Wang, Xi Ran
  • Literature: V.S. Sorokin, I.I. Blekhman, V.B. Vasilkov, Motion of a gas bubble in fluid under vibration, Nonlinear Dynamics, doi:10.1007/s11071-011-9966-9, (2011). 2) Grigory Falkovich, Fluid Mechanics, Cambridge University Press, 2011. 3) Kana, Daniel D. and Dodge, Franklin T., Bubble Behavior in Liquids Contained in Vertically Vibrated Tanks. Technical Report No. 4 prepared for the National Aeronautics and Space Administration, (1964, August 1).
  • Midterm presentation: March 28, 2013 (first presentation)
  • Midterm report: April 5, 2013
  • Final presentation April 30, 2013.
  • Final report May 7, 2013
  • Poster May 2, 2013
• Physics: Stability of inverted pendulum
  • Mentor: John Gemmer (jgemmer@math.arizona.edu ).
  • Team members: Ashley, Sean; D'Amelio, Avery Hope; Liu, Jiaying; Warren, Cameron
  • Literature: 1) Mechanics, L. D. Landau, E. M. Lifshitz, Third Edition: Volume 1 (Course of Theoretical Physics), Oxford ; New York : Pergamon Press, 1976. 2) Mark Levi, Geometry of Kapitsa's potentials, Nonlinearity, Volume 11, 1365, 1998.
  • Midterm presentation: March 26, 2013 (first presentation)
  • Midterm report: April 5, 2013
  • Final presentation April 25, 2013.
  • Final report May 7, 2013
  • Poster May 2, 2013
• Electrical engineering: Energy flows in smart grids
  • Mentor: Aalok Shah (ashah@math.arizona.edu )
  • Team members: Islam, Md Safatul; Johnson, Deanna Heather; Shayan, Homa; Utegaard, Jonathan Michael
  • Literature: 1) Jan Machowski, Janusz W. Bialek, James R. Bumby, POWER SYSTEM DYNAMICS Stability and Control, ISBN 978-0-470-72558-0, 2008 John Wiley & Sons, Ltd. 2) D Wang, K Turitsyn and M Chertkov, “DistFlow ODE: Modeling, Analyzing and Controlling Long Distribution Feeder”, Proceedings of, the 51st IEEE Conference on Decision and Control (2012) [http://arxiv.org/abs/1209.5776]; 3) M. Chertkov, S. Backhaus, K. Turtisyn, V. Chernyak, V. Lebedev, Voltage Collapse and ODE Approach to Power Flows: Analysis of a Feeder Line with Static Disorder in Consumption/Production, arXiv:1106.5003. 4) Charlie Duclut, Scott Backhaus, Michael Chertkov, Hysteresis, Phase Transitions and Dangerous Transients in Electrical Power Distribution Systems, arXiv:1212.0252.
  • Midterm presentation: March 28, 2013 (first presentation)
  • Midterm report: April 5, 2013
  • Final presentation April 25, 2013.
  • Final report May 7, 2013
  • Poster May 2, 2013

Homework: Homework will be assigned regularly. Selected homework will be graded, and a final score of points will be assigned. Homework is an essential component of the course, whether it is assigned for grading or not.