University of Arizona | Department
of Mathematics | Ildar Gabitov |
MATH 485/585
MATH 485/585
Mathematical Modeling
Section 002, Spring 2013
| Classroom: | PSYCH 204,
TR, 2:00–3:15pm |
| Instructor: | Ildar Gabitov
|
| 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
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.
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
Medicine and electrophysics : Electro-mechanical properties of bones
- Mentor: Ildar Gabitov (gabitov@math.arizona.edu )
- Team members: Kieu,Vy Thuy; Newton, Miyant'e Yuki; Peng, Ken; Sonera Ramos, Eric J
- Literature: Rafael Casas, Igor Sevostianov, Electrical resistivity of cortical bone: Micromechanical modeling and
experimental verification, International Journal of Engineering Science, 62, 106–112, (2013)
- 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
Homework:
Homework will be assigned regularly. Selected homework will be graded, and
a final score of 100 points will be assigned.
Homework is an essential component of the course, whether it is assigned
for grading or not.