University of Arizona | Department of Mathematics | Ildar Gabitov | MATH 485/585

MATH 485/585
Mathematical Modeling

Section 001, Spring 2010

Classroom:	PSYCH 207, TR, 11:00am–12:15pm
Instructor:	Ildar Gabitov office:  MATHE 249C e-mail:  gabitov@math.arizona.edu phone:  (520) 626-8853
Office Hours:	Tue 4–5pm, Wed 2–3pm, Thu 9:30–10:30am (subject to change) and by appointment
Text:	J. Lega, Mathematical Modeling, Class Notes, MATH 485/585, (University of Arizona, 2010)

MATH 485/585 Calendar / Syllabus

Grades: The total number of points available on tests and homework is 500 = 100(homeworks) + 100 (midterm presentation)+ 100(midterm report)+ 200(poster session and final report). The two in-class tests are scheduled for Tue, Sep 16 and Tue, Nov 04. The final exam is at Fri, May 07, 11:00am–1:00pm. 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 :

• Population dynamics: Competing species
  • Mentor: Sarah Mann (smann@math.arizona.edu).
  • Team members: David DeCesari, Jennifer Kanemaru, Daniel Weiss , Carolyn Wise
  • Literature: Coexistence and chaos in complex ecologies, by J.C. Sprott, J.A. Vano, J.C. Wildenberg, M.B. Anderson, and J.K. Noel, Phys. Lett. A 335, 207-212 (2005).
  • Midterm presentation: March 25, 2010 (first presentation)
  • Midterm report: April 1, 2010
  • Final report May 10, 2010
• Social interactions: Modeling traffic flow
  • Mentor: David Love (dlove@math.arizona.edu).
  • Team members: Robert G. Soimaru, Ran Kumada, Matthew I. Avetian, Lynette D. Guzman, Salim Zerkoune
  • Literature: Jam formation in traffic flow on a highway with some slowdown sections, by H. Hanaura, T. Nagatani, and K. Tanaka, Physica A 374, 419-430 (2007); Chaos control and schedule of shuttle buses, by T. Nagatani, Physica A 371, 683-691 (2006); The night driving behavior in a car-following model, by R. Jiang and Q.S. Wu, Physica A 375, 297-306 (2007).
  • Midterm presentation: March 25, 2010 (second presentation)
  • Midterm report: April 1, 2010
  • Final report May 10, 2010
• Social interactions: Modeling competition between languages
  • Mentor: Rebecca Stockbridge (rstockbridge@math.arizona.edu).
  • Team members: Brian Bilquist, Katie Goeldner, Erin Hittle, Samantha Vandermey.
  • Literature: Non-equilibrium and irreversible simulation of competition among languages, by D. Stauffer, C. Schulze, F.W.S. Lima, S. Wichmann, and S. Solomon, Physica A 371, 719-724 (2006); Coexistence of Languages is possible, by J.P. Pinasco and L. Romanelli, Physica A 361, 355-360 (2006); Microscopic Abrams-Strogatz model of language competition, by D. Stauffer, X. Castello, V.M. Eguiluz, and M. San Miguel, Physica A374, 835-842 (2007).
  • Midterm presentation: March 30, 2010 (first presentation)
  • Midterm report April 6, 2010
• Cancer and chemotherapy: Modeling tumor growth
  • Mentor: Hottovy, Scott (shottovy@math.arizona.edu).
  • Team members: Meggie Erickson, Daniel Lukaszewski, Wesley Jackson, Gustavo Miranda
  • Literature: A mathematical model of tumor-immune evasion and siRNA treatment, by J.C. Arciero, T.L. Jackson, and D.E. Kirschner, Disc. Cont. Dyn. Syst. B 4, 39-58 (2004).
  • Midterm presentation: March 30, 2010 (second presentation)
  • Midterm report: April 6, 2010
• Epidemics: Modeling the effect of pathogen mutation on the spread of epidemics
  • Mentor: Toby Shearman (tshearman@math.arizona.edu).
  • Team members: Nadia Flores, Daniel Jackson, Robert Phillips, Manuel Rivera, Zach Rogers.
  • Literature: Epidemics with pathogen mutation on small-world networks, by Z.-G. Shao, Z.-J. Tan, X.-W. Zou, and Z.-Z. Jin, Physica A 363, 561-566 (2006).
  • Midterm presentation: April 1, 2010 (first presentation)
  • Midterm report April 8, 2010
  • Final report May 10, 2010
• Physics: Invisibility and Optical cloaking
  • Mentor: I.G. (gabitov@math.arizona.edu)
  • Team members: Amanda Booth, David Dror, Daniel Frasquillo, Jaron Gubernick
  • Literature: Optical Conformal Mapping, by Ulf Leonhardt, Science, 312, 1777-1780, (2006); Controlling Electromagnetic Fields, J. B. Pendry, D. Schurig, D. R. Smith, Science, 312, 1780-1782, (2006), Optical cloaking with metamaterials, Wenshan Cai, Uday K. Chettiar, Alexander V. Kildishev & Vladimir M. Shalaev, Nature Photonics, 1, 224-27 (2007)
  • Midterm presentation: April 1, 2010 (second presentation)
  • Midterm report: April 8, 2010
• Physics: Stability of inverted pendulum
  • Mentor: Pennybacker, Matthew, (pennybacker@math.arizona.edu).
  • Team members: Vicki Springmann, Edward Montiel
  • Literature: Mechanics, L. D. Landau, E. M. Lifshitz, Third Edition: Volume 1 (Course of Theoretical Physics), Oxford ; New York : Pergamon Press, 1976.
  • Midterm presentation: April 6, 2010 (first presentation)
  • Midterm report: April 13, 2010
  • Final report May 10, 2010
• Physics: Atomic physics: Ground state calculations of atoms using Gaussian basis functions
  • Mentor: I.G. (gabitov@math.arizona.edu)
  • Team members: Keeper Sharkey
  • Literature: Relativistic corrections to the non-Born- Oppenheimer energies of the lowest singlet Rydberg states of He-3 and He-4, Stanke M, Kedziera D, Bubin S, Adamowicz L., JOURNAL OF CHEMICAL PHYSICS Volume 126 (19), 2007
  • Midterm presentation: April 6, 2010 (second presentation)
  • Midterm report: April 13, 2010
• Nanotechnology: Memristor – new electronic device
  • Mentor: Taft, Jefferson (jctaft@math.arizona.edu)
  • Team members:  Troy Comi, Aaron Gibson,   Joseph Padilla
  • Literature: The missing memristor found, by Dmitri B. Strukov, Gregory S. Snider, Duncan R. Stewart and R. Stanley Williams, Nature 453, 80-83 (1 May 2008), doi:10.1038/nature06932; Memristor - the missing circuit element, by L. O. Chua, IEEE Trans. Circuit Theory 18, 507–519 (1971)
  • Midterm presentation: April 8, 2010 (first presentation)
  • Midterm report: April 15, 2010
• Optics: Recognition of spectral patterns
  • Mentor: I.G. (gabitov@math.arizona.edu)
  • Team members: Victoria Hahn
  Literature:
  • Midterm presentation: April 8, 2010
  • Midterm report April 15, 2010 (second presentation)
  • Final report May 10, 2010
• Hydrodynamics: Rogue waves
  • Mentor: I.G. (gabitov@math.arizona.edu)
  • Team members: Alex Andrade
  • Literature: Physical mechanisms of the rogue wave phenomenon, by Kharif C, Pelinovsky E (2003) Eur J Fluid Mech B/Fluids 22:603–634; Rogue waves in the ocean, by Kharif C, Pelinovsky E, Slyunyaev A (2009) Springer, Berlin; Water waves, nonlinear Schrodinger equations and their solutions, by Peregrine DH (1983) J Aust Math Soc Ser B 25: 16–43; What makes the Peregrine soliton so special as a prototype of freak waves?, V. I. Shrira and V. V. Geogjae, Journal of Engineering Mathematics, DOI 10.1007/s10665-009-9347-2.
  • Midterm presentation: April 13, 2010 (first presentation)
  • Midterm report April 20, 2010
  • Final report May 10, 2010
• Aerodynamics: Flight of insects
  • Mentor: I.G. (gabitov@math.arizona.edu)
  • Team members: Fernando Rojano
  • Literature: Nonlinear time-periodic models of the longitudinal flight dynamics of desert locusts Schistocerca gregaria, by G. K. Taylor and R. Zbikowski, J. R. Soc. Interface (2005) 2, 197–221, doi:10.1098/rsif.2005.0036 (Published online 18 May 2005).
  • Midterm presentation: April 13, 2010 (second presentation)
  • Midterm report April 20, 2010
  • Final report May 10, 2010

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.