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University of Arizona | Department of Mathematics | |

Section ,

Section 001: , ,

Section 002: , ,

Office Hours: (subject to change) and by appointment.

Homework: Will be assigned regularly. Although the homework will not be collected, there will be regular quizzes comprised of selected problems from the homework assignments. Quiz dates will be posted in advance on the course website.

due Apr 17due Apr 17due Mar 6due Feb 27due Feb 18due Feb 7due Feb 7

Homework 7

Homework 6 Additional Materials

Syllabus | Grades: Section 001, Section 002

Math 485/585 modeling projects:

Past year examples midterm report , midterm presentation

Physics: Wave structures on a jet entering the bulk liquid
- Mentor: Gabitov Ildar ( gabitov@math.arizona.edu )
- Team members (section 1): He Yijun; Li Youxi; Zhu Zijia; Lin Liang; Corkill Ashley Christine
- Literature: 1) MATTHEW J. HANCOCK AND JOHN W. M. BUSH, Fluid pipes, J. Fluid Mech. (2002), vol. 466, pp. 285-304, 2002 Cambridge University Press DOI: 10.1017/S0022112002001258; 2) Lamb, H. (1994), Hydrodynamics (6th ed.), Cambridge University Press, ISBN 978-0-521-45868-9, OCLC 30070401
- Midterm presentation: March 11, 2014
- Midterm report:March 25, 2014
- Final presentation: BIO W 237, 11:00am - 11:18 am, May 1, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Astronomy: Stability of Lagrangian points: James Webb Space Telescope
- Mentor: Young Alexander (young@math.arizona.edu )
- Team members (section 1): Pearson Kyle Alexander; Hanson Jake; Cacolici Gianna Nicole; Lejoly Cassandra; Reynolds Katherine.
- Literature: 1) A Deprit, A Deprit-Bartholome, Stability of the triangular Lagrangian points THE ASTRONOMICAL JOURNAL VOLUME 72, NUMBER 2 MARCH 1967. 2) Kenneth R. Meyer, Glen R. Hall, Dan Of?n, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Springer (200), ISBN 978-0-387-09723-7, e-ISBN 978-0-387-09724-4, DOI 10.1007/978-0-387-09724-4
- Midterm presentation: March 11, 2014
- Midterm report: March 25, 2014
- Final presentation: BIO W 237, 11:18am-11:36am, May 1, 2014
- Final report: May 6, 2014
- Poster: May 8, 2014
Physics: Bubble dynamics in vibrating liquid
- Mentor: Gabitov Ildar ( gabitov@math.arizona.edu )
- Team members (section 1): Wymer James; Henzerling Jaggar; Kilgallon Aaron; McIntire Michael Zackery, Ghallab Mohammed Ghazi
- 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 11, 2014
- Midterm report: March 25, 2014
- Final presentation: BIO W 237, 11:36 am - 11:54 am, May 1, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Physics: Pendulum with vibrating base
- Mentor: Gabitov Ildar ( gabitov@math.arizona.edu )
- Team members (section 1): Bello Thomas Lawrence; Rumsey Kellin; Lopez Fabian Antonio; Tao Tao; Huang Emily.
- 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 11, 2014
- Midterm report: March 25, 2014
- Final presentation BIO W 237, 11:54 am - 12:12 pm, May 1, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
- Experiment: Oblique Vibrations , Vertical Vibrations
Electrical engineering: Energy flows in electric grids
- Mentor: Steven Rosenthal (wsrosenthal@gmail.com )
- Team members (section 1): Fan Ruolin; Jasim Ahmed Abdulla; Yang Chih-Wei; Peng WeiDe; Greiner Stephanie Anne.
- 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 13, 2014
- Midterm report: March 25, 2014
- Final presentation: BIO W 237, 11:00 am - 11:18 am, May 6, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Electrical Engineering: Synchronization in Electrical Power Networks
- Mentor: Dinius Joseph (jdinius@math.arizona.edu )
- Team members (section 1): Chi Tianye; Taylor Thomas Ryan; Alsairafi Maha Jalil; Gubler Austin; Lee Oren Robert.
- Literature: Adilson E. Motter1, Seth A. Myers, Marian Anghel and Takashi Nishikawa, Spontaneous synchrony in power-grid networks, NATURE PHYSICS VOL 9, MARCH 2013, www.nature.com/naturephysics
- Midterm presentation: March 13, 2014
- Midterm report: March 25, 2014
- Final presentation: BIO W 237, 11:18 am - 11:36 am, May 6, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Cardiology : Shock-induced termination of cardiac arrhythmias
- Mentor: Williams Katie (kwilliams@math.arizona.edu )
- Team members (section 1): Chavez-Diaz Baltazar; Schwenck Sarah; Wang Weide; Zhang Jinglei; Jiang Chen
- Literature: Jean Bragard, Ana Simic, Jorge Elorza, Roman O. Grigoriev, Elizabeth M. Cherry, Robert F. Gilmour, Jr., Niels F. Otani, and Flavio H. Fenton, Shock-induced termination of reentrant cardiac arrhythmias: Comparing monophasic and biphasic shock protocols, Chaos: An Interdisciplinary Journal of Nonlinear Science 23, 043119 (2013); doi: 10.1063/1.4829632 View online: http://dx.doi.org/10.1063/1.4829632
- Midterm presentation: March 13, 2014
- Midterm report: March 25, 2014
- Final presentation: BIO W 237, 11:36 am - 11:54 am, May 6, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Biology: Wing size determination in fly development
- Mentor: Veprauskas Amy (aveprauskas@math.arizona.edu )
- Team members (section 1): Starks Rebekah; Deloach Alana; Aaron David Arthur; Dong Xun; Lass Katherine Elizabeth.
- Literature: Lars Hufnagel, Aurelio A. Teleman, Hervé Rouault, Stephen M. Cohen, and Boris I. Shraiman, On the mechanism of wing size determination in fly development, Proc Natl Acad Sci U S A. 2007 Mar 6;104(10):3835-40.
- Midterm presentation: March 13, 2014
- Midterm report: March 25, 2014
- Final presentation: BIO W 237, 11:54 pm - 12:12 pm, May 6, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Physics: Dynamics of the elastic pendulum
- Mentor: Gibney Joseph (pianomanjoe@gmail.com)
- Team members (section 2): Xiao Qisong; Xia Shenghao; Zammit Corey Robert Martin; Balagopal Nirantha; Li Zijun.
- Literature: 1) Vitt, A and G Gorelik, 1933: Oscillations of an Elastic Pendulum as an Example of the Oscillations of Two Parametrically Coupled Linear Systems. Translated by Lisa Shields, with an Introduction by Peter Lynch. Historical Note No. 3, Met Éireann, Dublin (1999); 2)Lynch, Peter, 2002: Resonant Motions of the Three-dimensional Elastic Pendulum, J. Nonlin. Mech, 37, 345-367; 3) Lynch, Peter, 2002: The Swinging Spring: a Simple Model for Atmospheric Balance, Proceedings of the Symposium on the Mathematics of Atmosphere-Ocean Dynamics, Isaac Newton Institute, June-December, 1996. Cambridge University Press; 4) Holm, Darryl D. and Peter Lynch, 2002: Stepwise Precession of the Resonant Swinging Spring, SIAM Journal on Applied Dynamical Systems, 1, 44-64; 5) Lynch, Peter, and Conor Houghton, 2003: Pulsation and Precession of the Resonant Swinging Spring, Physica D Nonlinear Phenomena, 01/2004; DOI:10.1016/j.physd.2003.09.043
- Midterm presentation: March 11, 2014
- Midterm report: March 25, 2014
- Final presentation: PSYCH 204, 2:00pm-2:20pm, May 1, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Probability: Search for a car parked on a forest road
- Mentor: Zhelezov Gleb (glebzh@email.arizona.edu )
- Team members (section 2): Rickel Jayson Anthony; Nguyen Alex; Braun Rachel Anne; Alabkari Mohammed; Gong Yu
- Literature: Yu Baryshnikov and V Zharnitsky, Search on the brink of chaos, Nonlinearity, 25 (2012), 3023–3047, doi:10.1088/0951-7715/25/11/3023
- Midterm presentation: March 11, 2014
- Midterm report: March 25, 2014
- Final presentation: PSYCH 204, 2:20pm-2:40pm, May 1, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Networks: Properties of mythological networks
- Mentor: Todd George (gtodd@math.arizona.edu )
- Team members (section 2): Krishnaswamy Roopa; Huang Riqu; Fitzgerald Jamie; Villegas Manuel; Neal Riley Thomas
- Literature: Padraig Mac Carron and Ralph Kenna, Universal properties of mythological networks, EPL, 99 (2012) 28002, doi: 10.1209/0295-5075/99/28002,
- Midterm presentation: March 11, 2014
- Midterm report: March 25, 2014
- Final presentation: PSYCH 204, 2:40pm-3:00pm, May 1, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Biology: Search of the scent source in turbulent flows
- Mentor: Gabitov Ildar ( gabitov@math.arizona.edu )
- Team members (section 2): Nakolan Laura; Thompson Craig Anthony; Smith Steven Bruce; Hammer Noah Isaac; Retamoza Cristina Olivia.
- Literature: Balkovsky E. and Shraiman, B.I. “Olfactory search at high Reynolds number”, Proc Natl Acad Sci USA.99,1258993 (2002).
- Midterm presentation: March 13, 2014
- Midterm report: March 25, 2014
- Final presentation: PSYCH 204, 2:00pm-2:20pm, May 6, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Cooking: Science in the kitchen
- Mentor: Hyman Jeffrey (jhyman@math.arizona.edu )
- Team members (section 2): Arellano Jonathan, Borg Katherine, Rodriguez Karina, Godoy Cortes Victor; Villanueva,Denise.
- Literature: 1) Andrey Varlamov and Lev Aslamazov, The Wonders of Physics, World Scientific, 2012, ISBN: 978-981-4374-15-6 2) Peter Barham The Science of Cooking, Springer, 2001 ISBN-10: 3540674667, ISBN-13: 978-3540674665
- Midterm presentation: March 13, 2014
- Midterm report: March 25, 2014
- Final presentation: PSYCH 204, 2:20pm-2:40pm, May 6, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Energy: Energy Harvesting
- Mentor: Gabitov Ildar ( gabitov@math.arizona.edu )
- Team members (section 2): Pan Yuhao; Tang Joseph Shu; Szwez Larissa Irene; Sanchez Luis; Paul Joshua; Cook Brent.
- Literature: F. Cottone, L. Gammaitoni, H. Vocca, Nonlinear energy harvesting, arXiv:0808.0266, DOI: 10.1103/PhysRevLett.102.080601
- Midterm presentation: March 11, 2014
- Midterm report: March 25, 2014
- Final presentation: PSYCH 204, PSYCH 204, 2:40pm-3:00pm, May 6, 2014
- Final report: May 6, 2014
- Poster May 8, 2014
Medicine: Wave Patterns and Their Application to Migraine
- Mentor: Gabitov Ildar ( gabitov@math.arizona.edu )
- Team members (section 2): Pursell Erica; Xie Chenxing; Swartz Max; Zhang Fan.
- Literature: 1) Markus A. Dahlem · Thomas M. Isele, Transient Localized Wave Patterns and Their Application to Migraine, Journal of Mathematical Neuroscience (2013) 3:7 DOI 10.1186/2190-8567-3-7; 2) Markus A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in episodic migraine, Chaos: An Interdisciplinary Journal of Nonlinear Science 23, 046101 (2013); doi: 10.1063/1.4813815 View online: http://dx.doi.org/10.1063/1.4813815
- Midterm presentation: March 13, 2014
- Midterm report: March 25, 2014
- Final presentation: PSYCH 204, 3:00pm-3:20pm, May 6, 2014
- Final report: May 6, 2014
- Poster May 8, 2014