Math 485/585 modeling projects
Social interactions
- Modeling competition between languages
•
•
•
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. Castellò, V.M. Eguíluz,
and M. San Miguel, Physica A 374, 835-842 (2007).
- Modeling traffic flow
•
•
•
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).
Cancer and chemotherapy
- Modeling tumor growth
• 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).
- Modeling leukaemia chemotherapy
•
•
Cancer biology: Summing up cancer stem cells by J.P. Huntly and D.G. Gilliland,
Nature 435, 1169-1170 (2005).
Dynamics of chronic myeloid leukaemia by F. Michor, T.P. Hughes, Y. Iwasa, S. Branford, N.P. Shah, C.L.
Sawyers and M.A. Nowak, Nature 435, 1267-1270 (2005).
Viral infections
- Modeling Hepatitis C infection
•
Modelling how ribavirin improves interferon response rates in hepatitis C virus infection, by N.M. Dixit,
J.E. Layden-Almer, T. J. Layden, and A.S. Perelson, Nature 432, 922-924 (2004).
- Antibody-dependent enhancement
•
Dynamic effects of antibody-dependent enhancement on the fitness of viruses, by D.A.T. Cummings, I.B.
Schwartz, L. Billings, L.B. Shaw, and D.S. Burke, Proc. Natl. Acad. Sci. 102, 15259-15264 (2005).
Epidemics
- Modeling the effect of pathogen mutation on the spread of epidemics
•
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).
- Controlling the spread of epidemics
•
Simple model for tuberculosis in cattle and badgers, by D. R. Cox, C.A. Donnelly, F.J. Bourne, G.
Gettinby, J.P. McInerney, W.I. Morrison, and R. Woodroffe, Proc. Natl. Acad. Sci. 102, 17588-17593
(2005).
Population dynamics
- Predator-prey dynamics
•
•
•
Deer Browsing and Population Viability of a Forest Understory Plant, by J.B. McGraw and M.A. Furedi,
Science 307, 920 - 922 (2005).
Stability and bifurcation of a simple food chain in a chemostat with removal rates, by M.M.A. El-Sheikh
and S.A.A. Mahrouf, Chaos, Solitons and Fractals 23, 1475-1489 (2005).
Stabilization of Large Generalized Lotka-Volterra Foodwebs By Evolutionary Feedback, by G. J. Ackland
and I. D. Gallagher, Phys. Rev. Lett. 93, 158701 (2004).
- Competing species
•
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).
Physics
- Stability of inverted pendulum
•
Mechanics, L. D. Landau, E. M. Lifshitz, Third Edition: Volume 1 (Course of Theoretical Physics) ,
Oxford ; New York : Pergamon Press, 1976
-Invisibility
•
•
•
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)
Nanotechnology
- Memristor – new electronic device
•
•
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)