A Student Seminar in Nonlinear dynamics and chaos
Instructors:
Einat Aharonov,
Vered Rom-Kedar,
Uzi Smilansky
and
Eli Tziperman.
Day, time & location of seminar: Thursdays at
16:00-18:00 hrs in Sem. Rm A, Weissman Building. First meeting: April
11, 2002
Announcements Last updated: Apr 4.
Feel free to write or call me with any questions:
Vered, x3170, vered@wisdom.weizmann.ac.il
Nonlinear models arise in a variety of fields of science, including
fluid dynamics, geophysics, particle physics and biological models. The
analysis of these models results in many cases in complicated
bifurcation scenarios and sometimes chaotic dynamics. Interpretation of
these results leads to interesting insights regarding the behavior of
the systems. Students will be offered a variety of topics and papers to
study and present in front of the class. The study of the papers will be
guided by the corresponding researchers. Students are expected to have
basic familiarity in nonlinear dynamics.
- Controlling chaos; El Nino's chaos; Controlling El Nino's chaos
(Eli):
- Ott, E., and Grebogi, C., and Yorke, J., Controlling chaos,
Phys. Rev. Lett., 1990, 64, 1196-1199.
- Tziperman, E., M. A. Cane and S. Zebiak, 1995: Irregularity
and locking to the seasonal cycle in an ENSO prediction model as
explained by the quasi-periodicity route to chaos. Journal of the
Atmospheric Sciences, 52, 293-306.
here
- E. Tziperman, H. Scher, S. Zebiak and M. A. Cane, 1997:
Controlling spatiotemporal chaos in a realistic El Niņo prediction
model. Physical Review Letters, 79, 6, 1034-1037.
here
- Glacial dynamics: stochastic resonance, frequency locking and
entrainment, chaos and relaxation oscillations (Eli):
- R. Benzi and G. Parisi and A. Sutera and A. Vulpiani,
Stochastic resonance in climatic change, Tellus, 1982, 34, 10-16
- (?) R. Benzi, A. Sutera, A. Vulpiani, The mechanism of
stochastic resonance, J. Phys. A 14, L453-L457 (1981).
- a coherence resonance paper
- Ghil, M. Cryothermodynamics: the chaotic dynamics of
paleoclimate, Physica D 1994, 77, 130-159
- Gildor, H. and E. Tziperman, 2000. Sea ice as the glacial
cycles' climate switch: role of seasonal and orbital forcing.
Paleoceanography, 15, 605-615.
here
- Chaos synchronization, chaos synchronization in climate dynamics
(Eli):
- Pecora LM, Carroll TL Synchronization in chaotic systems Phys
Rev Lett 64 (8): 821-824 FEB 19 1990
- Duane GS, Tribbia JJ Synchronized chaos in geophysical fluid
dynamics Phys Rev Lett 86 (19): 4298-4301 MAY 7 2001
- Duane GS, Webster PJ, Weiss JB Go-occurrence of Northern and
Southern Hemisphere blocks as partially synchronized chaos J Atmos
Sci 56 (24): 4183-4205 DEC 15 1999
- Geodynamics: Friction as it relates to Earthquakes (Einat):
- Creep, stick-slip and dry friciton dynamics Heslot et al.
Phys Rev E, 49, pg. 4973, (1994)
- Non-linear dynamics of friction F Elmer J Phys A: Math Gen.
30, pg 6057 (1997)
- Transition from stick-slip to smooth sliding: An
earthquake-like model Braun OM, Roder J PHYSICAL REVIEW LETTERS 88
(9): art. no. 096102 MAR 4 2002
- "slider-block" chapter from fractals and chaos by Turcotte.
- Geodynamics: The Earth's magnetic field (Einat):
- "Rikitake dynamo" chapter from: fractals and chaos by turcotte book
- Cook and Roberts (1970).
- Fluid Mixing and Transport (Vered)
- V. Rom-Kedar, A. Leonard and S. Wiggins [1990] An Analytical
Study of Transport, Mixing and Chaos in an Unsteady Vortical Flow
, Journal of Fluid Mechanics, volume 214, pp. 347-394;
Rom-Kedar, V.; Poje, A. C. [1999] Universal properties of
chaotic transport in the presence of diffusion. Phys. Fluids 11,
no. 8, 2044-2057.
- G. Haller [2001], Lagrangian structures and the rate of
strain in a partition of two dimensional turbulence, Physics of
Fluids 13(11)
- Hamiltonian chaos (Vered):
- Bessi, Ugo; Chierchia, Luigi; Valdinoci, Enrico Upper bounds
on Arnold diffusion times via Mather theory. J. Math. Pures Appl.
(9) 80 (2001), no. 1, 105-129
- Haller, G. Diffusion at intersecting resonances in Hamiltonian
systems. Phys. Lett. A 200 (1995), no. 1, 34-42.
- Anna Litvak-Hinenzon and Vered Rom-Kedar [2002] Parabolic
resonances in 3 d.o.f. near integrable Hamiltonian systems,
Physica D, to appear.
- Dynamical systems with small noise (Vered)
- Nils Burglund and Barbara Gentz -selected preprints [2001-2];
e.g. "Metastability in simple climate models: Pathwise analysis of
slowly driven Langevin equations", or "The effect of additive
noise on dynamical hysteresis", etc.
- Hamiltonian systems with noise: Mark. I. Freidlin [1998]
"Random and Deterministic perturbatopms of nonlinear oscillators",
Doc. Math. J. DMV, 223-235.
- Mathematical models for cancer (Vered)
- Bellomo, N.; Preziosi, L. Modeling and mathematical problems related to
tumor evolution and its interaction with the
immune system. Math. Comput. Modelling 32 (2000), no. 3-4, 413-452
and references therein.
- Chaotic scattering of particles and waves (Uzy)
- U Smilansky in Chaos and Quantum Physics ed: M J Giannoni A
Voros and J Zinn-Justin (North Holland, Amsterdam, 1992)
- "Chaos" Focus issue on "Chaotic Scattering" Chaos, vol 3 No.
4. 1993. Quantum chaos
- Rom-Kedar, Vered and Turaev, Dmitry [1999] Big Islands in
dispersing billiard-like potentials. Phys. D 130, no. 3-4,
187-210.
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