 Chaotic bubble

Many dynamical processes that generate bubbles are nonlinear, many exhibiting patterns consistent with mathematically chaotic dynamics (chaos theory). In such cases, chaotic bubbles can be said to occur. In most systems they arise out of a forcing pressure that encounters some kind of resistance or shear factor, but the details vary depending on the particular context.
The most widely used application has been in studying bubbles in various forms of liquid media. Although there may have been an earlier use of the term, it was used in 1987 specifically in connection with a model of the motion of a single bubble in a fluid subject to periodically driven pressure oscillations (Smereka, Birnir, and Banerjee, 1987). For an overview of models of single bubble dynamics see Feng and Leal (1997). There has been a long literature on nonlinear analysis of dynamics of bubbles in liquids, with an important figure in this being Werner Lauterborn (1976). Lauterborn and Cramer (1981) would also play an important role in applying chaos theory to acoustics, in which bubble dynamics play a crucial part. This includes analysis of chaotic dynamics in an acoustic cavitation bubble field in a liquid (Lauterborn, Holzfuss, and Bilio, 1994). The study of the role of shear stresses in nonNewtonian fluids has been done by Li, Mouline, Choplin, and Midoux (1997).
A somewhat related interest has been the study of controlling such chaotic bubble dynamics (control of chaos) by converting them to periodic oscillations, with an important application to gas–solids in fluidized bed reactors, also applicable to the ammoxidation of propylene to acrylonitril (Kaart, Schouten, and van den Bleek, 1999). Sarnobat et al. (2000 & 2004) study the behavior of electrostatic fields on chaotic bubbling in attempt to control the chaos into a lower order periodicity.
An early attempted application that led to failure was in Alan H. Guth’s (1981) chaotic inflation theory of the early period of the universe. While he did not precisely use the term “chaotic bubbles,” his model involved “bubbles” in the original cosmic foam that collided chaotically. The model has since been modified due to the inability to find in the real universe some of the phenomena predicted by it, with improvements involving quantum fluctuations provided by Andrei D. Linde (1986).
In economics the bubbles in question have been those due to speculation in asset markets (economic bubble). The first to apply the term in this context was J. Barkley Rosser, Jr. in 1991. While not using the term, Richard H. Day and Weihong Huang (1990) showed that the interaction of fundamentalist and trendchasing traders could lead to chaotic dynamics in the price path of a speculative bubble. De Grauwe, Dewachter, and Embrechts (1983) applied such a model to foreign exchange rate dynamics.
References
 P. Smereka, B. Birnir, and S. Banerjee. “Regular and Chaotic Bubble Oscillations in Periodically Driven Pressure Fields.” Physics of Fluids November 1987, 30(11), pp. 3342–3350.
 Z.C. Feng and L.G. Leal. “Nonlinear Bubble Dynamics.” Annual Review of Fluid Mechanics January 1997, 29(1), pp. 201–243.
 Werner Lauterborn. “Numerical Investigation of Nonlinear Oscillations of Gas Bubbles in Liquids.” Journal of the Acoustical Society of America 1976, 59(2), pp. 283–293.
 Sarnobat, S.U., “Modification, Identification & Control of Chaotic Bubbling via Electrostatic Potential”, Masters Thesis, University of Tennessee, Knoxville, August 2000. online archive
 Sarnobat S.U. et al., "The impact of external electrostatic fields on gas–liquid bubbling dynamics", Chemical Engineering Science, Volume 59, Issue 1, January 2004, Pages 247–258 link
 W. Lauterborn and E. Cramer. “Subharmonic Route to Chaos Observed in Acoustics.” Physical Review Letters 1981, 47(20), pp. 1445–1448.
 W. Lauterborn, J. Holzfuss, and A. Bilio. “Chaotic Behavior in Acoustic Cavitation.” IEEE Ultrasonics Symposium Proceedings November 1994, 2(1–4), pp. 801–810.
 H.Z. Li, Y. Mouline, L. Choplin, and N. Midoux. “Chaotic Bubble Coalescence in NonNewtonian Fluids.” International Journal of Multiphase Flow August 1997, 23(4), pp. 713–723.
 Sander Kaart, Jaap C. Schouten, and Cor M. van den Bleek. “Improving Conversion and Selectivity of Catalytic Reactions in Bubbling GasSolid Fluidized Bed Reactors by Control of the Nonlinear Bubble Dynamics.” Catalysis Today January 27, 1999, 48(1–4), pp. 185–194.
 Alan H. Guth. “Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems.” Physical Review D January 1981, 23(2), pp. 347–356.
 Andrei D. Linde. “Eternally Existing SelfReproducing Chaotic Inflationary Universe.” Physical Letters B 1986, 175, pp. 395–400.
 J. Barkley Rosser, Jr. From Catastrophe to Chaos: A General Theory of Economic Discontinuities. Boston/Dordrecht: Kluwer Academic Publishers, 1991.
 Richard H. Day and Weihong Huang. “Bulls, Bears, and Market Sheep.” Journal of Economic Behavior and Organization December 1990, 14(3), pp. 299–329.
 Paul De Grauwe, Hans Dewachter, and Mark Embrechts. Exchange Rate Theory: Chaotic Models of Foreign Exchange Rate Markets. Oxford: Blackwell, 1993.
Categories:
Wikimedia Foundation. 2010.
Look at other dictionaries:
Chaotic Inflation theory — Physical cosmology Universe · Big Bang … Wikipedia
Chaotic Code Masters — In Chaotic , Code Masters are moderators of the Battle Dromes, the battle arenas in Chaotic. Each Battle Drome is also named after their respective Code Master, except for the Beta Drome which has no Code Master. Since there are seven official… … Wikipedia
Economic bubble — An economic bubble (sometimes referred to as a speculative bubble, a market bubble, a price bubble, a financial bubble, a speculative mania or a balloon) is trade in high volumes at prices that are considerably at variance with intrinsic values… … Wikipedia
List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… … Wikipedia
Inflation (cosmology) — Inflation model and Inflation theory redirect here. For a general rise in the price level, see Inflation. For other uses, see Inflation (disambiguation). Physical cosmology … Wikipedia
Cosmic inflation — In physical cosmology, cosmic inflation is the idea that the universe passed through a phase of exponential expansion that was driven by a negative pressure vacuum energy density. [Liddle and Lyth (2000) and Mukhanov (2005) are recent cosmology… … Wikipedia
Chaos theory — This article is about chaos theory in Mathematics. For other uses of Chaos theory, see Chaos Theory (disambiguation). For other uses of Chaos, see Chaos (disambiguation). A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 … Wikipedia
Universe — For other uses, see Universe (disambiguation). Physical cosmology … Wikipedia
List of Bobobobo Bobobo characters — The universe of the anime and manga series Bobobo bo Bo bobo is a home to a wide array of fictional characters. Contents 1 Main characters 1.1 Bobobo bo Bo bobo 1.2 Beauty 1.3 … Wikipedia
False vacuum — In quantum field theory, a false vacuum is a metastable sector of space that appears to be a perturbative vacuum, but is unstable due to instanton effects that may tunnel to a lower energy state. This tunneling can be caused by quantum… … Wikipedia