Chaos Nameplat
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

You Tube Flickr Twitter iResearch App Facebook

Search Issue | RSS Feeds RSS
Previous Issue

Dec 1991

Volume 1, Issue 4, pp. 379-481


A history of chemical oscillations and waves

Anatol M. Zhabotinsky

Chaos 1, 379 (1991); http://dx.doi.org/10.1063/1.165848 (8 pages) | Cited 39 times

Full Text: | Download PDF

Show Abstract
The history of the discovery and study of chemical oscillations and waves is presented from the very first accidental observations up to the systematic design of chemical oscillators. Special emphasis is devoted to the long‐term debate over the possibility of pure chemical oscillations, i.e., concentration oscillations in homogeneous closed systems.
Show PACS
82.40.Bj Oscillations, chaos, and bifurcations
82.40.-g Chemical kinetics and reactions: special regimes and techniques

Oscillations and chaos in CO+O2 combustion

B. R. Johnson, J. F. Griffiths, and S. K. Scott

Chaos 1, 387 (1991); http://dx.doi.org/10.1063/1.165849 (9 pages) | Cited 2 times

Full Text: | Download PDF

Show Abstract
The gas‐phase reaction between carbon monoxide and oxygen (in the presence of small amounts of hydrogen) shows bistability and oscillatory behavior. Typically, the oscillatory ignition has a period‐1 relaxation waveform. The limit cycle is born at a saddle‐node loop and terminates via a supercritical Hopf bifurcation. For a mean residence time of 8 s there is a period‐doubling to a period‐2 solution followed by period‐halving to quasisinusoidal period‐1 oscillations. At longer residence times, more period‐doublings forming a full cascade to chaos with subsequent periodic windows are observed. The chaotic attractor has an underlying single‐humped next maximum map.
Show PACS
82.33.Vx Reactions in flames, combustion, and explosions
05.45.-a Nonlinear dynamics and chaos

Fractal analysis of size effects and surface morphology effects in catalysis and electrocatalysis

D. Avnir, J. J. Carberry, O. Citri, D. Farin, M. Grätzel, and A. J. McEvoy

Chaos 1, 397 (1991); http://dx.doi.org/10.1063/1.165850 (14 pages) | Cited 2 times

Full Text: | Download PDF

Show Abstract
Fractal geometry tools are used in order to analyze several related problems in surface science, catalysis, and electrocatalysis. The effects of complex morphologies of adsorbents, catalysts, and electrodes on various molecular processes with these materials are determined both theoretically and experimentally. It is shown that fractal geometry provides a convenient and natural tool for the elucidation of geometry‐performance relations in heterogeneous chemistry. Issues covered are particle size effects in physisorption and chemisorption; morphology effects on a variety of catalytic processes with unsupported catalysts (including coal liquefaction, alkene polymerizations, oxidations, dehydrogenations, and esterifications); surface accessibility effects on molecular interactions in an Eley–Rideal mechanism; surface patterning effects on concentration profiles near the surface; and electrode‐morphology effects on a variety of electrochemical and electrocatalytic processes. The domains of applicability of the fractal approach to these problems is discussed.
Show PACS
82.65.+r Surface and interface chemistry; heterogeneous catalysis at surfaces
82.45.-h Electrochemistry and electrophoresis
02.40.-k Geometry, differential geometry, and topology
05.45.-a Nonlinear dynamics and chaos

Transition to chemical turbulence

Q. Ouyang and Harry L. Swinney

Chaos 1, 411 (1991); http://dx.doi.org/10.1063/1.165851 (10 pages) | Cited 100 times

Full Text: | Download PDF

Show Abstract
Experiments have been conducted on Turing‐type chemical spatial patterns and their variants in a quasi‐two‐dimensional open spatial reactor with a chlorite–iodide–malonic acid reaction. A variety of stationary spatial structures−hexagons, stripes, and mixed states−were observed, and transitions to these states were studied. For conditions beyond those corresponding to the emergence of patterns, a transition was observed from stationary spatial patterns to chemical turbulence, which is marked by a continuous motion of the pattern within a domain and of the grain boundaries between domains. The transition to chemical turbulence was analyzed by measuring the correlation length, the average pattern speed, and the total length of the domain boundaries. The emergence of chemical turbulence is accompanied by a large increase in the defects in the pattern, which suggests that this is an example of defect‐mediated turbulence.
Show PACS
82.40.-g Chemical kinetics and reactions: special regimes and techniques
47.27.Cn Transition to turbulence

Vortex dynamics in oscillatory chemical systems

Xiao‐Guang Wu, Merk‐Na Chee, and Raymond Kapral

Chaos 1, 421 (1991); http://dx.doi.org/10.1063/1.165852 (14 pages) | Cited 13 times

Full Text: | Download PDF

Show Abstract
Vortex core dynamics is studied in the Brusselator both near to and far from the Hopf bifurcation line for random and pair initial conditions. Extensive simulations are carried out for a pair of counter‐rotating vortices close to the Hopf bifurcation line. Provided the vortices are not so far apart that wave‐front annihilation produces strong gradients between their centers, the simulation results compare favorably with theories based on the complex Ginzburg–Landau equation. Far from the Hopf line the vortex core dynamics changes character and phenomena such as periodic motion of the vortex centers arise.
Show PACS
82.40.Bj Oscillations, chaos, and bifurcations
05.45.-a Nonlinear dynamics and chaos

Transverse coupling of chemical waves

Vilmos Gáspár, Jerzy Maselko, and Kenneth Showalter

Chaos 1, 435 (1991); http://dx.doi.org/10.1063/1.165853 (10 pages) | Cited 2 times

Full Text: | Download PDF

Show Abstract
The transverse coupling of chemical waves is investigated using a model scheme for excitable media. Chemical waves supported on the surfaces of a semipermeable membrane couple via diffusion through the membrane, resulting in new types of spatiotemporal behavior. The model studies show that spontaneous wave sources may develop from interacting planar waves, giving rise to a complex sequence of patterns accessible only by perturbation. Coupled circular waves result in the spontaneous formation of spiral waves, which subsequently develop patterns in distinct domains with characteristic features. The long time entrainment behavior of coupled spiral waves reveals regions of 1:2 phase locking.
Show PACS
82.39.Wj Ion exchange, dialysis, osmosis, electro-osmosis, membrane processes
82.40.-g Chemical kinetics and reactions: special regimes and techniques

Bifurcation structures of periodically forced oscillators

William N. Vance and John Ross

Chaos 1, 445 (1991); http://dx.doi.org/10.1063/1.165854 (9 pages) | Cited 9 times

Full Text: | Download PDF

Show Abstract
A theoretical investigation of bifurcation structures of periodically forced oscillators is presented. In the plane of forcing frequency and amplitude, subharmonic entrainment occurs in v‐shaped (Arnol’d) tongues, or entrainment bands, for small forcing amplitudes. These tongues terminate at higher forcing amplitudes. Between these two limits, individual tongues fit together to form a global bifurcation structure. The regime in which the forcing amplitude is much smaller than the amplitude of the limit cycle is first examined. Using the method of multiple time scales, expressions for solutions on the invariant torus, widths of Arnol’d tongues, and Liapunov exponents of periodic orbits are derived. Next, the regime of moderate to large forcing amplitudes is examined through studying a periodically forced Hopf bifurcation. In this case the forcing amplitude and the amplitude of the limit cycle can be of the same order of magnitude. From a study of the normal forms for this case, it is shown how Arnol’d tongues terminate and how complicated bifurcation structures are associated with strong resonances. Aspects of model and experimental chemical systems that show some of the phenomena predicted from the above theoretical results are mentioned.
Show PACS
05.45.-a Nonlinear dynamics and chaos
82.40.-g Chemical kinetics and reactions: special regimes and techniques

Geometric phases in dissipative systems

Thomas B. Kepler, Michael L. Kagan, and Irving R. Epstein

Chaos 1, 455 (1991); http://dx.doi.org/10.1063/1.165855 (7 pages) | Cited 4 times

Full Text: | Download PDF

Show Abstract
It is shown that a phenomenon analogous to the geometric phase shifts of Berry and Hannay occurs for dissipative oscillatory systems and can be detected in numerical simulations of chemical oscillators. The approach herein to the theory of geometric phases begins with a study of simple first‐order differential equations on the circle (circle dynamics). It is shown how more complicated systems exhibit geometric phases through reduction to a circle dynamics. In this way, the various manifestations of the phenomenon are seen from a single unified perspective. The results are illustrated in numerical experiments on several model systems ranging from analytically solvable, but contrived, to realistic models of chemical oscillators.
Show PACS
45.05.+x General theory of classical mechanics of discrete systems
03.65.Ca Formalism

Channeling and percolation in two‐dimensional chaotic dynamics

D. K. Chaĭkovsky and G. M. Zaslavsky

Chaos 1, 463 (1991); http://dx.doi.org/10.1063/1.165856 (10 pages) | Cited 26 times

Full Text: | Download PDF

Show Abstract
The Hamiltonian dynamics of a particle moving in a nearly periodic two‐dimensional (2‐D) potential of square symmetry is analyzed. The particle undergoes two types of unbounded stochastic or random walks in such a system: a quasi‐1‐D motion (a ‘‘stochastic channeling’’) and a 2‐D motion which results from a sort of stochastic percolation. A scenario for the onset of this stochastic percolation is analyzed. The threshold energy for percolation is found as a function of the perturbation parameter. Each type of random walk has the property of intermittency. The particle transport is anomalous in certain energy intervals.
Show PACS
61.85.+p Channeling phenomena (blocking, energy loss, etc.)
64.60.A- Specific approaches applied to studies of phase transitions
05.45.-a Nonlinear dynamics and chaos

Parameter dependence of stochastic layers in a quasicrystalline web

J. H. Lowenstein

Chaos 1, 473 (1991); http://dx.doi.org/10.1063/1.165857 (9 pages) | Cited 1 time

Full Text: | Download PDF

Show Abstract
Stochastic web maps with approximate quasicrystalline symmetry possess an infinite number of inequivalent fixed points embedded in stochastic layers of varying thickness. In this investigation exploratory steps are taken toward a systematic numerical determination of the widths of the stochastic layers as a function of the web map’s control parameter. The study concentrates on a particular stochastic layer in the approximately fivefold symmetric web. Computer graphics and a simple stretching‐and‐folding criterion provide a coarse view, which is supplemented at finer scales by Greene’s residue method. The exact reflection symmetries of invariant sets, as well as a five‐dimensional representation of the map, are exploited to improve numerical precision. As the control parameter varies, one finds not only variations expected from island chain structures, but also larger‐scale oscillations whose origin is not understood.
Show PACS
05.45.-a Nonlinear dynamics and chaos
Close

Google Calendar

ADVERTISEMENT

Go to AIP Home   © AIP Publishing LLC
close