Microscopic fluctuations and pattern formation in a supercritical oscillatory chemical system

2003 ◽  
Vol 119 (6) ◽  
pp. 3291-3296 ◽  
Author(s):  
Harold M. Hastings ◽  
Richard J. Field ◽  
Sabrina G. Sobel
Keyword(s):  
Pattern Formation ◽  
Chemical System ◽  
Oscillatory Chemical

Turing Pattern Formation by the CIMA Reaction in a Chemical System Consisting of Quaternary Alkyl Ammonium Cationic Groups

2011 ◽  
Vol 115 (14) ◽  
pp. 3959-3963 ◽  
Author(s):  
Kouichi Asakura ◽  
Ryo Konishi ◽  
Tomomi Nakatani ◽  
Takaya Nakano ◽  
Masazumi Kamata
Keyword(s):  
Pattern Formation ◽  
Chemical System ◽  
Turing Pattern ◽  
Alkyl Ammonium ◽  
Cima Reaction

scholarly journals A nonlinear two-species oscillatory system: bifurcation and stability analysis

2003 ◽  
Vol 2003 (31) ◽  
pp. 1981-1991 ◽  
Author(s):  
Malay Bandyopadhyay ◽  
Rakhi Bhattacharya ◽  
C. G. Chakrabarti
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Wave Train ◽  
Oscillatory System ◽  
Homogeneous System ◽  
Travelling Wave ◽  
Chemical System ◽  
Oscillatory Chemical ◽  
Bifurcation And Stability

The present paper dealing with the nonlinear bifurcation analysis of two-species oscillatory system consists of three parts. The first part deals with Hopf-bifurcation and limit cycle analysis of the homogeneous system. The second consists of travelling wave train solution and its linear stability analysis of the system in presence of diffusion. The last deals with an oscillatory chemical system as an illustrative example.

scholarly journals Spatial Heterogeneity and Imperfect Mixing in Chemical Reactions: Visualization of Density-Driven Pattern Formation

2009 ◽  
Vol 2009 ◽  
pp. 1-4 ◽  
Author(s):  
Sabrina G. Sobel ◽  
Harold M. Hastings ◽  
Matthew Testa
Keyword(s):  
Pattern Formation ◽  
Salt Water ◽  
Model System ◽  
Reaction Vessel ◽  
Chemical System ◽  
Industrial Processes ◽  
History Of ◽  
Convection Rolls ◽  
Belousov Zhabotinsky Reaction ◽  
Complex Ion

Imperfect mixing is a concern in industrial processes, everyday processes (mixing paint, bread machines), and in understanding salt water-fresh water mixing in ecosystems. The effects of imperfect mixing become evident in the unstirred ferroin-catalyzed Belousov-Zhabotinsky reaction, the prototype for chemical pattern formation. Over time, waves of oxidation (high ferriin concentration, blue) propagate into a background of low ferriin concentration (red); their structure reflects in part the history of mixing in the reaction vessel. However, it may be difficult to separate mixing effects from reaction effects. We describe a simpler model system for visualizing density-driven pattern formation in an essentially unmixed chemical system: the reaction of pale yellow Fe3+ with colorless SCN− to form the blood-red Fe(SCN)2+ complex ion in aqueous solution. Careful addition of one drop of Fe(NO3)3 to KSCN yields striped patterns after several minutes. The patterns appear reminiscent of Rayleigh-Taylor instabilities and convection rolls, arguing that pattern formation is caused by density-driven mixing.

scholarly journals Mechanism of Trees / Bushes Like Pattern in Chemical System

2009 ◽  
Vol 6 (3) ◽  
pp. 819-829
Author(s):  
P. K. Srivastava ◽  
Narendra Yadav
Keyword(s):  
Pattern Formation ◽  
Ir Spectra ◽  
Succinic Acid ◽  
Ammonium Sulphate ◽  
Cyclic Compound ◽  
Chemical System ◽  
Powder Spectrum ◽  
Initial Concentration ◽  
X Ray ◽  
Type Pattern

Trees / bushes like pattern have been investigated in succinic acid + ethylacetoacetate + BrO3−+ Fe (phen)3+2+ Ce+4+ H2SO4system at 30 °C in a petridish after 6 hours. These patterns are dependent on initial concentration of reactants and temperature. The system first shows fast appearing / disappearing blue and red pattern then bifurcate into concentric waves and finally shows a tree / bushes type pattern which grows in length and breadth against time. Microphotographs of trees / bushes pattern, succinic acid and ceric ammonium sulphate shows that a new compound has been formed which is responsible for this pattern. It is further confirmed by X-ray powder spectrum of trees / bushes pattern material and succinic acid. IR spectra of pattern material show that presence of cyclic compound in which Ce+4ion coordinated by hydroxyethylacetoacetate. A tentative mechanism of pattern formation is proposed.

scholarly journals Pattern Formation in Oscillatory Chemical Reactions

1976 ◽  
Vol 56 (3) ◽  
pp. 724-740 ◽  
Author(s):  
Y. Kuramoto ◽  
T. Yamada
Keyword(s):  
Pattern Formation ◽  
Chemical Reactions ◽  
Oscillatory Chemical

scholarly journals Temperature Control of Continuous Chemical Reactors Under Noisy Measurements and Model Uncertainties

2012 ◽  
Vol 10 (3) ◽  
Author(s):  
Ricardo Aguilar López ◽  
Rafael Martínez Guerra ◽  
Juan L. Mata Machuca
Keyword(s):  
Sliding Mode ◽  
System Stability ◽  
Chemical System ◽  
Control Law ◽  
Model Uncertainties ◽  
Uncertainty Estimator ◽  
The Face ◽  
Oscillatory Chemical ◽  
Error Dynamics ◽  
Noisy Measurements

The aim of this paper is to present the synthesis of a robust control law for the control of a class of nonlinear systems named Liouvillian. The control design is based on a sliding-mode uncertainty estimator developed under the framework of algebraic-differential concepts. The estimation convergence is done by the Lyapunov-type analysis and the closed-loop system stability is shown by means of the regulation error dynamics. Robustness of the proposed control scheme is tested in the face of noise output measurements and model uncertainties. The performance of the proposed control law is illustrated with numerical simulations in which a class of oscillatory chemical system is used as application example.

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