Citation
Coutsias, Evangelos A. (1980) Some effects of spatial nonuniformities in chemically reacting mixtures. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:12072012130738166
Abstract
In Part I, a method is developed for treating reactingdiffusing systems whose kinetics lead to a limit cycle behavior with frequency varying slowly with position. This is accomplished by including the effects of the spatial variation in a phase variable that is introduced to parametrize the limit cycles at each point. The normalization of this phase variable is chosen such that the limit cycles at each point have the same frequency with respect to this variable. The method is motivated by treating the weakly coupled behavior of two oscillators that, unlike previous works, are not nearly identical. The analogy between discrete oscillator systems and continuous chemically reacting mixtures is explored by treating a chain of coupled limit cycle oscillators and considering various limits as the number of oscillators tends to infinity.
In Part II a different effect of spatial nonuniformities is studied: the modification of the simple diffusion approximation to treat situations of large deviations from equilibrium distributions in a mixture or proximity to some critical temperature. A technique for treating bifurcation from the continuous spectrum by introducing a slow space scale is developed. Using this, the onset of a spatially nonuniform state in a model chemically reacting system is studied, occurring when some reaction rate crosses the values at which linearized theory predicts destabilization of the uniform steady state solutions admitted by the system. Subs critical bifurcation is also found possible.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Mathematics 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  14 August 1979 
Record Number:  CaltechTHESIS:12072012130738166 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:12072012130738166 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  7314 
Collection:  CaltechTHESIS 
Deposited By:  Benjamin Perez 
Deposited On:  11 Dec 2012 17:09 
Last Modified:  26 Dec 2012 04:46 
Thesis Files
PDF
 Final Version
Restricted to Caltech community only See Usage Policy. 11Mb 
Repository Staff Only: item control page