Path-following for disjoint bifurcation problems arising in ignition theory

E. Balakrishnan, A. Swift, G. C. Wake

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The correct formulation governing the ignition of a solid reactant undergoing slow oxidation gives rise to a nonlinear problem which in symmetrical geometries (infinite slab, cylinder, and sphere) is a two point boundary value problem. The discontinuity in the smallest branch of steady-states is the threshold for ignition. The solution branches are found by modifications of the path-following software (AUTO). Gross multiplicity of steady-states occurs for dimensions greater than two, and in all cases, the diagrams exhibit "disjointedness" for some parameter values which require special redefinition of the nonlinearity.

Original languageEnglish
Pages (from-to)9-15
Number of pages7
JournalMathematical and Computer Modelling
Volume19
Issue number9
DOIs
Publication statusPublished - 1994

Fingerprint

Path Following
Ignition
Disjoint
Branch
Bifurcation
Two-point Boundary Value Problem
Gross
Oxidation
Boundary value problems
Nonlinear Problem
Discontinuity
Multiplicity
Diagram
Nonlinearity
Software
Geometry
Formulation
Diagrams

Keywords

  • Combustion
  • Limit points
  • Nonlinear systems
  • Numerics

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Information Systems and Management
  • Control and Systems Engineering
  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

Path-following for disjoint bifurcation problems arising in ignition theory. / Balakrishnan, E.; Swift, A.; Wake, G. C.

In: Mathematical and Computer Modelling, Vol. 19, No. 9, 1994, p. 9-15.

Research output: Contribution to journalArticle

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AB - The correct formulation governing the ignition of a solid reactant undergoing slow oxidation gives rise to a nonlinear problem which in symmetrical geometries (infinite slab, cylinder, and sphere) is a two point boundary value problem. The discontinuity in the smallest branch of steady-states is the threshold for ignition. The solution branches are found by modifications of the path-following software (AUTO). Gross multiplicity of steady-states occurs for dimensions greater than two, and in all cases, the diagrams exhibit "disjointedness" for some parameter values which require special redefinition of the nonlinearity.

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