Path-following for disjoint bifurcation problems arising in ignition theory

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

doi:10.1016/0895-7177(94)90036-1

Path-following for disjoint bifurcation problems arising in ignition theory

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

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	9-15
Number of pages	7
Journal	Mathematical and Computer Modelling
Volume	19
Issue number	9
DOIs	https://doi.org/10.1016/0895-7177(94)90036-1
Publication status	Published - 1994

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

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T1 - Path-following for disjoint bifurcation problems arising in ignition theory

AU - Balakrishnan, E.

AU - Swift, A.

AU - Wake, G. C.

PY - 1994

Y1 - 1994

N2 - 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.

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.

KW - Combustion

KW - Limit points

KW - Nonlinear systems

KW - Numerics

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EP - 15

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 9

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