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 | |
| Publication status | Published - 1994 |
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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 journal › Article
}
TY - JOUR
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
UR - http://www.scopus.com/inward/record.url?scp=38149147232&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38149147232&partnerID=8YFLogxK
U2 - 10.1016/0895-7177(94)90036-1
DO - 10.1016/0895-7177(94)90036-1
M3 - Article
AN - SCOPUS:38149147232
VL - 19
SP - 9
EP - 15
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling
SN - 0895-7177
IS - 9
ER -