These two volumes represent the culmination of the Special Year '84-'85 in Reacting Flows held at Cornell University. As the proceedings of the 1985 AMS/SIAM Summer Seminar in Applied Mathematics, the volumes focus on both mathematical and computational questions in combustion and chemical reactors. They are addressed to researchers and graduate students in the theory of reacting flows. Together they provide a sound basis and many incentives for future research, especially in computational aspects of reacting flows. Although the theory of reacting flows has developed rapidly, researchers in the two subareas of combustion and chemical reactors have not communicated. The main goal of this seminar was to synthesize the mathematical theory and bring it to the interface with large-scale computing. All of the papers have high research value, but the first five introductory lectures should be especially noted.
Part 1: Introduction: Low Mach number combustion by G. S. Ludford S. The mathematical background of chemical reactor analysis. II. The stirred tank by R. Aris High Mach number combustion by A. Majda Numerical calculation of the interaction of pressure waves by H. A. Dwyer, A. Lutz, and R. J. Kee Computational methods in turbulent reacting flow by A. F. Ghoniem Combustion: Flame resonance and acoustics in the presence of heat loss by A. C. McIntosh The asymptotic analysis of ignition events with detailed kinetics by D. W. Mikolaitis Thermal expansion effects on perturbed premixed flames: a review by T. L. Jackson and A. K. Kapila Modeling end-gas knock in a rapid-compression machine: review and extension by F. J. Higuera and A. Linan Two asymptotic models for solid propellant combustion by S. B. Margolis and R. C. Armstrong Plane shock initiation of homogeneous and heterogeneous condensed phase. Explosives with a sensitive rate by D. S. Stewart The structure and stability of plane detonation waves for large activation energy by J. D. Buckmaster Stability theory for shocks in reacting media: Mach stems in detonation waves by R. R. Rosales Roles of perturbation methods for turbulent diffusion flame by F. A. Williams The lifting of turbulent diffusion flames and the noise they make by J. Buckmaster and N. Peters Part 2: Chemical reactors: Stability and Hopf bifurcation in isothermal catalysts by J. M. Vega and I. E. Parra Propagation of reaction fronts in exothermic heterogeneous noncatalytic systems solid-solid and solid-gas by J. Puszynski, J. Degreve, S. Kumar, and V. Hlavacek Optimal catalyst activity profiles in pellets by A. Varma Polymerization reactions in closed and open systems by T. A. Bak and L. Binglin Periodic and aperiodic regimes in linear and cyclic arrays of coupled reaction-diffusion cells by R. Raschman, I. Schreiber, and M. Marek Dynamic behavior of continuous stirred-tank reactors with extraneous thermal capacitance by J. B. Planeaux, K. F. Jensen, and W. W. Farr Steady-state multiplicity features of open chemically reacting systems by V. Balakotaiah Global bifurcations in simple models of a chemical reactor by J. Guckenheimer Methods of singularity theory in the analysis of dynamics of reactive systems by L. M. Pismen Mathematical questions: Solution profiles and thermal runaway by J. Bebernes and D. Kassoy Premixed laminar flames as travelling waves by D. H. Wagner Mathematical study of a model with no ignition temperature for laminar plane flames by M. Marion Well-posedness of the nonlinear equations for zero Mach number combustion by P. Embid Flame structure for reaction networks with chain branching and recombination by P. C. Fife and B. Nicolaenko The use of symmetry and bifurcation techniques in studying flame stability by B. L. Keyfitz, M. Golubitsky, M. Gorman, and P. Chosset Mathematical analysis of tubular reactors by R. Alexander Oscillating chemical reactions: the well-stirred and spatially distributed class by G. C. Wake, J. G. Graham-Eagle, and B. F. Gray A systematic derivation of the constitutive properties of mixtures of viscous-heat conducting fluids by I. Muller Computational question: Calculation of extinction limits for premixed laminar flames in a stagnation point flow by V. Giovangigli and M. D. Smooke Contribution to the numerical analysis of laminar stationary flames by M. Sermange Adaptive numerical methods for unsteady flame propagation by B. Larrouturou Using computers to answer fundamental questions in combustion theory: an example from droplet combustion by R. D. Janssen and P. J. O'Rourke actional step methods for reacting shock waves by P. Colella, A. Majda, and V. Roytburd Modelling and computation of deflagration-to-detonation transition (DDT) in reactive granular materials by M. R. Baer, R. E. Benner, R. J. Gross, and J. W. Nunziato On determining important aspects of combustion kinetics modelling with sensitivity analysis by H. Rabitz Singular perturbation for stiff equations using numerical computations by S. H. Lam.