Spectral quasi equilibrium manifold and intrinsic low dimensional manifold: A multi-step reaction mechanism

In this paper there are the collection of constructive methods to study slow invariant manifold of dynamic system. These techniques reduce the high dimensional complex problem to low dimensional and solve these problem without losing the information about the complex system. According to Gibbs rule we can estimate the degree of freedom (number of key components N-kc, in which we can reduce the system which is: N-k(c) = N-s - N-e where N-s and N-e are number of steps and number of elements respectively in a complex reaction. Several strategies have been used to reduce the detailed chemical kinetics. The method of Intrinsic low dimensional manifold (ILDM) and Spectral Quasi Equilibrium Manifold (SQEM) both methods are developed for homogeneous reactive system. In the absence of any transport system like diffusion, which can be modeled by system of ODE,s. the behavior of the reactive system is defined by trajectories in composition space starting from initials and approaches towards the chemical equilibrium. These methods are described in detail.