SOME DEVELOPMENTS AND APPLICATIONS OF NETWORK COMBING TECHNIQUE IN PROCESS DYNAMICS

The concept of network combing is extended to give the concentration history at all the nodes in a flow network whose nodes have exponential dynamic mixing characteristics with arbitrary time constants. It is shown that the transition matrix for the flow network is a special form of stochastic matrix whose power series has absolute convergence. This generalization results in a new, very stable method for handling any linear dynamic system which may be described by a set of first-order ordinary differential equations, even if the ratio of the largest to the smallest time constant is greater that 104. © 1969.