A finite state Markov model with continuous time parameter for physical and chemical cutting processes

Several processes in physics and chemistry are one-dimensional cutting processes. Grinding of fibers in a grinding mill as well as depolymerisation of polymers in an enzymatic solution are examples of these processes. One-dimensional chains of connected identical “atomic particles” are cut into smaller chains until only the, indivisible, atomic particles remain: the indivisible smallest fiber particles in the grinder and the monomers in the enzymatic solution. A mathematical model has been developed for controlling and optimizing these processes. It is characterized as a finite state Markov process with continuous time parameter. From a given distribution of the length of the chains at the start of the process and from a given cutting or transition intensity during the process, the model gives the length distribution on each moment during the process. The cutting intensity may vary during the process and can be dependent on the length of the chain or on the cutting location within the chain at the start or during the process. The model can be used for control systems in the process industry. For instance, it is possible to forecast the moment of achieving a desired length distribution of the chains.