The Colloquium of the Mathematics with Computer Science Program By Prof. Vadim Panfilov

Title

The Catastrophe Theory Application to Locate an Additional Stable Operating Regime

Speaker

Prof. Vadim Panfilov (GTIIT & University of Nevada)

Language

English

Location

E408 (Education Building, 4th floor)

Abstract

When we think how to control complex dynamical systems, at first instance, we focus on stable steady states of the system to look for appropriate operating conditions. The steady states correspond to the stationary states when the state variables of the mathematical models are not changing in time. For large heat capacity plants like chemical reactors, steel production furnaces, nuclear reactors the steady state operation is an only feasible option. We understand that dynamical systems may exhibit multiple steady states and the question of interest is how to locate, select a stable state for operation.

The bifurcation theory studies and classifies the qualitative nature of equation solutions depending of the (control) parameters of the equation. The Catastrophe Theory as a branch of bifurcation theory has been originated by the French mathematician Rene Thom in the 1960s. This theory introduced seven qualitative geometric structures called Elementary Catastrophes. Such geometric structures (and their names too) are so beautiful that they inspire famous Spanish artist Salvador Dali for his last painting “The Swallow’s Tail – Series of Catastrophes” (see attached picture).

We will consider the most complex 7th Butterfly Catastrophe. We will divide the 4-dimensional parametric space into the regions with different number of solutions. For Illustration purposes this procedure will be applied (in real-time!) to the 5-degree polynomial. We also show the catastrophe theory application to one of the most common models of perfectly mixed chemical reactors, namely, the Continuous Stirred Tank Reactor (CSTR).