טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentMirer Tatiana
SubjectApplication of the Theory of Catastrophes to the Analysis
of Elements of Power Plants
DepartmentDepartment of Quality Assurance and Reliability
Supervisor Dr. Phineas Dickstein


Abstract

This project is intended to apply the catastrophe theory to the analysis of the shape and behavior of a rotating liquid droplet free of gravitational affects.

The first part explains the basic principles of Catastrophe theory.  Catastrophe theory is mathematical modeling of sudden changes in the behavior of natural system, so called “catastrophes”, which may occur despite continuous changes of the system parameters.

The second part of the project is devoted to the application of a Cusp Catastrophe to the mathematical modeling of the possible shapes and stability of a rotating liquid droplet under microgravity conditions, based on the methodology and foundation developed by professor C.A.Ward from the University of Toronto, Canada. As the rotation rate increases, the initial shape, an oblate spheroid, transforms into biconcave spheroid and afterwards into torus.

We examined the characteristics of this process and found them appropriate to be simulated using the Cusp catastrophe model. The frequency of rotation and the external radius of torus are chosen to be the control parameters, though these parameters are not independent, and the radius of section of torus represents the state parameter. We consider the points where the simply connected shape transforms into a non-simply connected shape and vice versa to be catastrophes. By expanding Ward’s formulation of the Helmholtz function, for a non-simply connected shape, into a Taylor series, and by means of further mathematical transformations, the Cusp Catastrophe model is obtained for this system.