In this paper, we define the fundamental group of a topological space and explore its structure, and we proceed to prove Van-Kampen’s Theorem, a powerful result useful for calculating the fundamental groups of spaces which decompose into spaces whose fundamental groups are already known. With these tools, we show that the circle, 2-sphere, torus, and figure-8 space are topologically distinct. W...

We use reformulation techniques to model and solve a complex sphere covering problem occurring in the configuration of a gamma ray machine radiotherapy equipment unit.

We describe the first analytically tractable example of an instability of a nonorientable minimal surface under parametric variation of its boundary. A one-parameter family of incomplete Meeks Möbius surfaces is defined and shown to exhibit an instability threshold as the bounding curve is opened up from a double-covering of the circle. Numerical and analytical methods are used to determine the...

An extensive experimental investigation to study the flow structure over the wing of a fighter type configuration model has been conducted. The model used for this study was similar to the High Alpha Research Vehicle (HARV) that has been used in various European research centers for studying its force and moment characteristics. Tests were conducted at two subsonic speeds and at low to moderate...