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Full-Text Articles in Atomic, Molecular and Optical Physics
Critical Energy Of Torus Knots, Fred Hickling, Wesley Davis, Heather Woolverton
Critical Energy Of Torus Knots, Fred Hickling, Wesley Davis, Heather Woolverton
Journal of the Arkansas Academy of Science
The energy of a smoothly parameterized knot y(t) is defined as rr\ i i lp7 \\dn dsdt Jo Jo \||7M-7(0f (D(t(s),T(t))) 2 j\\ds \\dt where D(y (s), y(t)) is the arc length between the two points y (s) and y(t) on the curve. Simple calculus based arguments are used to locate critical values of the energy functional for torus knots. Explicitly the curves given parametrically by °(«*)W = (V2°iSri).JSSBe V2 C s7nS are CriticalP ° intS ° fthe energy functional whenever a and b are relatively prime.