Abstract
We construct a new method for inextensible flows of timelike curves in Minkowski space-time E14. Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a timelike curve in Minkowski space-time E14.
Highlights
Numerous processing operations of complex fluids involve free surface deformations; examples include spraying and atomization of fertilizers and pesticides, fiber-spinning operations, paint application, roll-coating of adhesives, and food processing operations such as container- and bottle-filling
Necessary and sufficient conditions for an inextensible curve flow first are expressed as a partial differential equation involving the curvature and torsion
They derived the corresponding equations for the inextensible flow of a developable surface and showed that it suffices to describe its evolution in terms of two inextensible curve flows [8]
Summary
Numerous processing operations of complex fluids involve free surface deformations; examples include spraying and atomization of fertilizers and pesticides, fiber-spinning operations, paint application, roll-coating of adhesives, and food processing operations such as container- and bottle-filling. Understanding such flows can be extremely difficult because of the large number of different forces that may be involved, including capillarity, viscosity, inertia, gravity, and the additional stresses resulting from the extensional deformation of the microstructure within the fluid. Necessary and sufficient conditions for an inextensible curve flow first are expressed as a partial differential equation involving the curvature and torsion. We give some characterizations for curvatures of a curve in Minkowski space-time
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