Double, Double, Toil and Trouble Double, Double, Toil and Trouble Double, Double, Toil and Trouble is a 1993 Halloween made-for-television children's film. It stars Mary-Kate and Ashley Olsen as two adventurous little girls who discover that their Great Aunt Sophia has been trapped and cursed by her evil twin sister Agatha. On the 7th year of her imprisonment, Sophia will be doomed to the netherworld unless the curse is broken by the magical spell of twins. The film's title is part of the famous line spoken by the three witches in Shakespeare's Macbeth (Act IV, Scene I): "Double, double toil and trouble; Fire burn and
Chaotic bubble fluid subject to periodically driven pressure oscillations (Smereka, Birnir, and Banerjee, 1987). For an overview of models of single-bubble dynamics see Feng and Leal (1997). There is extensive literature on nonlinear analysis of the dynamics of bubbles in liquids, with important contributions from (1976). Lauterborn and Cramer (1981) also applied chaos theory to acoustics, in which bubble dynamics play a crucial part. This includes analysis of chaotic dynamics in an acoustic cavitation bubble field in a liquid (Lauterborn, Holzfuss, and Bilio, 1994). The study of the role of shear stresses in non-Newtonian fluids has been done by Li, Mouline, Choplin,