TAILIEUCHUNG - Capillary graph-interfaces in-the-Large

This paper continues ongoing investigations into questions initiated by seventeenth-century experiments of Mariotte on mutual attractions and repulsions of floating objects, later reformulated mathematically by Laplace in the context of idealized surface tension theory. | Vietnam Journal of Mathematics (2019) 47: 113–132 Capillary Graph-Interfaces “in-the-Large” Robert Finn1 Received: 27 April 2017 / Accepted: 12 April 2018 / Published online: 28 September 2018 © Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018 Abstract This paper continues ongoing investigations into questions initiated by seventeenth-century experiments of Mariotte on mutual attractions and repulsions of floating objects, later reformulated mathematically by Laplace in the context of idealized surface tension theory. The characteristic nonlinearity in the governing equations imposes restrictions on behavior of solutions as graphs in the Laplace model, to the effect that a priori relations connecting height and inclination of a presumed surface interface occur, severely restricting the heights that can be achieved by solution curves. We develop below some relevant consequences of that phenomenon. The initial section provides general (perhaps inadequate) background, characterizes global qualitative behavior of all solutions of the underlying equations, and elucidates the significant distinctions in behavior that occur for solutions over an interval that extends unboundedly in one base direction. The section next following presents a non-existence result ensuing from the limitations imposed on such solutions (this result is elaborated in the Appendix). Next follow individual properties of general solutions. The remainder of the paper addresses the forces arising between partially submerged bodies. Theorem 6 offers an alternative derivation of a discovery due to Aspley, He, and McCuan, which displays a remarkable identification of net horizontal force with a first integral of the basic equations. These relations simplify significantly some earlier literature; additionally, as indicated in Section 5, they open the way to consideration of a much larger class of partially immersed .

• Toán học
• Partially immersed
• First integral
• Unlike menisci
• Repelling configuration
• Two plate configuration
• Horizontal force