On the Classification and Asymptotic Behavior of the Symmetric Capillary Surfaces

Multi-scale spectral methods for bounded radially symmetric capillary surfaces

“…They do, however, have self-intersections in this global setting of arbitrary s > 0. A classification of all of these global solutions and an exploration of the asymptotic behavior appears in the work of Bagley and Treinen [2]. For physical applications one is restricted to selecting connected pieces of these curves that avoid these self-intersections.…”

“…For example, in the configurations where ψ a , ψ b = −π, when 0 < a 1 and b is moderately sized, the performance of the base code [15] is poor or fails completely, depending on how small a is. These configurations correspond to a singular limiting process that was explored by Bagley and Treinen [2]. In that work the global solutions of (2.1)-(2.3) were considered for all arc-lengths.…”

Spectral Methods for capillary surfaces described by bounded generating curves

“…In either case, these solution curves form generating curves with total arclength 2ℓ. The global behavior can become quite complicated [3], though we specify boundary conditions that avoid the self-intersections appearing in that work.…”