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Abstract

We construct examples of nonparametric surfaces z = h(x, y) of zero mean curvature which satisfy contact angle boundary conditions in a cylinder in ‫ޒ‬ 3 over a convex domain with corners. When the contact angles for two adjacent walls of the cylinder differ by more than π−2α, where 2α is the opening angle between the walls, the (bounded) solution h is shown to be discontinuous at the corresponding corner. This is exactly the behavior predicted by the Concus-Finn conjecture. These examples currently constitute the largest collection of capillary surfaces for which the validity of the Concus-Finn conjecture is known and, in particular, provide examples for all contact angle data satisfying the condition above for opening angles 2α ∈ (π/2, π).

Chemotaxis in the Green Flagellate Alga Chlamydomonas

“…One can distinguish: 1) "real" orientation, when the direction of progressive movement of the cell coincides with the direction of the stimulus gradient; 2) so called "orientation by trial and error" (biased random walk). In microorganisms that freely swim in liquid medium along helical paths "real" orien tation can be achieved by so called "helical klinotaxis", which was first suggested as a theoretical model [66], and subsequently observed experimentally during chemotaxis in Paramecium [67], the ciliate Strombidium [68], and in the bacterium Thiovulum [69].…”