2012年5月2日 · Qualitatively, the catenoid looks like the meniscus depicted in Fig. 2.6a; it corresponds to zero capillary pressure and zero mean curvature of the interface (P c = 0 and H = 0). In this case H = 0 because the two principle curvatures have equal magnitude, but opposite sign, at each point of the catenoid. This is the reason why it is called ...

2021年6月15日 · Further, the catenoid plays a crucial role in the study of IFT. Four forces are considered to affect the formation of the catenoid height, namely gravity, IFT, tension of the ring, and pressure on both sides of the catenoid. Accordingly, the force analysis of the micro catenoid surface is as presented in Fig. 12.

2020年9月7日 · The catenoid is a surface of revolution of the catenary along some direction [29]. It has the remarkable property of being a minimal surface, i.e., a surface of least area [29]. As a result, the catenoid has negative Gaussian curvature whereas …

2019年10月12日 · The dynamics of a collapsing catenoid, analogous to those of a rupturing soap film, has been investigated computationally (Chopp and Sethian, 1993) and experimentally (Ito and Sato, 2010, Robinson and Steen, 2001), giving insight into the conditions required for film stability. With two rings of unequal radii, two different portions of catenoid ...

2021年8月1日 · The Professor Matthias Weber [21] has constructed numerically an example of a minimal surface of genus one, with one catenoid-type end and one Enneper-type end. That surface was also studied by S. Fujimori and T. Shoda, [8] .

2021年8月1日 · In [22], Matthias Weber suggested numerically that the surface S belongs to a one-parameter family of minimal surfaces with two catenoid ends and one Enneper end. In this section we will give an analytically prove that S is indeed a lie inside the one-parameter sub-family of genus one minimal surfaces S x with two catenoid ends and one Enneper end.

2017年11月1日 · The catenoid is the only non-planar rotational minimal surface in Euclidean space and it is generated by the catenary f (z) = (1 ∕ a) cosh (a z + b) when rotated around the z axis. Consider a piece of a catenoid bounded by two coaxial circles C 1 ∪ C 2 with the same radius r > 0 and separated by a distance h > 0 far apart.

2024年6月1日 · A catenoid is a minimal surface, and its geometry is equivalent to that of two-dimensional wormholes, as they represent possible solutions for traversable wormholes [14] (see also [15]). The curvature of the catenoid tends to approach zero asymptotically and concentrates around the bridge [16], and a catenoid may describe a bridge connecting ...

2024年8月1日 · The catenoid is of particular interest because it is a minimal surface [7] and minimizes the Willmore energy [8]. This makes the surface suitable for making connections between nanostructures of different materials, such as graphene and boron nitride [7] , [9] , and it has been studied using the Schrödinger formalism [21] , [22] .

2011年3月20日 · It is the unique portion of the catenoid cut out by a ball centered at the origin hich meets the boundary orthogonally; that is, it is a free boundary solution in the ball. We refer this portion of the catenoid as the “critical†catenoid. Supercritical annuli In this section we consider the annulus with an arbitrary metric.