Uniqueness of Closed Equilibrium Hypersurfaces for Anisotropic Surface Energy and Application to a Capillary Problem

We study a variational problem for hypersurfaces in the Euclidean space with an anisotropic surface energy. An anisotropic surface energy is the integral of an energy density that depends on the surface normal over the considered hypersurface, which was introduced to model the surface tension of a small crystal. The purpose of this paper is two-fold. First, we give uniqueness and nonuniqueness results for closed equilibria under weaker assumptions on the regularity of both considered hypersurfaces and the anisotropic surface energy density than previous works and apply the results to the anisotropic mean curvature flow. This part is an announcement of two forthcoming papers by the author. Second, we give a new uniqueness result for stable anisotropic capillary surfaces in a wedge in the three-dimensional Euclidean space.

Hygrothermal Characterization of Porous Building Materials-Experiment Research on Isothermal Sorption and Capillary Problem

The research on water vapor isothermal sorption of porous building materials have an important function on controlling and solving hygrothermal problems, such as durability, thermal insulation, mold growth and indoor air quality, when building materials are in hygrothermal environment, especially in the high humidity environment. The isothermal sorption is used to describe the maximum moisture sorption capacity, if moisture content exceeds the limitation, probably there will be liquid water appearance, which lead to the risk of mold growth, decreasing durability and increasing thermal conductivity, and so on. The classic testing method of isothermal sorption could be found in ASTM Standards C 1498-01. In this paper, the eco-stucco, eco-fiber batt and eco-fiber board is tested using traditional method. Meanwhile, pore size distribution and capillary condensation is analyzed which is challenge for the design basis of hygrothermal character for the building envelope.

Stability in a ball-partition problem

Stability for a capillary problem with surfaces meeting along a singular curve is analyzed using eigenvalue methods.