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house of 1000 doors family secrets keygen My research focusses on thin-film flows with/without contact lines, with additional complexities such as substrate heterogeneities and gas flow. One problem that we looked at recently is the spreading of a droplet on substrates that are chemically heterogeneous. Can we make a droplet to move in a specified direction? Is it possible to confine it within a given region? We explored such scenarios by developing a mathematical model for the droplet, spreading on an arbitrary substrate descargar cype crack español. For a sufficiently small droplet, we have shown via phase plane analysis that there exist multiple equilibrium droplet configurations. In solving this problem, we combine long-wave theory, matched asymptotics and numerics (spectral collocation method).
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resharper 8.0.2 keygen Below you can see a video of spreading of a two-dimensional droplet on a substrate where the heterogeneities are localized. The droplet gets pinned at the heterogeneity spots, where the contact angle is large (more hydrophobic).