Karl B. Glasner

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Lubrication theory for unstable thin liquid films on solid substrates is used to model the coarsening dynamics in the long-time behavior of dewetting films. The dominant physical effects that drive the fluid dynamics in dewetting films are surface tension and intermolecular interactions with the solid substrate. Instabilities in these films lead to rupture(More)
Fourth order thin film equations can have late stage dynamics that are analogous to the classical Cahn–Hilliard equation. We undertake a systematic asymptotic analysis of a class of equations that describe partial wetting with a stable precursor film introduced by intermolecular interactions. The limit of small precursor film thickness is considered,(More)
In many pattern forming systems, narrow two-dimensional domains can arise whose cross sections are roughly one-dimensional localized solutions. This paper investigates this phenomenon in the variational Swift–Hohenberg equation. Stability of straight line solutions is analyzed, leading to criteria for either curve buckling or curve disintegration. Matched(More)
This paper proposes the use of a variational framework to model fluid wetting dynamics. The central problem of infinite energy dissipation for a moving contact line is dealt with explicitly rather than by introducing a specific microscopic mechanism which removes it. We analyze this modelling approach in the context of the quasi-steady limit, where contact(More)
Interface dynamics of post contact states in regularized models of electrostatic-elastic interactions are analyzed. A canonical setting for our investigations is the field of MicroElectromechanical Systems (MEMS) in which flexible elastic structures may come into physical contact due to applied Coulomb forces. We study the dynamic features of a recently(More)
In canonical models of Micro-Electro Mechanical Systems (MEMS), an event called touchdown whereby the electrical components of the device come into contact, is characterized by a blow up in the governing equations and a non-physical divergence of the electric field. In the present work, we propose novel regularized governing equations whose solutions remain(More)
Above the critical temperature for the order-disorder transition, diblock copolymer melts have been observed to exhibit localized structures that exist within the homogeneous mixture. This paper uses an Ohta–Kawasaki-type density functional to explore this regime. Spatially localized peak-shaped equilibria are studied in one, two, and three dimensions,(More)
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