Related papers: Analytical validation of the Yound-Dupr\'e law for…
In this paper, we establish an $\varepsilon$-regularity theorem for minimizers of an Alt-Phillips type functional subject to constraint maps. We prove that under sufficiently small energy, the minimizers exhibit regularity, and hence…
The linear (Winkler) foundation is a simple model widely used for decades to account for the surface response of elastic bodies. It models the response as purely local, linear, and perpendicular to the surface. We extend this model to the…
We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly…
The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using stochastic thin-film equations (STFEs). Two canonical boundary conditions are employed to reveal the influence of the confinement: (1)…
This article presents theoretical results for the dynamic response of periodically surface-modulated ferromagnetic thin films. For such system, the role of the periodic dipolar field induced by the modulation is addressed by using the…
Investigations of the elastic behavior of bulk elastomers have traditionally proceeded on the basis of classical rubber elasticity, which regards chains as thermally fluctuating but disregards the thermal fluctuations of the cross-links.…
We present a detailed analysis of one-dimensional N\'eel walls in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Within the reduced one-dimensional thin film…
The mathematical model of a rotating electrohydrodynamic flow in a thin suspended liquid film is proposed and studied. The motion is driven by the given difference of potentials in one direction and constant external electrical field…
We investigate minimizers defined on a bounded domain in $\mathbb{R}^2$ for the Maier--Saupe Q--tensor energy used to characterize nematic liquid crystal configurations. The energy density is singular, as in Ball and Mujamdar's modification…
Probing the fluid dynamics of thin films is an excellent tool to study the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid due to the fact that the dewetting process, an internal…
We study the steady states and dynamics of a thin film-type equation with non-conserved mass in one dimension. The evolution equation is a nonlinear fourth-order degenerate parabolic PDE motivated by a model of volatile viscous fluid films…
The evolution of the vortex glass (VG) phase transition and vortex creep with decreasing film thickness is studied in ultrathin, polycrystalline niobium films, with thickness in the range 7.4 nm to 44 nm, using current-voltage…
We analyze a linear 3D/3D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic plate-like structure with the aim of deriving a simplified reduced model. Based on suitable energy dissipation…
The dynamics of thin films on a horizontal solid substrate is investigated in the case of non-Newtonian fluids exhibiting normal stress differences, the rheology of which is strongly non-linear. Two coupled equations of evolution for the…
Young's law fails on soft solid and liquid substrates where there are substantial deformations near the contact line. On liquid substrates, this is captured by Neumann's classic analysis, which provides a geometrical construction for…
In solution-processing of thin films, the material layer is deposited from a solution composed of several solutes and solvents. The final morphology and hence the properties of the film often depend on the time needed for the evaporation of…
A theoretical framework is developed to describe experiments on the structure of epitaxial thin films, particularly niobium on sapphire. We extend the hypothesis of dynamical scaling to apply to the structure of thin films from its…
Purpose: To determine whether evaporation, tangential flow, or a combination of the two cause tear film breakup in a variety of instances; to estimate related breakup parameters that cannot be measured in breakup during subject trials; and…
While the electrodynamic treatment of a superconducting thin film by Yeh et al. [Phys. Rev. B 48, 9861 (1993)] ostensibly has application for the "thin-film limit," their work is shown to employ bulk-like instead of thin-film…
We establish a local minimality sufficiency criterion, based on the strict positivity of the second variation, in the context of a variational model for the epitaxial growth of elastic films. Our result holds also in the three-dimensional…