Related papers: Solutions for a free-boundary problem modeling mul…
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 theoretically the profile evolution of a thin viscoelastic film supported onto a no-slip flat substrate. Due to the nonconstant initial curvature at the free surface, there is a flow driven by Laplace pressure and mediated by…
In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly…
We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with…
We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interfaces between stable homogeneous rest states. In many example…
Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a…
When a flexible plate is peeled off a thin and soft elastic film bonded to a rigid support, uniformly spaced fingering patterns develop along their line of contact. While, the wavelength of these patterns depends only on the thickness of…
On the basis of a previous theoretical approach to the plastic flow of highly refined materials, a physical explanation for diffusion bonding is essayed, which yields closed--form equations relating the bonding progress with time,…
We study a higher-dimensional thin film equation that incorporates competitive effects between aggregation and repulsion, where repulsion is modeled by fourth-order diffusion and aggregation by backward second-order degenerate diffusion,…
Many objects in nature and industry are wrapped in a thin sheet to enhance their chemical, mechanical, or optical properties. There are similarly a variety of methods for wrapping, from pressing a film onto a hard substrate, to using…
We introduce a mean-field model for the potential energy landscape of a thin fluid film confined between parallel substrates. The model predicts how the number of accessible basins on the energy landscape and, consequently, the film's ideal…
It is known that an axisymmetric viscous film flowing down the outside of a thin vertical fiber becomes unstable to interfacial perturbations. We present an experimental study using fluids with different densities, surface tensions and…
The paper presents analytical or semi-analytical solutions for the formation and evolution of localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. A variationally based formulation of explicit gradient…
We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity,…
This paper addresses the well posedness of a dynamical model of perfect plasticity with mixed boundary conditions for general closed and convex elasticity sets. The proof relies on an asymptotic analysis of the solution of a perfect…
We consider a linearly elastic body consisting of two equal symmetrically arranged layers (or half-planes) connected by a structured interface as a prospective crack path. The interface is comprised by periodic discrete system of bonds. In…
In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by…
We consider two thin layers of immiscible liquids on a heated solid horizontal substrate. The free liquid-liquid and liquid-gas interfaces of such a two-layer (or bilayer) liquid film may be unstable due to effective molecular interactions…
We extend the force-level ECNLE theory to treat the spatial gradients of the alpha relaxation time and glass transition temperature, and the corresponding film-averaged quantities, to the geometrically asymmetric case of finite thickness…
This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…