Using a rod theory formulation, we derive equations of state for a thin elastic membrane subjected to several different boundary conditions-clamped, simply supported, and periodic. The former is applicable to membranes supported on a softer substrate and subjected to uniaxial compression. We show that a wider family of quasistatic equilibrium shapes exist beyond the previously obtained analytic...

Phase-field-crystal (PFC) models constitute a field theoretical approach to solidification, melting, and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain elastic excitations associated with strain in crystalline bodies. However, instabilities that are diffusively driven towards equilibrium are often orders of magn...

In this paper, we consider the relationship between supply chain network equilibrium and transportation network equilibrium. We demonstrate that a supply chain network equilibrium model introduced earlier can be reformulated as a transportation network equilibrium model with elastic demands through a supernetwork reformulation of the former. This equivalence allows us to transfer the wealth of ...

We considered the issue of whether shifts in the metarhodopsin I (MI)-metarhodopsin II (MII) equilibrium from lipid composition are fully explicable by differences in bilayer curvature elastic stress. A series of six lipids with known spontaneous radii of monolayer curvature and bending elastic moduli were added at increasing concentrations to the matrix lipid 1-palmitoyl-2-oleoyl-sn-glycero-3-...

Recently, rod theory has been applied to the mathematical modeling of bacterial fibers and biopolymers (e.g. DNA), to study their mechanical properties and shapes (e.g. supercoiling). In static rod theory, an elastic rod in equilibrium is the critical point of an elastic energy. This induces a natural question of how to find elasticae. In this paper, we focus on how to find the critical points ...

In this paper we derive the general equilibrium equations of a polymer chain with a noncircular cross section by the variation of the free energy functional. From the equilibrium equation of the elastic ribbon we derive analytically the equilibrium conformations both of the helical ribbons and the twisted ribbons. We find that the pitch angle of the helical ribbons depends on the ratio of the t...

This article discusses the existence of positive solutions for systems of bending elastic beam equations. In mechanics, the problem describes the deformations of two elastic beams in equilibrium state, whose two ends are simply supported.