Radiation Conditions for Rough Surfaces in Linear Elasticity

Artificial conditions for the linear elasticity equations

In this paper, we consider the equations of linear elasticity in an exterior domain. We exhibit artificial boundary conditions on a circle, which lead to a non-coercive second order boundary value problem. In the particular case of an axisymmetric geometry, explicit computations can be performed in Fourier series proving the wellposedness except for a countable set of parameters. A perturbation...

Surface Energy, Elasticity and the Homogenization of Rough Surfaces

Due to a larger surface to volume ratio, phenomena at the nanoscale require consideration of surface energy effects and the latter are frequently used to interpret size-effects in material behavior. Extensive work exists on deriving homogenized constitutive responses for macroscopic composites— relating effective properties to various microstructural details. In the present work, we focus on ho...

Global existence for rough differential equations under linear growth conditions

We prove existence of global solutions for differential equations driven by a geometric rough path under the condition that the vector fields have linear growth. We show by an explicit counter-example that the linear growth condition is not sufficient if the driving rough path is not geometric. This settle a long-standing open question in the theory of rough paths. So in the geometric setting w...

Artificial boundary conditions to compute correctors in linear elasticity

Linear theory of unstable growth on rough surfaces

Unstable homoepitaxy on rough substrates is treated within a linear continuum theory. The time dependence of the surface width W (t) is governed by three length scales: The characteristic scale l0 of the substrate roughness, the terrace size lD and the Ehrlich-Schwoebel length lES . If lES ≪ lD (weak step edge barriers) and l0 ≪ lm ∼ lD √ lD/lES , then W (t) displays a minimum at a coverage θmi...