Displaying similar documents to “An analysis of the boundary layer in the 1D surface Cauchy–Born model∗”

An analysis of the boundary layer in the 1D surface Cauchy–Born model

Kavinda Jayawardana, Christelle Mordacq, Christoph Ortner, Harold S. Park (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The surface Cauchy–Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is 𝒪(1) in the mesh size; however, we are able to identify an alternative “approximation parameter” – the stiffness of the interaction potential – with respect to which the...

On surface braids of index four with at most two crossings

Teruo Nagase, Akiko Shima (2005)

Fundamenta Mathematicae

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Let Γ be a 4-chart with at most two crossings. We show that if the closure of the surface braid obtained from Γ is one 2-sphere, then the sphere is a ribbon surface.