The role of the patch test in 2D atomistic-to-continuum coupling methods∗

Christoph Ortner

Displaying similar documents to “The role of the patch test in 2D atomistic-to-continuum coupling methods∗”

The role of the patch test in 2D atomistic-to-continuum coupling methods

Christoph Ortner (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether (or, absence of ) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction, (iii) volumetric scaling...

Cramér type moderate deviations for Studentized U-statistics

Tze Leng Lai, Qi-Man Shao, Qiying Wang (2012)

ESAIM: Probability and Statistics

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Let be a Studentized U-statistic. It is proved that a Cramér type moderate deviation ( ≥ )/(1 − Φ()) → 1 holds uniformly in [0, ( )) when the kernel satisfies some regular conditions.

Morphisms preserving the set of words coding three interval exchange

Tomáš Hejda (2012)

RAIRO - Theoretical Informatics and Applications

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Any amicable pair , of Sturmian morphisms enables a construction of a ternary morphism which preserves the set of infinite words coding 3-interval exchange. We determine the number of amicable pairs with the same incidence matrix in SL(2,ℕ) and we study incidence matrices associated with the corresponding ternary morphisms .