Sentence examples for in a three dimensional case from inspiring English sources

In comparison with the conventional continuum model which has three independent degrees of freedom and six independent stress components in a three dimensional case, the Cosserat model for the stratified material will have six independent degrees of freedom and 10 independent stress components.

Now we attack this problem by deriving a specialized optimization algorithm based on two ingredients: first, a recently found necessary condition for the quasiconvexity of fourth-degree polynomials that distinguishes between both classes in the three dimensional case, and secondly, upon a characterization of rank-one convex fourth-degree polynomials in terms of infinitely many constraints.

We follow the approach of Schmitz and Ying (2012) on combining the nested dissection matrix factorization method with hierarchical matrices in two dimensions and extend it to the three dimensional case.

In this paper we design and analyze a class of high order numerical methods to delta function integrals appearing in level set methods in two dimensional case.

This was done in [204] in order to detect elastic inclusions, in [205] to detect inclusions in the two dimensional case for a large class of systems with inhomogeneous background, and in [165] for the case of inclusions contained in a slab.

In the case that M is an open, bounded subset of R n with smooth boundary, it is easy to see ([121]) that for n ≥ 3 Λ g = Λ γ (87 where ( g i j ) = ( det γ k l ) 1 n - 2 ( γ i j ) - 1, ( γ i j ) = ( det g k l ) 1 2 ( g i j ) - 1. (88)In the two dimensional case there is an additional obstruction since the Laplace-Beltrami operator is conformally invariant.

2.2 we consider the boundary rigidity in the two dimensional case and in Sect.

1.6, one can extend Theorem 1.5 to L ∞ conductivities in the two dimensional case.

In the two dimensional case they showed that (89) is the only obstruction to unique identifiability for smooth Riemannian surfaces.

The result above was proven in [64, 65] for the case of dimension n ≥ 3. The same basic construction works in the two dimensional case [112].

We remark that the reduction from the non-linear problem to the linear is also valid in the two dimensional case [98].