In this paper we obtain a limit model for a turbine blade fixed to a 3D solid. This model is a three-dimensional linear elasticity problem in the 3D part of the piece (the rotor) and a two-dimensional problem (the nonlinear shallow shell equations) in the 2D part (the turbine blade), with junction conditions in the part of the turbine blade fixed to the rotor. To obtain this model, we perform a...

Marginal stability plays an important role in nonlinear elasticity because the associated minimally stable states usually delineate failure thresholds. In this paper we study the local (material) aspect of marginal stability. The weak notion of marginal stability at a point, associated with the loss of strong ellipticity, is classical. States that are marginally stable in the strong sense are l...

where λ ∈ R. Next, we state the general hypotheses which will be assumed throughout the paper. (E) Assume that N , p satisfy the following relation N > p > 1. (G) g is a smooth function, at least C1,α(RN ) for some α∈ (0,1), such that g ∈ L∞(RN ) and g(x) > 0, on Ω+, with measure of Ω+, |Ω+| > 0. Also there exist R0 sufficiently large and k > 0 such that g(x) <−k, for all |x| > R0. Generally, p...

A data analytics flow typically operates on three layers: ingestion, analytics, and storage, each of which is provided by a data-intensive system. These systems are often available as cloud managed services, enabling the users to have painfree deployment of data analytics flow applications such as click-stream analytics. Despite straightforward orchestration, elasticity management of the flows ...

Purpose We used acoustic radiation force optical coherence elastography (ARF-OCE) to map out the elasticity of retinal layers in healthy and diseased in vivo rabbit models for the first time. Methods A healthy rabbit eye was proptosed and imaged using ARF-OCE, by measuring the tissue deformation after an acoustic force is applied. A diseased retinal inflammation model was used to observe the ...

The curvature elasticity of a polyelectrolyte brush monolayer attached to curved surface is investigated theoretically. An analytical method based on the strong-stretching theory for a Gaussian chain is developed to calculate the elastic modulus induced by a polyelectrolyte brush. In particular, the scaling relations for the bending or Gaussian modulus with respect to system parameters related ...

In this paper, we prove that the linearized elasticity system has no eigenvalues in two geometric situations: the whole space R and a local perturbation of the half-space. We consider the Lamé coefficients and the density varying in an unbounded part of the domain. For the whole space, we use the operations curl and div to reduce our system to a scalar problem and use a limiting absorption prin...

In this paper, we establish an optimal trace regularity theorem, also known as the hidden regularity theorem [L2], for the anisotropic linear elasticity equation on a bounded domain Ω with Lipschitz boundary. In its simplest form it provides a space-time L estimate for the trace of the normal derivative for the solution. Over the years, such sharp trace regularity theorems have proven to be cru...

In this paper, I argue that the two theoretical prerequisites of balanced growth purely labor augmenting technical progress and a unitary capital-labor elasticity are inconsistent with long-run evidence from a simple decomposition of the post-war U.S. economy into heterogeneous industries. My decomposition is motivated by empirical evidence that the degree of substitution between capital and la...