A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity

A generalized Cahn–Hilliard equation incorporating geometrically linear elasticity

We consider a generalisation of the Cahn–Hilliard equation that incorporates an elastic energy density which, being quasiconvex, incorporates microstructure formation on smaller length scales. We prove global existence of weak solutions in certain microstructural regimes in (one and) two dimensions and present sufficient conditions for uniqueness. Preliminary numerical computations to illustrat...

Generalized Stochastic Approach for Constitutive Equation in Linear Elasticity: A Random Matrix Model∗

This work is concerned with the construction of stochastic models for random elasticity matrices, allowing either for the generation of elasticity tensors exhibiting some material symmetry properties almost surely (integrating the statistical dependence between the random stiffness components), or for the modeling of random media that requires the mean of a stochastic anisotropy measure to be c...

Non-linear generalized elasticity of icosahedral quasicrystals

Quasicrystals can carry, in addition to the classical phonon displacement field, a phason displacement field, which requires a generalized theory of elasticity. In this paper, the third-order strain invariants (including phason strain) of icosahedral quasicrystals are determined. They are connected with 20 independent third-order elastic constants. By means of non-linear elasticity, phason stra...

Linear Elasticity and (Generalized) Stokes — Parallel Implementation

Generalized Partially Linear Mixed-effects Models Incorporating Mismeasured Covariates.

In this article we consider a semiparametric generalized mixed-effects model, and propose combining local linear regression, and penalized quasilikelihood and local quasilikelihood techniques to estimate both population and individual parameters and nonparametric curves. The proposed estimators take into account the local correlation structure of the longitudinal data. We establish normality fo...