1. NOTATION AND PRELIMINARIES Here we define our notation and some basic facts and identities from differential geometry. For further details and proofs of the results we state we refer to the book by Do Carmo [1]. Throughout Γ denotes a closed smooth oriented d − 1 dimensional hypersurface in R, d = 2, 3, with outward pointing unit normal ν. For x ∈ Γ we will make the slight abuse of notation ...

Microtubules are used as targets for anticancer drugs due to their crucial role in the process of mitosis. Recent studies show that carbon nanotubes (CNTs) can be classified as microtubule-stabilizing agents as they interact with protein microtubules (MTs), leading to interference in the mitosis process. CNTs hold a substantial promising application in cancer therapy in conjunction with other c...

Curls and curves of a shell interweave its various strain modes and link them together. This interactional behavior has yet frustrated all attempts for the construction of shell templates, which needs for an individual element test in traditional approaches. Such a test fails to work for shell elements and must be reconstructed. In this paper, it is tried to study shell interactional behavior a...

Steady state crack propagation produce substantial plastic strain gradients near the tip, which are accompanied by a high density of geometrically necessary dislocations and additional local strain hardening. Here, the objective is to study these gradient effects on Mode I toughness of a homogeneous rate-sensitive metal, using a higher order plasticity theory. Throughout, emphasis is on the tou...

In this article, we consider the misspecified optimization problem of minimizing a convex function $f(x;\theta ^*)$ in notation="LaTeX">$x$ over conic constraint set represented by notation="LaTeX">$h(x;\thet...

We consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin-Anand formulation [19]. The aim of the present model is to account for different phenomena: on the one hand the elastic stiffness reduces and the plastic yield surface shrinks due to material’s degradation, on ...

We study the following lesser-known low rank (LR) recovery problem: recover an $n \times q$ rank- notation="LaTeX">$r$ matrix, notation="LaTeX">${ \boldsymbol {X}}^{\ast}=[\boldsymbol {x}^{\ast}_{1}, {x}^{\ast}_{2}, \ldots, {x}^{\ast}...