Surface texturing has been frequently used for tribological purposes in the last three
decades due to its great potential to reduce friction and wear. Although biological systems …

Numerical homogenization is a methodology for the computational solution of multiscale
partial differential equations. It aims at reducing complex large-scale problems to simplified …

For more details about the topologies of the spaces P (Ω) and P/(Ω), see Yosida [1966], Vo-
Khac [1972a, 1972b], Hörmander [1983, Chapters 1–7], Duistermaat & Kolk [2010], and of …

We propose a method for fabricating deformable objects with spatially varying elasticity
using 3D printing. Using a single, relatively stiff printer material, our method designs an …

" The art of structure is where to put the holes" Robert Le Ricolais, 1894-1977 This is a
completely revised, updated and expanded version of the book titled" Optimization of …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

In the context of shape optimization, we seek minimizers of the sum of the elastic compliance
and of the weight of a solid structure under specified loading. This problem is known not to …

We introduce elastic textures: a set of parametric, tileable, printable, cubic patterns achieving
a broad range of elastic material properties: the softest pattern is over a thousand times …

Mathematics is playing an ever more important role in the physical and biological sciences,
provoking a blurring of boundaries between scienti? c disciplines and a resurgence of …

The focus of this book is the large-scale statistical behavior of solutions of divergence-form
elliptic equations with random coefficients, which is closely related to the long-time …