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We prove the existence of a (random) Lipschitz function F : Z d 1 ! Z + such that, for every x2 Z d 1 , the site(x, F(x)) is open in a site percolation process on Z d . The Lipschitz constant may beExpand
Lipschitz Percolation
We prove the existence of a (random) Lipschitz function F : Zd−1 → Z+ such that, for every x ∈ Zd−1, the site (x, F(x)) is open in a site percolation process on Zd . The Lipschitz constant may beExpand
A gradient system with a wiggly energy and relaxed EDP-convergence
If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic effects. We introduce a notion of evolutionaryExpand
Norm-resolvent convergence in perforated domains
For several different boundary conditions (Dirichlet, Neumann, Robin), we prove norm-resolvent convergence for the operator $-\Delta$ in the perforated domain $\Omega\setminus \bigcup_{ i\in 2\varepsilon\mathbb Z^d }B_{a_\varrepsilon}(i),$ . Expand
Optimization of the branching pattern in coherent phase transitions
Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and M\"uller studied a branching pattern with optimal scaling of theExpand
Lamination microstructure in shear deformed copper single crystals
We investigate the formation of microscopic patterns in a copper single crystal deformed in a shear experiment. Using high-resolution electron backscatter diffraction imaging, we find a band-likeExpand
Uniform regularity and convergence of phase-fields for Willmore’s energy
We investigate the convergence of phase fields for the Willmore problem away from the support of a limiting measure $$\mu $$μ. For this purpose, we introduce a suitable notion of essentially uniformExpand
Effective behavior of an interface propagating through a periodic elastic medium
We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that aExpand
Computational analysis of martensitic thin films using subdivision surfaces
This paper studies numerically the deformation of thin films made of materials undergoing martensitic phase transformations by using subdivision surfaces. These thin films have received interest asExpand
Optimization of Bone Scaffold Porosity Distributions
Additive manufacturing (AM) is a rapidly emerging technology that has the potential to produce personalized scaffolds for tissue engineering applications with unprecedented control of structural andExpand