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ELECTRONIC COMMUNICATIONS in PROBABILITY

- N. Dirr, P. Dondl, G. Grimmett, A. Holroyd
- Mathematics
- 2010

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 be… Expand

Lipschitz Percolation

- N. Dirr, P. Dondl, G. Grimmett, A. Holroyd, M. Scheutzow
- Mathematics
- 17 November 2009

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 be… Expand

A gradient system with a wiggly energy and relaxed EDP-convergence

- P. Dondl, T. Frenzel, A. Mielke
- Physics, Mathematics
- 1 December 2017

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 evolutionary… Expand

Norm-resolvent convergence in perforated domains

- K. Cherednichenko, P. Dondl, F. Rösler
- Mathematics, Computer Science
- Asymptot. Anal.
- 19 June 2017

TLDR

Optimization of the branching pattern in coherent phase transitions

- P. Dondl, Behrend Heeren, M. Rumpf
- Mathematics
- 21 December 2015

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 the… Expand

Lamination microstructure in shear deformed copper single crystals

- O. Dmitrieva, P. Dondl, S. Müller, D. Raabe
- Materials Science
- 1 July 2009

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-like… Expand

Uniform regularity and convergence of phase-fields for Willmore’s energy

- P. Dondl, Stephan Wojtowytsch
- Mathematics
- 29 December 2015

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 uniform… Expand

Effective behavior of an interface propagating through a periodic elastic medium

- P. Dondl, K. Bhattacharya
- Mathematics
- 12 June 2012

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 a… Expand

Computational analysis of martensitic thin films using subdivision surfaces

- P. Dondl, Ching-Ping Shen, K. Bhattacharya
- Materials Science
- 1 October 2007

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 as… Expand

Optimization of Bone Scaffold Porosity Distributions

- Patrina S P Poh, Dvina Valainis, K. Bhattacharya, M. van Griensven, P. Dondl
- Materials Science, Medicine
- Scientific Reports
- 24 June 2019

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 and… Expand

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