Bibtex

@article{Weichselberger:2022aa,
  abstract = {Cooperative morphogenesis of cell lineages underlies the development of functional units and organs. To study mechanisms driving the coordination of lineages, we investigated soma-germline interactions during oogenesis. From invertebrates to vertebrates, oocytes develop as part of a germline cyst that consists of the oocyte itself and so-called nurse cells, which feed the oocyte and are eventually removed. The enveloping somatic cells specialize to facilitate either oocyte maturation or nurse cell removal, which makes it essential to establish the right match between germline and somatic cells. We uncover that the transcriptional regulator Eya, expressed in the somatic lineage, controls bilateral cell--cell affinity between germline and somatic cells in Drosophila oogenesis. Employing functional studies and mathematical modelling, we show that differential affinity and the resulting forces drive somatic cell redistribution over the germline surface and control oocyte growth to match oocyte and nurse cells with their respective somatic cells. Thus, our data demonstrate that differential affinity between cell lineages is sufficient to drive the complex assembly of inter-lineage functional units and underlies tissue self-organization during Drosophila oogenesis.},
  author = {Weichselberger, Vanessa and Dondl, Patrick and Classen, Anne-Kathrin},
  date = {2022/10/26},
  date-added = {2022-10-26 20:59:33 +0200},
  date-modified = {2022-10-26 21:02:57 +0200},
  doi = {10.1038/s41467-022-33845-1},
  id = {Weichselberger2022},
  isbn = {2041-1723},
  journal = {Nature Communications},
  keywords = {Article},
  number = {1},
  pages = {6377},
  title = {Eya-controlled affinity between cell lineages drives tissue self-organization during \textit{Drosophila} oogenesis},
  volume = {13},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1038/s41467-022-33845-1}
}
@misc{2209.04538,
  author = {Patrick Dondl and Alberto Maione and Steve Wolff-Vorbeck},
  date-added = {2022-09-19 14:32:30 +0200},
  date-modified = {2022-09-19 14:32:38 +0200},
  eprint = {arXiv:2209.04538},
  keywords = {Preprints},
  title = {Multi-material model and shape optimization for bending and torsion of inextensible rods},
  year = {2022}
}
@misc{yeah,
  author = {Schorsch Henderson and Giorgio Spinetti},
  date-added = {2022-07-26 20:37:46 -0700},
  date-modified = {2022-08-01 07:53:54 -0500},
  howpublished = {{Rare} {Wiri} {Records}},
  keywords = {Other},
  title = {\emph{{Y}eah! {Y}eah! {Y}eah!}},
  url = {https://rarewirirecords.bandcamp.com/album/yeah-yeah-yeah},
  year = {2021},
  bdsk-url-1 = {https://rarewirirecords.bandcamp.com/track/yeah-yeah-yeah}
}
@article{Dondl_22a,
  author = {Wolff-Vorbeck, Steve and Speck, Olga and Langer, Max and Speck, Thomas and Dondl, Patrick W.},
  date-added = {2022-05-25 10:38:04 +0200},
  date-modified = {2022-06-22 14:55:13 +0200},
  doi = {10.1098/rsif.2022.0131},
  journal = {Journal of the Royal Society Interface},
  keywords = {Article},
  number = {20220131},
  title = {Charting the twist-to-bend ratio of plant axes},
  volume = {19},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1098/rsif.2022.0131}
}
@misc{north,
  author = {{North Coast Limited}},
  date-added = {2022-02-21 13:48:01 +0100},
  date-modified = {2022-08-01 07:52:35 -0500},
  howpublished = {{Rare} {Wiri} {Records}},
  keywords = {Other},
  title = {\emph{{N}orth {C}oast {L}imited}},
  url = {https://www.junodownload.com/products/north-coast-limited/5685704-02/},
  year = {2022},
  bdsk-url-1 = {https://rarewirirecords.bandcamp.com/track/yeah-yeah-yeah}
}
@misc{2112.11530,
  author = {Patrick Dondl and Marius Zeinhofer},
  date-added = {2021-12-26 20:54:53 +0100},
  date-modified = {2021-12-26 20:55:04 +0100},
  eprint = {arXiv:2112.11530},
  keywords = {Preprints},
  title = {Three Dimensional Optimization of Scaffold Porosities for Bone Tissue Engineering},
  year = {2021}
}
@misc{2112.09500,
  author = {Patrick Dondl and Marius Zeinhofer},
  date-added = {2021-12-20 07:36:55 +0100},
  date-modified = {2021-12-20 07:40:56 +0100},
  eprint = {arXiv:2112.09500},
  keywords = {Preprints},
  title = {${L}^p({I},{C}^\alpha({\Omega}))$ Regularity for Reaction-Diffusion Equations with Non-smooth Data},
  year = {2021}
}
@article{Dondl_21d,
  abstract = { We describe the implementation of a topological constraint in finite-element simulations of phase-field models, which ensures path-connectedness of preimages of intervals in the phase-field variable. The constraint takes the form of an energetic penalty for a suitable geodesic distance between all pairs of points in the domain. The main application of our method presented here is a discrete steepest descent of a phase-field version of a bending energy with spontaneous curvature and additional surface area penalty. This leads to disconnected surfaces without our topological constraint but connected surfaces with the constraint. Numerically, our constraint is treated by first transforming the double integral over all pairs of points in the domain to a weighted graph structure and then using Dijkstra's algorithm to calculate the distance between discrete connected components. },
  author = {Patrick Dondl and Stephan Wojtowytsch},
  date-added = {2021-12-14 06:49:08 +0100},
  date-modified = {2021-12-14 06:51:13 +0100},
  doi = {10.1177/17483026211054342},
  eprint = {arXiv:1806.04767},
  journal = {Journal of Algorithms \& Computational Technology},
  keywords = {Article},
  title = {Keeping it together: A phase-field version of path-connectedness and its implementation},
  volume = {15},
  year = {2021},
  bdsk-url-1 = {https://doi.org/10.1177/17483026211054342}
}
@article{Dondl_21c,
  author = {Patrina S. P. Poh and Thomas Lingner and Stefan Kalkhof and Sven M{\"a}rdian and Jan Baumbach and Patrick Dondl and Georg N. Duda and Sara Checa},
  date-added = {2021-12-07 23:44:51 +0100},
  date-modified = {2022-01-07 12:54:50 +0100},
  doi = {10.1016/j.copbio.2021.12.002},
  journal = {Current Opinion in Biotechnology},
  keywords = {Article},
  pages = {263--270},
  title = {Enabling technologies towards personalization of scaffolds for large bone defect regeneration},
  volume = {74},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1016/j.copbio.2021.12.002}
}
@article{2111.05637,
  author = {Patrick Dondl and Johannes M{\"u}ller and Marius Zeinhofer},
  date-added = {2021-11-15 00:05:50 +0100},
  date-modified = {2022-07-03 21:56:41 +0200},
  doi = {10.1186/s13662-022-03722-8},
  eprint = {arXiv:2111.05637},
  journal = {Advances in Continuous and Discrete Models},
  keywords = {Article},
  title = {Uniform Convergence Guarantees for the Deep {R}itz Method for Nonlinear Problems},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1186/s13662-022-03722-8}
}
@article{Wolff-Vorbeck:2021up,
  abstract = {During biological evolution, plants have developed a wide variety of body plans and concepts that enable them to adapt to changing environmental conditions. The trade-off between flexural and torsional rigidity is an important example of sometimes conflicting mechanical requirements, the adaptation to which can be quantified by the dimensionless twist-to-bend ratio. Our study considers the triangular flower stalk of Carex pendula, which shows the highest twist-to-bend ratios ever measured for herbaceous plant axes. For an in-depth understanding of this peak value, we have developed geometric models reflecting the 2D setting of triangular cross-sections comprised of a parenchymatous matrix with vascular bundles surrounded by an epidermis. We analysed the mathematical models (using finite elements) to measure the effect of either reinforcements of the epidermal tissue or fibre reinforcements such as collenchyma and sclerenchyma on the twist-to-bend ratio. The change from an epidermis to a covering tissue of corky periderm increases both the flexural and the torsional rigidity and decreases the twist-to-bend ratio. Furthermore, additional individual fibre reinforcement strands located in the periphery of the cross-section and embedded in a parenchymatous ground tissue lead to a strong increase of the flexural and a weaker increase of the torsional rigidity and thus resulted in a marked increase of the twist-to-bend ratio. Within the developed model, a reinforcement by 49 sclerenchyma fibre strands or 24 collenchyma fibre strands is optimal in order to achieve high twist-to-bend ratios. Dependent on the mechanical quality of the fibres, the twist-to-bend ratio of collenchyma-reinforced axes is noticeably smaller, with collenchyma having an elastic modulus that is approximately 20 times smaller than that of sclerenchyma. Based on our mathematical models, we can thus draw conclusions regarding the influence of mechanical requirements on the development of plant axis geometry, in particular the placement of reinforcements.},
  author = {Wolff-Vorbeck, Steve and Speck, Olga and Speck, Thomas and Dondl, Patrick W.},
  date-added = {2021-11-01 11:50:48 +0100},
  date-modified = {2022-08-17 15:48:56 +0200},
  doi = {10.1038/s41598-021-00569-z},
  journal = {Scientific Reports},
  keywords = {Article},
  number = {1},
  pages = {21232},
  title = {Influence of structural reinforcements on the twist-to-bend ratio of plant axes: a case study on \textit{Carex pendula}},
  volume = {11},
  year = {2021},
  bdsk-url-1 = {https://doi.org/10.1038/s41598-021-00569-z}
}
@article{2110.13728,
  author = {Patrick Dondl and Martin Jesenko and Martin Kru{\v z}{\'\i}k and Jan Valdman},
  date-added = {2021-10-27 09:27:25 +0200},
  date-modified = {2022-05-08 21:44:02 +0200},
  doi = {10.3934/mine.2023030},
  eprint = {arXiv:2110.13728},
  journal = {Mathematics in Engineering},
  keywords = {Article},
  number = {2},
  pages = {1--15},
  title = {Linearization and Computation for Large-Strain Viscoelasticity},
  volume = {5},
  year = {2023},
  bdsk-url-1 = {https://doi.org/10.3934/mine.2023030}
}
@misc{2110.12291,
  author = {Patrick Dondl and Brian Straughan},
  date-added = {2021-10-26 02:35:38 +0200},
  date-modified = {2021-10-26 02:35:48 +0200},
  eprint = {arXiv:2110.12291},
  keywords = {Preprints},
  title = {Thermal convection in a linearly viscous fluid overlying a bidisperse porous medium},
  year = {2021}
}
@article{2110.08672,
  author = {Patrick Dondl and Sergio Conti and Julia Orlik},
  date-added = {2021-10-19 06:48:32 +0200},
  date-modified = {2022-06-16 09:38:52 +0200},
  doi = {10.3934/mine.2023039},
  eprint = {arXiv:2110.08672},
  journal = {Mathematics in Engineering},
  keywords = {Article},
  number = {2},
  pages = {1--28},
  title = {Variational Modeling of Paperboard Delamination Under Bending},
  volume = {5},
  year = {2023},
  bdsk-url-1 = {https://doi.org/10.3934/mine.2023039}
}
@inproceedings{2110.07328,
  author = {Patrick Dondl and Marius Zeinhofer},
  booktitle = {IX International Conference on Computational Bioengineering},
  date-added = {2021-10-16 22:27:38 +0200},
  date-modified = {2022-10-05 21:09:10 +0200},
  editor = {Fernandes, Paulo R. and Folgado, Jo{\~a}o and Quental, Carlos and Castro, Andr{\'e}},
  eprint = {arXiv:2110.07328},
  keywords = {Other},
  publisher = {Instituto Superior T{\'e}cnico, Lisbon},
  title = {A parameter study on optimal scaffolds in a simple model for bone regeneration},
  url = {https://iccb2022.tecnico.ulisboa.pt/proceedings_ICCB2022/PDF/ID57_T2DM_Model_ICCB2022(1).pdf},
  year = {2022},
  bdsk-url-1 = {https://iccb2022.tecnico.ulisboa.pt/proceedings_ICCB2022/PDF/ID57_T2DM_Model_ICCB2022(1).pdf}
}
@article{Dondl_21b,
  abstract = {We consider a version of Gamow's liquid drop model with a short range attractive perimeter-penalizing potential and a long-range Coulomb interaction of a uniformly charged mass in . Here we constrain ourselves to minimizing among the class of shapes that are columnar, i.e., constant in one spatial direction. Using the standard perimeter in the energy would lead to non-existence for any prescribed cross-sectional area due to the infinite mass in the constant spatial direction. In order to overcome this issue we use a connected perimeter instead. We prove existence of minimizers for this connected isoperimetric problem with long-range interaction and study the shapes of minimizers in the small and large cross section regimes. For an intermediate regime we use an Ohta--Kawasaki phase field model with connectedness constraint to study the shapes of minimizers numerically.},
  author = {Patrick Dondl and Matteo Novaga and Stephan Wojtowytsch and Steve Wolff-Vorbeck},
  date-added = {2021-07-27 16:20:40 +0200},
  date-modified = {2022-10-06 10:34:06 +0200},
  doi = {10.1088/1361-6544/ac022f},
  eprint = {arXiv:2007.00136},
  journal = {Nonlinearity},
  keywords = {Article},
  number = {9},
  pages = {6120--6139},
  publisher = {{IOP} Publishing},
  title = {Connected Coulomb columns: analysis and numerics},
  volume = {34},
  year = 2021,
  bdsk-url-1 = {https://doi.org/10.1088/1361-6544/ac022f}
}
@article{2106.00798,
  author = {Luca Courte and Patrick Dondl and Michael Ortiz},
  date-added = {2021-06-03 11:14:57 +0200},
  date-modified = {2022-03-29 13:56:45 +0200},
  doi = {10.1007/s00205-022-01765-5},
  eprint = {arXiv:2106.00798},
  journal = {Archive for Rational Mechanics and Analysis},
  keywords = {Article},
  title = {A proof of {T}aylor scaling for curvature-driven dislocation motion through random arrays of obstacles},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1007/s00205-022-01765-5}
}
@article{Dondl_21a,
  author = {N{\"o}hring, Wolfram Georg and Grie{\ss}er, Jan and Dondl, Patrick and Pastewka, Lars},
  date-added = {2021-01-31 15:38:19 +0100},
  date-modified = {2021-12-27 13:59:52 +0100},
  doi = {10.1088/1361-651X/ac3ca2},
  eprint = {arXiv:2101.12519},
  journal = {Modelling and Simulation in Materials Science and Engineering},
  keywords = {Article},
  number = {1},
  pages = {015007},
  title = {Surface lattice {G}reen's functions for high-entropy alloys},
  volume = {30},
  year = {2021},
  bdsk-url-1 = {https://doi.org/10.1088/1361-651X/ac3ca2}
}
@article{2101.09128,
  author = {Patrick Dondl and Patrina S. P. Poh and Marius Zeinhofer},
  date-added = {2021-01-31 11:38:22 +0100},
  date-modified = {2022-06-09 20:56:52 +0200},
  doi = {10.1137/21M1401887},
  eprint = {arXiv:2101.09128},
  journal = {SIAM Journal on Applied Mathematics},
  keywords = {Article},
  number = {3},
  pages = {924-949},
  title = {An Efficient Model for Scaffold-Mediated Bone Regeneration},
  volume = {82},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1137/21M1401887}
}
@article{2010.06509,
  author = {Harbir Antil and Patrick Dondl and Ludwig Striet},
  date-added = {2020-10-14 13:53:25 +0200},
  date-modified = {2021-08-26 10:08:33 +0200},
  doi = {10.1137/20M1374122},
  eprint = {arXiv:2010.06509},
  journal = {SIAM J. Sci. Comput.},
  keywords = {Article},
  number = {4},
  pages = {A2897--A2922},
  title = {Approximation of Integral Fractional {L}aplacian and Fractional {PDE}s via sinc-Basis},
  volume = {43},
  year = {2021},
  bdsk-url-1 = {https://doi.org/10.1137/20M1374122}
}
@article{2007.07605,
  author = {Patrick Dondl and Martin Jesenko and Michael Scheutzow},
  date-added = {2020-07-16 09:57:56 +0200},
  date-modified = {2022-06-09 21:04:30 +0200},
  doi = {https://doi.org/10.1112/blms.12599},
  eprint = {arXiv:2007.07605},
  journal = {Bulletin of the London Mathematical Society},
  keywords = {Article},
  number = {2},
  pages = {760-771},
  title = {Infinite pinning},
  volume = {54},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1112/blms.12599}
}
@article{Dondl_19a,
  abstract = {The yield behavior of crystalline solids is determined by the motion of defects like dislocations, twin boundaries and coherent phase boundaries. These solids are hardened by introducing precipitates---small particles of a second phase. It is generally observed that the motion of line defects like dislocations are strongly inhibited or pinned by precipitates while the motion of surface defects like twin and phase boundaries are minimally affected. In this article, we provide insight into why line defects are more susceptible to the effect of precipitates than surface defects. Based on mathematical models that describe both types of motion, we show that for small concentrations of a nearly periodic arrangement of precipitates, the critical force that is required for a surface defect to overcome a precipitate is smaller than that required for a line defect. In particular, the critical forces for surface and line defects scale with the radius of precipitates to the second and first power, respectively.},
  author = {Courte, Luca and Bhattacharya, Kaushik and Dondl, Patrick},
  date-added = {2020-06-04 10:44:15 +0200},
  date-modified = {2020-06-04 10:45:28 +0200},
  doi = {10.1007/s00033-020-01327-3},
  eprint = {arXiv:1903.07505},
  journal = {Zeitschrift f{\"u}r angewandte Mathematik und Physik},
  keywords = {Article},
  number = {3},
  pages = {99},
  title = {Bounds on precipitate hardening of line and surface defects in solids},
  volume = {71},
  year = {2020},
  bdsk-url-1 = {https://doi.org/10.1007/s00033-020-01327-3}
}
@article{Dondl_19e,
  author = {Dondl, Patrick W. and Wojtowytsch, Stephan},
  date-added = {2020-06-01 21:36:51 +0200},
  date-modified = {2020-06-01 21:38:27 +0200},
  doi = {10.1017/prm.2018.100},
  eprint = {arXiv:1706.02160},
  fjournal = {Proceedings of the Royal Society of Edinburgh. Section A. Mathematics},
  issn = {0308-2105},
  journal = {Proc. Roy. Soc. Edinburgh Sect. A},
  keywords = {Article},
  mrclass = {49Q10 (35B25 35B65 35J20 49N60)},
  mrnumber = {3988633},
  number = {4},
  pages = {1017--1035},
  title = {On the boundary regularity of phase-fields for {W}illmore's energy},
  volume = {149},
  year = {2019},
  bdsk-url-1 = {https://doi.org/10.1017/prm.2018.100}
}
@article{Dondl_20b,
  author = {Patrick Dondl and Martin Jesenko and Michael Scheutzow},
  date-added = {2020-05-18 21:11:33 +0200},
  date-modified = {2021-08-26 10:10:31 +0200},
  doi = {10.4171/IFB/455},
  eprint = {arXiv:2002.00800},
  journal = {Interfaces and Free Boundaries},
  keywords = {Article},
  number = {3},
  pages = {305--321},
  title = {Pinning of interfaces in a random medium with zero mean},
  volume = {23},
  year = {2021},
  bdsk-url-1 = {https://doi.org/10.4171/IFB/455}
}
@article{MR4027693,
  author = {Dondl, Patrick and Frenzel, Thomas and Mielke, Alexander},
  date-added = {2020-03-13 10:04:51 +0100},
  date-modified = {2020-06-01 21:43:35 +0200},
  doi = {10.1051/cocv/2018058},
  eprint = {arXiv:1801.07144},
  fjournal = {ESAIM. Control, Optimisation and Calculus of Variations},
  issn = {1292-8119},
  journal = {ESAIM Control Optim. Calc. Var.},
  keywords = {Article},
  mrclass = {35K55 (35A15 35B27 49J40 49J45 49S05)},
  mrnumber = {4027693},
  pages = {Art. 68, 45},
  title = {A gradient system with a wiggly energy and relaxed {EDP}-convergence},
  volume = {25},
  year = {2019},
  bdsk-url-1 = {https://doi.org/10.1051/cocv/2018058}
}
@article{Dondl_20a,
  author = {Luca Courte and Patrick Dondl},
  date-added = {2020-03-13 10:02:49 +0100},
  date-modified = {2022-07-26 07:13:43 -0700},
  doi = {10.1080/00036811.2022.2102487},
  eprint = {arXiv:2003.05751},
  journal = {Applicable Analysis},
  keywords = {Article},
  title = {Viscosity Solutions for Doubly-Nonlinear Evolution Equations},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1080/00036811.2022.2102487}
}
@article{Dondl_19g,
  abstract = {Mechanical optimisation plays a key role in living beings either as an immediate response of individuals or as an evolutionary adaptation of populations to changing environmental conditions. Since biological structures are the result of multifunctional evolutionary constraints, the dimensionless twist-to-bend ratio is particularly meaningful because it provides information about the ratio of flexural rigidity to torsional rigidity determined by both material properties (bending and shear modulus) and morphometric parameters (axial and polar second moment of area). The determination of the mutual contributions of material properties and structural arrangements (geometry) or their ontogenetic alteration to the overall mechanical functionality of biological structures is difficult. Numerical methods in the form of gradient flows of phase field functionals offer a means of addressing this question and of analysing the influence of the cross-sectional shape of the main load-bearing structures on the mechanical functionality. Three phase field simulations were carried out showing good agreement with the cross-sections found in selected plants: (i) U-shaped cross-sections comparable with those of Musa sp. petioles, (ii) star-shaped cross-sections with deep grooves as can be found in the lianoid wood of Condylocarpon guianense stems, and (iii) flat elliptic cross-sections with one deep groove comparable with the cross-sections of the climbing ribbon-shaped stems of Bauhinia guianensis.},
  author = {Wolff-Vorbeck, Steve and Langer, Max and Speck, Olga and Speck, Thomas and Dondl, Patrick},
  date-added = {2019-11-27 10:15:28 +0100},
  date-modified = {2019-11-27 10:16:20 +0100},
  doi = {10.1038/s41598-019-52878-z},
  journal = {Scientific Reports},
  keywords = {Article},
  number = {1},
  pages = {17182},
  title = {Twist-to-bend ratio: an important selective factor for many rod-shaped biological structures},
  volume = {9},
  year = {2019},
  bdsk-url-1 = {https://doi.org/10.1038/s41598-019-52878-z}
}
@article{Dondl_20c,
  author = {Luca Courte and Patrick Dondl and Ulisse Stefanelli},
  date-added = {2019-09-12 16:02:42 +0200},
  date-modified = {2020-06-05 19:20:50 +0200},
  doi = {10.1016/j.jde.2020.06.005},
  eprint = {arXiv:1909.04717},
  journal = {Journal of Differential Equations},
  keywords = {Article},
  number = {9},
  pages = {7356--7381},
  title = {Pinning of Interfaces by Localized Dry Friction},
  volume = {269},
  year = {2020},
  bdsk-url-1 = {https://doi.org/10.1016/j.jde.2020.06.005}
}
@article{Dondl_19f,
  author = {Valainis, Dvina and Dondl, Patrick and Foehr, Peter and Burgkart, Rainer and Kalkhof, Stefan and Duda, Georg N and van Griensven, Martijn and Poh, Patrina S P},
  date-added = {2019-08-14 07:51:27 +0200},
  date-modified = {2019-10-14 06:56:48 +0200},
  doi = {10.1088/1748-605x/ab38c6},
  journal = {Biomedical Materials},
  keywords = {Article},
  number = {6},
  pages = {065002},
  title = {Integrated additive design and manufacturing approach for the bioengineering of bone scaffolds for favorable mechanical and biological properties},
  volume = {14},
  year = {2019},
  bdsk-url-1 = {https://doi.org/10.1088/1748-605X/ab38c6},
  bdsk-url-2 = {https://doi.org/10.1088/1748-605x/ab38c6}
}
@article{Dondl_19d,
  abstract = {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 functional design. Particularly for bone defect regeneration, the complex coupling of biological mechanisms to the scaffolds'properties has led to a predominantly trial-and-error approach. To mitigate this, shape or topology optimization can be a useful tool to design a scaffold architecture that matches the desired design targets, albeit at high computational cost. Here, we consider an efficient macroscopic optimization routine based on a simple one-dimensional time-dependent model for bone regeneration in the presence of a bioresorbable polymer scaffold. The result of the optimization procedure is a scaffold porosity distribution which maximizes the stiffness of the scaffold and regenerated bone system over the entire regeneration time, so that the propensity for mechanical failure is minimized.},
  author = {Patrina S. P. Poh and Dvina Valainis and Kaushik Bhattacharya and Martijn van Griensven and Patrick Dondl},
  da = {2019/06/24},
  date-added = {2019-07-12 14:49:39 +0200},
  date-modified = {2019-07-12 23:15:56 +0200},
  doi = {10.1038/s41598-019-44872-2},
  eprint = {1809.08179},
  id = {Poh2019},
  isbn = {2045-2322},
  journal = {Scientific Reports},
  keywords = {Article},
  number = {1},
  pages = {9170},
  title = {Optimization of Bone Scaffold Porosity Distributions},
  ty = {JOUR},
  volume = {9},
  year = {2019},
  bdsk-url-1 = {https://doi.org/10.1038/s41598-019-44872-2}
}
@article{Dondl_19c,
  abstract = { This paper deals with the simultaneous optimization of a subset O0 of some domain Ω and its complement O1=Ω∖O0¯ both considered as separate elastic objects subject to a set of loading scenarios. If one asks for a configuration which minimizes the maximal elastic cost functional both phases compete for space since elastic shapes usually get mechanically more stable when being enlarged. Such a problem arises in biomechanics where a bioresorbable polymer scaffold is implanted in place of lost bone tissue and in a regeneration phase, new bone tissue grows in the scaffold complement via osteogenesis. In fact, the polymer scaffold should be mechanically stable to bear loading in the early stage regeneration phase and at the same time, the new bone tissue grown in the complement of this scaffold should as well bear the loading. Here, this optimal subdomain splitting problem with appropriate elastic cost functionals is introduced and the existence of optimal two-phase configurations is established for a regularized formulation. Furthermore, based on a phase-field approximation, a finite-element discretization is derived. Numerical experiments are presented for the design of optimal periodic scaffold microstructure. },
  author = {Patrick Dondl and Patrina S. P. Poh and Martin Rumpf and Stefan Simon},
  date-added = {2019-07-12 14:48:42 +0200},
  date-modified = {2019-07-12 23:16:02 +0200},
  doi = {10.1098/rspa.2018.0718},
  eprint = {1809.07555},
  journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  keywords = {Article},
  number = {2227},
  pages = {20180718},
  title = {Simultaneous elastic shape optimization for a domain splitting in bone tissue engineering},
  volume = {475},
  year = {2019},
  bdsk-url-1 = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2018.0718},
  bdsk-url-2 = {https://doi.org/10.1098/rspa.2018.0718}
}
@article{Dondl_19b,
  author = {Patrick Dondl and Martin Jesenko},
  date-added = {2019-07-12 14:47:20 +0200},
  date-modified = {2020-06-01 21:41:06 +0200},
  doi = {10.3934/dcdss.2020329},
  eprint = {arXiv:1903.04952},
  journal = {Discrete and Continuous Dynamical Systems Series S},
  keywords = {Article},
  title = {Threshold phenomenon for homogenized fronts in random elastic media},
  year = {2019},
  bdsk-url-1 = {https://doi.org/10.3934/dcdss.2020329}
}
@article{Dondl_18h,
  author = {Dondl, Patrick W. and Novaga, Matteo and Wirth, Benedikt and Wojtowytsch, Stephan},
  date-added = {2018-10-16 07:41:09 +0200},
  date-modified = {2019-10-14 06:53:12 +0200},
  doi = {10.1137/18M1225197},
  eprint = {1810.05787},
  fjournal = {SIAM Journal on Mathematical Analysis},
  journal = {SIAM J. Math. Anal.},
  keywords = {Article},
  number = {5},
  pages = {3902--3920},
  title = {A {P}hase-field {A}pproximation of the {P}erimeter under a {C}onnectedness {C}onstraint},
  volume = {51},
  year = {2019},
  bdsk-url-1 = {https://doi.org/10.1137/18M1225197}
}
@article{Dondl_18a,
  author = {Patrick Dondl and Kirill Cherednichenko and Frank R{\"o}sler},
  date-added = {2018-10-09 15:43:39 +0200},
  date-modified = {2018-11-14 11:37:31 +0100},
  doi = {10.3233/ASY-181481},
  eprint = {1706.05859},
  journal = {Asymptotic Analysis},
  keywords = {Article},
  number = {3--4},
  pages = {163--184},
  title = {Norm-Resolvent Convergence in Perforated Domains},
  volume = {110},
  year = {2018},
  bdsk-url-1 = {https://doi.org/10.3233/ASY-181481}
}
@article{Dondl_18b,
  abstract = {We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model is based on a Peierls--Nabarro type energy penalizing non-integer slip and elastic stress. Forest dislocations are introduced as a perforation of the domain by small disks where slip is prohibited. The {\$}{\$}{\{}{\backslash}Gamma{\}}{\$}{\$}$\Gamma$-limit of this energy was deduced by Garroni and M{\"u}ller (SIAM J Math Anal 36(6):1943--1964, 2005, Arch Ration Mech Anal 181(3):535--578, 2006). Our main result shows that the gradient flows of these {\$}{\$}{\{}{\backslash}Gamma{\}}{\$}{\$}$\Gamma$-convergent energy functionals do not approach the gradient flow of the limiting energy. Indeed, the gradient flow dynamics remains a physically reasonable model in the case of non-monotone loading. Our proofs rely on the construction of explicit sub- and super-solutions to a fractional Allen--Cahn equation on a flat torus or in the plane, with Dirichlet data on a union of small discs. The presence of these obstacles leads to an additional friction in the viscous evolution which appears as a stored energy in the {\$}{\$}{\{}{\backslash}Gamma{\}}{\$}{\$}$\Gamma$-limit, but it does not act as a driving force. Extensions to related models with soft pinning and non-viscous evolutions are also discussed. In terms of physics, our results explain how in this phase field model the presence of forest dislocations still allows for plastic as opposed to only elastic deformation.},
  author = {Dondl, Patrick W. and Kurzke, Matthias W. and Wojtowytsch, Stephan},
  date-added = {2018-10-09 15:25:35 +0200},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1007/s00205-018-1317-2},
  eprint = {1707.07515},
  issn = {1432-0673},
  journal = {Archive for Rational Mechanics and Analysis},
  keywords = {Article},
  title = {The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Plastic Slip},
  year = {2018},
  bdsk-url-1 = {https://doi.org/10.1007/s00205-018-1317-2}
}
@inproceedings{Dondl_07c,
  author = {Dondl, Patrick W.},
  booktitle = {Oberwolfach Reports},
  date-added = {2016-09-26 10:54:59 +0000},
  date-modified = {2018-10-26 17:16:45 +0200},
  doi = {10.4171/OWR/2007/11},
  editor = {Dal {M}aso, Gianni and Francfort, Gilles and Mielke, Alexander and Roub{\'\i}{\v{c}}ek, Toma{\'s}},
  keywords = {Other},
  number = {1},
  pages = {608--610},
  publisher = {EMS Publishing House},
  title = {Evolution of martensitic phase boundaries in heterogeneous media},
  volume = {4},
  year = {2007},
  bdsk-url-1 = {http://dx.doi.org/10.4171/OWR/2007/11}
}
@incollection{Dondl_13a,
  author = {Dondl, Patrick W. and Reina, Celia},
  booktitle = {Oberwolfach Reports},
  date-added = {2016-09-26 10:50:46 +0000},
  date-modified = {2018-10-26 17:16:32 +0200},
  doi = {10.4171/OWR/2013/54},
  keywords = {Other},
  number = {4},
  publisher = {EMS Publishing House},
  title = {Mini-Workshop: Inelastic and Non-equilibrium Material Behavior: from Atomistic Structure to Macroscopic Constitutive Relations},
  volume = {10},
  year = {2013},
  bdsk-url-1 = {http://dx.doi.org/10.4171/OWR/2013/54}
}
@mastersthesis{Dondl_02a,
  author = {Dondl, Patrick W.},
  date-added = {2016-09-25 20:32:35 +0000},
  date-modified = {2018-10-26 17:16:07 +0200},
  keywords = {Theses},
  pdf = {Dondl - Diplomarbeit.pdf},
  school = {Technische Universit{\"a}t M{\"u}nchen},
  title = {Modeling and Analysis of Non-Diffusive Structural Phase Transitions in Crystals},
  year = {2002}
}
@article{Dondl_18g,
  author = {Anguige, Keith and Dondl, Patrick and Kru\v{z}\'{i}k, Martin},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1002/zamm.201700032},
  eprint = {1701.01033},
  fjournal = {ZAMM. Zeitschrift f\"{u}r Angewandte Mathematik und Mechanik. Journal of Applied Mathematics and Mechanics},
  issn = {0044-2267},
  journal = {ZAMM Z. Angew. Math. Mech.},
  keywords = {Article},
  mrclass = {74G65 (49Q12 74G25 74N15)},
  mrnumber = {3779412},
  mrreviewer = {Vito Crismale},
  number = {3},
  pages = {431--447},
  title = {On the existence of minimisers for strain-gradient single-crystal plasticity},
  volume = {98},
  year = {2018},
  bdsk-url-1 = {https://doi.org/10.1002/zamm.201700032}
}
@article{Dondl_17d,
  author = {Dondl, Patrick W. and Dorey, Patrick and R\"{o}sler, Frank},
  date-modified = {2018-10-26 23:25:41 +0200},
  doi = {10.1093/amrx/abw011},
  eprint = {1505.05719},
  fjournal = {Applied Mathematics Research Express. AMRX},
  issn = {1687-1200},
  journal = {Appl. Math. Res. Express. AMRX},
  keywords = {Article},
  mrclass = {35J10 (35P05 47A10)},
  mrnumber = {3749117},
  number = {2},
  pages = {271--296},
  title = {A bound on the pseudospectrum for a class of non-normal {S}chr\"{o}dinger operators},
  year = {2017},
  bdsk-url-1 = {https://doi.org/10.1093/amrx/abw011}
}
@article{Dondl_17b,
  author = {Dondl, Patrick W. and Wojtowytsch, Stephan},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1007/s00526-017-1178-9},
  eprint = {1512.08641},
  fjournal = {Calculus of Variations and Partial Differential Equations},
  issn = {0944-2669},
  journal = {Calc. Var. Partial Differential Equations},
  keywords = {Article},
  mrclass = {49Q20 (35B25 35B65 35J20 35J35 49N60 49Q10)},
  mrnumber = {3659639},
  mrreviewer = {Giovanni Pisante},
  number = {4},
  pages = {Art. 90, 22},
  title = {Uniform regularity and convergence of phase-fields for {W}illmore's energy},
  volume = {56},
  year = {2017},
  bdsk-url-1 = {https://doi.org/10.1007/s00526-017-1178-9}
}
@article{Dondl_17c,
  author = {Dondl, Patrick W. and Scheutzow, Michael},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1214/17-AAP1279},
  eprint = {1407.7379},
  fjournal = {The Annals of Applied Probability},
  issn = {1050-5164},
  journal = {Ann. Appl. Probab.},
  keywords = {Article},
  mrclass = {60K37 (34F05 60H10)},
  mrnumber = {3719956},
  number = {5},
  pages = {3189--3200},
  title = {Ballistic and sub-ballistic motion of interfaces in a field of random obstacles},
  volume = {27},
  year = {2017},
  bdsk-url-1 = {https://doi.org/10.1214/17-AAP1279}
}
@article{Dondl_17a,
  author = {Dondl, Patrick W. and Lemenant, Antoine and Wojtowytsch, Stephan},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1007/s00205-016-1043-6},
  eprint = {1507.01856},
  fjournal = {Archive for Rational Mechanics and Analysis},
  issn = {0003-9527},
  journal = {Arch. Ration. Mech. Anal.},
  keywords = {Article},
  mrclass = {74G65 (49J45 53Z05)},
  mrnumber = {3590663},
  mrreviewer = {Carolin Kreisbeck},
  number = {2},
  pages = {693--736},
  title = {Phase field models for thin elastic structures with topological constraint},
  volume = {223},
  year = {2017},
  bdsk-url-1 = {https://doi.org/10.1007/s00205-016-1043-6}
}
@article{Dondl_07d,
  abstract = {In this article, we study the role of defects in the quasistatic evolution of a martensitic phase boundary. The formulation of the model gives rise to a nonlocal free boundary problem, for which we present an implicit finite-time discretization. For an approximate model, assuming a nearly flat interface, we show that the phase boundary exhibits a sick-slip behavior in the presence of a heterogeneous environment, thus leading to a transition from viscous kinetics to rate-independent behavior. ({\^A}{\copyright} 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)},
  author = {Dondl, Patrick W. and Bhattacharya, Kaushik},
  date-added = {2016-09-25 20:23:16 +0000},
  date-modified = {2018-10-26 23:20:45 +0200},
  doi = {10.1002/pamm.200701003},
  issn = {1617-7061},
  journal = {PAMM},
  keywords = {Other},
  number = {1},
  pages = {1151207--1151208},
  publisher = {WILEY-VCH Verlag},
  title = {The effect of precipitates on the evolution of a martensitic phase boundary},
  volume = {7},
  year = {2007},
  bdsk-url-1 = {http://dx.doi.org/10.1002/pamm.200701003}
}
@inproceedings{Dondl_15d,
  abstract = {We consider a variational formulation of gradient elasto-plasticity, as they arise in the incremental formulation of the plastic evolution problem, subject to a class of single-slip side conditions. Such side conditions typically render the associated boundary-value problems non-convex. We first show that, for a large class of plastic deformations, a given single-slip condition (specification of Burgers' vectors and slip planes) can be relaxed by introducing a lamination microstructure. This yields a relaxed side condition which allows for arbitrary slip in a prescribed family of slip planes. This relaxed model can be thought of as an aid to simulating macroscopic plastic behavior without the need to resolve arbitrarily fine spatial scales. We also discuss issues of existence of solutions for the relaxed model.},
  author = {Dondl, Patrick W. and Anguige, Keith},
  booktitle = {Material Forming ESAFORM 2015},
  date-added = {2016-09-25 20:21:51 +0000},
  date-modified = {2018-10-26 17:16:45 +0200},
  doi = {10.4028/www.scientific.net/KEM.651-653.963},
  keywords = {Other},
  pages = {963--968},
  publisher = {Trans Tech Publications},
  series = {Key Engineering Materials},
  title = {Relaxation of the Non-Convex, Incremental Energy-Minimization Problem in Single-Slip Strain-Gradient Plasticity},
  volume = {651},
  year = {2015},
  bdsk-url-1 = {http://dx.doi.org/10.4028/www.scientific.net/KEM.651-653.963}
}
@article{Dondl_09b,
  author = {Dondl, Patrick W. and Hormann, Kai and Zimmer, Johannes},
  date-added = {2016-09-25 20:19:34 +0000},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1103/PhysRevB.79.104114},
  issue = {10},
  journal = {Phys. Rev. B},
  keywords = {Article},
  numpages = {12},
  pages = {104114},
  pdf = {Dondl - Transformation Paths.pdf},
  publisher = {American Physical Society},
  title = {Modeling transformation paths of multiphase materials: The triple point of zirconia},
  volume = {79},
  year = {2009},
  bdsk-url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.79.104114},
  bdsk-url-2 = {http://dx.doi.org/10.1103/PhysRevB.79.104114}
}
@article{Dondl_09a,
  abstract = {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 microstructure consisting of confined areas in the sample with rotated lattice. Digital image correlation allows us to exactly determine the macroscopic state of deformation of the sample. This data can be used as a side condition to calculate the lamination parameters from the theory of kinematically compatible lamination of separate material regions, each deforming in single slip. The parameters given by the theory agree with the measured properties, i.e. a lattice rotation of 3{\^A}$\,^{\circ}$ and a lamination normal rotated 7{\^A}$\,^{\circ}$ counterclockwise from a {\~a}€ˆ111{\~a}€‰ direction. },
  author = {Olga Dmitrieva and Patrick W. Dondl and Stefan M\"{u}ller and Dierk Raabe},
  date-added = {2016-09-25 20:16:56 +0000},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {http://dx.doi.org/10.1016/j.actamat.2009.03.035},
  issn = {1359-6454},
  journal = {Acta Materialia},
  keywords = {Article},
  number = {12},
  pages = {3439 - 3449},
  pdf = {Dondl - Lamination.pdf},
  title = {Lamination microstructure in shear deformed copper single crystals},
  volume = {57},
  year = {2009},
  bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S1359645409001943},
  bdsk-url-2 = {http://dx.doi.org/10.1016/j.actamat.2009.03.035}
}
@article{Dondl_14a,
  abstract = {We consider the variational formulation of both geometrically linear and geometrically nonlinear elasto-plasticity subject to a class of hard single-slip conditions. Such side conditions typically render the associated boundary-value problems non-convex. We show that, for a large class of non-smooth plastic distortions, a given single-slip condition (specification of Burgers vectors) can be relaxed by introducing a microstructure through a two-stage process of mollification and lamination. The relaxed model can be thought of as an aid to simulating macroscopic plastic behaviour without the need to resolve arbitrarily fine spatial scales.},
  author = {Anguige, Keith and Dondl, Patrick W.},
  date-added = {2016-09-25 20:12:08 +0000},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1098/rspa.2014.0098},
  eprint = {1402.0114},
  issn = {1364-5021},
  journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences},
  keywords = {Article},
  number = {2169},
  publisher = {The Royal Society},
  title = {Relaxation of the single-slip condition in strain-gradient plasticity},
  volume = {470},
  year = {2014},
  bdsk-url-1 = {http://rspa.royalsocietypublishing.org/content/470/2169/20140098},
  bdsk-url-2 = {http://dx.doi.org/10.1098/rspa.2014.0098}
}
@article{Dondl_16b,
  author = {Dondl, Patrick W. and Bhattacharya, Kaushik},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.4171/IFB/358},
  eprint = {1206.2578},
  fjournal = {Interfaces and Free Boundaries. Mathematical Analysis, Computation and Applications},
  issn = {1463-9963},
  journal = {Interfaces Free Bound.},
  keywords = {Article},
  mrclass = {74Q15 (35B27 35R11 35R35 74A50)},
  mrnumber = {3511342},
  number = {1},
  pages = {91--113},
  title = {Effective behavior of an interface propagating through a periodic elastic medium},
  volume = {18},
  year = {2016},
  bdsk-url-1 = {http://dx.doi.org/10.4171/IFB/358}
}
@article{Dondl_16a,
  author = {Dondl, Patrick and Heeren, Behrend and Rumpf, Martin},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1016/j.crma.2016.03.013},
  eprint = {1512.06620},
  fjournal = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
  issn = {1631-073X},
  journal = {C. R. Math. Acad. Sci. Paris},
  keywords = {Article},
  mrclass = {74N15},
  mrnumber = {3494336},
  number = {6},
  pages = {639--644},
  title = {Optimization of the branching pattern in coherent phase transitions},
  volume = {354},
  year = {2016},
  bdsk-url-1 = {http://dx.doi.org/10.1016/j.crma.2016.03.013}
}
@incollection{Dondl_15c,
  author = {Dmitrieva, Olga and Raabe, Dierk and M{\"u}ller, Stefan and Dondl, Patrick W.},
  booktitle = {Analysis and computation of microstructure in finite plasticity},
  date-modified = {2018-10-26 17:16:45 +0200},
  doi = {10.1007/978-3-319-18242-1_8},
  keywords = {Other},
  mrclass = {74A60 (74Cxx)},
  mrnumber = {3381466},
  pages = {205--218},
  publisher = {Springer, Cham},
  series = {Lect. Notes Appl. Comput. Mech.},
  title = {Microstructure in plasticity, a comparison between theory and experiment},
  volume = {78},
  year = {2015},
  bdsk-url-1 = {http://dx.doi.org/10.1007/978-3-319-18242-1_8}
}
@incollection{Dondl_15b,
  author = {Anguige, Keith and Dondl, Patrick W.},
  booktitle = {Analysis and computation of microstructure in finite plasticity},
  date-modified = {2018-10-26 17:16:45 +0200},
  doi = {10.1007/978-3-319-18242-1_6},
  keywords = {Other},
  mrclass = {74C05 (74G65)},
  mrnumber = {3381464},
  pages = {157--173},
  publisher = {Springer, Cham},
  series = {Lect. Notes Appl. Comput. Mech.},
  title = {Energy estimates, relaxation, and existence for strain-gradient plasticity with cross-hardening},
  volume = {78},
  year = {2015},
  bdsk-url-1 = {http://dx.doi.org/10.1007/978-3-319-18242-1_6}
}
@article{Dondl_15a,
  author = {Dondl, Patrick W. and Scheutzow, Michael and Throm, Sebastian},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1017/S0308210512001291},
  eprint = {1201.4836},
  fjournal = {Proceedings of the Royal Society of Edinburgh. Section A. Mathematics},
  issn = {0308-2105},
  journal = {Proc. Roy. Soc. Edinburgh Sect. A},
  keywords = {Article},
  mrclass = {35R11 (35Q74 60K37 74B20)},
  mrnumber = {3371564},
  number = {3},
  pages = {481--512},
  title = {Pinning of interfaces in a random elastic medium and logarithmic lattice embeddings in percolation},
  volume = {145},
  year = {2015},
  bdsk-url-1 = {http://dx.doi.org/10.1017/S0308210512001291}
}
@article{Dondl_14c,
  author = {Anguige, Keith and Dondl, Patrick},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1007/s00033-013-0379-0},
  eprint = {1304.7377},
  fjournal = {Zeitschrift f\"ur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Math\'ematiques et de Physique Appliqu\'ees},
  issn = {0044-2275},
  journal = {Z. Angew. Math. Phys.},
  keywords = {Article},
  mrclass = {74C05 (35J50 35J57 49S05 74N05)},
  mrnumber = {3263154},
  number = {5},
  pages = {1011--1030},
  title = {Optimal energy scaling for a shear experiment in single-crystal plasticity with cross-hardening},
  volume = {65},
  year = {2014},
  bdsk-url-1 = {http://dx.doi.org/10.1007/s00033-013-0379-0}
}
@article{Dondl_14b,
  author = {Dondl, Patrick W. and Mugnai, Luca and R{\"o}ger, Matthias},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1137/130921994},
  eprint = {1305.5054},
  fjournal = {SIAM Journal on Mathematical Analysis},
  issn = {0036-1410},
  journal = {SIAM J. Math. Anal.},
  keywords = {Article},
  mrclass = {49Q10 (53A10)},
  mrnumber = {3196943},
  mrreviewer = {Vladimir V. Kobelev},
  number = {2},
  pages = {1610--1632},
  title = {A phase field model for the optimization of the {W}illmore energy in the class of connected surfaces},
  volume = {46},
  year = {2014},
  bdsk-url-1 = {http://dx.doi.org/10.1137/130921994}
}
@article{Dondl_12a,
  author = {Dondl, Patrick W. and Scheutzow, Michael},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.3934/nhm.2012.7.137},
  eprint = {1102.5691},
  fjournal = {Networks and Heterogeneous Media},
  issn = {1556-1801},
  journal = {Netw. Heterog. Media},
  keywords = {Article},
  mrclass = {35K58 (35B40 35R60 60G60 60H25 60H30)},
  mrnumber = {2908614},
  mrreviewer = {Alexander A. Pankov},
  number = {1},
  pages = {137--150},
  title = {Positive speed of propagation in a semilinear parabolic interface model with unbounded random coefficients},
  volume = {7},
  year = {2012},
  bdsk-url-1 = {http://dx.doi.org/10.3934/nhm.2012.7.137}
}
@article{Dondl_11c,
  author = {Dondl, Patrick W. and Mugnai, Luca and R{\"o}ger, Matthias},
  coden = {SMJMAP},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1137/100805339},
  eprint = {1005.3668},
  fjournal = {SIAM Journal on Applied Mathematics},
  issn = {0036-1399},
  journal = {SIAM J. Appl. Math.},
  keywords = {Article},
  mrclass = {49Q10 (35R35 49J52 74G65)},
  mrnumber = {2873265},
  mrreviewer = {Andrzej M. My{\'s}li{\'n}ski},
  number = {6},
  pages = {2205--2226},
  title = {Confined elastic curves},
  volume = {71},
  year = {2011},
  bdsk-url-1 = {http://dx.doi.org/10.1137/100805339}
}
@article{Dondl_11a,
  author = {Dondl, Patrick W.},
  date-modified = {2018-11-24 21:36:14 +0100},
  doi = {10.1002/gamm.201110019},
  fjournal = {GAMM-Mitteilungen},
  issn = {0936-7195},
  journal = {GAMM-Mitt.},
  keywords = {Article},
  mrclass = {74N20 (35Q74 65K10)},
  mrnumber = {2843983},
  mrreviewer = {Xiaofeng Ren},
  number = {1},
  pages = {118--123},
  pdf = {Dondl - Numerical and Analytical.pdf},
  title = {Numerical and analytical aspects of the pinning of martensitic phase boundaries},
  volume = {34},
  year = {2011},
  bdsk-url-1 = {http://dx.doi.org/10.1002/gamm.201110019}
}
@article{Dondl_11b,
  author = {Dirr, Nicolas and Dondl, Patrick W. and Scheutzow, Michael},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.4171/IFB/265},
  eprint = {0911.4254},
  fjournal = {Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation},
  issn = {1463-9963},
  journal = {Interfaces Free Bound.},
  keywords = {Article},
  mrclass = {35R60 (35K15 35K55 74A40 74N20)},
  mrnumber = {2846018},
  number = {3},
  pages = {411--421},
  title = {Pinning of interfaces in random media},
  volume = {13},
  year = {2011},
  bdsk-url-1 = {http://dx.doi.org/10.4171/IFB/265}
}
@article{Dondl_10b,
  author = {Dondl, Patrick W. and Bhattacharya, Kaushik},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1007/s00205-009-0286-x},
  fjournal = {Archive for Rational Mechanics and Analysis},
  issn = {0003-9527},
  journal = {Arch. Ration. Mech. Anal.},
  keywords = {Article},
  mrclass = {74N05 (74E15 74G25 74G65)},
  mrnumber = {2660520},
  number = {2},
  pages = {599--617},
  pdf = {Dondl - Sharp interface Model.pdf},
  title = {A sharp interface model for the propagation of martensitic phase boundaries},
  volume = {197},
  year = {2010},
  bdsk-url-1 = {http://dx.doi.org/10.1007/s00205-009-0286-x}
}
@article{Dondl_10a,
  author = {Dirr, Nicolas and Dondl, Patrick W. and Grimmett, Geoffrey R. and Holroyd, Alexander E. and Scheutzow, Michael},
  date-modified = {2022-10-06 11:34:59 +0200},
  doi = {10.1214/ECP.v15-1521},
  eprint = {0911.3384},
  fjournal = {Electronic Communications in Probability},
  issn = {1083-589X},
  journal = {Electron. Commun. Probab.},
  keywords = {Article},
  mrclass = {60K35 (82B20 82B43)},
  mrnumber = {2581044},
  mrreviewer = {Aernout C. D. van Enter},
  pages = {14--21},
  title = {Lipschitz percolation},
  volume = {15},
  year = {2010},
  bdsk-url-1 = {http://dx.doi.org/10.1214/ECP.v15-1521}
}
@phdthesis{Dondl_07b,
  author = {Dondl, Patrick Werner},
  date-modified = {2018-10-26 23:15:36 +0200},
  keywords = {Theses},
  mrclass = {Thesis},
  mrnumber = {3078547},
  pages = {94},
  school = {California Institute of Technology},
  title = {Structure and evolution of martensitic phase boundaries},
  url = {http://resolver.caltech.edu/CaltechETD:etd-05292007-211950},
  year = {2007},
  bdsk-url-1 = {http://resolver.caltech.edu/CaltechETD:etd-05292007-211950}
}
@article{Dondl_07a,
  author = {Dondl, Patrick W. and Shen, Ching-Ping and Bhattacharya, Kaushik},
  coden = {IJNMBH},
  date-modified = {2018-10-26 17:15:09 +0200},
  doi = {10.1002/nme.2005},
  fjournal = {International Journal for Numerical Methods in Engineering},
  issn = {0029-5981},
  journal = {Internat. J. Numer. Methods Engrg.},
  keywords = {Article},
  mrclass = {74N99 (74G15 74K35 74S05)},
  mrnumber = {2353133},
  number = {1},
  pages = {72--94},
  pdf = {Dondl - Subdivision.pdf},
  title = {Computational analysis of martensitic thin films using subdivision surfaces},
  volume = {72},
  year = {2007},
  bdsk-url-1 = {http://dx.doi.org/10.1002/nme.2005}
}
@article{Dondl_04a,
  author = {Dondl, Patrick W. and Zimmer, Johannes},
  coden = {JMPSA8},
  date-modified = {2018-10-26 17:15:00 +0200},
  doi = {10.1016/j.jmps.2004.03.001},
  fjournal = {Journal of the Mechanics and Physics of Solids},
  issn = {0022-5096},
  journal = {J. Mech. Phys. Solids},
  keywords = {Article},
  mrclass = {74N15 (74S05)},
  mrnumber = {2085646},
  number = {9},
  pages = {2057--2077},
  pdf = {Dondl - Triple Point Zirconia.pdf},
  title = {Modeling and simulation of martensitic phase transitions with a triple point},
  volume = {52},
  year = {2004},
  bdsk-url-1 = {http://dx.doi.org/10.1016/j.jmps.2004.03.001}
}