Text icon 'UFR' standing for University of Freiburg
Department of Applied Mathematics
Seal element of the university of freiburg in the shape of a clover

Publications

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Preprints

5 Patrick Dondl and Oliver Suchan. Micro-macro coupling for optimizing scaffold mediated bone regeneration, 2025. bib | arXiv
4 Patrick Dondl, Akwum Onwunta, Ludwig Striet, and Stephan Wojtowytsch. Convex-concave splitting for the Allen-Cahn equation leads to ε2-slow movement of interfaces, 2025. bib | arXiv
3 Patrick Dondl, Martin Heida, and Simone Hermann. Non-local homogenization limits of discrete elastic spring network models with random coefficients, 2024. bib | arXiv
2 Oluwatosin Akande, Patrick Dondl, Kanan Gupta, Akwum Onwunta, and Stephan Wojtowytsch. Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs, 2024. bib | arXiv
1 Patrick Dondl and Marius Zeinhofer. Three dimensional optimization of scaffold porosities for bone tissue engineering, 2021. bib | arXiv

Journal Publications

57 Ludwig Striet, Max D. Mylo, Olga Speck, and Patrick W. Dondl. Modeling abscission of cacti branches. Journal of the Mechanics and Physics of Solids, 196:105965, 2025. bib | DOI
56 Patrick Dondl, Ludwig Striet, and Brian Straughan. Arbitrary precision computation of hydrodynamic stability eigenvalues. Accepted for publication in Proc R Soc A, 2025. bib | arXiv
55 Patrick Dondl and Brian Straughan. Thermal convection in a linearly viscous fluid overlying a bidisperse porous medium. Studies in Applied Mathematics, 154(1):e12799, 2024. bib | DOI | arXiv
54 Patrick Dondl, Alberto Maione, and Steve Wolff-Vorbeck. Multi-material model and shape optimization for bending and torsion of inextensible rods. ESAIM: COCV, 30:50, 2024. bib | DOI | arXiv
53 Patrick Dondl, Coffi Aristide Hounkpe, and Martin Jesenko. Γ-convergence of a discrete kirchhoff rod energy. ESAIM: COCV, 30:53, 2024. bib | DOI | arXiv
52 Patrick Dondl, Yongming Luo, Stefan Neukamm, and Steve Wolff-Vorbeck. Efficient uncertainty quantification for mechanical properties of randomly perturbed elastic rods. Multiscale Modeling & Simulation, 22(4):1267–1325, 2024. bib | DOI | arXiv
51 Luca Courte and Patrick Dondl. Viscosity solutions for doubly nonlinear evolution equations. Appl. Anal., 102(14):3923–3945, 2023. bib | DOI | arXiv
50 Patrick Dondl, Sergio Conti, and Julia Orlik. Variational modeling of paperboard delamination under bending. Mathematics in Engineering, 5(2):1–28, 2023. bib | DOI | arXiv
49 Patrick Dondl, Martin Jesenko, Martin Kružík, and Jan Valdman. Linearization and computation for large-strain viscoelasticity. Mathematics in Engineering, 5(2):1–15, 2023. bib | DOI | arXiv
48 Patrick Dondl and Marius Zeinhofer. Lp(I,Cα(Ω)) regularity for diffusion equations with non-smooth data. Results Math., 78(4):Paper No. 142, 22, 2023. bib | DOI | arXiv
47 Harbir Antil, Patrick W. Dondl, and Ludwig Striet. Analysis of a sinc-Galerkin method for the fractional Laplacian. SIAM Journal on Numerical Analysis, 61(6):2967–2993, 2023. bib | DOI | arXiv
46 Patrick Dondl, Martin Jesenko, and Michael Scheutzow. Infinite pinning. Bulletin of the London Mathematical Society, 54(2):760–771, 2022. bib | DOI | arXiv
45 Patrick Dondl, Patrina S. P. Poh, and Marius Zeinhofer. An efficient model for scaffold-mediated bone regeneration. SIAM Journal on Applied Mathematics, 82(3):924–949, 2022. bib | DOI | arXiv
44 Luca Courte, Patrick Dondl, and Michael Ortiz. A proof of Taylor scaling for curvature-driven dislocation motion through random arrays of obstacles. Arch. Ration. Mech. Anal., 244(2):317–341, 2022. bib | DOI | arXiv
43 Patrick Dondl, Johannes Müller, and Marius Zeinhofer. Uniform convergence guarantees for the deep Ritz method for nonlinear problems. Adv. Contin. Discrete Models, 49, 2022. bib | DOI | arXiv
42 Patrina S. P. Poh, Thomas Lingner, Stefan Kalkhof, Sven Märdian, Jan Baumbach, Patrick Dondl, Georg N. Duda, and Sara Checa. Enabling technologies towards personalization of scaffolds for large bone defect regeneration. Current Opinion in Biotechnology, 74:263–270, 2022. bib | DOI
41 Steve Wolff-Vorbeck, Olga Speck, Max Langer, Thomas Speck, and Patrick W. Dondl. Charting the twist-to-bend ratio of plant axes. Journal of the Royal Society Interface, 19(20220131), 2022. bib | DOI
40 Vanessa Weichselberger, Patrick Dondl, and Anne-Kathrin Classen. Eya-controlled affinity between cell lineages drives tissue self-organization during Drosophila oogenesis. Nature Communications, 13(1):6377, 2022. bib | DOI
39 Patrick Dondl, Martin Jesenko, and Michael Scheutzow. Pinning of interfaces in a random medium with zero mean. Interfaces and Free Boundaries, 23(3):305–321, 2021. bib | DOI | arXiv
38 Harbir Antil, Patrick Dondl, and Ludwig Striet. Approximation of integral fractional Laplacian and fractional PDEs via sinc-basis. SIAM J. Sci. Comput., 43(4):A2897–A2922, 2021. bib | DOI | arXiv
37 Wolfram Georg Nöhring, Jan Grießer, Patrick Dondl, and Lars Pastewka. Surface lattice Green’s functions for high-entropy alloys. Modelling and Simulation in Materials Science and Engineering, 30(1):015007, 2021. bib | DOI | arXiv
36 Patrick Dondl, Matteo Novaga, Stephan Wojtowytsch, and Steve Wolff-Vorbeck. Connected coulomb columns: analysis and numerics. Nonlinearity, 34(9):6120–6139, 2021. bib | DOI | arXiv
35 Steve Wolff-Vorbeck, Olga Speck, Thomas Speck, and Patrick W. Dondl. Influence of structural reinforcements on the twist-to-bend ratio of plant axes: a case study on Carex pendula. Scientific Reports, 11(1):21232, 2021. bib | DOI
34 Patrick Dondl and Stephan Wojtowytsch. Keeping it together: A phase-field version of path-connectedness and its implementation. Journal of Algorithms & Computational Technology, 15, 2021. bib | DOI | arXiv
33 Luca Courte, Patrick Dondl, and Ulisse Stefanelli. Pinning of interfaces by localized dry friction. Journal of Differential Equations, 269(9):7356–7381, 2020. bib | DOI | arXiv
32 Luca Courte, Kaushik Bhattacharya, and Patrick Dondl. Bounds on precipitate hardening of line and surface defects in solids. Zeitschrift für angewandte Mathematik und Physik, 71(3):99, 2020. bib | DOI | arXiv
31 Patrick W. Dondl, Matteo Novaga, Benedikt Wirth, and Stephan Wojtowytsch. A Phase-field Approximation of the Perimeter under a Connectedness Constraint. SIAM J. Math. Anal., 51(5):3902–3920, 2019. bib | DOI | arXiv
30 Patrick Dondl and Martin Jesenko. Threshold phenomenon for homogenized fronts in random elastic media. Discrete and Continuous Dynamical Systems Series S, 2019. bib | DOI | arXiv
29 Patrick Dondl, Patrina S. P. Poh, Martin Rumpf, and Stefan Simon. Simultaneous elastic shape optimization for a domain splitting in bone tissue engineering. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2227):20180718, 2019. bib | DOI | arXiv
28 Patrina S. P. Poh, Dvina Valainis, Kaushik Bhattacharya, Martijn van Griensven, and Patrick Dondl. Optimization of bone scaffold porosity distributions. Scientific Reports, 9(1):9170, 2019. bib | DOI | arXiv
27 Dvina Valainis, Patrick Dondl, Peter Foehr, Rainer Burgkart, Stefan Kalkhof, Georg N Duda, Martijn van Griensven, and Patrina S P Poh. Integrated additive design and manufacturing approach for the bioengineering of bone scaffolds for favorable mechanical and biological properties. Biomedical Materials, 14(6):065002, 2019. bib | DOI
26 Steve Wolff-Vorbeck, Max Langer, Olga Speck, Thomas Speck, and Patrick Dondl. Twist-to-bend ratio: an important selective factor for many rod-shaped biological structures. Scientific Reports, 9(1):17182, 2019. bib | DOI
25 Patrick Dondl, Thomas Frenzel, and Alexander Mielke. A gradient system with a wiggly energy and relaxed EDP-convergence. ESAIM Control Optim. Calc. Var., 25:Art. 68, 45, 2019. bib | DOI | arXiv
24 Patrick W. Dondl and Stephan Wojtowytsch. On the boundary regularity of phase-fields for Willmore’s energy. Proc. Roy. Soc. Edinburgh Sect. A, 149(4):1017–1035, 2019. bib | DOI | arXiv
23 Keith Anguige, Patrick Dondl, and Martin Kružík. On the existence of minimisers for strain-gradient single-crystal plasticity. ZAMM Z. Angew. Math. Mech., 98(3):431–447, 2018. bib | DOI | arXiv
22 Patrick W. Dondl, Matthias W. Kurzke, and Stephan Wojtowytsch. The effect of forest dislocations on the evolution of a phase-field model for plastic slip. Archive for Rational Mechanics and Analysis, 2018. bib | DOI | arXiv
21 Patrick Dondl, Kirill Cherednichenko, and Frank Rösler. Norm-resolvent convergence in perforated domains. Asymptotic Analysis, 110(3–4):163–184, 2018. bib | DOI | arXiv
20 Patrick W. Dondl, Antoine Lemenant, and Stephan Wojtowytsch. Phase field models for thin elastic structures with topological constraint. Arch. Ration. Mech. Anal., 223(2):693–736, 2017. bib | DOI | arXiv
19 Patrick W. Dondl and Michael Scheutzow. Ballistic and sub-ballistic motion of interfaces in a field of random obstacles. Ann. Appl. Probab., 27(5):3189–3200, 2017. bib | DOI | arXiv
18 Patrick W. Dondl and Stephan Wojtowytsch. Uniform regularity and convergence of phase-fields for Willmore’s energy. Calc. Var. Partial Differential Equations, 56(4):Art. 90, 22, 2017. bib | DOI | arXiv
17 Patrick W. Dondl, Patrick Dorey, and Frank Rösler. A bound on the pseudospectrum for a class of non-normal Schrödinger operators. Appl. Math. Res. Express. AMRX, 2017(2):271–296, 2017. bib | DOI | arXiv
16 Patrick Dondl, Behrend Heeren, and Martin Rumpf. Optimization of the branching pattern in coherent phase transitions. C. R. Math. Acad. Sci. Paris, 354(6):639–644, 2016. bib | DOI | arXiv
15 Patrick W. Dondl and Kaushik Bhattacharya. Effective behavior of an interface propagating through a periodic elastic medium. Interfaces Free Bound., 18(1):91–113, 2016. bib | DOI | arXiv
14 Patrick W. Dondl, Michael Scheutzow, and Sebastian Throm. Pinning of interfaces in a random elastic medium and logarithmic lattice embeddings in percolation. Proc. Roy. Soc. Edinburgh Sect. A, 145(3):481–512, 2015. bib | DOI | arXiv
13 Patrick W. Dondl, Luca Mugnai, and Matthias Röger. A phase field model for the optimization of the Willmore energy in the class of connected surfaces. SIAM J. Math. Anal., 46(2):1610–1632, 2014. bib | DOI | arXiv
12 Keith Anguige and Patrick Dondl. Optimal energy scaling for a shear experiment in single-crystal plasticity with cross-hardening. Z. Angew. Math. Phys., 65(5):1011–1030, 2014. bib | DOI | arXiv
11 Keith Anguige and Patrick W. Dondl. Relaxation of the single-slip condition in strain-gradient plasticity. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 470(2169), 2014. bib | DOI | arXiv
10 Patrick W. Dondl and Michael Scheutzow. Positive speed of propagation in a semilinear parabolic interface model with unbounded random coefficients. Netw. Heterog. Media, 7(1):137–150, 2012. bib | DOI | arXiv
9 Nicolas Dirr, Patrick W. Dondl, and Michael Scheutzow. Pinning of interfaces in random media. Interfaces Free Bound., 13(3):411–421, 2011. bib | DOI | arXiv
8 Patrick W. Dondl. Numerical and analytical aspects of the pinning of martensitic phase boundaries. GAMM-Mitt., 34(1):118–123, 2011. bib | DOI | .pdf
7 Patrick W. Dondl, Luca Mugnai, and Matthias Röger. Confined elastic curves. SIAM J. Appl. Math., 71(6):2205–2226, 2011. bib | DOI | arXiv
6 Nicolas Dirr, Patrick W. Dondl, Geoffrey R. Grimmett, Alexander E. Holroyd, and Michael Scheutzow. Lipschitz percolation. Electron. Commun. Probab., 15:14–21, 2010. bib | DOI | arXiv
5 Patrick W. Dondl and Kaushik Bhattacharya. A sharp interface model for the propagation of martensitic phase boundaries. Arch. Ration. Mech. Anal., 197(2):599–617, 2010. bib | DOI | .pdf
4 Olga Dmitrieva, Patrick W. Dondl, Stefan Müller, and Dierk Raabe. Lamination microstructure in shear deformed copper single crystals. Acta Materialia, 57(12):3439 — 3449, 2009. bib | DOI | .pdf
3 Patrick W. Dondl, Kai Hormann, and Johannes Zimmer. Modeling transformation paths of multiphase materials: The triple point of zirconia. Phys. Rev. B, 79:104114, 2009. bib | DOI | .pdf
2 Patrick W. Dondl, Ching-Ping Shen, and Kaushik Bhattacharya. Computational analysis of martensitic thin films using subdivision surfaces. Internat. J. Numer. Methods Engrg., 72(1):72–94, 2007. bib | DOI | .pdf
1 Patrick W. Dondl and Johannes Zimmer. Modeling and simulation of martensitic phase transitions with a triple point. J. Mech. Phys. Solids, 52(9):2057–2077, 2004. bib | DOI | .pdf

Other

10 Aiku. Fried Acid. Multi Culti, 2023. bib | http
9 Patrick Dondl and Marius Zeinhofer. A parameter study on optimal scaffolds in a simple model for bone regeneration. In Paulo R. Fernandes, João Folgado, Carlos Quental, and André Castro, editors, IX International Conference on Computational Bioengineering. Instituto Superior Técnico, Lisbon, 2022. bib | arXiv | .pdf
8 North Coast Limited. North Coast Limited. Rare Wiri Records, 2022. bib | http
7 Schorsch Henderson and Giorgio Spinetti. Yeah! Yeah! Yeah! Rare Wiri Records, 2021. bib | http
6 Keith Anguige and Patrick W. Dondl. Energy estimates, relaxation, and existence for strain-gradient plasticity with cross-hardening. In Analysis and computation of microstructure in finite plasticity, volume 78 of Lect. Notes Appl. Comput. Mech., pages 157–173. Springer, Cham, 2015. bib | DOI
5 Olga Dmitrieva, Dierk Raabe, Stefan Müller, and Patrick W. Dondl. Microstructure in plasticity, a comparison between theory and experiment. In Analysis and computation of microstructure in finite plasticity, volume 78 of Lect. Notes Appl. Comput. Mech., pages 205–218. Springer, Cham, 2015. bib | DOI
4 Patrick W. Dondl and Keith Anguige. Relaxation of the non-convex, incremental energy-minimization problem in single-slip strain-gradient plasticity. In Material Forming ESAFORM 2015, volume 651 of Key Engineering Materials, pages 963–968. Trans Tech Publications, 2015. bib | DOI
3 Patrick W. Dondl and Celia Reina. Mini-workshop: Inelastic and non-equilibrium material behavior: from atomistic structure to macroscopic constitutive relations. In Oberwolfach Reports, volume 10. EMS Publishing House, 2013. bib | DOI
2 Patrick W. Dondl and Kaushik Bhattacharya. The effect of precipitates on the evolution of a martensitic phase boundary. PAMM, 7(1):1151207–1151208, 2007. bib | DOI
1 Patrick W. Dondl. Evolution of martensitic phase boundaries in heterogeneous media. In Gianni Dal Maso, Gilles Francfort, Alexander Mielke, and Tomaś Roubíček, editors, Oberwolfach Reports, volume 4, pages 608–610. EMS Publishing House, 2007. bib | DOI

Theses

2 Patrick Werner Dondl. Structure and evolution of martensitic phase boundaries. PhD thesis, California Institute of Technology, 2007. bib | http
1 Patrick W. Dondl. Modeling and analysis of non-diffusive structural phase transitions in crystals. Master’s thesis, Technische Universität München, 2002. bib | .pdf