| 2019Sergio Conti, Martin Lenz, Nora Lüthen, Martin Rumpf and Barbara Zwicknagl
Geometry of martensite needles in shape memory alloys
2019
https://arxiv.org/abs/1912.02274
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| 2018M. Griebel, C. Rieger and B. Zwicknagl
Regularized Kernel-Based Reconstruction in Generalized Besov Spaces
Foundations of Computational Mathematics, 18(2): 459--508 2018
10.1007/s10208-017-9346-z
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| Michael Griebel, Christian Rieger and Peter Zaspel
Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations
2018
https://ins.uni-bonn.de/media/public/publication-media/INSPreprint1813.pdf
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| M. Gubinelli, B. E. Ugurcan and I. Zachhuber
Semilinear evolution equations for the Anderson Hamiltonian in two and three dimensions
ArXiv e-prints 2018
https://arxiv.org/abs/1807.06825
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| Diogo Oliveira e Silva, Christoph Thiele and Pavel Zorin-Kranich
Band-limited maximizers for a Fourier extension inequality on the circle
arXiv e-prints: arXiv:1806.06605 2018
https://ui.adsabs.harvard.edu/abs/2018arXiv180606605S
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| 2017Sergio Conti, Johannes Diermeier and Barbara Zwicknagl
Deformation concentration for martensitic microstructures in the limit of low volume fraction
Calc. Var. PDE, 56: 16 2017
10.1007/s00526-016-1097-1
Abstract: We consider a singularly-perturbed nonconvex energy functional which arises in the study of microstructures in shape memory alloys. The scaling law for the minimal energy predicts a transition from a parameter regime in which uniform structures are favored, to a regime in which the formation of fine patterns is expected. We focus on the transition regime and derive the reduced model in the sense of $Γ$-convergence. The limit functional turns out to be similar to the Mumford-Shah functional with additional constraints on the jump set of admissible functions. One key ingredient in the proof is an approximation result for $SBV^p$ functions whose jump sets have a prescribed orientation. |
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| S. Conti, M. Klar and B. Zwicknagl
Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity
Proc. Roy. Soc. A, 473(2203) 2017
http://rspa.royalsocietypublishing.org/content/473/2203/20170235
Abstract: We consider a partial differential inclusion problem which models stress-free martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory. We show that for specific parameter choices there exist piecewise affine continuous solutions for the square-to-oblique and the hexagonal-to-oblique phase transitions. This suggests that for specific crystallographic parameters the hysteresis of the phase transformation will be particularly small. |
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| Francesco Di Plinio, Shaoming Guo, Christoph Thiele and Pavel Zorin-Kranich
Square functions for bi-Lipschitz maps and directional operators
arXiv e-prints: arXiv:1706.07111 2017
https://ui.adsabs.harvard.edu/abs/2017arXiv170607111D
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| Angkana Rüland, Christian Zillinger and Barbara Zwicknagl
Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int($K^lc$)
2017
https://arxiv.org/abs/1709.02880
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| 2016Sergio Conti and Barbara Zwicknagl
Low volume-fraction microstructures in martensites and crystal plasticity
Math. Models Methods App. Sci.: 1319-1355 2016
10.1142/S0218202516500317
Abstract: We study microstructure formation in two nonconvex singularly-perturbed variational problems from materials science, one modeling austenite-martensite interfaces in shape-memory alloys, the other one slip structures in the plastic deformation of crystals. For both functionals we determine the scaling of the optimal energy in terms of the parameters of the problem, leading to a characterization of the mesoscopic phase diagram. Our results identify the presence of a new phase, which is intermediate between the classical laminar microstructures and branching patterns. The new phase, characterized by partial branching, appears for both problems in the limit of small volume fraction, that is, if one of the variants (or of the slip systems) dominates the picture and the volume fraction of the other one is small. |
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| Angkana Rüland, Christian Zillinger and Barbara Zwicknagl
Higher Sobolev regularity of convex integration solutions in elasticity
2016
https://arxiv.org/abs/1610.02529
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| 2015Peter Bella, Michael Goldman and Barbara Zwicknagl
Study of Island Formation in Epitaxially Strained Films on Unbounded Domains
Arch. for Ration. Mech. and Anal., 218(1): 163-217 2015
http://dx.doi.org/10.1007/s00205-015-0858-x
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| Michael Griebel, Christian Rieger and Barbara Zwicknagl
Multiscale approximation and reproducing kernel Hilbert space methods
SIAM Journal on Numerical Analysis, 53(2): 852-873 2015
http://dx.doi.org/10.1137/130932144
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| Christian Zillinger
Linear inviscid damping for monotone shear flows in a finite periodic channel, boundary effects, blow-up and critical Sobolev regularity
Archive for Rational Mechanics and Analysis 2015
http://link.springer.com/article/10.1007/s00205-016-0991-1
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| 2014Irene Fonseca, Aldo Pratelli and Barbara Zwicknagl
Shapes of Epitaxially Grown Quantum Dots
Archive for Rational Mechanics and Analysis, 214(2): 359-401 2014
http://dx.doi.org/10.1007/s00205-014-0767-4
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| Stefan Müller, Lucia Scardia and Caterina Ida Zeppieri
Geometric rigidity for incompatible fields and an application to strain-gradient plasticity
Indiana Univ. Math. J., 63(5): 1365-1396 2014
http://dx.doi.org/10.1512/iumj.2014.63.5330
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| Marc A. Schweitzer and Albert Ziegenhagel
Dispersion Properties of the Partition of Unity Method & Explicit Dynamics
In M. Griebel and M. A. Schweitzer, editor, Meshfree Methods for Partial Differential Equations VII, Volume 100 of Lecture Notes in Computational Science and Engineering
Chapter 14, page 269-292.
Publisher: Springer International
2014
http://dx.doi.org/10.1007/978-3-319-06898-5_14
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| Christian Zillinger
Linear Inviscid Damping for Monotone Shear Flows
2014
http://arxiv.org/abs/1410.7341
Abstract: In this article, we prove linear stability, scattering and inviscid damping with optimal decay rates for the linearized 2D Euler equations around a large class of strictly monotone shear flows, (U(y),0), in a periodic channel under Sobolev perturbations. Here, we consider the settings of both an infinite periodic channel of period L, TL×R, as well as a finite periodic channel, TL×[0,1], with impermeable walls. The latter setting is shown to not only be technically more challenging, but to exhibit qualitatively different behavior due to boundary effects. |
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| 2013Sven Beuchler, Veronika Pillwein and Sabine Zaglmayr
Sparsity optimized high order finite element functions for $H(\romancurl)$ on tetrahedra
Adv. in Appl. Math., 50(5): 749--769 2013
http://dx.doi.org/10.1016/j.aam.2012.11.004
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| Sven Beuchler, Veronika Pillwein and Sabine Zaglmayr
Fast summation techniques for sparse shape functions in tetrahedral $hp$-FEM
In Domain decomposition methods in science and engineering {XX}, Volume 91 of Lect. Notes Comput. Sci. Eng.
page 511--518.
Publisher: Springer, Heidelberg
2013
http://dx.doi.org/10.1007/978-3-642-35275-1_60
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