Preprints - IAM Publications


	2018 Sergio Conti, Stefan Müller and Michael Ortiz Data-driven problems in elasticity Arch. Ration. Mech. Anal., 229: 79-123 2018 10.1007/s00205-017-1214-0

	Peter Gladbach, Eva Kopfer and Jan Maas Scaling limits of discrete optimal transport arxiv e-print 1809.01092 2018 https://arxiv.org/abs/1809.01092

	Jani Lukkarinen, Mattheo Marcozzi and Alessia Nota Summability of connected correlation functions of coupled lattice fields J. Stat. Phys., 171 (2): 189-206 2018 https://link.springer.com/article/10.1007/s10955-018-2000-6

	Muhittin Mungan and M. Mert Terzi The structure of state transition graphs in hysteresis models with return point memory. I. General Theory 2018 https://arxiv.org/abs/1802.03096

	2017 David Bourne, Sergio Conti and Stefan Müller Energy bounds for a compressed elastic film on a substrate J. Nonlinear Science, 27: 453-494 2017 10.1007/s00332-016-9339-0 Abstract: We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum value of a suitable energy functional. The energy consists of two parts, describing the two main physical effects. The first part represents the elastic energy of the film, which is approximated using the von Kármán plate theory. The second part represents the fracture or delamination energy, which is approximated using the Griffith model of fracture. A simpler model containing the first term alone was previously studied with similar methods by several authors, assuming that the delaminated region is fixed. We include the fracture term, transforming the elastic minimization into a free-boundary problem, and opening the way for patterns which result from the interplay of elasticity and delamination. After rescaling, the energy depends on only two parameters: the rescaled film thickness, $σ$, and a measure of the bonding strength between the film and substrate, $γ$. We prove upper bounds on the minimum energy of the form $σ^a γ^b$ and find that there are four different parameter regimes corresponding to different values of $a$ and $b$ and to different folding patterns of the film. In some cases the upper bounds are attained by self-similar folding patterns as observed in experiments. Moreover, for two of the four parameter regimes we prove matching, optimal lower bounds.

	Sergio Conti, Adriana Garroni and Stefan Müller Homogenization of vector-valued partition problems and dislocation cell structures in the plane Boll. Unione Mat. Ital., 10(1): 3--17 2017 10.1007/s40574-016-0083-z

	Jan Maas, Martin Rumpf and Stefan Simon Transport based image morphing with intensity modulation In Proc. of International Conference on Scale Space and Variational Methods in Computer Vision Publisher: Springer, Cham 2017 http://dx.doi.org/10.1007/978-3-319-58771-4_45

	Stefan Müller and Florian Schweiger Estimates for the Green's function of the discrete bilaplacian in dimensions 2 and 3 arXiv e-prints: arXiv:1712.02587 2017 https://ui.adsabs.harvard.edu/abs/2017arXiv171202587M

	2016 Stefan Adams, Roman Kotecký and Stefan Müller Strict Convexity of the Surface Tension for Non-convex Potentials 2016 http://arxiv.org/abs/1606.09541v1

	Sergio Conti, Adriana Garroni and Stefan Müller Dislocation microstructures and strain-gradient plasticity with one active slip plane J. Mech. Phys. Solids, 93: 240-251 2016 10.1016/j.jmps.2015.12.008

	Jan Maas, Martin Rumpf and Stefan Simon Generalized optimal transport with singular sources 2016 http://arxiv.org/abs/1607.01186

	Patrick Müller Path large deviations for interacting diffusions with local mean-field interactions 2016 http://arxiv.org/abs/1512.05323 Abstract: We consider a system of Nd spins, with a local mean field type interaction. Each spin has a fixed spacial position on the torus Td and a spin value in R that evolves according to a space dependent Langevin dynamic. The interaction between two spins depends on their spacial distance. We investigate the path large deviation principle from the hydrodynamic (or local mean field McKean-Vlasov) limit and characterise the rate function, for both the space dependent empirical process and the space dependent empirical measure of the paths. To this end, we generalize an approach of Dawson and G\"artner. By the space dependency, this requires new ingredients compared to mean field type interactions. Moreover, we prove the large deviation principle by using second approach. This requires a generalisation of Varadhan's lemma to nowhere continuous functions.

	2015 Anton Bovier and Hannah Mayer A conditional strong large deviation result and a functional central limit theorem for the rate function ALEA Lat. Am. J. Probab. Math. Stat., 12(1): 533--550 2015 http://alea.impa.br/articles/v12/12-21.pdf

	Sergio Conti, Adriana Garroni and Annalisa Massaccesi Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity Calc. Var. PDE, 54(2): 1847-1874 2015 http://dx.doi.org/10.1007/s00526-015-0846-x Abstract: In the modeling of dislocations one is lead naturally to energies concentrated on lines, where the integrand depends on the orientation and on the Burgers vector of the dislocation, which belongs to a discrete lattice. The dislocations may be identified with divergence-free matrix-valued measures supported on curves or with 1-currents with multiplicity in a lattice. In this paper we develop the theory of relaxation for these energies and provide one physically motivated example in which the relaxation for some Burgers vectors is nontrivial and can be determined explicitly. From a technical viewpoint the key ingredients are an approximation and a structure theorem for 1-currents with multiplicity in a lattice.

	Matthias Erbar, Jan Maas and Prasad Tetali Ricci curvature bounds for Bernoulli-Laplace and random transposition models Ann. Fac. Sci. Toulouse Math., ArXiv e-prints, 24(4): 781-800 2015 http://arxiv.org/abs/1409.8605 Abstract: We calculate a Ricci curvature lower bound for some classical examples of random walks, namely, a chain on a slice of the $n$-dimensional discrete cube (the so-called Bernoulli-Laplace model) and the random transposition shuffle of the symmetric group of permutations on $n$ letters.

	Max Fathi and Jan Maas Entropic Ricci curvature bounds for discrete interacting systems Ann. Appl. Prob. 2015 http://arxiv.org/abs/1501.00562

	Aicke Hinrichs, Lev Markhasin, Jens Oettershagen and Tino Ullrich Optimal quasi-Monte Carlo rules on higher order digital nets for the numerical integration of multivariate periodic functions 2015 http://arxiv.org/pdf/1501.01800v1

	Jan Maas and Daniel Matthes Long-time behavior of a finite volume discretization for a fourth order diffusion equation ArXiv e-prints 2015 http://arxiv.org/abs/1505.03178

	2014 Sergio Conti, Georg Dolzmann and Stefan Müller Korn's second inequality and geometric rigidity with mixed growth conditions Calc. Var., 50: 437-454 2014 http://dx.doi.org/10.1007/s00526-013-0641-5 Abstract: Geometric rigidity states that a gradient field which is $ L^p$ -close to the set of proper rotations is necessarily $ L^p$ -close to a fixed rotation, and is one key estimate in nonlinear elasticity. In several applications, as for example in the theory of plasticity, energy densities with mixed growth appear. We show here that geometric rigidity holds also in $ L^p+L^q$ and in $ L^p,q$ interpolation spaces. As a first step we prove the corresponding linear inequality, which generalizes Korn's inequality to these spaces.

	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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