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