10 papers
Stacking faults in the limit of a discrete model for partial edge dislocations
Annika Bach, Marco Cicalese, Adriana Garroni +1
In the limit of vanishing lattice spacing we provide a rigorous variational coarse-graining result for a next-to-nearest neighbor lattice model of a simple crystal. We show that th…
Stochastic homogenization of functionals defined on finite partitions
Annika Bach, Matthias Ruf
We prove a stochastic homogenization result for integral functionals defined on finite partitions assuming the surface tension to be stationary and possibly ergodic. We also consid…
Gradient damage models for heterogeneous materials
Annika Bach, Teresa Esposito, Roberta Marziani +1
In this paper we study the asymptotic behaviour of phase-field functionals of Am brosio and Tortorelli type allowing for small-scale oscillations both in the volume and in the diff…
Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions
Annika Bach, Matthias Ruf
In this paper we derive quantitative estimates in the context of stochastic homogenization for integral functionals defined on finite partitions, where the random surface integrand…
-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals
Annika Bach, Roberta Marziani, Caterina Ida Zeppieri
We study the limit behaviour of singularly-perturbed elliptic functionals of the form \[ \mathcal F_k(u,v)=\int_A v^2\,f_k(x,\nabla u)dx+\frac{1}{\varepsilon_k}\int_A g_k(x,v,\vare…
The antiferromagnetic XY model on the triangular lattice: topological singularities
Annika Bach, Marco Cicalese, Leonard Kreutz +1
We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the two-dimensional triangular lattice in the vortex regime. Within this regime, the spin…
The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling
Annika Bach, Marco Cicalese, Leonard Kreutz +1
We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the two-dimensional triangular lattice. The system is fully frustrated and displays two fa…
Discrete-to-continuum limits of multi-body systems with bulk and surface long-range interactions
Annika Bach, Andrea Braides, Marco Cicalese
We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interact…
Random finite-difference discretizations of the Ambrosio-Tortorelli functional with optimal mesh size
Annika Bach, Marco Cicalese, Matthias Ruf
We propose and analyze a finite-difference discretization of the Ambrosio-Tortorelli functional. It is known that if the discretization is made with respect to an underlying period…
Quantitative analysis of finite-difference approximations of free-discontinuity problems
Annika Bach, Andrea Braides, Caterina Ida Zeppieri
Motivated by applications to image reconstruction, in this paper we analyse a \emph{finite-difference discretisation} of the Ambrosio-Tortorelli functional. Denoted by $\varepsilon…