Zobrazeno 1 - 10
of 75
pro vyhledávání: '"Bach, Annika"'
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 the $\Gamma$-limit of suitable scaled versions of the model leads to an
Externí odkaz:
http://arxiv.org/abs/2407.03975
Autor:
Bach, Annika, Ruf, Matthias
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 consider the convergence of boundary value problems when we impose a boundar
Externí odkaz:
http://arxiv.org/abs/2303.14024
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 diffuse surface term. The functionals under examination can be interpreted
Externí odkaz:
http://arxiv.org/abs/2205.13966
Autor:
Bach, Annika, Ruf, Matthias
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 is assumed to be stationary. Requiring the integrand to satisfy in ad
Externí odkaz:
http://arxiv.org/abs/2105.13846
We study the limit behaviour of singularly-perturbed elliptic functionals of the form \[ \mathcal F_k(u,v)=\int_A v^2\,f_k(x,\nabla u)\.dx+\frac{1}{\varepsilon_k}\int_A g_k(x,v,\varepsilon_k\nabla v)\.dx\,, \] where $u$ is a vector-valued Sobolev fun
Externí odkaz:
http://arxiv.org/abs/2102.09872
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 system cannot overcome the energetic barrier of chirality transitions,
Externí odkaz:
http://arxiv.org/abs/2011.10445
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 families of ground states distinguished by the chirality of the spin fie
Externí odkaz:
http://arxiv.org/abs/2004.01416
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 interactions between all points of the lattice and we give conditions that ens
Externí odkaz:
http://arxiv.org/abs/1910.00346
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 periodic lattice of spacing $\delta$, the discretized functionals $\Gamma$-c
Externí odkaz:
http://arxiv.org/abs/1902.08437
Motivated by applications to image reconstruction, in this paper we analyse a \emph{finite-difference discretisation} of the Ambrosio-Tortorelli functional. Denoted by $\varepsilon$ the elliptic-approximation parameter and by $\delta$ the discretisat
Externí odkaz:
http://arxiv.org/abs/1807.05346