18 citations · 40 across the 10 of their papers we have counts for
10 papers
On surface energies in scaling laws for singular perturbation problems for martensitic phase transitions
Angkana Rüland, Camillo Tissot, Antonio Tribuzio +1
The objective of this article is to compare different surface energies for multi-well singular perturbation problems associated with martensitic phase transformations involving hig…
Second-order asymptotics of fractional Gagliardo seminorms as and convergence of the associated gradient flows
Andrea Kubin, Valerio Pagliari, Antonio Tribuzio
We study the second-order asymptotic expansion of the -fractional Gagliardo seminorm as in terms of a higher order nonlocal functional. We prove a Mosco-convergence re…
On a -Structure in Geometrically Linearized Elasticity: Qualitative and Quantitative Analysis and Numerical Simulations
Roman Indergand, Dennis Kochmann, Angkana Rüland +2
We study the rigidity properties of the -structure for the symmetrized gradient from \cite{BFJK94} qualitatively, quantitatively and numerically. More precisely, we complement…
On the Effect of Geometry on Scaling Laws for a Class of Martensitic Phase Transformations
Janusz Ginster, Angkana Rüland, Antonio Tribuzio +1
We study scaling laws for singular perturbation problems associated with a class of two-dimensional martensitic phase transformations and deduce a domain dependence of the scaling…
Energy barriers for boundary nucleation in a two-well model without gauge invariance
Antonio Tribuzio, Konstantinos Zemas
We study energy scaling laws for a simplified, singularly perturbed, double-well nucleation problem confined in a half-space, in the absence of gauge invariance and for an inclusio…
On Scaling Properties for a Class of Two-Well Problems for Higher Order Homogeneous Linear Differential Operators
Bogdan Raiţă, Angkana Rüland, Camillo Tissot +1
We study the scaling behaviour of a class of compatible two-well problems for higher order, homogeneous linear differential operators. To this end, we first deduce general lower sc…
On the Scaling of the Cubic-to-Tetragonal Phase Transformation with Displacement Boundary Conditions
Angkana Rüland, Antonio Tribuzio
We provide (upper and lower) scaling bounds for a singular perturbation model for the cubic-to-tetragonal phase transformation with (partial) displacement boundary data. We illustr…
On Scaling Laws for Multi-Well Nucleation Problems without Gauge Invariances
Angkana Rüland, Antonio Tribuzio
In this article we study scaling laws for simplified multi-well nucleation problems without gauge invariances which are motivated by models for shape-memory alloys. Seeking to expl…
On the Energy Scaling Behaviour of Singular Perturbation Models with Prescribed Dirichlet Data Involving Higher Order Laminates
Angkana Rüland, Antonio Tribuzio
Motivated by complex microstructures in the modelling of shape-memory alloys and by rigidity and flexibility considerations for the associated differential inclusions, in this arti…
On the Energy Scaling Behaviour of a Singularly Perturbed Tartar Square
Angkana Rüland, Antonio Tribuzio
In this article we derive an (almost) optimal scaling law for a singular perturbation problem associated with the Tartar square. As in \cite{W97, C99}, our upper bound quantifies t…