114 citations · 392 across the 27 of their papers we have counts for
34 papers
The energy scaling behaviour of singular perturbation models of staircase type in linearized elasticity for higher order laminates
Lennart Machill, Angkana Rüland
We investigate the scaling behaviour of a singular perturbation model within the geometrically linearized theory of elasticity involving data of higher lamination order. We study b…
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 Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation
Angkana Rüland, Theresa M. Simon
We classify all exactly stress-free solutions to the cubic-to-trigonal phase transformation within the geometrically linearized theory of elasticity, showing that only simple lamin…
On Scaling Properties for Two-State Problems and for a Singularly Perturbed Structure
Bodgan Raiţă, Angkana Rüland, Camillo Tissot
In this article we study quantitative rigidity properties for the compatible and incompatible two-state problems for suitable classes of -free operators and for a sing…
Minimal Energy for Geometrically Nonlinear Elastic Inclusions in Two Dimensions
Ibrokhimbek Akramov, Hans Knüpfer, Martin Kružík +1
We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigat…
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 Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
Giovanni Covi, María Ángeles García-Ferrero, Angkana Rüland
In this article we consider direct and inverse problems for -stable, elliptic nonlocal operators whose kernels are possibly only supported on cones and which satisfy the structu…
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…
Higher Regularity for the Signorini Problem for the Homogeneous, Isotropic Lamé System
Angkana Rüland, Wenhui Shi
In this note we discuss the (higher) regularity properties of the Signorini problem for the homogeneous, isotropic Lamé system. Relying on an observation by Schumann \cite{Schumann…
On instability mechanisms for inverse problems
Herbert Koch, Angkana Rüland, Mikko Salo
In this article we present three robust instability mechanisms for linear and nonlinear inverse problems. All of these are based on strong compression properties (in the sense of s…
On a probabilistic model for martensitic avalanches incorporating mechanical compatibility
Francesco Della Porta, Angkana Rüland, Jamie M Taylor +1
Building on the work in \cite{BCH15,CH18,TIVP17}, in this article we propose and study a simple, geometrically constrained, probabilistic algorithm geared towards capturing some as…
On Single Measurement Stability for the Fractional Calderón Problem
Angkana Rüland
In this short note we prove the logarithmic stability of the single measurement uniqueness result for the fractional Calderón problem which had been derived in \cite{GRSU18}. To th…
On some partial data Calderón type problems with mixed boundary conditions
Giovanni Covi, Angkana Rüland
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible b…
On Two Methods for Quantitative Unique Continuation Results for Some Nonlocal Operators
María Ángeles García-Ferrero, Angkana Rüland
In this article we present two mechanisms for deducing logarithmic quantitative unique continuation bounds for certain classes of integral operators. In our first method, expanding…
Discrete Carleman estimates and three balls inequalities
Aingeru Fernández-Bertolin, Luz Roncal, Angkana Rüland +1
We prove logarithmic convexity estimates and three balls inequalities for discrete magnetic Schrödinger operators. These quantitatively connect the discrete setting in which the un…
On Runge approximation and Lipschitz stability for a finite-dimensional Schrödinger inverse problem
Angkana Rüland, Eva Sincich
In this note we reprove the Lipschitz stability for the inverse problem for the Schrödinger operator with finite-dimensional potentials by using quantitative Runge approximation re…
The Calderón problem for a space-time fractional parabolic equation
Ru-Yu Lai, Yi-Hsuan Lin, Angkana Rüland
In this article we study an inverse problem for the space-time fractional parabolic operator with in any space dimension. We uniquely determine the unk…
Exact constructions in the (non-linear) planar theory of elasticity: From elastic crystals to nematic elastomers
Pierluigi Cesana, Francesco Della Porta, Angkana Rüland +2
In this article we deduce necessary and sufficient conditions for the presence of `Conti-type', highly symmetric, exactly-stress free constructions in the geometrically non-linear,…
The Calderón problem for the fractional Schrödinger equation with drift
Mihajlo Cekić, Yi-Hsuan Lin, Angkana Rüland
We investigate the Calderón problem for the fractional Schrödinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultane…
Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations
Angkana Rüland, Jamie M. Taylor, Christian Zillinger
We study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is two-fold, treating both rigidity and flexibility propert…
Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
Tuhin Ghosh, Angkana Rüland, Mikko Salo +1
We show global uniqueness in the fractional Calderón problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cit…
A Compactness and Structure Result for a Discrete Multi-Well Problem with Symmetry in Arbitrary Dimension
Georgy Kitavtsev, Gianluca Lauteri, Stephan Luckhaus +1
In this note we combine the "spin-argument" from [KLR15] and the -dimensional incompatible, one-well rigidity result from [LL16], in order to infer a new proof for the compactne…