Related papers: Reconstruction of a fully anisotropic elasticity t…
A method to reconstruct weakly anisotropic inhomogeneous dielectric tensors inside a transparent medium is proposed. The mathematical theory of Integral Geometry is cast into a workable framework which allows the full determination of…
We develop an algorithm for reconstruction of elastic strain fields from their Longitudinal Ray Transform (LRT) in either two or three dimensions. In general, the LRT only determines the solenoidal part of a symmetric tensor field, but…
We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality Ultrasound Modulated…
A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic…
Transient Elastography enables detection and characterization of tissue abnormalities. In this paper we assume that the displacements are modeled by linear isotropic elasticity system and the tissue displacement has been obtained by the…
This paper concerns the reconstruction of a complex-valued anisotropic tensor $\gamma=\sigma+\i\omega\varepsilon$ from knowledge of several internal magnetic fields $H$, where $H$ satisfies the anisotropic Maxwell system on a bounded domain…
We study inverse problems in anisotropic elasticity using tools from algebraic geometry. The singularities of solutions to the elastic wave equation in dimension $n$ with an anisotropic stiffness tensor have propagation kinematics captured…
We present a general, constructive procedure to find the basis for tensors of arbitrary order subject to linear constraints by transforming the problem to that of finding the nullspace of a linear operator. The proposed method utilizes…
A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…
We present a straightforward analytical-numerical methodology for determining polynomially complete and irreducible scalar-valued invariant sets for anisotropic hyperelasticity. By applying the proposed technique, we obtain irreducible…
We derive closed-form solutions for reverberant elastography in anisotropic elastic media by adapting the framework used in electromagnetic theory to treat transverse isotropic materials. Different sample-setup geometries are analyzed,…
We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate…
A fully algebraic approach to reconstructing one-dimensional reflectionless potentials is described. A simple and easily applicable general formula is derived, using the methods of the theory of determinants. In particular, useful…
We consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a…
Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress-strain data, we employ classical representation theory, novel…
We propose an effective geometrical approach to recover the normal form of a given Elasticity tensor, once we know its symmetry class. In other words, we produce a rotation which brings an Elasticity tensor onto its normal form, given its…
We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying…
In this paper, we present an analytic non-iterative approach for recovering a planar isotropic elastic inclusion embedded in an unbounded medium from the elastic moment tensors (EMTs), which are coefficients for the multipole expansion of…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…