arXiv research

Paper demonstrates triaxial strain tomography using neutron imaging.

New method reconstructs strain and lattice spacing from neutron data.

New method for sensing non-planar surfaces using ERT.

We study the problem of finding strain-minimising stream surfaces in a divergence-free vector field. These surfaces are generated by motions of seed curves that propagate through the field in a strain minimising manner, i.e., they move without stretching or shrinking, preserving the length of their arbitrary arc. In ge…

Unified framework for strain-gradient plasticity from dislocations.

Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape? Motivated by this concern, we first classify, and quantify, the translational, ro…

The paper proves properties of strain tensors on surfaces with changing Gauss curvature.

Unified theory solves strain compatibility and elasticity of origami metamaterials.

We consider various notions of strains; quantitative measures for the deviation of a linear transformation from an isometry. The main approach, which is motivated by physical applications and follows the work of Patrizio Neff and co-workers , is to select a Riemannian metric on $\text{GL}_n$, and use its induced geodes…

CNN improves frame selection for ultrasound elastography.

Emergenet predicts animal influenza strain emergence, outperforming current methods.

We consider the two logarithmic strain measures\[ω_{\rm iso}=\|\mathrm{dev}_n\log U\|=\|\mathrm{dev}_n\log \sqrt{F^TF}\|\quad\text{ and }\quad ω_{\rm vol}=|\mathrm{tr}(\log U)|=|\mathrm{tr}(\log\sqrt{F^TF})|\,,\]which are isotropic invariants of the Hencky strain tensor $\log U$, and show that they can be uniquely char…

Paper derives formulas for surface variations in shell theory.

We discuss several issues regarding material homogeneity and strain compatibility for materially uniform thin elastic shells from the viewpoint of a 3-dimensional theory, with small thickness, as well as a 2-dimensional Cosserat theory. A relationship between inhomogeneity and incompatibility measures under the two des…

TIER uses extended strain data to improve gravitational wave detection sensitivity.

Model trains passing events on a bridge using multilevel Gaussian process.

Study travel time tomography for transversely isotropic media using modified pseudodifferential calculus.

Summary of tensor tomography proofs on manifolds with boundaries.

Paper addresses travel time tomography stability and statistical inversion.

Physics-informed deep learning approximates strain gradient plasticity solutions.

Symmetries in shell theory lead to multiple deformation possibilities.

Study uses machine learning to solve photoacoustic tomography's inverse problem.

These are lecture notes for the course "Analysis and X-ray tomography". The course is a broad overview of various tools in analysis that can be used to study X-ray tomography. The focus is on tools and ideas, not so much on technical details and minimal assumptions. Only very basic functional analysis is assumed as bac…

Sketch Tomography improves quantum state estimation accuracy.

Deep network improves electrical tomography across multiple frequencies.

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various ki…

The paper develops GPR models for hyperelastic materials, improving accuracy and rotational invariance.

We propose a general strategy to derive null-homotopy operators for differential complexes based on the Bernstein-Gelfand-Gelfand (BGG) construction and properties of the de Rham complex. Focusing on the elasticity complex, we derive path integral operators $\mathscr{P}$ for elasticity satisfying $\mathscr{D}\mathscr{P…

TANNs integrate thermodynamics into ANN models for accurate, consistent predictions.

Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is developed to analytically predict the equilibrium deformed helical shape of an initiall…

A new method speeds up quantum state estimation.

Improved computed tomography reconstruction with deep learning and deep image prior.

Gradient flows for knot energies ensure long-term existence of knotted loops.

A new method quantifies uncertainty in brain injury simulations.

Deep learning speeds up gravitational wave analysis.

We develop a 2D travel time tomography method which regularizes the inversion by modeling groups of slowness pixels from discrete slowness maps, called patches, as sparse linear combinations of atoms from a dictionary. We propose to use dictionary learning during the inversion to adapt dictionaries to specific slowness…

New method uses MRI data to improve PET tomography uncertainty quantification.

Geometrically reformulates Cosserat solid mechanics using differential geometry.

Sharp stability estimate for tensor tomography in non-positive curvature.

Study inverse problems for twisted geodesic flows on manifolds.

We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer's law. The algorithm promotes solutions that are sparse in the pixel/voxel-differences domain by introduci…

TomOpt optimizes muon detector designs using differentiable programming.

Deep kernel learning for complex function modeling.

Dissertation tackles geodesic ray transform on Riemannian manifolds.

The distribution of absorbed dose in radionuclide therapy with Lu$^{177}$ can be approximated by convolving an image of the time-integrated activity distribution with a dose voxel kernel representing different tissue types. This fast but inaccurate approximation is unsuitable for personalised dosimetry because it negle…

Bayesian approach for adaptive radio tomography using SLFs.

Study online learning of quantum processes, showing feasibility for certain types.

Extends magnetic flow theory results to higher dimensions.