Publications (26)
Universal Phase Contrast in Micro-CT Systems
Grammatiki Lioliou, Alberto Astolfo, Marco Endrizzi +3
Conventional high-resolution micro-CT systems are regarded as attenuation-based unless visible Fresnel fringes reveal the presence of propagation-based phase contrast. Here we show…
Characterising 1-rectifiable metric spaces via connected tangent spaces
David Bate, Phoebe Valentine
We prove that in a complete metric space , -rectifiability of a set with and positive lower density -a.e. is implied by…
Fragment-wise differentiable structures
David Bate, Sylvester Eriksson-Bique, Elefterios Soultanis
The -modulus of curves, test plans, upper gradients, charts, differentials, approximations in energy and density of directions are all concepts associated to the theory of Sobol…
Laboratory-based x-ray microtomography with directional dark-field sensitivity
Carlos Navarrete-Leon, Alvaro Jose Gonzalez-Grajales, Harry Allan +9
We demonstrate dark-field x-ray microtomography in a compact, laboratory-based system capable of resolving attenuation, phase, and anisotropic scattering signals with micrometer-sc…
Differentiability and Poincaré-type inequalities in metric measure spaces
David Bate, Sean Li
We demonstrate the necessity of a Poincaré type inequality for those metric measure spaces that satisfy Cheeger's generalization of Rademacher's theorem for all Lipschitz function…
Structure of Metric -currents: approximation by normal currents and representation results
David Bate, Emanuele Caputo, Jakub TakÃ¡Ä +2
We prove the -dimensional flat chain conjecture in any complete and quasiconvex metric space, namely that metric -currents can be approximated in mass by normal -currents.…