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Vanishing of the atomic form factor derivatives in non-spherical structural refinement – a key approximation scrutinized in the case of Hirshfeld atom refinement (2021)
Journal Article
Midgley, L., Bourhis, L. J., Dolomanov, O. V., Grabowsky, S., Kleemiss, F., Puschmann, H., & Peyerimhoff, N. (2021). Vanishing of the atomic form factor derivatives in non-spherical structural refinement – a key approximation scrutinized in the case of Hirshfeld atom refinement. Acta Crystallographica Section A: Foundations and Advances, 77(6), 519-533. https://doi.org/10.1107/s2053273321009086

When calculating derivatives of structure factors, there is one particular term (the derivatives of the atomic form factors) that will always be zero in the case of tabulated spherical atomic form factors. What happens if the form factors are non-sph... Read More about Vanishing of the atomic form factor derivatives in non-spherical structural refinement – a key approximation scrutinized in the case of Hirshfeld atom refinement.

Eigenfunctions and the Integrated Density of States on Archimedean Tilings (2021)
Journal Article
Peyerimhoff, N., & Taeufer, M. (2021). Eigenfunctions and the Integrated Density of States on Archimedean Tilings. Journal of Spectral Theory, 11(2), 461-488. https://doi.org/10.4171/jst/347

We study existence and absence of ` 2 -eigenfunctions of the combinatorial Laplacian on the 11 Archimedean tilings of the Euclidean plane by regular convex polygons. We show that exactly two of these tilings (namely the .3:6/2 “kagome” tiling and the... Read More about Eigenfunctions and the Integrated Density of States on Archimedean Tilings.

Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds (2021)
Journal Article
Egidi, M., Liu, S., Muench, F., & Peyerimhoff, N. (2021). Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds. Communications in Analysis and Geometry, 29(5), 1127-1156. https://doi.org/10.4310/cag.2021.v29.n5.a4

In this paper, we present a Lichnerowicz type estimate and (higher order) Buser type estimates for the magnetic Laplacian on a closed Riemannian manifold with a magnetic potential. These results relate eigenvalues, magnetic fields, Ricci curvature, a... Read More about Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds.