A new proof of the analyticity of the electronic density of molecules

We give a new, short proof of the regularity away from the nuclei of the electronic density of a molecule obtained in [1,2]. The new argument is based on the regularity properties of the Coulomb interactions underlined in [3,4] and on well-known elliptic technics. [1] S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oe stergaard Soerensen: The electron density is smooth away from the nuclei. Comm. Math. Phys. 228, no. 3 (2002), 401-415. [2] S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oestergaard Soerensen: Analyticity of the density of electronic wave functions. Ark. Mat. 42, no. 1 (2004), 87-106. [3] W. Hunziker: Distortion analyticity and molecular resonances curves. Ann. Inst. H. Poincar\'e, s. A, t. 45, no 4, 339-358 (1986). [4] M. Klein, A. Martinez, R. Seiler, X.P. Wang: On the Born-Oppenheimer expansion for polyatomic molecules. Comm. Math. Phys. 143, no. 3, 607-639 (1992). The paper is published in Letters in Mathematical Physics 93, number 1, pp. 73-83, 2010. The original publication is available at " www.springerlink.com "

Fifty thousand years of Arctic vegetation and megafaunal diet

Although it is generally agreed that the Arctic flora is among the youngest and least diverse on Earth, the processes that shaped it are poorly understood. Here we present 50 thousand years (kyr) of Arctic vegetation history, derived from the first large-scale ancient DNA metabarcoding study of circumpolar plant diversity. For this interval we also explore nematode diversity as a proxy for modelling vegetation cover and soil quality, and diets of herbivorous megafaunal mammals, many of which became extinct around 10 kyr bp (before present). For much of the period investigated, Arctic vegetation consisted of dry steppe-tundra dominated by forbs (non-graminoid herbaceous vascular plants). During the Last Glacial Maximum (25-15 kyr bp), diversity declined markedly, although forbs remained dominant. Much changed after 10 kyr bp, with the appearance of moist tundra dominated by woody plants and graminoids. Our analyses indicate that both graminoids and forbs would have featured in megafaunal diets. As such, our findings question the predominance of a Late Quaternary graminoid-dominated Arctic mammoth steppe