On the definition and examples of cones and finsler spacetimes

The authors warmly acknowledge Professor Daniel Azagra (Universidad Complutense, Madrid) his advise on approximation of convex functions as well as Profs. Kostelecky (Indiana University), Fuster (University of Technology, Eindhoven), Stavrinos (University of Athens), Pfeifer (University of Tartu), Perlick (University of Bremen) and Makhmali (Institute of Mathematics, Warsaw) their comments on a preliminary version of the article. The careful revision by the referee is also acknowledged. This work is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Region de Murcia, Spain, by Fundacion Seneca, Science and Technology Agency of the Region de Murcia. MAJ was partially supported by MINECO/FEDER project reference MTM2015-65430-P and Fundacion Seneca project reference 19901/GERM/15, Spain and MS by Spanish MINECO/ERDF project reference MTM2016-78807-C2-1-P.A systematic study of (smooth, strong) cone structures C and Lorentz–Finsler metrics L is carried out. As a link between both notions, cone triples (Ω,T,F), where Ω (resp. T) is a 1-form (resp. vector field) with Ω(T)≡1 and F, a Finsler metric on ker(Ω), are introduced. Explicit descriptions of all the Finsler spacetimes are given, paying special attention to stationary and static ones, as well as to issues related to differentiability. In particular, cone structures C are bijectively associated with classes of anisotropically conformal metrics L, and the notion of cone geodesic is introduced consistently with both structures. As a non-relativistic application, the time-dependent Zermelo navigation problem is posed rigorously, and its general solution is provided.MINECO/FEDER project, Spain MTM2015-65430-PFundacion Seneca 19901/GERM/15Spanish MINECO/ERDF project MTM2016-78807-C2-1-

Diverging climate trends in Mongolian taiga forests influence growth and regeneration of Larix sibirica

Central and semiarid north-eastern Asia was subject to twentieth century warming far above the global average. Since forests of this region occur at their drought limit, they are particularly vulnerable to climate change. We studied the regional variations of temperature and precipitation trends and their effects on tree growth and forest regeneration in Mongolia. Tree-ring series from more than 2,300 trees of Siberian larch (Larix sibirica) collected in four regions of Mongolia’s forest zone were analyzed and related to available weather data. Climate trends underlie a remarkable regional variation leading to contrasting responses of tree growth in taiga forests even within the same mountain system. Within a distance of a few hundred kilometers (140–490 km), areas with recently reduced growth and regeneration of larch alternated with regions where these parameters remained constant or even increased. Reduced productivity could be correlated with increasing summer temperatures and decreasing precipitation; improved growth conditions were found at increasing precipitation, but constant summer temperatures. An effect of increasing winter temperatures on tree-ring width or forest regeneration was not detectable. Since declines of productivity and regeneration are more widespread in the Mongolian taiga than the opposite trend, a net loss of forests is likely to occur in the future, as strong increases in temperature and regionally differing changes in precipitation are predicted for the twenty-first century

Gauging the spacetime metric -- looking back and forth a century later

H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local scale gauge (later called {\em Weyl geometry}) was motivated by mathematical, philosophical and physical considerations. It was the starting point of his unified field theory of electromagnetism and gravity. After getting disillusioned with this research program and after the rise of a convincing alternative for the gauge idea by translating it to the phase of wave functions and spinor fields in quantum mechanics, Weyl no longer considered the original scale gauge as physically relevant. About the middle of the last century the question of conformal and/or local scale gauge transformation were reconsidered by different authors in high energy physics (Bopp, Wess, et al.) and, independently, in gravitation theory (Jordan, Fierz, Brans, Dicke). In this context Weyl geometry attracted new interest among different groups of physicists (Omote/Utiyama/Kugo, Dirac/Canuto/Maeder, Ehlers/Pirani/Schild and others), often by hypothesizing a new scalar field linked to gravity and/or high energy physics. Although not crowned by immediate success, this ``retake'' of Weyl geometrical methods lives on and has been extended a century after Weyl's first proposal of his basic geometrical structure. It finds new interest in present day studies of elementary particle physics, cosmology, and philosophy of physics.Comment: 56 pages, contribution to Workshop Hundred Years of Gauge Theory Bad Honnef, July 30 - August 3, 201