Optimally Dense Packings for Fully Asymptotic Coxeter Tilings by Horoballs of Different Types

The goal of this paper to determine the optimal horoball packing arrangements and their densities for all four fully asymptotic Coxeter tilings (Coxeter honeycombs) in hyperbolic 3-space $\mathbb{H}^3$. Centers of horoballs are required to lie at vertices of the regular polyhedral cells constituting the tiling. We allow horoballs of different types at the various vertices. Our results are derived through a generalization of the projective methodology for hyperbolic spaces. The main result states that the known B\"or\"oczky--Florian density upper bound for "congruent horoball" packings of $\mathbb{H}^3$ remains valid for the class of fully asymptotic Coxeter tilings, even if packing conditions are relaxed by allowing for horoballs of different types under prescribed symmetry groups. The consequences of this remarkable result are discussed for various Coxeter tilings.Comment: 26 pages, 10 figure

On commensurable hyperbolic Coxeter groups

For Coxeter groups acting non-cocompactly but with finite covolume on real hyperbolic space Hn, new methods are presented to distinguish them up to (wide) commensurability. We exploit these ideas and determine the commensurability classes of all hyperbolic Coxeter groups whose fundamental polyhedra are pyramids over a product of two simplices of positive dimensions

Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra

We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorithm that detects the geometric decomposition of good 3-orbifolds with planar singular locus and underlying manifold the 3-sphere. The volume bounds follow from techniques related to the proof of Thurston's Orbifold Theorem, Schl\"afli's formula, and previous results of the author giving volume bounds for right-angled hyperbolic polyhedra.Comment: 36 pages, 19 figure

Global ocean heat content in the Last Interglacial

The Last Interglacial (129-116 ka) represents one of the warmest climate intervals of the last 800,000 years and the most recent time when sea level was meters higher than today. However, the timing and magnitude of peak warmth varies between reconstructions, and the relative importance of individual sources contributing to elevated sea level (mass gain versus seawater expansion) during the Last Interglacial remains uncertain. Here we present the first mean ocean temperature record for this interval from noble gas measurements in ice cores and constrain the thermal expansion contribution to sea level. Mean ocean temperature reaches its maximum value of 1.1±0.3°C warmer-than-modern at the end of the penultimate deglaciation at 129 ka, resulting in 0.7±0.3m of elevated sea level, relative to present. However, this maximum in ocean heat content is a transient feature; mean ocean temperature decreases in the first several thousand years of the interglacial and achieves a stable, comparable-to-modern value by ~127 ka. The synchroneity of the peak in mean ocean temperature with proxy records of abrupt transitions in oceanic and atmospheric circulation suggests that the mean ocean temperature maximum is related to the accumulation of heat in the ocean interior during the preceding period of reduced overturning circulation

Global ocean heat content in the Last Interglacial

The Last Interglacial (129–116 thousand years ago (ka)) represents one of the warmest climate intervals of the past 800,000 years and the most recent time when sea level was metres higher than today. However, the timing and magnitude of the peak warmth varies between reconstructions, and the relative importance of individual sources that contribute to the elevated sea level (mass gain versus seawater expansion) during the Last Interglacial remains uncertain. Here we present the first mean ocean temperature record for this interval from noble gas measurements in ice cores and constrain the thermal expansion contribution to sea level. Mean ocean temperature reached its maximum value of 1.1 ± 0.3 °C warmer-than-modern values at the end of the penultimate deglaciation at 129 ka, which resulted in 0.7 ± 0.3 m of thermosteric sea-level rise relative to present level. However, this maximum in ocean heat content was a transient feature; mean ocean temperature decreased in the first several thousand years of the interglacial and achieved a stable, comparable-to-modern value by ~127 ka. The synchroneity of the peak in mean ocean temperature with proxy records of abrupt transitions in the oceanic and atmospheric circulation suggests that the mean ocean temperature maximum is related to the accumulation of heat in the ocean interior during the preceding period of reduced overturning circulation

Volume formula for a Z2\mathbb{Z}_2-symmetric spherical tetrahedron through its edge lengths

The present paper considers volume formulae, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. The tetrahedron possesses a certain symmetry: namely rotation through angle $\pi$ in the middle points of a certain pair of its skew edges.Comment: 27 pages, 2 figures; enhanced and improved exposition, typos corrected; Arkiv foer Matematik, 201

Evidence for self-similar bedload transport on Andean alluvial fans, Iglesia basin, south Central Argentina

Self‐similar downstream grain‐size fining trends in fluvial deposits are being increasingly used to simplify equilibrium sediment transport dynamics in numerical models. Their ability to collapse time‐averaged behavior of a depositional system into a simple mass balance framework makes them ideal for exploring the sensitivity of sediment routing systems to their climatic and tectonic boundary conditions. This is important if we want to better understand the sensitivity of landscapes to environmental change over timescales >102 years. However, the extent to which self‐similarity is detectable in the deposits of natural rivers is not fully constrained. In transport‐limited rivers, stored sediment can be remobilized or “recycled” and this behavior has been highlighted as a mechanism by which externally forced grain‐size fining trends are distorted. Here we evaluate evidence of self‐similarity in surface gravel‐size distributions on three geomorphically diverse alluvial fans in the Iglesia basin, south Central Argentine Andes. We find that size distributions are self‐similar, deviating from that condition only when significant variability occurs in the coarse tails of the distributions. Our analysis indicates a strong correlation between the degree of sediment recycling and the proportion of coarse clasts present on the bed surface. However, by fitting a relative mobility transfer function, we demonstrate that size‐selectivity alone can explain the bulk size distributions observed. This strengthens the application of self‐similar grain size fining models to solving problems of mass balance in a range of geomorphic settings, with an aim for reconstructing environmental boundary conditions from stratigraphy

Klärung der Elternschaft der Apfelsorte ‘Meran’

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