Earth’s polar night boundary layer as an analogue for dark side inversions on synchronously rotating terrestrial exoplanets

A key factor in determining the potential habitability of synchronously rotating planets is the strength of the atmospheric boundary layer inversion between the dark side surface and the free atmosphere. Here we analyse data obtained from polar night measurements at the South Pole and Alert Canada, which are the closest analogues on Earth to conditions on the dark sides of synchronously rotating exoplanets without and with a maritime influence, respectively. On Earth, such inversions rarely exceed 30 K in strength, because of the effect of turbulent mixing induced by phenomena such as so-called mesoscale slope winds, which have horizontal scales of 10s to 100s of km, suggesting a similar constraint to near-surface dark side inversions. We discuss the sensitivity of inversion strength to factors such as orography and the global-scale circulation, and compare them to a simulation of the planet Proxima Centauri b. Our results demonstrate the importance of comparisons with Earth data in exoplanet research, and highlight the need for further studies of the exoplanet atmospheric collapse problem using mesoscale and eddy-resolving models

Comment on star-star relations in statistical mechanics and elliptic gamma-function identities

We prove a recently conjectured star-star relation, which plays the role of an integrability condition for a class of 2D Ising-type models with multicomponent continuous spin variables. Namely, we reduce this relation to an identity for elliptic gamma functions, previously obtained by Rains.Comment: 8 pages, 3 figure

Neoproterozoic Microfossils from the Margin of the East European Platform and the Search for a Biostratigraphic Model of Lower Ediacaran Rocks

A ca. 600 m thick siliciclastic succession in northern Russia contains abundant and diverse microfossils that document early to middle Ediacaran deposition along the northeastern margin of the East European Platform. The Vychegda Formation is poorly exposed but is well documented by a core drilled in the Timan trough region (Kel’tminskaya-1 borehole). Vychegda siliciclastics lie unconformably above Tonian to lower Cryogenian strata and below equivalents of the late Ediacaran Redkino succession that is widely distributed across the platform. The basal 10 m of the formation preserve acritarchs and fragments of problematic macrofossils known elsewhere only from pre-Sturtian successions. In contrast, the upper, nearly 400 m of the succession contains abundant and diverse large acanthomorphic acritarchs attributable to the Ediacaran Complex Acanthomorph Palynoflora (ECAP). This distinctive set of taxa is known elsewhere only from lower, but not lowermost, Ediacaran rocks. In between lies an additional assemblage of relatively simple filaments and stratigraphically long ranging sphaeromorphic acritarchs interpreted as early Ediacaran in age. Bearing in mind that knowledge of late Cryogenian (post-Strurtian/pre-Marinoan) microfossils is sparse, the Vychegda record is consistent with data from Australia and China which suggest that diverse ECAP microfossil assemblages appeared well into the Ediacaran Period. Accumulating paleontological observations underscore both the promise and challenges for the biostratigraphic characterization of the early Ediacaran Period.Organismic and Evolutionary Biolog

Ediacaran Microfossils from the Ura Formation, Baikal-Patom Uplift, Siberia: Taxonomy and Biostratigraphic Significance

Abundant and diverse microfossils from shales of the uppermost Ura Formation, central Siberia, document early to middle Ediacaran life along the southeastern margin of the Siberian Platform. The Ura Formation is well exposed in a series of sections in the Lena River basin but the best microfossil assemblages come from a locality along the Ura River. Here, the uppermost twenty meters of the formation contain diverse microfossils exceptionally well preserved as organic compressions. Fossils include nearly two dozen morphospecies of large acanthomorphic microfossils attributable to the Ediacaran Complex Acanthomorph Palynoflora (ECAP), a distinctive assemblage known elsewhere only from lower, but not lowermost, to middle Ediacaran rocks. Discovery of ECAP in strata previously considered Mesoproterozoic through Cryogenian confirms inferences from chemostratigraphy, dramatically changing stratigraphic interpretation of sedimentary successions and Proterozoic tectonics on the Siberian Platform. Systematic paleontology is reported for 36 taxa (five described informally) assigned to 23 genera of both eukaryotic and prokaryotic microfossils. One new genus and two new species are proposed: Ancorosphaeridium magnum n. gen. n. sp. and A. minor n. gen. n. sp.Organismic and Evolutionary Biolog

Coherent vortex structures in quantum turbulence

This report addresses an important question discussed by the quantum turbulence community during the last decade: do quantized vortices form, in zero-temperature superfluids, coherent structures similar to vortex tubes in ordinary, viscous turbulence? So far the evidence provided by numerical simulations is that bundles of quantized vortices appear in finite-temperature superfluids, but from the interaction with existing coherent structures in the turbulent (viscous) normal fluid, rather than due to the intrinsic superfuid dynamics. In this report we show that, in very intense quantum turbulence (whose simulation was made possible by a tree algorithm), the vortex tangle contains small coherent vortical structures (bundles of quantized vortices) which arise from the Biot-Savart dynamics alone, and which are similar to the coherent structures observed in classical viscous turbulence.Comment: 6 pages, 6 figure

Weak localization effect on thermomagnetic phenomena

The quantum transport equation (QTE) is extended to study weak localization (WL) effects on galvanomagnetic and thermomagnetic phenomena. QTE has many advantages over the linear response method (LRM): (i) particle-hole asymmetry which is necessary for the Hall effect is taken into account by the nonequilibrium distribution function, while LRM requires expansion near the Fermi surface, (ii) when calculating response to the temperature gradient, the problem of WL correction to the heat current operator is avoided, (iii) magnetic field is directly introduced to QTE, while the LRM deals with the vector potential and and special attention should be paid to maintain gauge invariance, e.g. when calculating the Nernst effect the heat current operator should be modified to include the external magnetic field. We reproduce in a very compact form known results for the conductivity, the Hall and the thermoelectric effects and then we study our main problem, WL correction to the Nernst coefficient (transverse thermopower).Comment: 20 pages 2 figure

The structure of the Kac-Wang-Yan algebra

The Lie algebra $\mathcal{D}$ of regular differential operators on the circle has a universal central extension $\hat{\mathcal{D}}$. The invariant subalgebra $\hat{\mathcal{D}}^+$ under an involution preserving the principal gradation was introduced by Kac, Wang, and Yan. The vacuum $\hat{\mathcal{D}}^+$-module with central charge $c\in\mathbb{C}$, and its irreducible quotient $\mathcal{V}_c$, possess vertex algebra structures, and $\mathcal{V}_c$ has a nontrivial structure if and only if $c\in \frac{1}{2}\mathbb{Z}$. We show that for each integer $n>0$, $\mathcal{V}_{n/2}$ and $\mathcal{V}_{-n}$ are $\mathcal{W}$-algebras of types $\mathcal{W}(2,4,\dots,2n)$ and $\mathcal{W}(2,4,\dots, 2n^2+4n)$, respectively. These results are formal consequences of Weyl's first and second fundamental theorems of invariant theory for the orthogonal group $\text{O}(n)$ and the symplectic group $\text{Sp}(2n)$, respectively. Based on Sergeev's theorems on the invariant theory of $\text{Osp}(1,2n)$ we conjecture that $\mathcal{V}_{-n + 1/2}$ is of type $\mathcal{W}(2,4,\dots, 4n^2+8n+2)$, and we prove this for $n=1$. As an application, we show that invariant subalgebras of $\beta\gamma$-systems and free fermion algebras under arbitrary reductive group actions are strongly finitely generated.Comment: Final versio

Late Ediacaran Redox Stability and Metazoan Evolution

The Neoproterozoic arrival of animals fundamentally changed Earth's biological and geochemical trajectory. Since the early description of Ediacaran and Cambrian animal fossils, a vigorous debate has emerged about the drivers underpinning their seemingly rapid radiation. Some argue for predation and ecology as central to diversification, whereas others point to a changing chemical environment as the trigger. In both cases, questions of timing and feedbacks remain unresolved. Through these debates, the last fifty years of work has largely converged on the concept that a change in atmospheric oxygen levels, perhaps manifested indirectly as an oxygenation of the deep ocean, was causally linked to the initial diversification of large animals. What has largely been absent, but is provided in this study, is a multi-proxy stratigraphic test of this hypothesis. Here, we describe a coupled geochemical and paleontological investigation of Neoproterozoic sedimentary rocks from northern Russia. In detail, we provide iron speciation data, carbon and sulfur isotope compositions, and major element abundances from a predominantly siliciclastic succession (spanning>1000 m) sampled by the Kel'tminskaya-1 drillcore. Our interpretation of these data is consistent with the hypothesis that the $pO_2$ threshold required for diversification of animals with high metabolic oxygen demands was crossed prior to or during the Ediacaran Period. Redox stabilization of shallow marine environments was, however, also critical and only occurred about 560 million years ago (Ma), when large motile bilaterians first enter the regional stratigraphic record. In contrast, neither fossils nor geochemistry lend support to the hypothesis that ecological interactions altered the course of evolution in the absence of environmental change. Together, the geochemical and paleontological records suggest a coordinated transition from low oxygen oceans sometime before the Marinoan (~635 Ma) ice age, through better oxygenated but still redox-unstable shelves of the early Ediacaran Period, to the fully and persistently oxygenated marine environments characteristic of later Ediacaran successions that preserve the first bilaterian macrofossils and trace fossils.Earth and Planetary SciencesOrganismic and Evolutionary Biolog

Microfossils from the lower Mesoproterozoic Kaltasy Formation, East European Platform

Basinal shales of the lower Mesoproterozoic Kaltasy Formation, sampled from three boreholes drilled into the southeastern East European Platform, Russia, contain abundant and moderately well preserved microfossils. 34 distinct entities have been identified, most assigned to simple sphaeromorphic or small filamentous taxa found widely and characterized by long stratigraphic ranges. Ornamented microfossils found in coastal successions of other lower Mesoproterozoic basins are absent, but large filamentous microfossils interpreted as possible benthic photosynthetic eukaryotes are recorded, drawing comparisons to relatively deep water shales in Siberia. In overall aspect, the Kaltasy microfossils are consistent with other broadly coeval assemblages, but they highlight the importance of environment, as well as age, in determining the distributions of remains that record the early diversification of marine eukaryotes. Rectia magna is described as a new species.Organismic and Evolutionary Biolog