Time-vectorized numerical integration for systems of ODEs

Stiff systems of ordinary differential equations (ODEs) and sparse training data are common in scientific problems. This paper describes efficient, implicit, vectorized methods for integrating stiff systems of ordinary differential equations through time and calculating parameter gradients with the adjoint method. The main innovation is to vectorize the problem both over the number of independent times series and over a batch or "chunk" of sequential time steps, effectively vectorizing the assembly of the implicit system of ODEs. The block-bidiagonal structure of the linearized implicit system for the backward Euler method allows for further vectorization using parallel cyclic reduction (PCR). Vectorizing over both axes of the input data provides a higher bandwidth of calculations to the computing device, allowing even problems with comparatively sparse data to fully utilize modern GPUs and achieving speed ups of greater than 100x, compared to standard, sequential time integration. We demonstrate the advantages of implicit, vectorized time integration with several example problems, drawn from both analytical stiff and non-stiff ODE models as well as neural ODE models. We also describe and provide a freely available open-source implementation of the methods developed here

Modeling hyperthermal events in the Mesozoic-Paleogene periods: a review

Hyperthermal events, which are characterized by rapid and extreme warming, occurred at several points throughout the Mesozoic to Paleogene periods. Model simulation studies have been conducted to investigate the mechanisms behind these events, including the carbon fluxes required to drive observed warming and isotope dynamics, the impact of warming on continental weathering, seawater pH, ocean anoxia, and the mechanism that terminated the warming. Studies using simple box models, Earth system box models, or 3D Earth system models have suggested that warming had a significant biogeochemical impact and would enhance continental weathering, increase ocean anoxia, and drive marine acidification. However, the magnitudes of these impacts remain debated and require further modeling work, as do the reconstructions of carbon fluxes and compositions. This review provides an overview of the current state of knowledge on hyperthermal events and proposes possible modeling development directions to better understand the causes and impacts of these events. Particularly, new long-term ‘semi-spatial’ Earth system models are promising tools for providing new solutions and perspectives on the biogeochemical responses to warming events and the carbon fluxes behind hyperthermal events from the Mesozoic to Paleogene periods

Optical studies of structural phase transition in the vanadium-based kagome metal ScV6Sn6

In condensed matter physics, materials with kagome lattice exhibit exotic emergent quantum states, including charge density wave (CDW), superconductivity and magnetism. Very recently, hexagonal kagome metal ScV6Sn6 was found to undergo fascinating first-order structural phase transition at around 92 K and a 3x3x3 CDW modulation. The bulk electronic band properties are enlightened for comprehending the origin of the structural phase transition. Here, we perform a optical spectroscopy study on the monocrystalline compound across the transition temperature. The structural transition gives rise to the abrupt changes of optical spectra without observing gap development behavior. The optical measurements revealed a sudden reconstruction of the band structure after transition. We emphasize that the phase transition is of the first order and distinctly different from the conventional density-wave type condensation. Our results provide insight into the origin of the structural phase transition in the new kagome metal compound.Comment: 7 pages, 4 figure

Pump-induced terahertz conductivity response and peculiar bound state in Mn3Si2Te6

We report the significant enhancement on ultrafast terahertz optical conductivity and the unexpected formation of a polaronic-like state in semiconductor Mn3Si2Te6 at room temperature. With the absorption of pump photons, the low-frequency terahertz photoconductivity spectrum exhibits a significant rise, quickly forming a broad peak and subsequently shifting to higher energy. The short-lived nature of the broad peak, as well as the distribution of optical constants, strongly points towards a transient polaron mechanism. Our study not only provides profound insights into the remarkable photoelectric response of Mn3Si2Te6 but also highlights its significant potential for future photoelectric applications

Strong nonlinear optical response and transient symmetry switching in Type-II Weyl semimetal β\beta-WP2

The topological Weyl semimetals with peculiar band structure exhibit novel nonlinear optical enhancement phenomena even for light at optical wavelengths. While many intriguing nonlinear optical effects were constantly uncovered in type-I semimetals, few experimental works focused on basic nonlinear optical properties in type-II Weyl semimetals. Here we perform a fundamental static and time-resolved second harmonic generation (SHG) on the three dimensional Type-II Weyl semimetal candidate $\beta$-WP$_2$. Although $\beta$-WP$_2$ exhibits extremely high conductivity and an extraordinarily large mean free path, the second harmonic generation is unscreened by conduction electrons, we observed rather strong SHG response compared to non-topological polar metals and archetypal ferroelectric insulators. Additionally, our time-resolved SHG experiment traces ultrafast symmetry switching and reveals that polar metal $\beta$-WP$_2$ tends to form inversion symmetric metastable state after photo-excitation. Intense femtosecond laser pulse could optically drive symmetry switching and tune nonlinear optical response on ultrafast timescales although the interlayer coupling of $\beta$-WP$_2$ is very strong. Our work is illuminating for the polar metal nonlinear optics and potential ultrafast topological optoelectronic applications.Comment: 8 pages, 5 figure

Phonon promoted charge density wave in topological kagome metal ScV6_{6}Sn6_{6}

Charge density wave (CDW) orders in vanadium-based kagome metals have recently received tremendous attention due to their unique properties and intricate interplay with exotic correlated phenomena, topological and symmetry-breaking states. However, the origin of the CDW order remains a topic of debate. The discovery of ScV$_{6}$Sn$_{6}$, a vanadium-based bilayer kagome metal exhibiting an in-plane $\sqrt{3}$ x $\sqrt{3}$ $\textit{R}$30${\deg}$ CDW order with time-reversal symmetry breaking, provides a novel platform to explore the underlying mechanism behind the unconventional CDW. Here, we combine high-resolution angle-resolved photoemission spectroscopy, Raman scattering measurements and density functional theory to investigate the electronic structures and phonon modes of ScV$_{6}$Sn$_{6}$ and their evolution with temperature. We identify topologically nontrivial Dirac surface states and multiple van Hove singularities (VHSs) in the vicinity of the Fermi level, with one VHS near the K point exhibiting nesting wave vectors in proximity to the $\sqrt{3}$ x $\sqrt{3}$ $\textit{R}$30${\deg}$ CDW wave vector. Additionally, Raman measurements indicate a strong intrinsic electron-phonon coupling in ScV$_{6}$Sn$_{6}$, as evidenced by the presence of a two-phonon mode and a large frequency amplitude mode. Our findings highlight the fundamental role of lattice degrees of freedom in promoting the CDW in ScV$_{6}$Sn$_{6}$ and provide important insights into the fascinating correlation phenomena observed in kagome metals

A short-lived oxidation event during the early Ediacaran and delayed oxygenation of the Proterozoic ocean

The Ediacaran Period was characterised by major carbon isotope perturbations. The most extreme of these, the ∼570 Ma Shuram/DOUNCE (Doushantuo Negative Carbon isotope Excursion) anomaly, coincided with early radiations of benthic macrofauna linked to a temporary expansion in the extent of oxygenated seawater. Here we document an earlier negative excursion (the ∼610 Ma WANCE (Weng'An Negative Carbon isotope Excursion)) anomaly in the Yangtze Gorges area, South China, that reached equally extreme carbon isotope values and was associated with a similar degree of environmental perturbation. Specifically, new uranium isotope data evidence a significant, but transient, shift towards more oxygenated conditions in tandem with decreasing carbon isotope values, while strontium and sulfur isotope data support an increase in continental weathering through the excursion. We utilize a biogeochemical modelling approach to demonstrate that the influx of such a weathering pulse into an organically-laden, largely anoxic ocean, fully reproduces each of these distinct isotopic trends. Our study directly supports the hypothesis that a large dissolved marine organic pool effectively buffered against widespread oxygenation of the marine environment through the Proterozoic Eon, and in doing so, substantially delayed the radiation of complex aerobic life on Earth

Effective use of cerium anomalies as a redox proxy in carbonate-dominated marine settings

Rare earth elements and yttrium (REY) have a distinct distribution pattern in seawater, and this pattern may be faithfully preserved in carbonate sediments and rocks. Anomalous concentrations of redox-sensitive cerium (Ce) compared with neighbouring REY originate in oxic water column conditions, and as such, Ce anomalies can provide a potentially useful redox proxy in carbonate-dominated marine settings. The methods used to extract REY from carbonates vary widely, and may suffer from widespread leaching of REY from accessory non-carbonate minerals and organic matter, limiting the application of Ce anomalies for palaeo-redox reconstruction. We have systematically compared different methods on 195 carbonate samples with varying purity (% carbonate) from both modern and ancient environments. We used sequential leaching experiments in nitric acid to identify the most ‘seawater-like’ portion of the carbonate sample where contributions from non-carbonate minerals and organic matter are minimised. We also compared the results of sample dissolution in different types and strengths of acid. Our results confirm that REY concentrations can be inadvertently contaminated by partial leaching of clays and Fe (oxyhydr)oxides during a single-step digestion, and we suggest a pre-leach of 20% of the sample, followed by a partial leach of 40% of the sample to selectively dissolve carbonate. We suggest that REY studies are optimised in carbonates with > 85% CaCO₃, and show that dolomites behave differently during the leaching process and must be treated separately. We present REY patterns for modern carbonate-rich sediments from a range of environments, and show that seawater REY are faithfully preserved in some non-skeletal carbonate, but modified leaching procedures are necessary for impure, unlithified or organic rich carbonate sediments. We combine REY with Fe-speciation data to identify how Fe oxides and clays contribute to the REY signal and explore how the two proxies can be used together to provide a complex and high-resolution redox reconstruction in carbonate-dominated marine environments