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The effects of local variations in conditions on carbon storage and release in the continental mantle

National Science Review 2024年第6期11卷 22-36页

作者： Stephen F.Foley Chunfei Chen Dorrit E.Jacob school of Natural sciences Macquarie University Research school of Earth sciences Australian National University State Key Laboratory of Geological Processes and Mineral Resources School of Earth Sciences China University of Geosciences

Recent advances indicate that the amount of carbon released by gradual degassing from the mantle needs to be revised upwards, whereas the carbon supplied by plumes may have been overestimated in the *** in rock types and oxidation state may be very local and exert strong influences on carbon storage and release mechanisms. Deep subduction may be prevented by diapirism in thick sedimentary packages,whereas carbonates in thinner sequences may be subducted. Carbonates stored in the mantle transition zone will melt when they heat up, recognized by coupled stable isotope systems(e.g. Mg, Zn, Ca). There is no single ‘mantle oxygen fugacity’, particularly in the thermal boundary layer(TBL) and lowermost lithosphere, where very local mixtures of rock types coexist. Carbonate-rich melts from either subduction or melting of the uppermost asthenosphere trap carbon by redox freezing or as carbonate-rich dykes in this zone. Deeply derived, reduced melts may form further diamond reservoirs, recognized as polycrystalline diamonds associated with websteritic silicate minerals. Carbon is released by either edge-driven convection,which tears sections of the TBL and lower lithosphere down so that they melt by a mixture of heating and oxidation, or by lateral advection of solids beneath rifts. Both mechanisms operate at steps in lithosphere thickness and result in carbonate-rich melts, explaining the spatial association of craton edges and carbonate-rich magmatism. High-pressure experiments on individual rock types, and increasingly on reactions between rocks and melts, are fine-tuning our understanding of processes and turning up unexpected results that are not seen in studies of single rocks. Future research should concentrate on elucidating local variations and integrating these with the interpretation of geophysical signals. Global concepts such as average sediment compositions and a uniform mantle oxidation state are not appropriate for small-scale processes; an increa

关键词： lithospheric mantle carbonate melts deep carbon cycle craton destruction continental rifts

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Rational Solutions of First Order Algebraic Ordinary Differential Equations

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Journal of Systems Science & Complexity 2024年第2期37卷 567-580页

作者： FENG Shuang SHEN Liyong school of Physical and Mathematical sciences Nanjing Tech UniversityNanjing 211816China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

Let f(t,y,y')=∑ _(i=0)^(n )a_(i)(t,y)y'^(i)=0 be an irreducible first order ordinary differential equation with polynomial *** in 1998 proved that there exists a constant C such that every rational solution of f(t,y,y')=0 is of degree not greater than *** show that this degree bound C depends not only on the degrees of f in t,y,y' but also on the coefficients of f viewed as the polynomial in t,y,y'.In this paper,the authors show that if f satisfies deg(f,y)0,then the degree bound C only depends on the degrees of f in t,y,y',and furthermore we present an explicit expression for C in terms of the degrees of f in t,y,y'.

关键词： Degree bound first order AODE height rational solution

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The great catastrophe: causes of the Permo-Triassic marine mass extinction

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National Science Review 2024年第1期11卷 37-50页

作者： Paul B.Wignall David P.G.Bond school of Earth & Environment University of Leeds school of Environmental sciences University of Hull

The marine losses during the Permo-Triassic mass extinction were the worst ever experienced. All groups were badly affected, especially amongst the benthos(e.g. brachiopods, corals, bryozoans, foraminifers,ostracods). Planktonic populations underwent a fundamental change with eukaryotic algae being replaced by nitrogen-fixing bacteria, green-sulphur bacteria, sulphate-reducing bacteria and prasinophytes. Detailed studies of boundary sections, especially those in South China, have resolved the crisis to a ～55 kyr interval straddling the Permo-Triassic boundary. Many of the losses occur at the beginning and end of this interval painting a picture of a two-phase extinction. Improved knowledge of the extinction has been supported by numerous geochemical studies that allow diverse proposed extinction mechanisms to be studied. A transition from oxygenated to anoxic-euxinic conditions is seen in most sections globally, although the intensity and timing shows regional variability. Decreased ocean ventilation coincides with rapidly rising temperatures and many extinction scenarios attribute the losses to both anoxia and high *** kill mechanisms include ocean acidification for which there is conflicting support from geochemical proxies and, even less likely, siltation(burial under a massive influx of terrigenous sediment) which lacks substantive sedimentological evidence. The ultimate driver of the catastrophic changes at the end of the Permian was likely Siberian Trap eruptions and their associated carbon dioxide emissions with consequences such as warming, ocean stagnation and acidification. Volcanic winter episodes stemming from Siberian volcanism have also been linked to the crisis, but the short-term nature of these episodes(

关键词： ocean anoxia ocean acidification siltation productivity collapse volcanic winter

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Number of Solitons Emerged in the Initial Profile of Shallow Water Using Convolutional Neural Networks

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Journal of Systems Science & Complexity 2024年第2期37卷 463-479页

作者： WANG Zhen CUI Shikun school of Mathematical sciences Dalian University of TechnologyDalian 116024China school of Mathematical sciences Beihang UniversityBeijing 100191China

The soliton resolution conjecture proposes that the initial value problem can evolve into a dispersion part and a soliton ***,the problem of determining the number of solitons that form in a given initial profile remains unsolved,except for a few specific *** this paper,the authors use the deep learning method to predict the number of solitons in a given initial value of the Korteweg-de Vries(KdV)*** leveraging the analytical relationship between Asech^(2)(x)initial values and the number of solitons,the authors train a Convolutional Neural Network(CNN)that can accurately identify the soliton count from spatio-temporal *** trained neural network is capable of predicting the number of solitons with other given initial values without any additional *** extensive calculations,the authors demonstrate the effectiveness and high performance of the proposed method.

关键词： Convolutional neural network deep learning method KdV equation soliton

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A Note on the Entropy for Heisenberg Group Actions on the Torus

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2324-2336页

作者： Yu ZHANG Yu Jun ZHU school of Mathematical sciences Xiamen University

In this paper,the entropy of discrete Heisenberg group actions is *** α be a discrete Heisenberg group action on a compact metric space *** types of entropies,■ and h(α)are introduced,in which ■ is defined in Ruelle’s way and h(α) is defined via the natural extension of α.It is shown that when X is the torus and α is induced by integer matrices then ■ is zero and h(α) can be expressed via the eigenvalues of the matrices.

关键词： Entropy Heisenberg group action natural extension torus

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Optimal pivot path of the simplex method for linear programming based on reinforcement learning

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Science China Mathematics 2024年第6期67卷 1263-1286页

作者： Anqi Li Tiande Guo Congying Han Bonan Li Haoran Li school of Mathematical sciences University of Chinese Academy of SciencesBeijing100049China

Based on the existing pivot rules,the simplex method for linear programming is not polynomial in the worst ***,the optimal pivot of the simplex method is *** this paper,we propose the optimal rule to find all the shortest pivot paths of the simplex method for linear programming problems based on Monte Carlo tree ***,we first propose the SimplexPseudoTree to transfer the simplex method into tree search mode while avoiding repeated basis ***,we propose four reinforcement learning models with two actions and two rewards to make the Monte Carlo tree search suitable for the simplex ***,we set a new action selection criterion to ameliorate the inaccurate evaluation in the initial *** is proved that when the number of vertices in the feasible region is C_(n)^(m),our method can generate all the shortest pivot paths,which is the polynomial of the number of *** addition,we experimentally validate that the proposed schedule can avoid unnecessary search and provide the optimal pivot ***,this method can provide the best pivot labels for all kinds of supervised learning methods to solve linear programming problems.

关键词： simplex method linear programming pivot rules reinforcement learning

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NeuroPrim:An attention-based model for solving NP-hard spanning tree problems

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Science China Mathematics 2024年第6期67卷 1359-1376页

作者： Yuchen Shi Congying Han Tiande Guo school of Mathematical sciences University of Chinese Academy of SciencesBeijing100049China

Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential ***,there has been growing interest in end-to-end deep neural networks for solving routing ***,such methods typically produce sequences of vertices,which make it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges,as in various spanning tree *** this paper,we propose NeuroPrim,a novel framework for solving various spanning tree problems by defining a Markov decision process for general combinatorial optimization problems on *** approach reduces the action and state space using Prim's algorithm and trains the resulting model using *** apply our framework to three difficult problems on the Euclidean space:the degree-constrained minimum spanning tree problem,the minimum routing cost spanning tree problem and the Steiner tree problem in *** results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 ***,we find that our model has strong generalization ability with no significant degradation observed on problem instances as large as 1,*** results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.

关键词： degree-constrained minimum spanning tree problem minimum routing cost spanning tree problem Steiner tree problem in graphs Prim's algorithm reinforcement learning

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Rethinking the egg

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National Science Review 2024年第6期11卷 81-82页

作者： Michael J.Benton school of Earth sciences University of Bristol

Our image of early dinosaur eggs must change. Early dinosaur eggs are portrayed as soft-shelled, like those of modern lizards or snakes [1], and yet all the evidence is that early dinosaurs at least laid leathery-shel...

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Atomically self-healing of structural defects in monolayer WSe2

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Chinese Physics B 2024年第9期33卷 53-59页

作者：李康舒李俊贤韩小藏周武赵晓续 school of Materials Science and Engineering Peking University school of Physical sciences University of Chinese Academy of Sciences AI for Science Institute

Minimizing disorder and defects is crucial for realizing the full potential of two-dimensional transition metal dichalcogenides(TMDs) materials and improving device performance to desired properties. However, the methods in defect control currently face challenges with overly large operational areas and a lack of precision in targeting specific defects. Therefore,we propose a new method for the precise and universal defect healing of TMD materials, integrating real-time imaging with scanning transmission electron microscopy(STEM). This method employs electron beam irradiation to stimulate the diffusion migration of surface-adsorbed adatoms on TMD materials grown by low-temperature molecular beam epitaxy(MBE),and heal defects within the diffusion range. This approach covers defect repairs ranging from zero-dimensional vacancy defects to two-dimensional grain orientation alignment, demonstrating its universality in terms of the types of samples and defects. These findings offer insights into the use of atomic-level focused electron beams at appropriate voltages in STEM for defect healing, providing valuable experience for achieving atomic-level precise fabrication of TMD materials.

关键词： atom manipulation design fabrication nanoscale materials and structures: fabrication and characterization new materials: theory scanning transmission electron microscopy (STEM)

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Uncertainty Principles on Clifford Modules

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2537-2570页

作者： Pan LIAN school of Mathematical sciences Tianjin Normal University

In this paper, we derive the optimal Cauchy–Schwarz inequalities on a class of Hilbert and Krein modules over a Clifford algebra, which heavily depend on the Clifford algebraic *** obtained inequalities further lead to very general uncertainty inequalities on these modules. Some new phenomena arise, due to the non-commutative nature, the Clifford-valued inner products and the Krein geometry. Taking into account applications, special attention is given to the Dirac operator and the Howe dual pair Pin(m) × osp(1|2). Moreover, it is surprisingly to find that the recent highly nontrivial uncertainty relation for triple observables is indeed a direct consequence of our Cauchy–Schwarz inequality. This new observation leads to refined uncertainty relations in terms of the Wigner–Yanase–Dyson skew information for mixed states and other generalizations. These show that the obtained uncertainty inequalities on Clifford modules can be considered as new uncertainty relations for multiple observables.

关键词： 30G35 81P45 Clifford algebra Fischer decomposition Krein space uncertainty principle Wigner–Yanase–Dyson skew information

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