A global weak solution to the Lorentzian harmonic map flow

Han, Xiaohui; Liu, Lei; Zhao, Liang

doi:10.1007/s11425-018-9304-1

Cited by 3 publications

(1 citation statement)

References 18 publications

(26 reference statements)

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“…To an extent, it implies that the HER would deplete protons/electrons and compete with the NRR. There are three ways to solve the awkward situation: (i) limit proton and electron transfer kinetics via increasing the concentration of alkali metal ions − or building a hydrophobic layer, − (ii) change the chemical equilibrium of the HER, such as by changing the reaction temperature , and pressure, , and (iii) design reasonable electrocatalysts through preparing reasonable transition metal catalysts and atomic catalysts that possess intrinsic restrictions to the HER.…”

Section: Fundamentals Of Electrochemical N2 Reductionmentioning

confidence: 99%

Review on Electrochemical Reduction of Nitrogen by Graphdiyne-Based Catalysts: Recent Advances and Outlook

Zou

et al. 2023

Energy Fuels

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The present industrial ammonia synthesis is overdependent on the Haber–Bosch process operating under harsh conditions, which consumes enormous global energy together with gigatons of greenhouse gas emissions annually. The electrochemical nitrogen reduction reaction (NRR) offers a green and sustainable approach to ammonia synthesis under mild reaction conditions while its efficiency has been plagued by sluggish reactivity. Recently, novel engineering of catalysts and the development of electrolyzers have highlighted compelling opportunities to optimize the performance of the electrochemical NRR. In this review, emphasis was paid to summarizing a novel family of graphdiyne-based nitrogen reduction electrocatalysts together with a brief introduction to the fundamentals of the electrochemical NRR. In the beginning, mechanisms of the electrochemical NRR are discussed, followed by the elucidation of different types of electrolyzers together with experimental aspects of catalyst evaluation. Then, the advances in graphdiyne-based electrocatalysts are highlighted. Finally, the critical challenges and outlook for the emerging paradigms in the rational design of nitrogen reduction electrocatalysts are proposed.

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Section: Fundamentals Of Electrochemical N2 Reductionmentioning

confidence: 99%

Review on Electrochemical Reduction of Nitrogen by Graphdiyne-Based Catalysts: Recent Advances and Outlook

Zou

et al. 2023

Energy Fuels

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Boundary blow-up analysis for approximate Dirac-harmonic maps into stationary Lorentzian manifolds

Ai,

Liu,

Zhu

2024

Sci. China Math.

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Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold

Liu

2019

Pacific J. Math.

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In this paper, we will study the partial regularity theorem for stationary harmonic maps from a Riemannian manifold into a Lorentzian manifold. For a weakly stationary harmonic map (u, v) from a smooth bounded open domain Ω ⊂ R m to a Lorentzian manifold with Dirichlet boundary condition, we prove that it is smooth outside a closed set whose (m − 2)-dimension Hausdorff measure is zero. Moreover, if the target manifold N does not admit any harmonic sphere S l , l = 2, ..., m − 1, we will show (u, v) is smooth.

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A global weak solution to the Lorentzian harmonic map flow

Cited by 3 publications

References 18 publications

Review on Electrochemical Reduction of Nitrogen by Graphdiyne-Based Catalysts: Recent Advances and Outlook

Review on Electrochemical Reduction of Nitrogen by Graphdiyne-Based Catalysts: Recent Advances and Outlook

Boundary blow-up analysis for approximate Dirac-harmonic maps into stationary Lorentzian manifolds

Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold

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