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An extended framework of continuous-stage Runge-Kutta methods

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arXiv 2018年

We propose an extended framework for continuous-stage Runge-Kutta methods which enables us to treat more complicated cases especially for the case weighting on infinite intervals. By doing this, various types of weighted orthogonal polynomials (e.g., Jacobi polynomials, Laguerre polynomials, Hermite polynomials etc.) can be used in the construction of Runge-Kutta-type methods. Particularly, families of Runge-Kutta-type methods with geometric properties can be constructed in this new framework. As examples, some new symmetric and symplectic integrators by using Legendre polynomials, Laguerre polynomials and Hermite polynomials are constructed. Copyright © 2018, The Authors. All rights reserved.

关键词： Runge Kutta methods

Symplectic integration with Jacobi polynomials

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arXiv 2018年

In this paper, we study symplectic integration of canonical Hamiltonian systems with Jacobi polynomials. The relevant theoretical results of continuous-stage Runge-Kutta methods are revisited firstly and then symplectic methods with Jacobi polynomials will be established. A few numerical experiments are well performed to verify the efficiency of our new methods. Copyright © 2018, The Authors. All rights reserved.

关键词： Runge Kutta methods

Energy-preserving integration of non-canonical Hamiltonian systems by continuous-stage methods

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arXiv 2018年

As is well known, energy is generally deemed as one of the most important physical invariants in many conservative problems and hence it is of remarkable interest to consider numerical methods which are able to preserve it. In this paper, we are concerned with the energy-preserving integration of non-canonical Hamiltonian systems by continuous-stage methods. Algebraic conditions in terms of the Butcher coefficients for ensuring the energy preservation, symmetry and quadratic-Casimir preservation respectively are presented. With the presented condition and in use of orthogonal expansion techniques, the construction of energy-preserving integrators is examined. A new class of energy-preserving integrators which is symmetric and of order 2m is constructed. Some numerical results are reported to verify our theoretical analysis and show the effectiveness of our new methods. Copyright © 2018, The Authors. All rights reserved.

关键词： Numerical methods

Bulk-Phase Reconstruction Enables Robust Zinc Metal Anodes for Aqueous Zinc-Ion Batteries

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Angewandte Chemie 2023年第35期135卷

作者： Zefang Yang Chao Hu Qi Zhang Tingqing Wu Chunlin Xie Hao Wang Prof. Yougen Tang Prof. Xiaobo Ji Prof. Haiyan Wang Hunan Provincial Key Laboratory of Chemical Power Sources College of Chemistry and Chemical Engineering Central South University Changsha 410083 P. R. China Contribution: Conceptualization (lead) Formal analysis (lead) Writing - original draft (lead) Contribution: Methodology (lead) Writing - original draft (lead) Contribution: Conceptualization (equal) Methodology (equal) Validation (equal) Contribution: Data curation (supporting) Formal analysis (supporting) Software (supporting) Contribution: Data curation (supporting) Software (supporting) Contribution: Data curation (supporting) Validation (supporting) Contribution: Conceptualization (supporting) Supervision (equal) Validation (supporting) Contribution: Supervision (supporting) Visualization (supporting)

Aqueous zinc-ion batteries are inherently safe, but the severe dendrite growth and corrosion reaction on zinc anodes greatly hinder their practical applications. Most of the strategies for zinc anode modification refer to the research of lithium metal anodes on surface regulation without considering the intrinsic mechanisms of zinc anode. Herein, we first point out that surface modification cannot permanently protect zinc anodes due to the unavoidable surface damage during the stripping process by solid–liquid conversion. A bulk-phase reconstruction strategy is proposed to introduce abundant zincophilic sites both on the surface and inside the commercial zinc foils. The bulk-phase reconstructed zinc foil anodes exhibit uniform surfaces with high zincophilicity even after deep stripping, significantly improving the resistance to dendrite growth and side reactions. Our proposed strategy suggests a promising direction for the development of dendrite-free metal anodes for practical rechargeable batteries with high sustainability.

关键词： Aqueous Zinc-Ion Batteries Bulk-Phase Reconstruction Surface Damage Zinc Anodes

Discovering the Intrinsic Causes of Dendrite Formation in Zinc Metal Anodes: Lattice Defects and Residual Stress

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Angewandte Chemie 2023年第16期135卷

作者： Chunlin Xie Shengfang Liu Zefang Yang Huimin Ji Shuhan Zhou Hao Wu Chao Hu Yougen Tang Xiaobo Ji Qi Zhang Haiyan Wang Hunan Provincial Key Laboratory of Chemical Power Sources College of Chemistry and Chemical Engineering Central South University Changsha 410083 P. R. China Contribution: Conceptualization (lead) Data curation (lead) Formal analysis (lead) Investigation (lead) Visualization (lead) Writing - original draft (lead) College of Chemistry and Chemical Engineering Northwest Normal University Lanzhou 730070 China Contribution: Conceptualization (equal) Data curation (equal) Formal analysis (equal) Contribution: Validation (equal) Visualization (equal) Contribution: Investigation (equal) Methodology (equal) Contribution: Investigation (equal) Contribution: Project administration (equal) Resources (equal) Contribution: Conceptualization (equal) Data curation (equal) Resources (equal)

Developing a highly stable and dendrite-free zinc anode is essential to the commercial application of zinc metal batteries. However, the understanding of zinc dendrites formation mechanism is still insufficient. Herein, for the first time, we discover that the interfacial heterogeneous deposition induced by lattice defects and epitaxial growth limited by residual stress are intrinsic and critical causes for zinc dendrite formation. Therefore, an annealing reconstruction strategy was proposed to eliminate lattice defects and stresses in zinc crystals, which achieve dense epitaxial electrodeposition of zinc anode. The as-prepared annealed zinc anodes exhibit dendrite-free morphology and enhanced electrochemical cycling stability. This work first proves that lattice defects and residual stresses are also very important factors for epitaxial electrodeposition of zinc in addition to crystal orientation, which can provide a new mechanism for future researches on zinc anode modification.

关键词： Crystal Defects Dendrite Epitaxial Growth Residual Stress Zinc Anode

A Universal Molten Salt Method for Direct Upcycling of Spent Ni-rich Cathode towards Single-crystalline Li-rich Cathode

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Angewandte Chemie 2023年第25期135卷

作者： Zuoyu Qin Dr. Ying Zhang Wuqing Luo Tao Zhang Tao Wang Lianshan Ni Haoji Wang Prof. Ning Zhang Prof. Xiaohe Liu Jiang Zhou Prof. Gen Chen School of Materials Science and Engineering Hunan Provincial Key Laboratory of Electronic Packaging and Advanced Functional Materials Central South University 410083 Changsha Hunan P. R. China Contribution: Conceptualization (equal) Data curation (lead) Formal analysis (lead) Investigation (equal) Writing - original draft (lead) Zhongyuan Critical Metals Laboratory and School of Chemical Engineering Zhengzhou University 450001 Zhengzhou Henan P. R. China Contribution: Investigation (supporting) Visualization (lead) Writing - review & editing (equal) Contribution: Validation (lead) Contribution: Investigation (supporting) Resources (lead) Visualization (supporting) School of Metallurgy and Environment Central South University 410083 Changsha Hunan P. R. China Contribution: Investigation (supporting) Writing - review & editing (supporting) College of Chemistry and Chemical Engineering Central South University 410083 Changsha Hunan P. R. China Contribution: Formal analysis (supporting) Investigation (supporting) Contribution: Validation (supporting) Writing - review & editing (supporting) Contribution: Methodology (supporting) Writing - review & editing (supporting) Contribution: Project administration (supporting) Writing - review & editing (supporting) Contribution: Conceptualization (equal) Funding acquisition (equal) Investigation (lead) Project administration (supporting) Supervision (supporting) Writing - review & editing (lead) Contribution: Conceptualization (equal) Funding acquisition (lead) Investigation (equal) Project administration (lead) Supervision (lead)

With ever-increasing pursuit for high-value output in recycling spent lithium-ion batteries (LIBs), traditional recycling methods of cathodes tend to be obsolete because of the complicated procedures. Herein, we first upcycle spent polycrystal LiNi 0.88 Co 0.095 Al 0.025 O 2 (S-NCA) to high value-added single-crystalline and Li-rich cathode materials through a simple but feasible LiOH-Na 2 SO 4 eutectic molten salt strategy. The in situ X-ray diffraction technique and a series of paratactic experiments record the evolution process of upcycling and prove that excessive Li occupies the transition metal (TM) layers. Beneficial from the single-crystalline and Li-rich nature, the regenerated NCA (R-NCA) exhibits remarkably enhanced electrochemical performances in terms of long-term cyclability, high-rate performance and low polarization. This approach can also be successfully extended to other cathode materials e.g., LiNi x Co y Mn z O 2 (NCM) and mixed spent NCAs with varied degree of Li loss.

关键词： Li-Rich Cathode Single-Crystalline Spent LiNi0.88Co0.095Al0.025O2 Upcycling

Explicit representation for a class of Type 2 constacyclic codes over the ring F2m[u]/(u2λ) with even length

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arXiv 2019年

作者： Cao, Yuan Cao, Yonglin Dinh, Hai Q. Sriboonchitta, Songsak Wang, Guidong School of Mathematics and Statistics Shandong University of Technology Zibo Shandong255091 China Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and Statistics Hubei University Wuhan430062 China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha Hunan410114 China Division of Computational Mathematics and Engineering Institute for Computational Science Ton Duc Thang University Ho Chi Minh City Viet Nam Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Viet Nam Faculty of Economics Chiang Mai University Chiang Mai 52000 Thailand

Let F2m be a finite field of cardinality 2m, λ and k be integers satisfying λ, k ≥ 2 and denote R = F2m[u]/hu2λ. Let δ, α ∞ F2m. For any odd positive integer n, we give an explicit representation and enumeration for all distinct (δ+αu2)-constacyclic codes over R of length 2kn, and provide a clear formula to count the number of all these codes. As a corollary, we conclude that every (δ + αu2)-constacyclic code over R of length 2kn is an ideal generated by at most 2 polynomials in the residue class ring R[x]/(x2kn-(δ + αu2). Copyright © 2019, The Authors. All rights reserved.

关键词： Codes (symbols)

Construction and enumeration for self-dual cyclic codes of even length over F2m + uF2m

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arXiv 2019年

作者： Caoa, Yuan Cao, Yonglin Dinh, Hai Q. Fu, Fang-Wei Ma, Fanghui School of Mathematics and Statistics Shandong University of Technology Zibo Shandong255091 China Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and Statistics Hubei University Wuhan430062 China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha Hunan410114 China Division of Computational Mathematics and Engineering Institute for Computational Science Ton Duc Thang University Ho Chi Minh City Viet Nam Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Viet Nam Chern Institute of Mathematics and LPMC Nankai University Tianjin300071 China

Let F2m be a finite field of cardinality 2m, R = F2m + uF2m (u2 = 0) and s, n be positive integers such that n is odd. In this paper, we give an explicit representation for every self-dual cyclic code over the finite chain ring R of length 2sn and provide a calculation method to obtain all distinct codes. Moreover, we obtain a clear formula to count the number of all these self-dual cyclic codes. As an application, self-dual and 2-quasi-cyclic codes over F2m of length 2s+1n can be obtained from self-dual cyclic code over R of length 2sn and by a Gray map preserving orthogonality and distances from R onto F22m. Copyright © 2019, The Authors. All rights reserved.

关键词：

An efficient method to construct self-dual cyclic codes of length ps over Fpm + uFpm

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arXiv 2019年

作者： Cao, Yuan Cao, Yonglin Dinh, Hai Q. Jitman, Somphong School of Mathematics and Statistics Shandong University of Technology Zibo Shandong255091 China Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and Statistics Hubei University Wuhan430062 China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha Hunan410114 China Division of Computational Mathematics and Engineering Institute for Computational Science Ton Duc Thang University Ho Chi Minh City Viet Nam Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Viet Nam Department of Mathematics Faculty of Science Silpakorn University Nakhon Pathom73000 Thailand

Let p be an odd prime number, Fpm be a finite field of cardinality pm and s a positive integer. Using some combinatorial identities, we obtain certain properties for Kronecker product of matrices over Fp with a specific type. On that basis, we give an explicit representation and enumeration for all distinct self-dual cyclic codes of length ps over the finite chain ring Fpm+uFpm (u2 = 0). Moreover, We provide an efficient method to construct every self-dual cyclic code of length ps over Fpm + uFpm precisely. Copyright © 2019, The Authors. All rights reserved.

关键词： Matrix algebra