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r-matrix and algebraic-geometric symplectic map

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Chinese Science Bulletin 1999年第2期44卷 114-118页

作者： QIAO ZhijunInstitute of Mathematics and School of Mathematical Sciences, Peking University, Beijing 100871, China Institute of Mathematics and School of Mathematical Sciences Peking University Beijing China

A new Lax matrix is introduced for the integrable symplectic map (ISM), and the non-dynamical(i. e. constant) r-matrix of ISM is obtained. Moreover, an effective approach is systematically presented to construct the explicit solution(here, the explicit solution means algebraic-geometric solution expressed by the riemann-Theta function) of a soliton system or nonlinear evolution equation from Lax matrix, r-matrix, and the theory of nonlinearization through taking the Toda lattice as an example. The given algebraic-geometric solution of the Toda lattice is almost-periodic and includes the periodic and finite-band solution.

关键词： symplectic map r-matrix algebraic-geometric solution.

A Few Integrable Dynamical Systems,recurrence Operators,Expanding Integrable Models and Hamiltonian Structures by the r-matrix Method

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Communications in Theoretical Physics 2017年第10期67卷 463-470页

作者：张玉峰 Iqbal Muhammad 岳超 College of Mathematics China University of Mining and Technology College of Medical Information Engineering Taishan Medical University

We extend two known dynamical systems obtained by Blaszak, et al. via choosing Casimir functions and utilizing Novikov-Lax equation so that a series of novel dynamical systems including generalized Burgers dynamical system, heat equation, and so on, are followed to be generated. Then we expand some differential operators presented in the paper to deduce two types of expanding dynamical models. By taking the generalized Burgers dynamical system as an example, we deform its expanding model to get a half-expanding system, whose recurrence operator is derived from Lax representation, and its Hamiltonian structure is also obtained by adopting a new way. Finally, we expand the generalized Burgers dynamical system to the （29-1）-dimensional case whose Hamiltonian structure is derived by Poisson tensor and gradient of the Casimir function. Besides, a kind of （29-1）-dimensional expanding dynamical model of the （29-1）-dimensionaJ dynamical system is generated as well.

关键词： r-matrix poisson tensor expanding dynamical system

Quantum Yang-Baxter equation and constant r-matrix over Grassmann algebra

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第10期6卷 1065-1079页

作者： DUPLIJ Steven KOTULSKA Olga SADOVNIKOV Alexander Department of Physics and Technology V.N. Karazin Kharkov National University Svoboda Sq. 4 Kharkov 61077 UkraineDepartment of Physics and Technology V.N. Karazin Kharkov National University Svoboda Sq. 4 Kharkov 61077 UkraineDepartment of Physics and Technology V.N. Karazin Kharkov National University Svoboda Sq. 4 Kharkov 61077 Ukraine

Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex r-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when r-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular r-matrices which appear in weak Hopf algebras are considered.

关键词： Constant solution Grassmann algebra regularity r-matrix

Error propagation with r-matrix model fitting

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Science China(Physics,Mechanics & Astronomy) 2003年第3期46卷 225-234页

作者：陈振鹏张瑞孙业英刘挺进 Department of Physics Tsinghua UniversityBeijing 100084China Department of Materials Tsinghua UniversityBeijing 100084China China Nuclear Data Center Beijing 102413China

The error propagation features with r-matrix model fitting 7Li, 11B and 17O systems have been researched systematically. Some laws of error propagation have been revealed, an experience formula for describing standard error propagation has been established, and the most possible error range for evaluated standard cross section of 6Li (n, α), 10B (n, α) and 10B (n, α1) has been determined.

关键词： r-matrix model, error propagation, covariance, nuclear standard cross section.

The r-matrix for constrained flows

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Chinese Science Bulletin 1996年第9期41卷 705-708页

作者：曾云波 Department of Applied Mathematics Tsinghua University Beijing 100084 China

The classical r-matrix and Poisson structure play an important role in our studying ofintegrable systems, since they contain underlying property of the system. recently, inter-est has developed in the study of dynamical r-matrix structure, which depends also on thedynamical variables, and associated generalized Yang-Baxter equations. However,

关键词： r-matrix Poisson structure constrained flow.

CLASSICAL r-matrix APPrOACH TO THE SYSTEM ASSOCIATED WITH THE THrEE-WAVE INTErACTION EQUATIONS

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Annals of Differential Equations 2000年第4期16卷 401-406页

作者：张磊朱思铭

The r-matrix is established for the system associated with the three-wave Interaction equations. Via the r-matrix, 3N functionally independent and involutive integrals of motion are obtained, which shows that the sys... 详细信息

关键词： r-matrix Liouville integrabilit4

Cosmic implications of the 12C(n, γ)13C reaction: a nuclear astrophysical perspective

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Chinese Physics C 2024年第2期48卷 171-174页

作者： Soumya Saha Department of Physics Bidhan Chandra CollegeRishra31G.T.Road(East)Hooghly-712248India Department of Physics University of Calcutta92Acharya Prafulla Chandra RoadKolkata-700009India

We conducted a comprehensive study of the neutron capture cross section of 12C within the relevant astrophysical energy *** rigorous r-matrix analysis,we determined the Maxwellian-averaged cross section to be 11.98±0.25μb at kT=30 *** result is approximately four times higher than the thermal neutron capture cross section estimated in earlier studies assuming the 1/v *** implications of our findings extend to the region of inhomogeneous Big-Bang models in nuclear astrophysics,where understanding the behaviour of neutron capture cross sections plays a crucial role in elucidating the intricate processes that shaped the early universe.

关键词： reaction cross section r-matrix reaction rates spectroscopic factors

面向轻量级新工具链:GNDS-JSON格式核数据的共振重建

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现代应用物理 2024年第1期15卷 34-43,58页

作者：刘畅源新计算实验室北京100025

为了验证基于GNDS-JSON格式处理评价核数据能否用于粒子输运模拟,构建了一个新的轻量级工具链。新工具链无须先将ENDF-6或GNDS格式的数据转换为自定义的内部数据结构,可以直接在读入的GNDS-JSON格式数据上进行处理。作为该轻量级工具链... 详细信息

为了验证基于GNDS-JSON格式处理评价核数据能否用于粒子输运模拟,构建了一个新的轻量级工具链。新工具链无须先将ENDF-6或GNDS格式的数据转换为自定义的内部数据结构,可以直接在读入的GNDS-JSON格式数据上进行处理。作为该轻量级工具链的第一步,成功实现了可分辨共振截面重建功能,并在ENDF/B-VIII.0数据库上与NJOY程序进行了比较。计算结果表明,除少数核素外,重建截面的最大相对偏差小于10^(-5),均方根相对偏差约为10^(-6),验证了基于GNDS-JSON打造轻量级新工具链的可行性。同时也发现了自研程序和Fudge程序在处理40 Ca的复杂r-matrix形式共振参数时的错误。工具链的轻量化可为核数据处理工具的敏捷开发提供参考。

关键词： GNDS-JSON ENDF-6 共振截面 r-matrix

A Few Discrete Lattice Systems and Their Hamiltonian Structures,Conservation Laws

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Communications in Theoretical Physics 2017年第4期67卷 396-406页

作者：郭秀荣张玉峰张祥芝岳嵘 College of Mathematics China University of Mining and Technology Basic Courses Shandong University of Science and Technology

With the help of three shift operators and r-matrix theory, a few discrete lattice systems are obtained which can be reduced to the well-known Toda lattice equation with a constraint whose Hamiltonian structures are generated by Poisson tensors of some induced Lie–Poisson bracket. The recursion operators of these lattice systems are constructed starting from Lax representations. Finally, reducing the given shift operators to get a simpler one and its expanding shift operators, we produce a lattice system with three vector fields whose recursion operator is given. Furthermore,we reduce the lattice system with three vector fields to get a lattice system whose Lax pair and conservation laws are obtained, respectively.

关键词： discrete lattice system r-matrix Hamiltonian structure