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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (4): 511-521.doi: 10.3969/j.issn.1005-3085.2022.04.001

• •    下一篇

等离子体物理中分数阶模型数值解法研究进展

梅立泉,  郭士民   

  1. 西安交通大学数学与统计学院，西安 710049
  • 出版日期:2022-08-15 发布日期:2022-10-15
  • 基金资助:
    国家自然科学基金 (12171385)；科学挑战专题 (TZ2016002).

Research Progress and Future Prospect of Numerical Solutions of Fractional Model in Plasma Physics

MEI Liquan,  GUO Shimin   

  1. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Online:2022-08-15 Published:2022-10-15
  • Supported by:
    The National Natural Science Foundation of China (12171385); the Science Challenge Project (TZ2016002).

PDF (PC)

385

摘要：

宇宙中超过 99% 的可见物质由等离子体组成，天体物理以及空间物理中观测到的大量现象都可由等离子体的原理和规律描述。这些现象包括行星形成、太阳耀斑、恒星形成、太阳以及恒星星风、粒子加速、黑洞吸积与喷流、伽玛射线暴、超新星爆发、星系形成与演化、宇宙大尺度结构等等。与整数阶模型相比，分数阶方程可以精细地刻画等离子体中基于反常扩散过程的流体动力学行为的历史依赖性与长程相关性，将分数阶模型应用到等离子体物理领域将有重要的意义和前景。等离子体物理中分数阶模型数值解法的研究现状得到综述，并对未来的发展进行展望。

关键词: 离子体物理, 分数阶模型, 非线性色散, 磁流体, 数值解法

Abstract:

Over 99% of the baryonic matter in the universe is in the state of plasmas. Many phenomena observed in astrophysics and space physics are described by principles and laws of plasma. These phenomena include planetary formation, solar flares, star formation, solar and stellar winds, particle acceleration, black hole accretion and jet, Gamma ray bursts, supernova explosions, Galaxy formation and evolution, large-scale structure of the universe, etc. Compared with the integer order model, the fractional order equation can describe more precisely the historical dependence and long-range dependence of the hydrodynamic behavior based on the anomalous diffusion process in plasma. It is of great significance and prospect to apply the fractional order model to the field of plasma physics. The research status of the numerical solution of the fractional order model in plasma physics is reviewed, and the future development is also envisioned.

Key words: plasma physics, fractional model, nonlinear dispersive equation, MHD, numerical solution

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