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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (5): 537-542    DOI: 10.3785/j.issn.1008-9497.2019.05.004
数学与计算机科学     
二元体相分离模型的静态分歧
闫东明
浙江财经大学 数据科学学院，浙江 杭州 310018
On the steady state bifurcation of the binary alloys system.
YAN Dongming
School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou 310018, China
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摘要： 运用非线性分歧理论，研究二元体相分离模型的静态分歧，给出了一个与该模型线性问题第一特征值相关的临界值。当参数超过该临界值时，二元体相分离模型有静态分歧发生，此时相应的二元体有相分离现象发生。此外，提出影响二元体相分离现象发生的主要因素是晶格间距和二元体所在区域的形状。
关键词： 二元体模型;  分歧理论;  Fredholm 算子;  静态分歧;  相分离    
Abstract: In this paper, the steady state bifurcation of the binary alloys system is investigated. By using the nonlinear bifurcation theory, we prove that this system bifurcates from the trivial solution to the nontrivial solution branch when the parameter crosses certain critical value, which is related to the first eigenvalue of the relevant linear problem. In this case phase separation will occur in binary alloys. Furthermore, we obtain that lattice spacing and the shape of the domain are the key factors that affect the phase separation in binary alloys.
Key words: binary alloys    bifurcation theory    Fredholm operator    steady state bifurcation    phase separation
收稿日期: 2018-12-11 出版日期: 2019-09-25
CLC:  O175.8  
作者简介: 闫东明(1982—)，ORCID: http://orcid.org/0000-0002-2893-4871，男，博士,讲师，主要从事分歧理论研究，E-mail：13547895541@126.com.
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引用本文:

闫东明. 二元体相分离模型的静态分歧[J]. 浙江大学学报（理学版）, 2019, 46(5): 537-542.

YAN Dongming. On the steady state bifurcation of the binary alloys system.. Journal of ZheJIang University(Science Edition), 2019, 46(5): 537-542.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.05.004    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I5/537

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