合金凝固过程中等轴枝晶生长的数学模型

The Topological Representation and Detection of Isomorphism Among Geared Linkage Kinematic Chains

在枝晶晶粒的尺度上，从同时满足溶质守恒与热平衡的原则出发，提出了合金凝固过程中等轴枝晶生长的数学模型。该模型由４个相互联系的微分方程组成，可通过计算机求解，为模拟枝晶合金凝固组织的形成过程奠定了初步基础。

Proceeded from the topological characteristics of Geared Linkage Mechanisms(GLM) structure, a fully new graph, combinatorial graph, which can be used to describe the topological relationship in a Geared Linkage Kinematic Chain (GLKC), is firstly proposed. Then the corresponding matrix, combinatorial matrix, and the structural invariants of GLKC are presented. Based on the structural invariants, the difficult problem for detecting isomorphism among GLKCs is solved successfully using the powers of combinatorial matrix. Finally, the method for detecting isomorphism among GLKCs, which based on strong basis of graph theory, is suggested. A computer program based on these procedures has been applied successfully for detecting isomorphism among both the planar kinematic chains and GLKCs.