The symmetries of wave equations on new lattices

This paper focuses on studying the symmetry of a practical wave equation on new lattices. It is a new step in that the new lattice equation is applied to reduce the discrete problem of motion of an elastic thin homogeneous bar. The equation of motion of the bar can be changed into a discrete wave equation. With the new lattice equation, the translational and scaling invariant, not only is the infinitesimal transformation given, but the symmetry and Lie algebras are also calculated. We also give a new form of invariant called the ratio invariant, which can reduce the process of the computing invariant with the characteristic equation.     

聚乙二醇/氮化硼复合材料相变导热性能及其结晶行为

本文采用熔融共混浇筑的方法制备了聚乙二醇/氮化硼(PEG/BN)相变复合材料,并研究了不同尺度片状BN对相变复合材料导热性能和结晶行为的影响。 通过扫描电子显微镜(SEM)、热常数分析仪、红外热成像分析仪和差示扫描量热仪(DSC)研究了相变复合材料的微观形貌、导热系数和相变过程,并利用莫志深法对DSC结果进行了非等温结晶动力学分析。 结果表明,较大片状直径(50 μm)的BN可以更有效地提高聚乙二醇的导热系数,当BN填料质量分数为40%时,相变复合材料的导热系数可达到5.04 W/(m·K)。 在快速降温条件下,片径为50 μm的BN填料可以缩短PEG的半结晶时间,提高结晶速率,使相变复合材料具有较大的相变焓。     

Reductions and conserved quantities for discrete compound KdV–Burgers equations

We present two methods to reduce the discrete compound KdV–Burgers equation, which are reductions of the independent and dependent variables: the translational invariant method has been applied in order to reduce the independent variables; and a discrete spectral matrix has been introduced to reduce the number of dependent variables. Based on the invariance of a discrete compound KdV--Burgers equation under infinitesimal transformation with respect to its dependent and independent variables, we present the determining equations of transformation Lie groups for the KdV--Burgers equation and use the characteristic equations to obtain new forms of invariants.