Graphene(Gr)has unique properties including high electrical conductivity;Thus,graphene/copper(Gr/Cu)composites have attracted increasing attention to replace traditional Cu for electrical applications. However,the pro...Graphene(Gr)has unique properties including high electrical conductivity;Thus,graphene/copper(Gr/Cu)composites have attracted increasing attention to replace traditional Cu for electrical applications. However,the problem of how to control graphene to form desired Gr/Cu composite is not well solved. This paper aims at exploring the best parameters for preparing graphene with different layers on Cu foil by chemical vapor deposition(CVD)method and studying the effects of different layers graphene on Gr/Cu composite’s electrical conductivity. Graphene grown on single-sided and double-sided copper was prepared for Gr/Cu and Gr/Cu/Gr composites. The resultant electrical conductivity of Gr/Cu composites increased with decreasing graphene layers and increasing graphene volume fraction. The Gr/Cu/Gr composite with monolayer graphene owns volume fraction of less than 0.002%,producing the best electrical conductivity up to59.8 ×10^(6)S/m,equivalent to 104.5% IACS and 105.3% pure Cu foil.展开更多
The aim of this paper is to given an algebraic computational method for finding maximal independent sets as well as the independent number of an arbitrary finite graph of n vertices G by strengthening the problem of f...The aim of this paper is to given an algebraic computational method for finding maximal independent sets as well as the independent number of an arbitrary finite graph of n vertices G by strengthening the problem of finding maximal independent sets of G to the problem of finding k-independent sets in G for. It is shown that the existence of k-independent sets in G is equivalent to the existence of solutions of a system of multivariate polynomial equations. It follows that the problem of finding k-independent sets can be realized by using Gröbner bases of polynomial ideals. Since the number of k-independent sets is finite, the triangular equations composed by Gröbner bases are easier to be solved. Consequently, the maximal independent sets and the independent number of G are obtained after solving at most n such equations. Finally, the numerical example is presented to illustrate the effectiveness of this algebraic computational method.展开更多
基金supported substantially by the Southwest Jiaotong University for Material and Financial Support。
文摘Graphene(Gr)has unique properties including high electrical conductivity;Thus,graphene/copper(Gr/Cu)composites have attracted increasing attention to replace traditional Cu for electrical applications. However,the problem of how to control graphene to form desired Gr/Cu composite is not well solved. This paper aims at exploring the best parameters for preparing graphene with different layers on Cu foil by chemical vapor deposition(CVD)method and studying the effects of different layers graphene on Gr/Cu composite’s electrical conductivity. Graphene grown on single-sided and double-sided copper was prepared for Gr/Cu and Gr/Cu/Gr composites. The resultant electrical conductivity of Gr/Cu composites increased with decreasing graphene layers and increasing graphene volume fraction. The Gr/Cu/Gr composite with monolayer graphene owns volume fraction of less than 0.002%,producing the best electrical conductivity up to59.8 ×10^(6)S/m,equivalent to 104.5% IACS and 105.3% pure Cu foil.
文摘The aim of this paper is to given an algebraic computational method for finding maximal independent sets as well as the independent number of an arbitrary finite graph of n vertices G by strengthening the problem of finding maximal independent sets of G to the problem of finding k-independent sets in G for. It is shown that the existence of k-independent sets in G is equivalent to the existence of solutions of a system of multivariate polynomial equations. It follows that the problem of finding k-independent sets can be realized by using Gröbner bases of polynomial ideals. Since the number of k-independent sets is finite, the triangular equations composed by Gröbner bases are easier to be solved. Consequently, the maximal independent sets and the independent number of G are obtained after solving at most n such equations. Finally, the numerical example is presented to illustrate the effectiveness of this algebraic computational method.