Characterizations of Network Structures Using Eigenmode Analysis

Abstract

Abstract:We introduced an analysis to identify structural characterization of two-dimensional regular and amorphous networks. The analysis was shown to be reliable to determine the global network rigidity and can also identify local floppy regions in the mixture of rigid and floppy regions. The eigenmode analysis explores the structural properties of various networks determined by eigenvalue spectra. It is useful to determine the general structural stability of networks that the traditional Maxwell counting scheme based on the statistics of nodes (degrees of freedom) and bonds (constraints) does not provide. A visual characterization scheme was introduced to examine the local structure characterization of the networks. The eigenmode analysis is under development for various practical applications on more general network structures characterized by coordination numbers and nodal connectivity such as graphenes and proteins.

Grain Size Effect on Mechanical Properties of Polycrystalline Graphene

“…We conjecture that this result may hold up to the limit of infinite grain size corresponding to the single crystalline graphene. Similarly, the other limit of small grain size corresponding to the amorphous materials [13,14] can be addressed as well. Some other mechanical properties such as fracture energy and the interfacial characteristics between the grains will be investigated for deeper understanding of fracture mechanism and optimal design of polycrystalline graphene.…”

Solving Multi-Objective Matrix Games with Fuzzy Payoffs through the Lower Limit of the Possibility Degree

“…Single objective fuzzy game problems and related problems have attracted a wide range of research [6][7][8][9][10][11]. Therefore, fuzzy games theory has been extensively studied in some fields, such as economics, engineering and management science [12][13][14][15][16][17][18][19]. In order to deal with the fuzzy matrix games problem, a method of robust ranking is formulated by Bhaumik [20].…”