Network Methods in Engineering

2008 ◽  
Author(s):  
Offer Shai ◽  
Kenneth Preiss
Keyword(s):  
Graph Theory ◽  
Systems Engineering ◽  
Solid Mechanics ◽  
Main Idea ◽  
Mathematical Representation ◽  
Network Graph ◽  
Electric Circuits ◽  
Engineering Theory ◽  
Network Methods ◽  
Engineered Systems

This paper reviews the main idea underlying the use of network graph theory for analysis or for design of physical engineered systems. A physical engineered system is a system built from physical components, as compared with a system built only from symbols or software. The term includes structures, mechanisms, electric circuits and more. Different engineered systems may be represented as the same graph, or as graphs that show a known mathematical relationship between them. We then have a single mathematical representation that is applicable to more than one engineered system. The properties of the graph, as known from graph theory, are applicable to all the engineered systems in domains that match that graph. The graph can be regarded as a generalized representation suitable for various engineered systems. Engineering theory is commonly divided into domains, solid mechanics, mechanisms, fluid mechanics, heat transfer, and more. When dealing with engineered systems using the language and mathematical formality of graph theory such divisions become unnecessary. Network graph theory can apply similar or even identical theory to many engineering domains.

River System Connectivity Analysis of Wuxi’s Central Urban Area Based on Graph Theory

2012 ◽  
Vol 212-213 ◽  
pp. 543-548 ◽  
Author(s):  
Liu Yan Wang ◽  
You Peng Xu ◽  
Ming Jing Yu
Keyword(s):  
Graph Theory ◽  
Urban Area ◽  
Water Environment ◽  
River System ◽  
Yangtze River Delta ◽  
River Network ◽  
Structure Stability ◽  
Network Graph ◽  
Stream Structure ◽  
Wuxi City

Wuxi City is located in the hinterland of Taihu Basin and an important city in Yangtze River Delta Region with a prosperous economy. In the process of urban development, the river system pattern changes a lot. It has an impact on water environment, water ecology and other fields. The central urban area of Wuxi City was selected as the study area. Based on the river system of three periods: 1960s, 1980s and 2009, the rivers were classified into three levels according to the width of channels. The length, acreage and stream structure parameters were calculated. Then from the view of Graph Theory, river system was expressed as network graph, and the vertices, edges and degree of vertices were analyzed. The results show that the changes of rivers of different levels and lakes are not completely the same, but still appear a decreasing trend in general. The river network density and water surface ratio become smaller. Also the complexity and structure stability of river network weaken. The conclusions that the river evolution tends to be trunk and single, the stream structure is simplified and the connectivity of rivers and lakes reduces are verified by the analysis based on Graph Theory as well.

The 3D graph approach for breakdown voltage calculation in BaTiO3 ceramics

2021 ◽  
pp. 2150103
Author(s):  
Vojislav V. Mitic ◽  
Branislav Randjelovic ◽  
Ivana Ilic ◽  
Srdjan Ribar ◽  
An-Lu Chun ◽  
...  
Keyword(s):  
Graph Theory ◽  
Crystal Structures ◽  
Breakdown Voltage ◽  
Main Idea ◽  
Experimental Results ◽  
Grain Structure ◽  
Mathematical Approach ◽  
Electronic Parameters ◽  
Mathematical Graph

After pioneering attempts for the introduction of graph theory in the field of ceramics and microstructures, where 1D and 2D graphs were used, in this paper we applied 3D graphs for the breakdown voltage calculation in BaTiO3 sample with some predefined constraints. We have described the relations between grains in the sample and established a mathematical approach for the calculation of breakdown voltage using experimental results. As a result, we introduced mapping between the property of sample and grain structure, then between the grain structure and mathematical graph, using various crystal structures. The main idea was to apply 3D graph theory for the distribution of electronic parameters between the neighboring grains. With this study, we successfully confirmed the possibilities for applications of graphs as a tool for the determination of properties even at the intergranular level.

An interdisciplinary strategy to advance systems engineering theory: The case of abstraction and elaboration

2020 ◽  
Vol 23 (6) ◽  
pp. 673-683
Author(s):  
Taylan G. Topcu ◽  
Konstantinos Triantis ◽  
Richard Malak ◽  
Paul Collopy
Keyword(s):  
Systems Engineering ◽  
Engineering Theory

scholarly journals Sun Toughness Conditions for P 2 and P 3 Factor Uniform and Factor Critical Avoidable Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shu Gong ◽  
Haci Mehmet Baskonus ◽  
Wei Gao
Keyword(s):  
Graph Theory ◽  
Computer Networks ◽  
The Sun ◽  
Graph Structure ◽  
Network Graph ◽  
The Given ◽  
Path Factor

The security of a network is closely related to the structure of the network graph. The denser the network graph structure is, the better it can resist attacks. Toughness and isolated toughness are used to characterize the vulnerable programs of the network which have been paid attention from mathematics and computer scholars. On this basis, considering the particularity of the sun component structures, sun toughness was introduced in mathematics and applied to computer networks. From the perspective of modern graph theory, this paper presents the sun toughness conditions of the path factor uniform graph and the path factor critical avoidable graph in P ≥ 2 -factor and P ≥ 3 -factor settings. Furthermore, examples show that the given boundaries are sharp.

Sign in / Sign up

Export Citation Format

Share Document