Application of Matrix Model Based on Graph Theory in Hydraulic Calculation of Pipe Network.

2021 ◽  
Author(s):  
Raymond Frye
2011 ◽  
Vol 374-377 ◽  
pp. 606-609
Author(s):  
Jian Jun Hu ◽  
Hua Yang ◽  
Chun Hua Sun ◽  
Cheng Ying Qi ◽  
Guo Qiang Xia

In heat source ability sufficient situation, Yuhua network in Shijiazhuang had some phenomenon, such as uneven heating, serious disorders, the far-end heating reliability was insufficient. Based on the basic principle of Graph theory, this article carried on the detailed hydraulic calculation to the annular pipe network, determined and implemented the reasonable transformation program, finally carried on the investigation and study test to the actual operation network after reformation. The results show that after reformation, the actual heating network runs well, improves the heating security and reliability, so the hydraulic calculation method based on Graph theory is accurate, and has certain guiding sense to other pipe networks' energy conservation reformation.


2011 ◽  
Vol 317-319 ◽  
pp. 2266-2270
Author(s):  
Li Xin Wei ◽  
Jiang Bo Wen ◽  
Lu Ying Zhang ◽  
Yan Chun Xu ◽  
Peng Li

On the basis of analyzing process and structure characteristics of branch shape water-injection pipe network, this paper established a hydraulic calculation method of branch shape water-injection pipe network based on binary tree. This method has many advantages, such as calculation speed is fast, occupying less memory, having high calculation accuracy, and so on. According to it, this paper compiled a computer program and presented an actual example.


2011 ◽  
Vol 186 ◽  
pp. 61-65
Author(s):  
Yong Shan Liu ◽  
Wei Jie Gu

The xoy and xoz planes are divided into nine areas in three-dimensional space respectively by the MBR (Minimum Bounding Rectangle), which are produced by the reference objects’ projection to their planes. The intersecting situations between the projection of target objects and the two of reference objects are expressed by two 3×3 matrices. Then, a directional relations matrix model based on double projections is put forward. A combinational reasoning method is proposed by using the computational performance of matrices based on this model. Moreover, a combinational reasoning experiment is given and the result matches the reality.


2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Mauricio Soto ◽  
Christopher Thraves-Caro

Graph Theory International audience In this document, we study the scope of the following graph model: each vertex is assigned to a box in ℝd and to a representative element that belongs to that box. Two vertices are connected by an edge if and only if its respective boxes contain the opposite representative element. We focus our study on the case where boxes (and therefore representative elements) associated to vertices are spread in ℝ. We give both, a combinatorial and an intersection characterization of the model. Based on these characterizations, we determine graph families that contain the model (e. g., boxicity 2 graphs) and others that the new model contains (e. g., rooted directed path). We also study the particular case where each representative element is the center of its respective box. In this particular case, we provide constructive representations for interval, block and outerplanar graphs. Finally, we show that the general and the particular model are not equivalent by constructing a graph family that separates the two cases.


2014 ◽  
Vol 1046 ◽  
pp. 165-168
Author(s):  
Zhi Bin Luo

On the basis of the pipe network hydraulic calculation of basic theory, the pipe network utilization, using graph theory and peak array build relationships and storage node and pipe sections between the pipeline node associated with the hydraulic parameters of pipe sections linked together establish a common heating pipe network hydraulic calculation models. Matrix for the model were derived solving ideas based on the finite element method and linearization method for existing node equation method to improve to get a new heating network hydraulic calculation methods common to construct a new iterative calculation equation, to improve the convergence of iterative calculation.


2021 ◽  
Author(s):  
Dun Wu ◽  
chao wei ◽  
yunfei li

Abstract China is a country short of water resources, and the leakage of urban water pipe network not only aggravates the current situation of water shortage, but also causes major accidents such as ground collapse, so it is of great significance to study the discrimination of urban underground pipe leakage. In this paper, the conventional ions and hydrogen and oxygen isotopes of water samples are determined by ion chromatograph and inductively coupled plasma mass spectrometer, and the characteristic factors are selected by cluster analysis and principal component analysis, and the mixed water discrimination model based on conventional ions is established According to the difference of hydrogen and oxygen isotope content between buried pipe water and groundwater, a discrimination model based on hydrogen and oxygen isotope is established, and the two models are combined to discriminate the leakage of buried pipe. The results show that, in terms of conventional ion content characteristics, the water in the pipe network is high in K++Na+ and Cl−, while the shallow groundwater near the pipe network is low in K++Na+ and Cl−, and the accuracy of the discriminant model based on conventional ions reaches 87.5%. In the aspect of hydrogen and oxygen isotope content characteristics, the water in the pipe network is closer to the precipitation line than the shallow groundwater, and establishing a discriminant model based on hydrogen and oxygen isotope can determine the leakage of buried pipes. This study provides a scientific basis for judging the leakage of urban underground pipes.


Author(s):  
Stuart Wood

This article arises out of my research in a number of consecutive community music therapy projects,[1] and presents the model that resulted from these research periods. It is part of an ongoing study in which I track the development of my own community music therapy projects and explore a theoretical modelling to underpin it. The article proposes a model based on a matrix formation. It begins with a description of the 'matrix model' and goes on to set out the theoretical background, then survey the music therapy research data that led to its formulation. The article concludes with a discussion of how this model contributes to the evaluation of community music therapy practice.


CICTP 2020 ◽  
2020 ◽  
Author(s):  
Ouyu Wang ◽  
Jinliang Xu ◽  
Menghua Yan ◽  
Yingying Yang

2020 ◽  
Vol 35 (23) ◽  
pp. 2050137 ◽  
Author(s):  
Chun-Hong Zhang ◽  
Rui Wang

We construct two realizations of the [Formula: see text] algebra in the classical Calogero model based on the [Formula: see text] constraints for the Hermitian one-matrix model. We also discuss the quantum Calogero model and construct the new operators which yield the closed [Formula: see text][Formula: see text]-algebra. The super [Formula: see text][Formula: see text]-algebra is derived for the supersymmetric quantum Calogero model.


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