The following information was submitted:
Transactions: INTERNATIONAL JOURNAL of MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES
Transactions ID Number: 19-916
Full Name: Nobutoshi Ikeda
Position: Associate Professor
Age: ON
Sex: Male
Address: 1-18-2, Izumi-ku, Sendai 981-8585
Country: JAPAN
Tel: +81-22-272-7512
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E-mail address: nobikeda@mishima.ac.jp
Other E-mails: ikenobu@jupiter.ocn.ne.jp
Title of the Paper: time evolution of the edge length distribution of networks generated by random transports on a one-dimensional lattice
Authors as they appear in the Paper: Nobutoshi Ikeda
Email addresses of all the authors: nobikeda@mishima.ac.jp
Number of paper pages: 9
Abstract: The restriction on the Euclidian edge length is an important consideration in the study of geographical network modeling. We herein investigate a network model developed in a one-dimensional (1-D) lattice, in which the restriction on the Euclidian edge length is a result of dynamical processes on the network, the prosperity of random transports represented by a random walker, and the ageing of edges. Based on numerical calculations, we show that the time evolution of the distribution of the edge length is subject to the 1-D heat conduction equation with a radiation term. According to this equation, the typical equilibrium length of edges is determined by a balance between the diffusion rate and the decrease rate of the edge length density. We can relate these rates to a model parameter that adjusts the aging of edges by comparing the solution of the equation with numerical results. The calculation of the mean shortest path length and the sum of the edge length alon!
g the shortest paths shows that the model assumption provides a large traffic capacity on the network and an automatic mechanism causes a natural extinction of the unapproachable area for the walker with the consequent removal of circuitous routes with long edges. The calculation of the clustering coefficient also reveals that the local clustering strength on each vertex is stabilized for a certain value, regardless of the vertex degree. These global and local properties of resulting networks emerge spontaneously from random events in the network, the movement of the random walker, and the aging of edges.
Keywords: Network modeling, Euclidian length of edges, Heat conduction equation, Random walk, Clustering coefficient
EXTENSION of the file: .pdf
Special (Invited) Session: Euclidian Edge Length and Topology of Networks Generated by Random Transports on One-Dimensional Lattice
Organizer of the Session: 638-221R
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