Study on the chaotic behavior of mining rock seepage system
One dimensional non-steady, non-Darcy flow of water in a rock stratum was reduced into a system described by six ordinary differential equations involving five controlling parameters. Through response computations and time series analysis, chaotic behavior in the reduced system was discussed in deta...
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| Veröffentlicht in: | Mining science and technology (China) 2011-11, Vol.21 (6), p.755-759 |
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| creator | Wan, Shiwen Xu, Jinhai Li, Chong |
| description | One dimensional non-steady, non-Darcy flow of water in a rock stratum was reduced into a system described by six ordinary differential equations involving five controlling parameters. Through response computations and time series analysis, chaotic behavior in the reduced system was discussed in details. Firstly, the dynamical response of the reduced system under a set of parameters was calculated, and the power spectrum of the attractor was obtained through fast Lagrangian transformation; then the phase space was reconstructed by fixing embedding dimension to be 6 and delay time to range from 1 to 20, and the correlation dimension of the attractor was calculated based on the curves under the coordinates of logarithm of correlation integral vs. logarithm of covering radius; and lastly, the Lyapunov indices of the attractor were calculated by using Gram-Schmit’s orthogonalization method. The results show that the power spectrum of the attractor is continuous; the correlation dimension of the attractor is equal to 2.36; among the Lyapunov indices, LE1, LE2, LE3 are positive, LE5, LE6 are negative, and LE4 fluctuates near zero. All the analysis indicates that there may exist chaos in the system of non-steady, non-Darcy flow. |
| doi_str_mv | 10.1016/j.mstc.2011.12.001 |
| format | Article |
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Through response computations and time series analysis, chaotic behavior in the reduced system was discussed in details. Firstly, the dynamical response of the reduced system under a set of parameters was calculated, and the power spectrum of the attractor was obtained through fast Lagrangian transformation; then the phase space was reconstructed by fixing embedding dimension to be 6 and delay time to range from 1 to 20, and the correlation dimension of the attractor was calculated based on the curves under the coordinates of logarithm of correlation integral vs. logarithm of covering radius; and lastly, the Lyapunov indices of the attractor were calculated by using Gram-Schmit’s orthogonalization method. The results show that the power spectrum of the attractor is continuous; the correlation dimension of the attractor is equal to 2.36; among the Lyapunov indices, LE1, LE2, LE3 are positive, LE5, LE6 are negative, and LE4 fluctuates near zero. All the analysis indicates that there may exist chaos in the system of non-steady, non-Darcy flow.</description><identifier>ISSN: 1674-5264</identifier><identifier>EISSN: 2212-6066</identifier><identifier>DOI: 10.1016/j.mstc.2011.12.001</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Chaos ; Chaos theory ; Correlation ; Correlation dimension ; Dynamical systems ; Dynamics ; Logarithms ; Lyapunov indices ; Lyapunov指数 ; Mathematical analysis ; Mining ; Non-Darcy flow ; Power spectrum ; Rock ; 岩石 ; 开采 ; 时间序列分析 ; 混沌行为 ; 渗流系统 ; 维数计算 ; 非达西流</subject><ispartof>Mining science and technology (China), 2011-11, Vol.21 (6), p.755-759</ispartof><rights>2012</rights><rights>Copyright © Wanfang Data Co. Ltd. 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Through response computations and time series analysis, chaotic behavior in the reduced system was discussed in details. Firstly, the dynamical response of the reduced system under a set of parameters was calculated, and the power spectrum of the attractor was obtained through fast Lagrangian transformation; then the phase space was reconstructed by fixing embedding dimension to be 6 and delay time to range from 1 to 20, and the correlation dimension of the attractor was calculated based on the curves under the coordinates of logarithm of correlation integral vs. logarithm of covering radius; and lastly, the Lyapunov indices of the attractor were calculated by using Gram-Schmit’s orthogonalization method. The results show that the power spectrum of the attractor is continuous; the correlation dimension of the attractor is equal to 2.36; among the Lyapunov indices, LE1, LE2, LE3 are positive, LE5, LE6 are negative, and LE4 fluctuates near zero. All the analysis indicates that there may exist chaos in the system of non-steady, non-Darcy flow.</description><subject>Chaos</subject><subject>Chaos theory</subject><subject>Correlation</subject><subject>Correlation dimension</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>Logarithms</subject><subject>Lyapunov indices</subject><subject>Lyapunov指数</subject><subject>Mathematical analysis</subject><subject>Mining</subject><subject>Non-Darcy flow</subject><subject>Power spectrum</subject><subject>Rock</subject><subject>岩石</subject><subject>开采</subject><subject>时间序列分析</subject><subject>混沌行为</subject><subject>渗流系统</subject><subject>维数计算</subject><subject>非达西流</subject><issn>1674-5264</issn><issn>2212-6066</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kEFv1DAQhS0EEqvSP8DJ3JBQUo_XO3EEF1QVilSJA3C2HGeS9XZjb-1s6fLr8SoVR-Ywc_nmPb3H2FsQNQjAq1095dnVUgDUIGsh4AVbSQmyQoH4kq0AG1VtJKrX7DLnnSiz1roFvWIff8zH_sRj4POWuNvaOHvHO9raRx8TjwOffPBh5Cm6e56JDnYknk95pukNezXYfabL53vBfn25-Xl9W919__rt-vNd5SQCVLaxg8Kh0VrZRvcobIPWqU6i1GW1VmhsW9SK7CC6vu-HDhxulG5w0wCo9QX7sOj-tmGwYTS7eEyhOJo_4_2pf3rqDJ3DCyzRC_1-oQ8pPhwpz2by2dF-bwPFYzalshYVlvwFlQvqUsw50WAOyU82nQp05tDszLlac1Y3IM2i_2l5ohL50VMy2XkKjnqfyM2mj_7_7--ePbcxjA-l2n-mCpRo1Vqs_wJIrotd</recordid><startdate>20111101</startdate><enddate>20111101</enddate><creator>Wan, Shiwen</creator><creator>Xu, Jinhai</creator><creator>Li, Chong</creator><general>Elsevier B.V</general><general>State Key Laboratory of Coal Resources and Mine Safety, School of Mines, China University of Mining & Technology, Xuzhou 221008, China</general><general>Shaanxi Lu'an Mining Group, Changzhi 046204, China%State Key Laboratory of Coal Resources and Mine Safety, School of Mines, China University of Mining & Technology, Xuzhou 221008, China</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>W92</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8BQ</scope><scope>8FD</scope><scope>FR3</scope><scope>JG9</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20111101</creationdate><title>Study on the chaotic behavior of mining rock seepage system</title><author>Wan, Shiwen ; Xu, Jinhai ; Li, Chong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2611-a7af46f7884a78d60a76ac4b2628b269a08699684eaf0bdddfb1c654876571143</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Chaos</topic><topic>Chaos theory</topic><topic>Correlation</topic><topic>Correlation dimension</topic><topic>Dynamical systems</topic><topic>Dynamics</topic><topic>Logarithms</topic><topic>Lyapunov indices</topic><topic>Lyapunov指数</topic><topic>Mathematical analysis</topic><topic>Mining</topic><topic>Non-Darcy flow</topic><topic>Power spectrum</topic><topic>Rock</topic><topic>岩石</topic><topic>开采</topic><topic>时间序列分析</topic><topic>混沌行为</topic><topic>渗流系统</topic><topic>维数计算</topic><topic>非达西流</topic><toplevel>online_resources</toplevel><creatorcontrib>Wan, Shiwen</creatorcontrib><creatorcontrib>Xu, Jinhai</creatorcontrib><creatorcontrib>Li, Chong</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库-工程技术</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Materials Research Database</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Mining science and technology (China)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wan, Shiwen</au><au>Xu, Jinhai</au><au>Li, Chong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Study on the chaotic behavior of mining rock seepage system</atitle><jtitle>Mining science and technology (China)</jtitle><addtitle>Mining Science and Technology</addtitle><date>2011-11-01</date><risdate>2011</risdate><volume>21</volume><issue>6</issue><spage>755</spage><epage>759</epage><pages>755-759</pages><issn>1674-5264</issn><eissn>2212-6066</eissn><abstract>One dimensional non-steady, non-Darcy flow of water in a rock stratum was reduced into a system described by six ordinary differential equations involving five controlling parameters. Through response computations and time series analysis, chaotic behavior in the reduced system was discussed in details. Firstly, the dynamical response of the reduced system under a set of parameters was calculated, and the power spectrum of the attractor was obtained through fast Lagrangian transformation; then the phase space was reconstructed by fixing embedding dimension to be 6 and delay time to range from 1 to 20, and the correlation dimension of the attractor was calculated based on the curves under the coordinates of logarithm of correlation integral vs. logarithm of covering radius; and lastly, the Lyapunov indices of the attractor were calculated by using Gram-Schmit’s orthogonalization method. The results show that the power spectrum of the attractor is continuous; the correlation dimension of the attractor is equal to 2.36; among the Lyapunov indices, LE1, LE2, LE3 are positive, LE5, LE6 are negative, and LE4 fluctuates near zero. 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| ispartof | Mining science and technology (China), 2011-11, Vol.21 (6), p.755-759 |
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| source | Alma/SFX Local Collection |
| subjects | Chaos Chaos theory Correlation Correlation dimension Dynamical systems Dynamics Logarithms Lyapunov indices Lyapunov指数 Mathematical analysis Mining Non-Darcy flow Power spectrum Rock 岩石 开采 时间序列分析 混沌行为 渗流系统 维数计算 非达西流 |
| title | Study on the chaotic behavior of mining rock seepage system |
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