摘要
In the thesis, we apply mean-field theory to discuss the critical phenomena in two-dimensional sandpile model. With the concept of mean-field theory, every site in the system is assumed to be independent of each other. Following the investigation of A. Vespignani and S. Zapperi[5], we have derived higher-order correction to various single-site densities of sand grains. In the calculation, we include the two-site correlation function between two nearest-neighbor sites, which contributes to the higher-order correction to the previous calculated densities. Last of all, we discuss the correction to critical exponents due to the higher-order correction of densities.
參考文獻
[1] Shang-Keng Ma, Statistical Mechanics (World Scientific, 1985).
[4] A. van der Ziel, Physica 16, 359 (1950).
[5] A. Vespignani, S. Zapperi, Phys. Rev. E 57, 6345 (1998).
[2] 楊朝順, 沙堆模型之自組臨界性的理論與數值分析 (2005).
[3] P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. A 38, 364 (1988).
延伸閱讀
- Dey, T. (2012). A Bimodal Spike and Slab Model for Variable Selection and Model Exploration. Journal of Data Science, 10(3), 363-383. https://doi.org/10.6339/JDS.2012.10(3).1032
- Fadhel, F. S., Eidi, J. H., & Wali, H. M. (2022). Contraction Mapping Theorem in Partial Fuzzy Metric Spaces. 淡江理工學刊, 25(2), 453-460. https://doi.org/10.6180/jase.202204_25(2).0020
- Chiaselotti, G., Gentile, T., G.Marino, & Oliverio, P. A. (2013). Parallel Rank of Two Sandpile Models of Signed Integer Partitions. Journal of Applied Mathematics, 2013(), 772-783-190. https://doi.org/10.1155/2013/292143
- Dimastrogiovanni, E., Bartolo, N., Matarrese, S., & Riotto, A. (2010). Non-Gaussianity and Statistical Anisotropy from Vector Field Populated Inflationary Models. Advances in Astronomy, 2010(), 847-867. https://doi.org/10.1155/2010/752670
- Yan, Z. L., Chai, H. J., Jia, X. M., & Li, H. P. (2014). A Discrete Constitutive Model for Course Granular Soil. Study of Civil Engineering and Architecture, 3(), 116-120. https://www.airitilibrary.com/Article/Detail?DocID=P20150415001-201412-201504150027-201504150027-116-120