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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 胡進錕(Chin-Kun Hu) | |
| dc.contributor.author | Guan-Rong Huang | en |
| dc.contributor.author | 黃冠榮 | zh_TW |
| dc.date.accessioned | 2021-05-14T17:48:48Z | - |
| dc.date.available | 2017-12-01 | |
| dc.date.available | 2021-05-14T17:48:48Z | - |
| dc.date.copyright | 2015-12-01 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-09-22 | |
| dc.identifier.citation | [1] Nir Friedman, Long Cai Long Cai, and X. Sunney Xie. Linking stochastic dynamics to population distribution: An analytical framework of gene expression. Phys. Rev. Lett., 97(168302), 2006.
[2] Richard Losick and Claude Desplan. Stochasticity and cell fate. Science, 320(5872):65–68, 2008. [3] Leo P. Kadanoff. Hip bone is connected to ... Physicstoday, 62:8, 2009. [4] Hao Ge and Hong Qian. Thermodynamic limit of a nonequilibrium steady state: Maxwell-type construction for a bistable biochemical system. Phys. Rev. Lett., 103(148103), 2009. [5] Paul J. Choi, X. Sunney Xie, and Eugene I. Shakhnovich. Stochastic switching in gene networks can occur by a single-molecule event or many molecular steps. Journal of Molecular Biology, 396:230–244, 2010. [6] Yao-Chen Hung and Chin-Kun Hu. Constructive role of noise in p53 regulatory network. Computer Physics Communications, 182:249–250, 2011. [7] K. Ito. Stochastic integral. Proc. Imperial Acad. Tokyo, 20:519–524, 1944. [8] L. Onsager and S. Machlup. Fluctuations and irreversible process. Phys. Rev., 91:1505–1512, 1953. [9] H. Haken. Generalized onsager-machlup function and classes of path integral solutions of the fokker-planck equation and the master equation. Zeit. Physik. B, 24:321– 326, 1976. [10] H. Dekker. Functional integration and the onsager-machlup lagrangian for continuous markov processes in riemannian geometries. Phys. Rev. A, 19:2102–2111, 1979. [11] G. Hu. Chinese Phys. Letters, 2(217), 1988. [12] M. I. Dykman, Eugenia Mori, John Ross, and P. M. Hunt. Large fluctuations and optimal paths in chemical kinetics. J. Chem. Phys., 100:5735–5750, 1994. [13] C. Escudero and A. Kamenev. Switching rates of multistep reactions. Phys. Rev. E, 79(041149), 2009. [14] M. Assaf and B. Meerson. Extinction of metastable stochastic populations. Phys. Rev. E, 81(021116), 2010. [15] A. Martirosyan and D. B. Saakian. Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations. Phys. Rev. E, 84(021122), 2011. [16] S. Karlin and H.M. Taylor. A First Course in Stochastic Processes. Academic Press, New York, 2nd edition, 1975. [17] S. Karlin and H.M. Taylor. A Second Course in Stochastic Processes. Academic Press, New York, 2nd edition, 1980. [18] H. Ge and H.Qian. Analytical mechanics in stochastic dynamics: Most probable path, large-deviation rate function and hamilton-jacobi equation. 2011. [19] Van Kampen N. G. Stochastic processes in Physics and Chemistry. North-Holland, Elsevier Science, 2007. [20] E. Baake and W. Gabriel. Biological evolution through mutation, selection, and drift: An introductory review. Annu. Rev. Comput. Phys., 7:203–264, 2000. [21] M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58(10):465–523, 1971. [22] M. Eigen, J. McCaskill, and P. Schuster. The molecular quasispecies. Adv. Chem. Phys., 75:149–263, 1989. [23] D. B. Saakian and C.-K. Hu. Eigen model as a quantum spin chain: Exact dynamics. Phys. Rev. E, 69(021913), 2004. [24] J. F. Crow and M. Kimura. An Introduction to Population Genetics Theory. Harper Row, New York, 1970. [25] E. Baake, M. Baake, and H. Wagner. Ising quantum chain is equivalent to a model of biological evolution. Phys. Rev. Lett., 78(559), 1997. [26] D. B. Saakian and C.-K. Hu. Solvable biological evolution model with a parallel mutation-selection scheme. Phys. Rev. E, 69(046121), 2004. [27] M. Eigen. Error catastrophe and antiviral strategy. Proc. Natl. Acad. Sci. USA, 99:13374–13376, 2002. [28] Bocharov G, Ford NJ, Edwards J, Breinig T, Wain-Hobson S, and Meyerhans A. A genetic-algorithm approach to simulating human immunodeficiency virus evolution reveals the strong impact of multiply infected cells and recombination. J. Gen. Virol., 86:3109–18, 2005. [29] S.A. Meguid, G. Shagal, J.C. Stranart, and J. Daly. Three-dimensional dynamic finite element analysis of shot-peening induced residual stresses. Finite Elements in Analysis and Design, 31:179–191, 1999. [30] M Kobayashi, T Matsui, and Y Murakami. Mechanism of creation of compressive residual stress by shot peening. International Journal of Fatigue, 20(5):351–357, 1998. [31] N. R. Tao, M. L. Sui, J. Lu, and K Lua. Surface nanocrystallization of iron induced by ultrasonic shot peening. Nanostruct. Mater., 11(4):433–440, 1999. [32] G. Liu, J. Lu, and K. Lu. Surface nanocrystallization of 316l stainless steel induced by ultrasonic shot peening. Mater Sci Eng A., 286:91–95, 2000. [33] H.L. Chan, H.H. Ruan, A.Y. Chen, and J. Lu. Optimization of the strain rate to achieve exceptional mechanical properties of 304 stainless steel using high speed ultrasonic surface mechanical attrition treatment. Acta Materialia, 58(15):5086–5096, 2010. [34] N.R. Tao, Z.B. Wang, W.P. Tong, M.L. Sui, J. Lu, and K. Lu. An investigation of surface nanocrystallization mechanism in fe induced by surface mechanical attrition treatment. Acta Mater., 50(4603-4616), 2002. [35] N.W. Zhang, Z.K. Hei, G. Liu, J. Lu, and K. Lu. Formation of nanostructured surface layer on aisi 304 stainless steel by means of surface mechanical attrition treatment. Acta Mater., 51(1871-1881), 2003. [36] K. Wang, N.R. Tao, G. Liu, J. Lu, and K. Lu. Plastic strain-induced grain refinement at the nanometer scale in copper. Acta Mater., 54:5281–5291, 2006. [37] K. Lu and J. Lu. Nanostructured surface layer on metallic materials induced by surface mechanical attrition treatment. Mater. Sci. Eng. A, 375:38–45, 2004. [38] X. Wu, N. Tao, Y. Hong, B. Xu G. Liu, J. Lu, and K. Lu. Strain-induced grain refinement of cobalt during surface mechanical attrition treatment. Acta Mater., 53:681– 691, 2005. [39] K.Y. Zhu, A. Vassel, F. Brisset, K. Lu, and J. Lu. Nanostructure formation mechanism of £titanium using smat. Acta Mater., 52:4101–4110, 2004. [40] X. Wu, N. Tao, B. Xu Y. Hong, J. Lu, and K. Lu. Microstructure and evolution of mechanically-induced ultrafine grain in surface layer of al-alloy subjected to ussp. Acta Mater., 50:2075–2084, 2002. [41] N. R. Tao, J. Lu, and K. Lu. Surface nanocrystallization by surface mechanical attrition treatment. Materials Science Forum, 579:91–108, 2008. [42] Cynthia L. Kelchner, S. J. Plimpton, and J. C. Hamilton. Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B, 58(11085), 1998. [43] H. Van Swygenhoven and P. M. Derlet. Grain-boundary sliding in nanocrystalline fcc metals. Phys. Rev. B, 64(224105), 2001. [44] Y. H. Zhao, K. Lu, and K. Zhang. Microstructure evolution and thermal properties in nanocrystalline cu during mechanical attrition. Phys. Rev. B, 66(085404), 2002. [45] H. Goldstein. Classical Mechanics. Addison-Wesley, 3rd edition, 2000. [46] S. R. S. Varadhan. Asymptotic probabilities and differential equations. Comm. Pure Appl. Math., 19:261–286, 1966. [47] W. Y. Tsai, J. C. Huang, Yu Jia Gao, Y. L. Chung, and Guan-Rong Huang. Relationship between microstructure and properties for ultrasonic surface mechanical attrition treatment. Scripta Mater., 103:45–48, 2015. [48] L.Cai, N. Friedman, and X.S. Xie. Stochastic protein expression in individual cells at the single molecule level. Nature, 440(7082):358–362, 2006. [49] Harry Bateman. Higher Transcendental Functions, volume 1. McGraw-Hill, 1953. [50] Pahle J, Challenger J D, Mendes P, and McKane A J. Biochemical fluctuations, optimisation and the linear noise approximation. BMC Syst. Biol., 6:86, 2012. [51] Z. Kirakosyan, D. B. Saakian, and C.-K. Hu. Finite genome length corrections for the mean fitness and gene probabilities in evolution models. J. Stat. Phys., 144:198– 212, 2011. [52] J.-M. Park and M. W. Deem. Schwinger boson formulation and solution of the crowkimura and eigen models of quasispecies theory. J. Stat. Phys., 125:975–1015, 2006. [53] R. Wurschum, S. Herth, and U. Brossmann. Diffusion in nanocrystalline metals and alloys-a status report. Adv. Eng. Mater., 5:365–372, 2003. [54] P. Shewmon. Diffusion in Solids. John Wiley & Sons, Inc„ 2nd edition, 1989. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4853 | - |
| dc.description.abstract | In macro, the method and concept of statistical physics can be a powerful tool in analytical and numerical computation and applied to many fields such as chemical reaction, bio-evolution, and material science. In our work, the methods of statistical physics: chemical master equation (CME), Hamilton-Jacobi equation (HJE), and canonical ensemble are used to calculate various physical quantities. Our work is organized in three topics: the CME with the Gaussian and compound Poisson noise, bio-evolution of Eigen model, and energy conversion in the surface mechanical attrition treatment (SMAT) experiment.
In the CME part, the chemical reaction among DNA, mRNA, and protein can be regarded as a stochastic process. We consider the CME with compound Poisson and Gaussian noises and obtain the exact solution of steady state probability density function (PDF) verified by the algorithm of forward finite difference in large-scale time. Without Gaussian white noise, the solution of CME (set diffusion coefficient ϵ = 0) can be returned to that of CME derived by Long Cai, et al. In the bio-evolution part, we use the method of expansion in O(1/N) to obtain the HJE for probability distribution in Hamming class which is applied to calculate the correction of O(1/N) accuracy for the steady-state probability distribution in Hamming class and mean fitness in Eigen model. The steady-state distributions of O(1/N) correction are well-consistent with the Runge-Kutta simulation with relative errors less than 1 %, while the mean fitness of O( 1/N) is the same one derived by Michael Deem, et al. in quantum field theory. In the SMAT part, we consider the collisions among the 304-steel balls, motor top, and chamber bottom, where the chamber or motor can be treated as a hot reservoir. Since we assume that all the collisions among them are elastic except the ball-sample collisions, the balls with negligible potential among them can be regarded as the canonical ensemble. By this concept, we construct the link for energy conversion among the motor top, sample bottom, and balls, where the kinetic energy, heat energy, and internal energy are included in the energy conversion. We also introduce the one-dimensional heat equation with uniform-distributed heat source to obtain the temperature distribution of sample, and we use this temperature distribution of sample to connect the Zenner-Hollmann parameter and the heat energy and surface hardness of sample. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-14T17:48:48Z (GMT). No. of bitstreams: 1 ntu-104-D01222004-1.pdf: 1641391 bytes, checksum: b23c2b08f2fd81cac0ec6f5fe47e52fa (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | Contents
致謝i Abstract ii Contents iv List of Figures vii List of Tables xi 1 Introduction 1 1.1 Chemical Master Equation . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Bio-evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 SMAT modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 Basic theory for CME, Bio-evolution, and SMAT 10 2.1 Hamilton-Jacobi Equation . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 Canonical Transformation . . . . . . . . . . . . . . . . . . . . . 11 2.1.2 Hamilton-Jacobi Equation . . . . . . . . . . . . . . . . . . . . . 12 2.1.3 HJE Application in CME . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Diffusion Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.1 Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.2 Itõ’s Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.3 Kolmogorov Forward Equation . . . . . . . . . . . . . . . . . . 21 2.3 Bio-evolution Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.1 Crow-Kimura Model . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.2 Eigen Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4 Collision and Heat Equation . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.1 Collision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.2 Heat Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Advanced Theory for CME, Bio-evolution, and SMAT 32 3.1 Formalism of Chemical Master Equation . . . . . . . . . . . . . . . . . . 33 3.1.1 Solution of Linear-Drift Process . . . . . . . . . . . . . . . . . . 33 3.1.2 Path Integral Formalism in Stochastic Process . . . . . . . . . . . 36 3.1.3 Formalism for CME with Compound Poisson Noise . . . . . . . 38 3.2 Formalism of Bio-evolution Model in Hamming Class . . . . . . . . . . 41 3.2.1 Crow-Kimura Model in Hamming Class . . . . . . . . . . . . . . 42 3.2.2 HJE Method in Crow-Kimura Model . . . . . . . . . . . . . . . 44 3.2.3 Modified Eigen Model in Hamming Class . . . . . . . . . . . . . 54 3.3 SMAT Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.1 The Kinetic Energy of balls . . . . . . . . . . . . . . . . . . . . 55 3.3.2 The Loss of Kinetic Energy for Balls . . . . . . . . . . . . . . . 60 4 Analytical and Numerical Solution 63 4.1 CME Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.1.1 Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . 64 4.1.2 Analytical Solution of Van Kampen CME without Diffusion Term 68 4.1.3 Asymptotic Solution of Van Kampen CME with Diffusion Term . 71 4.1.4 Analytical Solution of Van Kampen CME with Diffusion Term . . 77 4.1.5 Dynamic Simulation of Van Kampen CME with Diffusion Term . 85 4.2 Finite correction of Modified Eigen Model in Hamming Class . . . . . . 86 4.2.1 The derivation for Hamilton-Jacobi equation . . . . . . . . . . . 86 4.2.2 Comparison with Numerics . . . . . . . . . . . . . . . . . . . . 96 4.3 Solution of Heat Equation in SMAT . . . . . . . . . . . . . . . . . . . . 97 4.3.1 The Heat Source . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.3.2 The Temperature Distribution of Steady State . . . . . . . . . . . 98 4.3.3 The internal energy of sample . . . . . . . . . . . . . . . . . . . 101 4.3.4 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . 102 4.3.5 Relating strain rate and temperature with sample micro-structure in SMAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5 Conclusion 105 5.1 Van Kampen CME with Gaussian White Noise . . . . . . . . . . . . . . 105 5.2 Finite Correction of Eigen Model . . . . . . . . . . . . . . . . . . . . . . 107 5.3 SMAT Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 .1 The Coefficient of Finite Difference . . . . . . . . . . . . . . . . . . . . 110 .2 The Power Series Expansion of Kummer’s Function . . . . . . . . . . . . 111 Bibliography 112 Figures and Tables 117 | |
| dc.language.iso | en | |
| dc.subject | 表面機械研磨處理 | zh_TW |
| dc.subject | 化學主方程式 | zh_TW |
| dc.subject | 艾根模型 | zh_TW |
| dc.subject | compound Poisson noise | en |
| dc.subject | energy conversion | en |
| dc.subject | collision | en |
| dc.subject | SMAT | en |
| dc.subject | Eigen model | en |
| dc.subject | chemical master equation | en |
| dc.subject | Gaussian white noise | en |
| dc.subject | bio-evolution | en |
| dc.title | 統計物理在化學主方程式、艾根模型及表面機械研磨處理的應用 | zh_TW |
| dc.title | Application of Statistical Physics in Chemical Master Equation, Eigen Model, and Surface Mechanical Attrition Treatment | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-1 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 黃志青,林財鈺,余瑞琳,陳企寧,馬文忠 | |
| dc.subject.keyword | 化學主方程式,艾根模型,表面機械研磨處理, | zh_TW |
| dc.subject.keyword | chemical master equation,Gaussian white noise,compound Poisson noise,bio-evolution,Eigen model,SMAT,collision,energy conversion, | en |
| dc.relation.page | 133 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2015-09-23 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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