博碩士論文 111222016 詳細資訊

本論文永久網址:   


以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:10 、訪客IP:3.133.107.176
姓名 湯偉佑(Wei-You Tang)  查詢紙本館藏   畢業系所 物理學系
論文名稱
(Entropy production and Information rates in non-equilibrium network dynamics)
相關論文
★ Case study of an extended Fitzhugh-Nagumo model with chemical synaptic coupling and application to C. elegans functional neural circuits★ 二維非彈性顆粒子之簇集現象
★ 螺旋狀高分子長鏈在拉力下之電腦模擬研究★ 顆粒體複雜流動之研究
★ 高分子在二元混合溶劑之二維蒙地卡羅模擬研究★ 帶電高分子吸附在帶電的表面上之研究
★ 自我纏繞繩節高分子之物理★ 高分子鏈在強拉伸流場下之研究
★ 利用雷射破壞方法研究神經網路的連結及同步發火的行為★ 最佳化網路成長模型的理論研究
★ 高分子鏈在交流電場或流場下的行為★ 驟放式發火神經元的數值模擬
★ DNA在微通道的熱泳行為★ 皮膚細胞增生與腫瘤生長之模擬
★ 耦合在非線性系統中的影響:模型探討以及非線性分析★ 從網路節點時間序列分析網路特性並應用在體外培養神經及心臟細胞
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 我們採用隨機力推斷(SFI)方法來研究布朗粒子在非線性力場下的噪聲網絡動力學。然後我們考慮了噪聲網絡動力學的情況,在這種情況下,每個節點的固有動力學是上述的一維布朗粒子,並且節點之間通過有向加權連接進行相互作用。我們分析了熵產生和信息速率,以揭示網絡屬性如何影響網絡的耗散,並探討非平衡集體動態與網絡結構的關聯。
摘要(英) We employ the stochastic force inference (SFI) method to investigate the noisy network dynamics of Brownian particles under a non-linear force field. We then consider the case of noisy network dynamics in which each node’s intrinsic dynamics is the above one-dimensional Brownian particle and the nodes are interacting with directed and weighted connections. The entropy production and information rates are analyzed to reveal how network properties affect the dissipation of the network and relate the non-equilibrium collective dynamics in terms of the network structures.
關鍵字(中) ★ 熵生成
★ 信息速率
★ 噪聲網絡動力學
★ 非平衡動力學
★ 布朗粒子
關鍵字(英) ★ Entropy production
★ Information rate
★ Noisy network dynamics
★ Non-equilibrium dynamics
★ Brownian particles
論文目次 Abstract iii
1 Introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Brownian Dynamics . . . . . . . . . . . . . . . . . . . . . . 2
Free Brownian Motion . . . . . . . . . . . . . . . . . . . . . 2
Einstein Relation . . . . . . . . . . . . . . . . . . . . . . . . 3
Langevin Equation . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Entropy Production Rate . . . . . . . . . . . . . . . . . . . 5
1.2.3 Information Rate . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 Network Property [11] . . . . . . . . . . . . . . . . . . . . 7
Weighted Mean degree . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 Modularity [12, 13] . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.3 Network Structure . . . . . . . . . . . . . . . . . . . . . . . 10
Erd˝os-Rényi random network . . . . . . . . . . . . . . . . . 10
Hierarchical network . . . . . . . . . . . . . . . . . . . . . . 10
Hyper-cubic structure . . . . . . . . . . . . . . . . . . . . . 11
Bethe lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Triangular Lattice . . . . . . . . . . . . . . . . . . . . . . . . 11
BCC Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Method 13
2.1 SFI [20] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Information in Brownian trajectory . . . . . . . . . . . . . . 13
2.1.2 Stochastic Force Inference . . . . . . . . . . . . . . . . . . . 15
2.2 Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Result 19
3.1 Analytic result for a single Brownian particle in two-dimension . 19
Pure anti-symmetric case . . . . . . . . . . . . . . . . . . . 21
General case . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Inference F and D for Network Dynamics(2.12) . . . . . . . . . . 23
3.3 Heterogeneous Diffusion coefficients . . . . . . . . . . . . . . . . . 24
3.4 Mean degree ¯k & Weighted Mean degree ¯W . . . . . . . . . . . . . 27
3.5 Symmetric level μ & Anti-Symmetric level ν . . . . . . . . . . . . 29
3.6 Modularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.7 Different Network structures . . . . . . . . . . . . . . . . . . . . . 32
4 Conclusion 35
4.1 Entropy Production Rate . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Information Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
A Appendix 37
A.1 Analytic result for a single Brownian particle in two-dimension . 37
A.1.1 Calculation of Entropy Production . . . . . . . . . . . . . . 38
A.1.2 Calculation of Information Rate . . . . . . . . . . . . . . . 40
A.2 Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
A.2.1 Generating Network . . . . . . . . . . . . . . . . . . . . . . 40
A.2.2 Using SFI to calculate the ˙S and I˙ by solving Langevin
equation in network dynamics . . . . . . . . . . . . . . . . 48
Bibliography 57
參考文獻 [1] Kerson Huang. Statistical Mechanics. 2nd ed. John Wiley & Sons, 1987.
[2] C. Jarzynski. “Equilibrium free-energy differences from nonequilibrium
measurements: A master-equation approach”. In: Phys. Rev. E 56 (5 1997),
pp. 5018–5035. DOI: 10.1103/PhysRevE.56.5018. URL: https://
link.aps.org/doi/10.1103/PhysRevE.56.5018.
[3] Gavin E. Crooks. “Entropy production fluctuation theorem and the
nonequilibrium work relation for free energy differences”. In: Phys. Rev.
E 60 (3 1999), pp. 2721–2726. DOI: 10.1103/PhysRevE.60.2721. URL:
https://link.aps.org/doi/10.1103/PhysRevE.60.2721.
[4] Denis J. Evans and Debra J. Searles. “Equilibrium microstates which generate
second law violating steady states”. In: Phys. Rev. E 50 (2 1994),
pp. 1645–1648. DOI: 10.1103/PhysRevE.50.1645. URL: https://
link.aps.org/doi/10.1103/PhysRevE.50.1645.
[5] Denis J. Evans, E. G. D. Cohen, and G. P. Morriss. “Probability of second
law violations in shearing steady states”. In: Phys. Rev. Lett. 71 (15 1993),
pp. 2401–2404. DOI: 10.1103/PhysRevLett.71.2401. URL: https:
//link.aps.org/doi/10.1103/PhysRevLett.71.2401.
[6] G. Gallavotti and E. G. D. Cohen. “Dynamical Ensembles in Nonequilibrium
Statistical Mechanics”. In: Phys. Rev. Lett. 74 (14 1995), pp. 2694–2697.
DOI: 10.1103/PhysRevLett.74.2694. URL: https://link.aps.
org/doi/10.1103/PhysRevLett.74.2694.
[7] Ken Sekimoto. “Langevin Equation and Thermodynamics”. In: Progress of
Theoretical Physics Supplement 130 (Jan. 1998), pp. 17–27. ISSN: 0375-9687.
DOI: 10.1143/PTPS.130.17. eprint: https://academic.oup.com/
ptps/article-pdf/doi/10.1143/PTPS.130.17/5213518/130-
17.pdf. URL: https://doi.org/10.1143/PTPS.130.17.
[8] Udo Seifert. “Stochastic thermodynamics, fluctuation theorems and
molecular machines”. In: Reports on Progress in Physics 75.12 (2012),
p. 126001. DOI: 10.1088/0034-4885/75/12/126001. URL: https:
//dx.doi.org/10.1088/0034-4885/75/12/126001.
[9] Shoichi Toyabe et al. “Experimental test of a new equality: Measuring heat
dissipation in an optically driven colloidal system”. In: Phys. Rev. E 75 (1
2007), p. 011122. DOI: 10.1103/PhysRevE.75.011122. URL: https:
//link.aps.org/doi/10.1103/PhysRevE.75.011122.
[10] Takahiro Harada and Shin-ichi Sasa. “Equality Connecting Energy Dissipation
with a Violation of the Fluctuation-Response Relation”. In: Phys.
Rev. Lett. 95 (13 2005), p. 130602. DOI: 10 . 1103 / PhysRevLett .
95 . 130602. URL: https : / / link . aps . org / doi / 10 . 1103 /
PhysRevLett.95.130602.
[11] Mark Newman. Networks: An Introduction. Oxford University Press,
Mar. 2010. ISBN: 9780199206650. DOI: 10 . 1093 / acprof : oso /
9780199206650.001.0001. URL: https://doi.org/10.1093/
acprof:oso/9780199206650.001.0001.
[12] Roger Guimerà, Marta Sales-Pardo, and Luís A. Nunes Amaral. “Modularity
from fluctuations in random graphs and complex networks”. In:
Phys. Rev. E 70 (2 2004), p. 025101. DOI: 10 . 1103 / PhysRevE . 70 .
025101. URL: https://link.aps.org/doi/10.1103/PhysRevE.
70.025101.
[13] M. E. J. Newman. “Modularity and community structure in networks”. In:
Proceedings of the National Academy of Sciences 103.23 (2006), pp. 8577–8582.
DOI: 10.1073/pnas.0601602103. eprint: https://www.pnas.org/
doi/pdf/10.1073/pnas.0601602103. URL: https://www.pnas.
org/doi/abs/10.1073/pnas.0601602103.
[14] M. E. J. Newman and M. Girvan. “Finding and evaluating community
structure in networks”. In: Phys. Rev. E 69 (2 2004), p. 026113. DOI: 10.
1103/PhysRevE.69.026113. URL: https://link.aps.org/doi/
10.1103/PhysRevE.69.026113.
[15] Vincent D Blondel et al. “Fast unfolding of communities in large networks”.
In: Journal of Statistical Mechanics: Theory and Experiment 2008.10
(Oct. 2008), P10008. ISSN: 1742-5468. DOI: 10.1088/1742-5468/2008/
10/p10008. URL: http://dx.doi.org/10.1088/1742- 5468/
2008/10/P10008.
[16] Paul L. Erdos and Alfréd Rényi. “On random graphs. I.” In: Publicationes
Mathematicae Debrecen (1959). DOI: https : / / doi . org / 10 . 5486 %
2FPMD.1959.6.3-4.12. URL: https://api.semanticscholar.
org/CorpusID:253789267.
[17] Wikimedia Commons. File:Hierarchical network model example.svg — Wikimedia
Commons, the free media repository. [Online; accessed 13-May-2024].
2020. URL: https://commons.wikimedia.org/w/index.php?
title = File : Hierarchical _ network _ model _ example . svg &
oldid=512303617.
[18] M. Ostilli. “Cayley Trees and Bethe Lattices: A concise analysis for mathematicians
and physicists”. In: Physica A: Statistical Mechanics and its Applications
391.12 (2012), pp. 3417–3423. ISSN: 0378-4371. DOI: https :
/ / doi . org / 10 . 1016 / j . physa . 2012 . 01 . 038. URL:
https : / / www . sciencedirect . com / science / article / pii /
S0378437112000647.
[19] Wikimedia Commons. File:Reseau de Bethe.svg — Wikimedia Commons, the
free media repository. [Online; accessed 14-May-2024]. 2020. URL: https:
//commons.wikimedia.org/w/index.php?title=File:Reseau_
de_Bethe.svg&oldid=499918548.
[20] Anna Frishman and Pierre Ronceray. “Learning Force Fields from Stochastic
Trajectories”. In: Phys. Rev. X 10 (2 2020), p. 021009. DOI: 10.1103/
PhysRevX.10.021009. URL: https://link.aps.org/doi/10.
1103/PhysRevX.10.021009.
[21] Thomas M. Cover and Joy A. Thomas. Elements of Information Theory 2nd
Edition (Wiley Series in Telecommunications and Signal Processing). Wiley-
Interscience, 2006. ISBN: 0471241954.
[22] Marco Baiesi and Gianmaria Falasco. “Inflow rate, a time-symmetric
observable obeying fluctuation relations”. In: Phys. Rev. E 92 (4 2015),
p. 042162. DOI: 10 . 1103 / PhysRevE . 92 . 042162. URL: https : / /
link.aps.org/doi/10.1103/PhysRevE.92.042162.
[23] Udo Seifert. “Stochastic thermodynamics, fluctuation theorems and
molecular machines”. In: Reports on Progress in Physics 75.12 (2012),
p. 126001. DOI: 10.1088/0034-4885/75/12/126001. URL: https:
//dx.doi.org/10.1088/0034-4885/75/12/126001.
59
指導教授 黎璧賢(Pik-Yin Lai) 審核日期 2024-7-11
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明