|
|
Noise-induced phase transition in the Vicsek model through eigen microstate methodology |
Yongnan Jia(贾永楠), Jiali Han(韩佳丽), and Qing Li(李擎)† |
School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China |
|
|
Abstract This paper presents a comprehensive framework for analyzing phase transitions in collective models such as the Vicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of social animals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noise remains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and non-equilibrium states, the eigen microstate method is employed here for a quantitative examination of the phase transitions in the Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phase transitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for these phase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions with escalation of population density.
|
Received: 15 April 2024
Revised: 14 June 2024
Accepted manuscript online: 24 June 2024
|
PACS:
|
87.80.-y
|
(Biophysical techniques (research methods))
|
|
Fund: This work was supported by the National Natural Science Foundation of China (Grant No. 62273033). |
Corresponding Authors:
Qing Li
E-mail: liqing@ies.ustb.edu.cn
|
Cite this article:
Yongnan Jia(贾永楠), Jiali Han(韩佳丽), and Qing Li(李擎) Noise-induced phase transition in the Vicsek model through eigen microstate methodology 2024 Chin. Phys. B 33 090501
|
[1] Butt T, Mufti T, Humayun A, Rosenthal P B, Khan S, Khan S and Molloy J E 2010 J. Biol. Chem. 285 4964 [2] Herbert-Read J E, Perna A, Mann R P, Schaerf T M, Sumpter D J T and Ward A J W 2011 Proc. Natl. Acad. Sci. USA 108 18726 [3] Becco C, Vandewalle N, Delcourt J and Poncin P 2006 Physica A 367 487 [4] Ballerini M, Cabibbo N, Candelier R, Cavagna A, Cisbani E, Giardina I, Lecomte V, Orlandi A, Parisi G, Procaccini A, Viale M and Zdravkovic V 2008 Proc. Natl. Acad. Sci. USA 105 1232 [5] Nagy M, Kos Z, Biro D and Vicsek T 2010 Nature 464 890 [6] Dalmao F and Ordecki E 2011 SLAM J. Appl. Math. 71 1307 [7] Jia Y N and Vicsek T 2019 New J. Phys. 21 093048 [8] Du J M 2019 Appl. Math. Comput. 363 124629 [9] Wang C H and DeBeer S 2021 Chem. Soc. Rev. 50 8743 [10] Du J M and Wu Z R 2022 Appl. Math. Comput. 430 127295 [11] Du J M and Wu Z R 2024 Knowledge-Based Systems 284 111287 [12] Reynolds C W 1987 ACM Siggraph Comput. Graph. 21 25 [13] Vicsek T, Czirok A, Ben-Jacob E, Cohen I and Shochet O 1995 Phys. Rev. Lett. 75 1226 [14] Cucker F and Smale S 2007 IEEE Trans. Automat. Control 52 852 [15] Barbaro A B T, Canizo J A, Carrillo J A and Degond P 2015 Multiscale Modeling and Simulation 14 1063 [16] Pearce D J G and Turner M S 2014 New J. Phys. 16 082002 [17] Aldana M and Huepe C 2003 J. Stat. Phys. 112 135 [18] Barbaro A B T and Degond P 2014 Discrete and Continuous Dynamical Systems B 19 1249 [19] Escaff D and Delpiano R 2020 Chaos 30 083137 [20] Du G L and Ye F F 2022 Chin. Phys. B 31 086401 [21] Vahabli D and Vicsek T 2023 Commun. Phys. 6 56 [22] Binder K 1981 Z. Phys. B 43 119 [23] Grégoire G and Chate H 2004 Phys. Rev. Lett. 92 025702 [24] Nagy M, Duruka I and Vicsek T 2007 Physica A 373 445 [25] Baglietto G and Albano E V 2009 Phys. Rev. E 80 050103 [26] Sun Y, Hu G K, Zhang Y W, Lu B, Lu Z H, Fan J F, Li X T, Deng Q M and Chen X S 2021 Commun. Theor. Phys. 73 065603 [27] Li X, Xue T T, Sun Y, Fan J F, Li H, Liu M X, Han Z G, Di Z R and Chen X S 2021 Chin. Phys. B 30 128703 [28] Hadamard J 1906 Bull. Am. Math. Soc. 12 194 [29] Strang G 1993 Am. Math. Mon. 100 848 [30] Lutz H O, Stein J, Datz S and Moak C D 1972 Phys. Rev. Lett. 28 8 [31] Privman V and Fisher M E 1984 Phys. Rev. B 30 322 [32] Privman V, Aharony A and Hohenberg P C 1991 Phase Transitions and Critical Phenomena (New York: Academic Press) [33] Hu G K, Liu T, Liu M X, Chen W and Chen X S 2019 Sci. China Phys. Mech. Astron. 62 990511 |
[1] |
LIN WEI-ZHU (林位株), PENG WEN-JI (彭文基), QIU ZHI-REN (丘志仁), ZHOU XUE-CONG (周学聪), MO DANG (莫党). DYNAMICS OF CARRIER CAPTURE IN AlGaAs/GaAs MULTIPLE QUANTUM WELLS[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(1): 63
-68
. |
[2] |
PENG WEN-JI (彭文基), LI QING-XING (李庆行), YU ZHEN-XIN (余振新), AN NING (安宁), XU MAI (徐迈). STUDIES ON THE DYNAMICS OF OPTICAL BISTABILITY SWITCHING IN THE INTERNAL FABRY-PEROT CAVITY WITH A CdSxSe1-x-DOPED GLASS CHANNEL WAVEGUIDE[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(3): 183
-190
. |
[3] |
WANG REN-ZHI (王仁智), KE SAN-HUANG (柯三黄), HUANG MEI-CHUN (黄美纯). AB INITIO CALCULATIONS OF OPTICAL PHONON DEFORMATION POTENTIALS IN DIAMOND AND ZINC-BLENDE SEMICONDUCTORS[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(3): 202
-210
. |
[4] |
HU CHENG-ZHENG (胡承正), DING DI-HUA (丁棣华), YANG WEN-GE (杨文革). EXPRESSION OF THE ELASTIC ENERGY IN TWO-DIMENSIONAL QUASICRYSTALS[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(1): 42
-47
. |
[5] |
LIU JUN-MING (刘俊明), LIU ZHI-GUO (刘治国), WU ZHUANG-CHUN (吴状春). SCALING LAW FOR CBr4-C2Cl6 LAMELLAR EUTECTIC IN DIRECTIONAL SOLIDIFICATION[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(10): 782
-790
. |
[6] |
LIU XIN-TIAN (刘心田), SHI BAO-AN (石保安), YANG DE-JIA (杨德嘉), CHEN ZHAO-JIA (陈兆甲). A DEMONSTRATION OF 1×8 LINEAR ARRAY YBCO TRANSITION EDGE IR BOLOMETER[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(4): 248
-251
. |
[7] |
YUAN SHI-QI (袁世齐), GU BEN-YUAN (顾本源). PROPERTIES OF PROPAGATION OF GUIDED ELECTRON WAVES IN COUPLED ASYMMETRIC QUANTUM WELLS[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(4): 286
-299
. |
[8] |
LIN MEI-RONG (林美荣), CHEN WEN-JU (陈文驹), ZHANG BAO-ZHENG (张包铮), LIU YAO-MING (刘耀明), LI LIN-FENG (李林枫). EFFECT OF THE LASER TRANSVERSE SPATIAL DISTRIBUTION ON MULTIPHOTON IONIZATION PROCESSES[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(5): 345
-355
. |
[9] |
QIANG LIANG-SHENG (强亮生), ZHANG HONG-XI (张洪喜), XU CHONG-QUAN (徐崇泉), XU YU-HENG (徐玉恒). THERMODYNAMIC ANALYSIS AND FORMATION ENTHALPY CALCULATION OF OXYGEN VACANCY DEFECT IN DOPED LITHIUM NIOBATE CRYSTALS[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(7): 523
-527
. |
[10] |
LIU GUO-ZHI (刘国治), QIU AI-CI (邱爱慈), ZHANG JIA-SHENG (张嘉生), LIU NAI-QUAN (刘乃泉), XIE XI (谢羲). EXPERIMENTAL STUDY ON THE UNIFORMITY OF LARGE AREA INTENSE RELATIVISTIC ELECTRON BEAMS[J]. Acta Physica Sinica (Overseas Edition), 1994, 3(1): 45
-50
. |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|