Kardar-Parisi-Zhang universality class for the critical dynamics of reaction-diffusion fronts. (English) Zbl 1459.82148
Summary: We have studied front dynamics for the discrete \(A+A \leftrightarrow A\) reaction-diffusion system, which in the continuum is described by the (stochastic) Fisher-Kolmogorov-Petrovsky-Piscunov equation. We have revisited this discrete model in two space dimensions by means of extensive numerical simulations and an improved analysis of the time evolution of the interface separating the stable and unstable phases. In particular, we have measured the full set of scaling exponents which characterize the spatio-temporal fluctuations of such front for different lattice sizes, focusing mainly in the front width and correlation length. These exponents are in very good agreement with those computed in [E. Moro, “Internal fluctuations effects on Fisher waves”, Phys. Rev. Lett. 87, Article ID 238303, 4 p. (2001; doi:10.1103/PhysRevLett.87.238303)] and correspond to those of the Kardar-Parisi-Zhang (KPZ) universality class for one-dimensional interfaces. Furthermore, we have studied the one-point statistics and the covariance of rescaled front fluctuations, which had remained thus far unexplored in the literature and allows for a further stringent test of KPZ universality.
MSC:
| 82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
References:
| [1] | Cross M and Greenside H 2009 Pattern Formation and Dynamics in Nonequilibrium Systems (Cambridge: Cambridge University Press) · Zbl 1177.82002 · doi:10.1017/CBO9780511627200 |
| [2] | Epstein I R and Pojman J A 1998 An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos (Oxford: Oxford University Press) |
| [3] | Tsimring L S 2014 Rep. Prog. Phys.77 026601 · doi:10.1088/0034-4885/77/2/026601 |
| [4] | Pastor-Satorras R, Castellano C, Van Mieghem P and Vespignani A 2015 Rev. Mod. Phys.87 925 · doi:10.1103/RevModPhys.87.925 |
| [5] | Boffetta G and Mazzino A 2017 Annu. Rev. Fluid Mech.49 119 · Zbl 1359.76136 · doi:10.1146/annurev-fluid-010816-060111 |
| [6] | Fisher R A 1937 Ann. Eugenics7 355 · JFM 63.1111.04 · doi:10.1111/j.1469-1809.1937.tb02153.x |
| [7] | Kolmogorov A, Petrosvky I and Piscounov N 1937 Mosc. Univ. Bull. Math. A 1 1-7 |
| [8] | Murray J D 2002 Mathematical Biology: an Introduction, volume (New York: Springer) · Zbl 1006.92001 · doi:10.1007/b98868 |
| [9] | van Saarloos W 2003 Phys. Rep.386 29 · Zbl 1042.74029 · doi:10.1016/j.physrep.2003.08.001 |
| [10] | Zadorin A S, Rondelez Y, Galas J C and Estevez-Torres A 2015 Phys. Rev. Lett.114 068301 · doi:10.1103/PhysRevLett.114.068301 |
| [11] | Tanaka H, Zeravcic Z and Brenner M P 2016 Phys. Rev. Lett.117 238004 · doi:10.1103/PhysRevLett.117.238004 |
| [12] | Zadorin A S, Rondelez Y, Gines G, Dilhas V, Urtel G, Zambrano A, Galas J C and Estevez-Torres A 2017 Nat. Chem.9 990 · doi:10.1038/nchem.2770 |
| [13] | Sun G Q, Jusup M, Jin Z, Wang Y and Wang Z 2016 Phys. Life Rev.19 43 · doi:10.1016/j.plrev.2016.08.002 |
| [14] | Hui C and Richardson D M 2017 Invasion Dynamics (Oxford: Oxford University Press) · Zbl 1358.92004 · doi:10.1093/acprof:oso/9780198745334.001.0001 |
| [15] | Sagués F, Sancho J M and García-Ojalvo J 2007 Rev. Mod. Phys.79 829 · doi:10.1103/RevModPhys.79.829 |
| [16] | Hallatschek O 2011 Proc. Natl Acad. Sci. USA108 1783 · doi:10.1073/pnas.1013529108 |
| [17] | Täuber U C 2014 Critical Dynamics: a Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior (Cambridge: Cambridge University Press) |
| [18] | Nesic S, Cuerno R and Moro E 2014 Phys. Rev. Lett.113 180602 · doi:10.1103/PhysRevLett.113.180602 |
| [19] | Ódor G 2004 Rev. Mod. Phys.76 663 · Zbl 1205.82102 · doi:10.1103/RevModPhys.76.663 |
| [20] | Panja D 2004 Phys. Rep.393 87 · doi:10.1016/j.physrep.2003.12.001 |
| [21] | Ben-Avraham D, Burschka M A and Doering C R 1990 J. Stat. Phys.60 695 · Zbl 1086.82556 · doi:10.1007/BF01025990 |
| [22] | Pechenik L and Levine H 1999 Phys. Rev. E 59 3893 · doi:10.1103/PhysRevE.59.3893 |
| [23] | Doering C R, Mueller C and Smereka P 2003 Physica A 325 243 · Zbl 1025.60027 · doi:10.1016/S0378-4371(03)00203-6 |
| [24] | Moro E 2004 Phys. Rev. E 70 045102 · doi:10.1103/PhysRevE.70.045102 |
| [25] | Henkel M, Hinrichsen H and Lübeck S 2008 Non-Equilibrium Phase Transitions. Absorbing Phase Transitions vol 1 (Dordrecht: Springer) · Zbl 1165.82002 |
| [26] | Barabási A L and Stanley H E 1995 Fractal Concepts in Surface Growth (Cambridge: Cambridge University Press) · Zbl 0838.58023 · doi:10.1017/CBO9780511599798 |
| [27] | Krug J 1997 Adv. Phys.46 139 · doi:10.1080/00018739700101498 |
| [28] | Riordan J, Doering C R and Ben-Avraham D 1995 Phys. Rev. Lett.75 565 · doi:10.1103/PhysRevLett.75.565 |
| [29] | Tripathy G and Van Saarloos W 2000 Phys. Rev. Lett.85 3556 · doi:10.1103/PhysRevLett.85.3556 |
| [30] | Moro E 2001 Phys. Rev. Lett.87 238303 · doi:10.1103/PhysRevLett.87.238303 |
| [31] | Tripathy G, Rocco A, Casademunt J and van Saarloos W 2001 Phys. Rev. Lett.86 5215 · doi:10.1103/PhysRevLett.86.5215 |
| [32] | Moro E 2004 Phys. Rev. E 69 060101 · doi:10.1103/PhysRevE.69.060101 |
| [33] | Kardar M, Parisi G and Zhang Y C 1986 Phys. Rev. Lett.56 889 · Zbl 1101.82329 · doi:10.1103/PhysRevLett.56.889 |
| [34] | Kriecherbauer T and Krug J 2010 J. Phys. A: Math. Theor.43 403001 · Zbl 1202.82058 · doi:10.1088/1751-8113/43/40/403001 |
| [35] | Halpin-Healy T and Takeuchi K A 2015 J. Stat. Phys.160 794 · Zbl 1327.82065 · doi:10.1007/s10955-015-1282-1 |
| [36] | Takeuchi K A 2018 Physica A 504 77 · Zbl 1514.82024 · doi:10.1016/j.physa.2018.03.009 |
| [37] | Fortin J Y and Clusel M 2015 J. Phys. A: Math. Theor.48 183001 · Zbl 1312.82008 · doi:10.1088/1751-8113/48/18/183001 |
| [38] | Prähofer M and Spohn H 2002 J. Stat. Phys.108 1071 · Zbl 1025.82010 · doi:10.1023/A:1019791415147 |
| [39] | Bornemann F, Ferrari P L and Prähofer M 2008 J. Stat. Phys.133 405 · Zbl 1161.82340 · doi:10.1007/s10955-008-9621-0 |
| [40] | Quastel J 2011 Curr. Dev. Math.2011 125 · doi:10.4310/CDM.2011.v2011.n1.a3 |
| [41] | Corwin I, Quastel J and Remenik D 2013 Commun. Math. Phys.317 347 · Zbl 1257.82112 · doi:10.1007/s00220-012-1582-0 |
| [42] | Alves S G, Oliveira T J and Ferreira S C 2014 Phys. Rev. E 90 020103 · doi:10.1103/PhysRevE.90.020103 |
| [43] | Hallatschek O, Hersen P, Ramanathan S and Nelson D R 2007 Proc. Natl Acad. Sci. USA104 19926 · doi:10.1073/pnas.0710150104 |
| [44] | Takeuchi K A, Sano M, Sasamoto T and Spohn H 2011 Sci. Rep.1 34 · doi:10.1038/srep00034 |
| [45] | Almeida R A L, Ferreira S O, Oliveira T J and Reis F D A A 2014 Phys. Rev. B 89 045309 · doi:10.1103/PhysRevB.89.045309 |
| [46] | Nicoli M, Cuerno R and Castro M 2013 J. Stat. Mech. P11001 · Zbl 1459.82190 · doi:10.1088/1742-5468/2013/11/P11001 |
| [47] | Van Beijeren H 2012 Phys. Rev. Lett.108 180601 · doi:10.1103/PhysRevLett.108.180601 |
| [48] | Mendl C B and Spohn H 2013 Phys. Rev. Lett.111 230601 · doi:10.1103/PhysRevLett.111.230601 |
| [49] | Yunker P J, Lohr M A, Still T, Borodin A, Durian D J and Yodh A G 2013 Phys. Rev. Lett.110 035501 · doi:10.1103/PhysRevLett.110.035501 |
| [50] | Santalla S N, Rodríguez-Laguna J, Lagatta T and Cuerno R 2015 New J. Phys.17 33018 · doi:10.1088/1367-2630/17/3/033018 |
| [51] | Córdoba-Torres P, Santalla S N, Cuerno R and Rodríguez-Laguna J 2018 J. Stat. Mech. 063212 · Zbl 1459.82116 · doi:10.1088/1742-5468/aac745 |
| [52] | Altman E, Sieberer L M, Chen L, Diehl S and Toner J 2015 Phys. Rev. X 5 011017 · doi:10.1103/PhysRevX.5.011017 |
| [53] | Chen L, Lee C F and Toner J 2016 Nat. Commun.7 12215 · doi:10.1038/ncomms12215 |
| [54] | Nahum A, Ruhman J, Vijay S and Haah J 2017 Phys. Rev. X 7 031016 · doi:10.1103/PhysRevX.7.031016 |
| [55] | Takeuchi K A 2012 J. Stat. Mech. P05007 · doi:10.1088/1742-5468/2012/05/P05007 |
| [56] | Alves S G, Oliveira T J and Ferreira S C 2013 J. Stat. Mech. P05007 · Zbl 1459.82165 · doi:10.1088/1742-5468/2013/05/P05007 |
| [57] | Saito Y, Dufay M and Pierre-Louis O 2012 Phys. Rev. Lett.108 8522 · doi:10.1103/PhysRevLett.108.245504 |
| [58] | Young P 2012 (arXiv:1210.3781) |
| [59] | Efron B 1982 The Jackknife, the Bootstrap, and Other Resampling Plans (Philadelphia, PA: SIAM) · Zbl 0496.62036 · doi:10.1137/1.9781611970319 |
| [60] | Pimpinelli A and Villain J 1998 Physics of Crystal Growth (Cambridge: Cambridge University Press) · Zbl 0934.76002 · doi:10.1017/CBO9780511622526 |
| [61] | Siegert M 1996 Phys. Rev. E 53 3209 · doi:10.1103/PhysRevE.53.3209 |
| [62] | Bornemann F 2010 Markov Process. Relat.16 803 · Zbl 1222.60013 |
| [63] | Bornemann F 2010 Math. Comput.79 871 · Zbl 1208.65182 · doi:10.1090/S0025-5718-09-02280-7 |
| [64] | Alves S G, Oliveira T J and Ferreira S C 2011 Europhys. Lett.96 48003 · doi:10.1209/0295-5075/96/48003 |
| [65] | Oliveira T J, Ferreira S C and Alves S G 2012 Phys. Rev. E 85 040102 · doi:10.1103/PhysRevA.85.040102 |
| [66] | Carrasco I S S and Oliveira T J 2016 Phys. Rev. E 94 050801 · doi:10.1103/PhysRevE.94.050801 |
| [67] | Rodríguez-Fernández E and Cuerno R 2019 Phys. Rev. E 99 042108 · doi:10.1103/PhysRevE.99.042108 |
| [68] | Nesic S 2015 Stochastic dynamics of substrate-confined systems: Fisher fronts and thin liquid films PhD Thesis Universidad Carlos III de Madrid Leganés, Spain |
| [69] | Scalise D and Schulman R 2019 Ann. Rev. Biomed. Eng.21 469 · doi:10.1146/annurev-bioeng-060418-052357 |
| [70] | Zenk J, Scalise D, Wang K, Dorsey P, Fern J, Cruz A and Schulman R 2017 RSC Adv.7 18032 · doi:10.1039/C7RA00824D |
| [71] | Lovrak M, Hendriksen W E, Kreutzer M T, Van Steijn V, Eelkema R and Van Esch J H 2019 Soft Matter15 4276 · doi:10.1039/C8SM02588F |
| [72] | Chou T, Mallick K and Zia R K P 2011 Rep. Prog. Phys.74 116601 · doi:10.1088/0034-4885/74/11/116601 |
| [73] | Yllanes D 2011 Rugged free-energy landscapes in disordered spin systems PhD Thesis Universidad Complutense de Madrid |
| [74] | Michael C 1994 Phys. Rev. D 49 2616 · doi:10.1103/PhysRevD.49.2616 |
| [75] | Lulli M, Parisi G and Pelissetto A 2016 Phys. Rev. E 93 032126 · doi:10.1103/PhysRevE.93.032126 |
| [76] | Seibert D 1994 Phys. Rev. D 49 6240 · doi:10.1103/PhysRevD.49.6240 |
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