Artículo
Capanna, M.; Soprano-Loto, N. "Turing Instability in a Model with Two Interacting Ising Lines: Non-equilibrium Fluctuations" (2019) Journal of Statistical Physics. 174(2):365-403
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Abstract:
This is the second of two articles on the study of a particle system model that exhibits a Turing instability type effect. About the hydrodynamic equations obtained in Capanna and Soprano (Markov Proc Relat Fields 23(3):401–420, 2017), we find conditions under which Turing instability occurs around the zero equilibrium solution. In this instability regime: for long times at which the process is of infinitesimal order, we prove that the non-equilibrium fluctuations around the hydrodynamic limit are Gaussian; for times converging to the critical time defined as the one at which the process starts to be of finite order, we prove that the ±1-Fourier modes are uniformly away from zero. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Registro:
| Documento: | Artículo |
| Título: | Turing Instability in a Model with Two Interacting Ising Lines: Non-equilibrium Fluctuations |
| Autor: | Capanna, M.; Soprano-Loto, N. |
| Filiación: | Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina Università degli Studi dell’Aquila, L’Aquila, 67100, Italy Gran Sasso Science Institute, L’Aquila, 67100, Italy |
| Palabras clave: | Ising; Kac potential; Non-equilibrium fluctuations; Turing instability |
| Año: | 2019 |
| Volumen: | 174 |
| Número: | 2 |
| Página de inicio: | 365 |
| Página de fin: | 403 |
| DOI: | http://dx.doi.org/10.1007/s10955-018-2206-7 |
| Título revista: | Journal of Statistical Physics |
| Título revista abreviado: | J. Stat. Phys. |
| ISSN: | 00224715 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v174_n2_p365_Capanna |
Referencias:
- Asslani, M., Di Patti, F., Fanelli, D., Stochastic turing patterns on a network (2012) Phys. Rev. E, 86, p. 046105
- Andreu-Vaillo, F., Mazón, J.M., Rossi, J.D., Toledo-Melero, J.J., (2010) Nonlocal Diffusion Problems. Mathematical Surveys and Monographs, 165. , American Mathematical Society, Providence
- Biancalani, T., Fanelli, D., Di Patti, F., Stochastic turing patterns in the Brusselator model (2010) Phys. Rev. E, 81, p. 046215
- Brémaud, P., (1999) Markov Chains: Gibbs Fields, Monte Carlo Simulation and Queues, Texts in Applied Mathematics, , Springer, New York
- Cao, Y., Erban, R., (2010) Stochastic Turing patterns: Analysis of compartment-based approaches
- Capanna, M., Soprano-Loto, N., Turing instability in a model with two interacting Ising lines: hydrodynamic limit (2017) Markov Proc. Relat. Fields, 23 (3), pp. 401-420
- De Masi, A., Ferrari, P.A., Lebowitz, J.L., Reaction–diffusion equations for interacting particle systems (1986) J. Stat. Phys., 44 (3), pp. 589-644
- Han, Q., (2011) A Basic Course in Partial Differential Equations, Graduate Studies in Mathematics, 120. , American Mathematical Society, Providence
- Kipnis, C., Landim, C., (1999) Scaling Limits of Interacting Particle Systems, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 320. , Springer, Berlin
- Meester, R., Roy, R., (1996) Continuum Percolation, Cambridge Tracts in Mathematics, 119. , Cambridge University Press, Cambridge
- Murray, J.D., (2003) Mathematical Biology. Interdisciplinary Applied Mathematics, 18. , 3, Spatial Models and Biomedical Applications, Springer, New York
- Perthame, B., (2015) Parabolic Equations in Biology, Lecture Notes on Mathematical Modelling in the Life Sciences, , Growth, Reaction, Movement and Diffusion, Springer, Cham
- Pollard, D., (1984) Convergence of Stochastic Processes, , Springer Series Statistics, Springer, New York
- Scarsoglio, S., Laio, F., D’Odorico, P., Ridolfi, L., Spatial pattern formation induced by Gaussian white noise (2011) Math. Biosci., 229 (2), pp. 174-184
- Terras, A., (1999) Fourier Analysis on Finite Groups and Applications, London Mathematical Society Student Texts, 43. , Cambridge University Press, Cambridge
- Turing, A.M., The chemical basis of morphogenesis (1952) Philos. Trans. R. Soc. Lond. Ser. B, 237 (641), pp. 37-72
- Zheng, Q., Wang, Z., Shen, J., Iqbal, A., Muhammad, H., Turing bifurcation and pattern formation of stochastic reaction–diffusion system (2017) Adv. Math. Phys., , https://doi.org/10.1155/2017/9648538
Citas:
---------- APA ----------
Capanna, M. & Soprano-Loto, N. (2019) . Turing Instability in a Model with Two Interacting Ising Lines: Non-equilibrium Fluctuations. Journal of Statistical Physics, 174(2), 365-403.http://dx.doi.org/10.1007/s10955-018-2206-7
---------- CHICAGO ----------
Capanna, M., Soprano-Loto, N. "Turing Instability in a Model with Two Interacting Ising Lines: Non-equilibrium Fluctuations" . Journal of Statistical Physics 174, no. 2 (2019) : 365-403.http://dx.doi.org/10.1007/s10955-018-2206-7
---------- MLA ----------
Capanna, M., Soprano-Loto, N. "Turing Instability in a Model with Two Interacting Ising Lines: Non-equilibrium Fluctuations" . Journal of Statistical Physics, vol. 174, no. 2, 2019, pp. 365-403.http://dx.doi.org/10.1007/s10955-018-2206-7
---------- VANCOUVER ----------
Capanna, M., Soprano-Loto, N. Turing Instability in a Model with Two Interacting Ising Lines: Non-equilibrium Fluctuations. J. Stat. Phys. 2019;174(2):365-403.http://dx.doi.org/10.1007/s10955-018-2206-7
