Prediction of catastrophes: An experimental model

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 86, Issue 2, 2012, Pages

  Peters, Randall D ^a   Le Berre, Martine ^b   Pomeau, Yves ^c  

^a MERCER UNIVERSITY   (United States)

^b INSTITUT DES SCIENCES MOLÉCULAIRES D ORSAY   (France)

^c University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COLLECTIVE MOTIONS; CONSTANT STRESS; CRITICAL SLOWING DOWN; DYNAMICAL MODEL; EXPERIMENTAL APPROACHES; EXPERIMENTAL MODELS; NOISY SIGNALS; PRECURSOR EFFECT; REALISTIC PHYSICAL MODEL; SOLDER WIRES; TIME-DEPENDENT;

ABSTRACTING;

DISASTERS;

EID: 84865345045     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.86.026207     Document Type: Article

References (31)

1. G. Ananthakrishna, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2006.10. 003 440, 113 (2007).
2. Y. Pomeau and M. Le Berre, arXiv: 1102.5637;
3. Y. Pomeau, M. Le Berre, J.-L. Le Mouël, C. Narteau, and P. Fromy, Comptes-rendus de la 14e Rencontre du Non Linéaire, edited by, C. Josserand, M. Lefranc, and, C. Letellier, (Non-Linéaire, Saint-Etienne du Rouvray, 2011).
4. G. Ananthakrishna and D. Sahoo, J. Phys. D JPAPBE 0022-3727 10.1088/0022-3727/14/11/015 14, 2081 (1981).
5. M. C. Valsakumar and G. Ananthakrishna, J. Phys. D JPAPBE 0022-3727 10.1088/0022-3727/16/6/014 16, 1055 (1983).
6. A. A. Dorodnicyn, Am. Math. Soc. Transl. Seri. One 4, 1 (1953)
7. A. A. Dorodnicyn, [translated from Priklad Mat. Mek. 11, 313 (1947)].
8. V. A. Dubrovskiy and V. N. Sergeev, GEOS, Moscow 1, 222 (2001) (in Russian);
9. V. A. Dubrovskiy and V. N. Sergeev, Dok. Phys. DOPHFU 1028-3358 10.1134/1.1753617 49, 231 (2004). (Pubitemid 38782397)
10. V. A. Dubrovskiy and V. N. Sergeev, Ital. J. Eng. Geol. Environ., Spec. Issue 1, 183 (2006).
11. D. Sornette and J. V. Andersen, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2006-10036-6 74, 778 (2006). (Pubitemid 43874889)
12. Y. Haung, H. Salem, C. Sammis, and D. Sornette, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i1998-00113-x 41, 43 (1994);
13. C. G. Bufe and D. J. Varnes, J. Geophys. Res. JGREA2 0148-0227 10.1029/93JB00357 98, 9871 (1990);
14. A. Guarino, S. Ciliberto, A. Garcimartín, M. Zei, and R. Scorretti, Eur. Phys. J. B 10.1140/epjb/e20020075 26, 141 (2002);
15. R. De and G. Ananthakrishna, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-10255-3 66, 715 (2004); (Pubitemid 39015031)
16. see Nature Debates (1999) http://helix.nature.com/debates/earthquake.
17. Y. Pomeau and M. Le Berre, in Chaos, CNN, Memristors and Beyond, edited by, A. Adamatzky, and, G. Chen, (World Scientific, Singapore, 2012) (to be published);
18. see also Y. Pomeau and M. Le Berre, arXiv: 1107.3331.
19. US Patent No. 5461319 (1995). A description of the sensor is provided at http://telatomic.com/mechanics/sensor.html.
20. http://telatomic.com/mechanics/cavendish-balance.html. The support electronics for this balance employs a novel capacitive to digital converter (AD7745), which was marketed by Analog Devices soon after the demise of the NE5521n.
21. The USB4CH is described online at http://www.symres.com.
22. The VolksMeter is described online at http://psn.quake.net/volksmeter/ State-of-the-art-Digital-Seismograph.pdf.
23. The Earthquake data are shown at http://physics.mercer.edu/hpage/CSP/ bounce.html.
24. R. Thom, Stabilité structurelle et morphogénese (Benjamin, New York, 1972);
25. V. I. Arnol'd, Catastrophe Theory, 3rd ed. (Springer-Verlag, New York, 1992).
26. Sweeping bifurcation in dynamical systems has been studied before. To the best of our knowledge it has been considered in continuous transitions in the following two cases: first, from the point of view of bifurcation theory with a time direction inverse of ours, namely in the direction where a pair of equilibria appears in forward time; see T. Erneux and P. Mandel, SIAM J Appl. Math. SMJMAP 0036-1399 10.1137/0146001 46, 1 (1986);
27. see D. Sornette, J. Phys. I (France) JPGCE8 1155-4304 10.1051/jp1:1994133 4, 209 (1994).
28. J.-P. Bouchaud and R. Cont, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050582 6, 543 (1998)
29. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1965), Chap. 10.
30. C. Kuehn, Physica D PDNPDT 0167-2789 10.1016/j.physd.2011.02.012 240, 1020 (2011), and references herein.
31. R. D. Peters, M. Le Berre, and Y. Pomeau, arXiv: 1204.1551.