Weak-noise limit of a piecewise-smooth stochastic differential equation

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

Volumn 88, Issue 5, 2013, Pages

  Chen, Yaming ^a   Baule, Adrian ^a   Touchette, Hugo ^b,c   Just, Wolfram ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b National Institute for Theoretical Physics   (South Africa)

^c STELLENBOSCH UNIVERSITY   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

HIGHER-ORDER; INSTANTONS; NOISE POWER; PATH INTEGRAL; SADDLE POINT; SIMPLE MODELING; SOLID FRICTION; STOCHASTIC DIFFERENTIAL EQUATIONS;

QUANTUM THEORY;

DIFFERENTIAL EQUATIONS;

EID: 84888147708     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.88.052103     Document Type: Article

References (39)

1. A. F. Filippov, Differential Equations with Discontinuous Righthand Sides (Kluwer, Dordrecht, 1988).
2. M. di Bernardo, C. Budd, A. Champneys, and P. Kowalczyk, Piecewise-Smooth Dynamical Systems: Theory and Applications (Springer, Berlin, 2008).
3. O. Makarenkov and J. S. W. Lamb, Physica D PDNPDT 0167-2789 10.1016/j.physd.2012.08.002 241, 1826 (2012).
4. B. J. J. Biemond, N. van de Wouw, and H. Nijmeijer, Physica D PDNPDT 0167-2789 10.1016/j.physd.2011.05.006 241, 1882 (2012).
5. A. Colombo, M. di Bernardo, S. J. Hogan, and M. R. Jeffrey, Physica D PDNPDT 0167-2789 10.1016/j.physd.2011.09.017 241, 1845 (2012).
6. F. P. Bowden and D. Tabor, Friction and Lubrication of Solids (Oxford University Press, Oxford, 1950).
7. F.-J. Elmer, J. Phys. A: Math. Gen. JPHAC5 0305-4470 10.1088/0305-4470/ 30/17/015 30, 6057 (1997). (Pubitemid 127117284)
8. B. N. J. Persson, Sliding Friction: Physical Principles and Applications (Springer, Berlin, 1998).
9. E. J. Berger, Appl. Mech. Rev. AMREAD 0003-6900 10.1115/1.1501080 55, 535 (2002). (Pubitemid 40225720)
10. M. R. Jeffrey, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106. 254103 106, 254103 (2011).
11. P. Reimann, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(01)00081-3 361, 57 (2002).
12. T. K. Caughey and J. K. Dienes, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1777094 32, 2476 (1961).
13. J. D. Atkinson and T. K. Caughey, Int. J. Nonlin. Mech. IJNMAG 0020-7462 10.1016/0020-7462(68)90028-0 3, 399 (1968).
14. P.-G. de Gennes, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-005-4650- 4 119, 953 (2005). (Pubitemid 41125303)
15. H. Hayakawa, Physica D PDNPDT 0167-2789 10.1016/j.physd.2004.12.011 205, 48 (2005). (Pubitemid 40753175)
16. A. Baule and P. Sollich, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/97/20001 97, 20001 (2012).
17. H. Touchette, E. V. der Straeten, and W. Just, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/43/44/445002 43, 445002 (2010).
18. M. K. Chaudhury and S. Mettu, Langmuir LANGD5 0743-7463 10.1021/la8003728 24, 6128 (2008).
19. P. S. Goohpattader, S. Mettu, and M. K. Chaudhury, Langmuir LANGD5 0743-7463 10.1021/la901111u 25, 9969 (2009).
20. P. S. Goohpattader and M. K. Chaudhury, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3460530 133, 024702 (2010).
21. A. Gnoli, A. Puglisi, and H. Touchette, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/102/14002 102, 14002 (2013).
22. D. J. W. Simpson and R. Kuske, arXiv: 1204.5792.
23. I. Karatzas and S. E. Shreve, Ann. Prob. APBYAE 0091-1798 10.1214/aop/1176993230 12, 819 (1984).
24. W. Zhang, IEEE Trans. Automat. Contr. IETAA9 0018-9286 10.1109/9.58517 35, 980 (1990). (Pubitemid 20738757)
25. V. E. Benes, L. A. Shepp, and H. S. Witsenhausen, Stochastics STOCB2 0090-9491 10.1080/17442508008833156 4, 39 (1980).
26. S. Browne and W. Whitt, in Advances in Queueing, edited by, J. Dshalalow, (CRC, Boca Raton, FL, 1995), pp. 463-480.
27. M. Gradinaru, S. Herrmann, and B. Roynette, Ann. Inst. Poincaré B AHPBAR 0246-0203 10.1016/S0246-0203(01)01075-5 37, 555 (2001).
28. A. P. Korostelev and S. L. Leonov, Prob. Theory Relat. Fields PTRFEU 0178-8051 10.1007/BF01199247 94, 317 (1993).
29. T.-S. Chiang and S.-J. Sheu, Ann. Prob. 10.1214/aop/1019160115 28, 140 (2000).
30. M. Boué, P. Dupuis, and R. S. Ellis, Prob. Theory Relat. Fields PTRFEU 0178-8051 10.1007/PL00008720 116, 125 (2000).
31. M. Chaichian and A. Demichev, Path Pntegrals in Physics: Stochastic Processes and Quantum Mechanics (IOP, London, 2001), Vol. 1.
32. R. Graham, in Noise in Nonlinear Dynamical Systems, edited by, F. Moss, and, P. V. E. McClintock, (Cambridge University Press, Cambridge, 1989), Vol. 1, pp. 225-278.
33. H. Touchette, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2009.05.002 478, 1 (2009).
34. A. Baule, E. G. D. Cohen, and H. Touchette, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/43/2/025003 43, 025003 (2010).
35. A. Baule, H. Touchette, and E. G. D. Cohen, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/24/2/001 24, 351 (2011).
36. M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, Grundlehren der Mathematischen Wissenschaften Vol. 260 (Springer, New York, 1984).
37. P. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, Berlin, 1992).
38. R. Graham and T. Tél, Phys. Rev. A 0556-2791 10.1103/PhysRevA.31. 1109 31, 1109 (1985).
39. W. Cassing and J. Knoll, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(81)90253-7 106, 443 (1981).