Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:C4L-D

Session:

Number:495

Stochasticity and Non-locality in Various Systems

Toru Ohira,  

pp.495-498

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.495

PDF download (809.4KB)

We discuss here three different systems, which address concepts of stochasticity and non-locality; human stick balancing, chase and escapes, and simple quantum mechanical problem. Though these problems are rather distant from each other, they show rich behaviors which are brought in by these two factors, separately or together.

[1] T. Ohira and J. G. Milton, “Delayed Random Walks”, Physical Review E, 52 3277 (1995).

[2] T. Ohira and T. Yamane, “Delayed Stochastic Systems”, Physical Review E, 61 1247 (2000).

[3] T. Ohira, “Stochasticity and Non-locality of Time”, Physica A, 379, 483-490, (2007)

[4] T. Ohira, “Temporal Stochasticity and Non-locality”, J. of Statistical Mechanics, 2009-01, P01032, (2009)

[5] J. L. Cabrera and J. G. Milton, “On-off intermittency in a human balancing task”, Phys. Rev. Lett. 89, 158702, (2002).

[6] J. L. Cabrera and J. G. Milton, “Human stick balancing: Tuning Lévy flights to improve balance control”, Chaos 14, 691-698, (2004).

[7] T. Ohira and T. Hosaka: “Control in Delayed Stochastic Systems”, In Proc. of DETC05, 2005 ASME Design Engineering Technical Conference (September, 2005, Long Beach, U.S.A.), DETC2005-84883, (2005).

[8] T. Hosaka and T. Ohira: “Delayed Random Walks and Control”, In Flow Dynamics: The second international conference on flow dynamics (AIP Conf. Porc. 832) (November, 2005, Sendai, Japan), 487, (2005).

[9] T. Hosaka, T. Ohira, C. Luciani, J. L. Cabrera, J. G. Milton, “Balancing with noise and delay”, Prog. Theor. Phys., S 161, 314 (2006).

[10] J. G. Milton, J. Cummins, J. Gunnoe, M. Tollefson, J.L. Cabrera, T. Ohira, “Resource allocation in neural networks for motor control”, Bull. of the APS (March Meeting 2006) 51, 1529 (2006).

[11] J.Milton, T. Ohira, J. L. Cabrera, R.M.Fraiser, J.B.Gyoffy, F.K.Ruiz, M.A.Strauss, E.C.Balch, P.J.Marin, J.L.Alexander, “Balancing with Vibration: A Prelude for ‘Drift and Act’ Balance Control” , PLoS One, 0007427 (2009).

[12] P. J. Nahin, Chases and Escapes: The mathematics of pursuit and evasion, (Princeton University Press, Princeton, 2007).

[13] T. Ohira, A. Kamimura, J. G. Milton, “Pursuit-escape with distance-dependent delay”, In Proceedings of ENOC2011: 7th European Nonlinear Dynamics, Conferences, (July, 2011, Rome, Italy) (2011).

[14] J. G. Milton, A. Fuerte, C. Belair, J. Lippai, A. Kamimura, T. Ohira, “Delayed pursuit.escape as a model for virtual stick balancing”, Nonlinear Theory and Its Applications (NOLTA, IEICE) E96-N, (2013).

[15] A. Kamimura, T. Ohira, “Group Chase and Escape”, New Journ. Phys. 12, 053013, (2010).

[16] J. A. Wheeler, and W. H. Zurek (eds.), Quantum Theory and Measurement, (Princeton University Press, 1984).

[17] J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, (Cambridge University Press, 2004).

[18] D.Bohm, Quantum Theory, (Prentice-Hall,1951).

[19] L. L. Chang, L. Esaki, and R. Tsu, “Resonant tunneling in double barriers”, Appl. Phys. Lett. 24, 593-595, (1974).

[20] A. Peruzzo, P. Shadbolt, N. Brunner, S. Popescu, and J. L. O'Brien, “A Quantum Delayed-Choice Experiment”, Science 338, 634-637, (2012).

[21] T. Ohira, “Stochasticity and non-locality of Time”, Physica A 379, 483-490, (2007).

[22] T. Ohira, “Temporal stochasticity and non-locality”, J. Stat. Mech. 2009-1, P01032, (2009).

[23] L. I. Schiff, Quantum Mechanics, (McGraw-Hill, 1969).

[24] Note that the wave function Ψ(x) itself does not satisfy the differential equation.