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
[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.