Beyond Brownian Motion
DOI: 10.1063/1.881487
Newtonian physics began with an attempt to make precise predictions about natural phenomena, predictions that could be accurately checked by observation and experiment. The goal was to understand nature as a deterministic, “clockwork” universe. The application of probability distributions to physics developed much more slowly. Early uses of probability arguments focused on distributions with well‐defined means and variances. The prime example was the Gaussian law of errors, in which the mean traditionally represented the most probable value from a series of repeated measurements of a fixed quantity, and the variance was related to the uncertainty of those measurements.
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References
1. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco (1982).
2. A. Einstein, Annalen der Physik 17, 549 (1905).
3. Lévy Flights and Related Topics in Physics, M. Shlesinger, G. Zaslavsky, U. Frisch, Eds., Springer, Berlin (1995).
4. T. Geisel, J. Nierwetberg, A. Zacherl, Phys. Rev. Lett. 54, 616 (1985).https://doi.org/PRLTAO
5. M. Shlesinger, B. West, J. Klafter, Phys. Rev. Lett. 58, 1100 (1987). https://doi.org/PRLTAO
M. Shlesinger, J. Klafter, Y. M. Wong, J. Stat. Phys. 27, 499 (1982).https://doi.org/JSTPBS6. F. Hayot, Phys. Rev. A. 43, 806 (1991).https://doi.org/PLRAAN
7. A. Ott, J. Bouchaud, D. Langevin, and W. Urbach, Phys. Rev. Lett. 65, 2201 (1990). https://doi.org/PRLTAO
J. Bouchaud, A. Georges, Phys. Reports 195, 127 (1980).https://doi.org/PRPLCM8. J. Viecelli, Phys. Fluids A 5, 2484 (1993).https://doi.org/PFADEB
9. T. Solomon, E. Weeks, H. Swinney, Phys. Rev. Lett. 71, 3975 (1993).https://doi.org/PRLTAO
10. G. Zumofen, J. Klafter, Chem. Phys. Lett. 219, 303 (1994).https://doi.org/CHPLBC
11. T. Geisel, A. Zacherl, G. Radons, Z. Phys. B. 71, 117 (1988).
12. A. Chernikov, B. Petrovichev, A. Rogalsky, R. Sagdeev, G. Zaslavsky, Phys. Lett. A 144, 127 (1990).https://doi.org/PYLAAG
13. D. Chaikovsky, G. Zaslavsky, Chaos 1, 463 (1991).https://doi.org/CHAOEH
14. I. Aranson, M. Rabinovich, L. Tsimring, Phys. Lett. A 151, 523 (1990).
15. J. Klafter, G. Zumofen, Phys. Rev. E 49, 4873 (1994).https://doi.org/PLEEE8
16. M. Shlesinger, G. Zaslavsky, J. Klafter, Nature 363, 31 (1993).https://doi.org/NATUAS
17. R. Ramashanker, D. Berlin, J. Gollub, Phys. Fluids A 2, 1955 (1980).
18. O. Baychuk, B. O’Shaughnessy, Phys. Rev. Lett. 74, 1795 (1985). https://doi.org/PRLTAO
S. Stapf, R. Kimmich, R. Seitter, Phys. Rev. Lett. 75, 2855 (1995).https://doi.org/PRLTAO19. G. Zimbardo, P. Veltrei, G. Basile, S. Principato, Phys. Plasma 2, 2653 (1995). https://doi.org/PHPAEN
R. Balescu, Phys. Rev. E 51, 4807 (1995).https://doi.org/PLEEE820. A. Carasso, in Mathematical Methods in Medical Imaging II, SPIE vol. 2035 (1993), p. 255.
21. R. Fleischmann, T. Geisel, R. Ketzmerick, Europhys. Lett. 25, 219 (1994).https://doi.org/EULEEJ
More about the authors
Joseph Klafter, Tel Aviv University, Israel.
Michael F. Shlesinger, Office of Naval Research, Arlington, Virginia.
Gert Zumofen, Laboratory for Physical Chemistry of the Eidgenössische Technische Hochschule, Zurich, Switzerland.
