Theory of electrical noise induced in a wire loop by the thermal motions of ions in solution

Journal of Applied Physics

Volumn 83, Issue 6, 1998, Pages 3118-3128

  Gillespie, Daniel T ^a  

^a NAVAL AIR WARFARE CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041944855     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.367068     Document Type: Article

References (17)

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4. P. Langevin, Comptes Rendues 146, 530 (1908).
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9. D. T. Gillespie, Am. J. Phys. 64, 225 (1996).
10. - ions, the number of hydrating water molecules is often taken to be about 6, although various measurement techniques have yielded a rather broad range of estimates. See H. Ohtaki and T. Radnal, Chem. Rev. 93, 1157 (1993).
11. Monte Carlo integration techniques are discussed at length in many places; e.g., M. H. Kalos and P. A. Whitlock, Monte Carlo Methods, Vol. I: Basics (Wiley, New York, 1986), and D. T. Gillespie, The Monte Carlo method of evaluating integrals (Naval Weapons Center Tech. Pub. #7514, China Lake, CA, 1975) No. NWC TP7514.
12. Monte Carlo integration techniques are discussed at length in many places; e.g., M. H. Kalos and P. A. Whitlock, Monte Carlo Methods, Vol. I: Basics (Wiley, New York, 1986), and D. T. Gillespie, The Monte Carlo method of evaluating integrals (Naval Weapons Center Tech. Pub. #7514, China Lake, CA, 1975) No. NWC TP7514.
13. D. T. Gillespie, Phys. Rev. E 55, 2588 (1997); see particularly Sec. IV.
14. D. T. Gillespie, Am. J. Phys. 64, 1246 (1996).
15. For the simple OU process, Eqs. (2.2a) and (2.2b) are, respectively, the "standard form" Langevin equation and the "white-noise form" Langevin equation. A detailed discussion of those two equivalent Langevin equation forms for a general multivariate continuous Markov process can be found in Ref. 12, Sec. II.
16. See, for instance, M. D. Springer, in The Algebra of Random Variables (Wiley, New York, 1979), pp. 70-75.
17. See, for instance, Ref. 8, Sec. II D.