Jeffery Lewins, Martin Becker's Advances in Nuclear Science and Technology: Volume 26 PDF

By Jeffery Lewins, Martin Becker

ISBN-10: 0306461102

ISBN-13: 9780306461101

ISBN-10: 0306470888

ISBN-13: 9780306470882

Due to the fact its initiation in 1962, this sequence has awarded authoritative reports of crucial advancements in nuclear technology and engineering, from either theoretical and utilized views. furthermore, many unique contributions are incorporated.

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Additional resources for Advances in Nuclear Science and Technology: Volume 26 (Advances in Nuclear Science & Technology)

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111) as (113) where R(ξ) and f(ξ) are slowly varying variables. Following the method of KBM, one can put (114) 38 H. (113) into (116) in noticing that mω 2 0 = 1, we obtain (117) Substituting (113) and (114) into (117), we obtain (118) Averaging the cosine terms in the coefficients of R, R 2 and R 3 over one cycle [0,2π] of oscillation, one obtains (119) where (120) Similarly, application of the above averaging procedure to the equation of the phase, (121) leads to (122) where (123) 6. Experimental verification (a) complex normal form In the previous section, we have derived a van der Pol type equation with additive noise (111) for a small amplitude limit cycle oscillation near the onset of Hopf bifurcation.

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When h' can be ignored the phase motion becomes independent of the amplitude motion. However, the amplitude motion is still under the parametric influence from the phase motion. To discuss the pdfs identified experimentally in the previous section, let us derive approximate analytical expressions for the amplitude and phase pdfs at the steady-state. Let us begin with the phase pdf. (128) with (133) Note that when h' = 0, the phase motion is independent of the amplitude without the mean field approximation.

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Advances in Nuclear Science and Technology: Volume 26 (Advances in Nuclear Science & Technology) by Jeffery Lewins, Martin Becker


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