Dynamics of Nonlinear Stochastic Systems
Dynamics of Nonlinear Stochastic Systems
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In our eReader you can find the full English version of the book. Read Dynamics of Nonlinear Stochastic Systems Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Dynamics of Nonlinear Stochastic Systems
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, (b^) -l[S(p)]-2[fi(p)]2j(3)(p) . (^. Is, - 37 - Combining our results (and suppressing the argument p) we have, finally, Eliminating H and J from (7. 6) and (7. I7), we obtain (b^> ^G^ ♦ p( ♦ ap2)G^ - ( ♦ 3ap^)G^ ♦ 3apO - a - . (7. 18) The relevant branch of (7. 18) is the one for which G(co) • n" Re {G(-iw)} reduces to (5. 6) when a ■ 0, and it is easily verified that such a branch exists. Let us examine the behavior of G((a) on this branch as a is varied. For sufficiently small a, it is p...lausible to assume that our assignment of values to the C's is realizable. As we increase a, we may plausibly anticipate that G(co) will begin to violate (2. U), or at least will exhibit some discontinuous change in its dependence on a, when a critical value is reached for which the C »s are unrealizable by any assignment of values to the Jjf's consistwit with (U. U). This argument is supported by the example of Section 6« The behavior of (7. 18) is accessible by standard techniques for quartic equations.
What to read after Dynamics of Nonlinear Stochastic Systems?
You can find similar books in the "Read Also" column, or choose other free books by R H Kraichnan to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
, (b^) -l[S(p)]-2[fi(p)]2j(3)(p) . (^. Is, - 37 - Combining our results (and suppressing the argument p) we have, finally, Eliminating H and J from (7. 6) and (7. I7), we obtain (b^> ^G^ ♦ p( ♦ ap2)G^ - ( ♦ 3ap^)G^ ♦ 3apO - a - . (7. 18) The relevant branch of (7. 18) is the one for which G(co) • n" Re {G(-iw)} reduces to (5. 6) when a ■ 0, and it is easily verified that such a branch exists. Let us examine the behavior of G((a) on this branch as a is varied. For sufficiently small a, it is p...lausible to assume that our assignment of values to the C's is realizable. As we increase a, we may plausibly anticipate that G(co) will begin to violate (2. U), or at least will exhibit some discontinuous change in its dependence on a, when a critical value is reached for which the C »s are unrealizable by any assignment of values to the Jjf's consistwit with (U. U). This argument is supported by the example of Section 6« The behavior of (7. 18) is accessible by standard techniques for quartic equations.
What to read after Dynamics of Nonlinear Stochastic Systems?
You can find similar books in the "Read Also" column, or choose other free books by R H Kraichnan to read onlineMoreLess
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