921 resultados para Non-linear time series


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Daily sea surface temperatures have been acquired at the Hopkins Marine Station in Pacific Grove, California since January 20, 1919.This time series is one of the longest oceanographic records along the U.S. west coast. Because of its length it is well-suited for studying climate-related and oceanic variability on interannual, decadal, and interdecadal time scales. The record, however, is not homogeneous, has numerous gaps, contains possible outliers, and the observations were not always collected at the same time each day. Because of these problems we have undertaken the task of reconstructing this long and unique series. We describe the steps that were taken and the methods that were used in this reconstruction. Although the methods employed are basic, we believe that they are consistent with the quality of the data. The reconstructed record has values at every time point, original, or estimated, and has been adjusted for time-of-day variations where this information was available. Possible outliers have also been examined and replaced where their credibility could not be established. Many of the studies that have employed the Hopkins time series have not discussed the issue of data quality and how these problems were addressed. Because of growing interest in this record, it is important that a single, well-documented version be adopted, so that the results of future analyses can be directly compared. Although additional work may be done to further improve the quality of this record, it is now available via the internet. [PDF contains 48 pages]

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The general theory of Whitham for slowly-varying non-linear wavetrains is extended to the case where some of the defining partial differential equations cannot be put into conservation form. Typical examples are considered in plasma dynamics and water waves in which the lack of a conservation form is due to dissipation; an additional non-conservative element, the presence of an external force, is treated for the plasma dynamics example. Certain numerical solutions of the water waves problem (the Korteweg-de Vries equation with dissipation) are considered and compared with perturbation expansions about the linearized solution; it is found that the first correction term in the perturbation expansion is an excellent qualitative indicator of the deviation of the dissipative decay rate from linearity.

A method for deriving necessary and sufficient conditions for the existence of a general uniform wavetrain solution is presented and illustrated in the plasma dynamics problem. Peaking of the plasma wave is demonstrated, and it is shown that the necessary and sufficient existence conditions are essentially equivalent to the statement that no wave may have an amplitude larger than the peaked wave.

A new type of fully non-linear stability criterion is developed for the plasma uniform wavetrain. It is shown explicitly that this wavetrain is stable in the near-linear limit. The nature of this new type of stability is discussed.

Steady shock solutions are also considered. By a quite general method, it is demonstrated that the plasma equations studied here have no steady shock solutions whatsoever. A special type of steady shock is proposed, in which a uniform wavetrain joins across a jump discontinuity to a constant state. Such shocks may indeed exist for the Korteweg-de Vries equation, but are barred from the plasma problem because entropy would decrease across the shock front.

Finally, a way of including the Landau damping mechanism in the plasma equations is given. It involves putting in a dissipation term of convolution integral form, and parallels a similar approach of Whitham in water wave theory. An important application of this would be towards resolving long-standing difficulties about the "collisionless" shock.