Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this paper, it was shown that for autoresonance to appear, the pump amplitude must exceed some threshold value, i.e., the amplitude of the pump is larger than a threshold value.
Abstract: Autoresonance is one of the most interesting phenomena in nonlinear oscillations. The energy of forced oscillations of a nonlinear system substantially increases in the course of time, although the driving force remains small. This phenomenon, observed in various physical systems [1–8], is used, for example, for accelerating relativistic particles [9–12]. Numerical experiments based on various mathematical models have shown that, for autoresonance to appear, it is necessary that the pump amplitude exceed some threshold value [13, 14]. In the present paper, we obtain a result of this sort analytically by an asymptotic analysis of the equations
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TL;DR: The plane-wave asymptotic expansion of the wave function for two electrons in a Coulomb field has been investigated in the case when the total orbital momentum, L, is equal to zero as mentioned in this paper.
Abstract: The plane-wave asymptotic expansion of the wavefunction for two electrons in a Coulomb field has been investigated in the case when the total orbital momentum, L, is equal to zero Analytic solutions are obtained for the first term of the asymptotic expansion The second term is found by numerical integration along classical trajectories Analytic solutions are obtained for the the Altick (1982-3) asymptotic equations It is shown that the Altick asymptotic form represents the asymptotic expression of the authors' asymptotic form The branch point of the later Altick asymptotic form has been discussed and the conclusion is made that this asymptotic form cannot be applied
5 citations