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, the authors examined a general technique for deriving the small time asymptotic expansion of a correlation from the large frequency asymPTotic form of the associated spectrum.
Abstract: We examine a general technique for deriving the small time asymptotic expansion of a correlation from the large frequency asymptotic form of the associated spectrum ( conjugate asymptotic properties). Our analysis explicitly takes into account the form of approach of the spectrum to its asymptotic limit (i.e. asymptotic convergence), and the resulting impact on the correlation asymptotic expansion. We fully evaluate the two lowest-order terms in the small time asymptotic expansion of the correlation for the important special case of the large frequency asymptotic behaviour of the spectrum being a negative power of frequency. Included in our analysis is a determination of sufficient conditions on the rapidity of approach of the spectrum towards its asymptotic form (i.e. convergence rate), for the derived correlation asymptotic approximation to be accurate to second order. We comment on how small time must be for our correlation asymptotic approximations to be valid. To motivate this analysis we propose circumstances under which these results could be of utility in physics.
3 citations
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TL;DR: The wave packet formalism is applied to the Vlasov-Poisson equations to derive a K-dV equation and also to the problem of the wave modulation by taking an example of the Bussinesque equation as discussed by the authors.
Abstract: Some asymptotic methods except for the reductive perturbation method are presented. The wave packet formalism is applied to the Vlasov-Poisson equations to derive a K-dV equation and also to the problem of the wave modulation by taking an example of the Bussinesque equation. The derivative expansion method and the extended Krylov Bogoliubov-Mitropolsky method are also discussed.
3 citations
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TL;DR: In this article, the authors used the renormalization-group equation and the loop expansion to obtain the asymptotic behavior of the effective potential in the classical field variable, and applied it to √ √ ε = 0.
Abstract: We use the renormalization-group equation and the loop expansion to obtain the asymptotic behavior of the effective potential in the classical field variable. This is applied to ${\ensuremath{\varphi}}^{4}$ theory as an explicit example. Some remarks on possible uses and extensions are given.
3 citations
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3 citations
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TL;DR: In this paper, a new systematic method to obtain discrete asymptotic numerical models for incompressible free-surface flows is discussed, which consists of first discretizing the Euler equations in the horizontal direction, keeping both the vertical and time derivatives continuous, and then performing an analysis on the resulting system.
Abstract: In this paper, we discuss a new systematic method to obtain discrete asymptotic numerical models for incompressible free-surface flows. The method consists of first discretizing the Euler equations in the horizontal direction, keeping both the vertical and time derivatives continuous, and then performing an asymptotic analysis on the resulting system. The asymptotics involve the ratios wave amplitude over depth, denoted by $\varepsilon$, and depth over wavelength, denoted by $\sigma$. For simplicity, in this paper we only consider the weakly nonlinear scaling in which both $\sigma^4$ and $\varepsilon\sigma^2$ are very small and of the same order. We investigate the properties of the fully discrete Boussinesq model obtained by neglecting terms proportional to these quantities. Our study reveals that if the interaction between terms arising from the discretization and from the PDE is properly accounted for, the resulting discrete system has improved linear dispersion and shoaling approximations w.r.t. the d...
3 citations