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 article, it was shown that there does not exist a classical asymptotic expansion for short time in terms of fractional powers of t with locally computable coefficients.
Abstract: The spectral problem where the field satisfies Dirichlet conditions on one part of the boundary of the relevant domain and Neumann on the remainder is discussed. It is shown that there does not exist a classical asymptotic expansion for short time in terms of fractional powers of t with locally computable coefficients.
28 citations
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TL;DR: In this article, an asymptotic analysis of the system of differential equations describing the transient behavior of a p-n-junction device (i.e., a diode) is carried out.
Abstract: In this paper we carry out an asymptotic analysis of the system of differential equations describing the transient behavior of a p-n-junction device (i.e., a diode). We determine the different time scales present in the equations and investigate which of them actually occur in physical situations. We derive asymptotic expansions of the solution and perform some numerical experiments.
27 citations
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TL;DR: In this article, the authors studied the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary and showed that the leading terms of the expansion for the eigenelements of the eigenvalue of the limit problem can be obtained from the spectral equation.
Abstract: We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics.
27 citations
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TL;DR: In this article, a diffusing particle in one dimension is subject to a time-dependent drift or potential field, and a reflecting barrier constrains the particle's position to the half-line X ≥ 0.
Abstract: We consider a diffusing particle in one dimension that is subject to a time-dependent drift or potential field. A reflecting barrier constrains the particle's position to the half-line X ≥ 0. Such models arise naturally in the study of queues with time-dependent arrival rates, as well as in advection-diffusion problems of mathematical physics. We solve for the probability distribution of the particle as a function of space and time. Then we do a detailed study of the asymptotic properties of the solution, for various ranges of space and time. We also relate our asymptotic results to those obtained by probabilistic approaches, such as central limit theorems and large deviations. We consider drifts that are either piecewise constant or linear functions of time.
27 citations