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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, the radial distribution of temperature field in a well is used to illustrate the application of a modification of the asymptotic method for solving a number of problems in subterranean thermodynamics.
Abstract: The example of the problem on radial distribution of temperature field in a well is used to illustrate the application of a modification of the asymptotic method for solving a number of problems in subterranean thermodynamics. The problem is represented in the form of a set of equations of mixed types for the respective coefficients of expansion, remainder term, and boundary-layer functions. Analytical expressions are constructed for coefficients of zero-order and first-order expansion and for boundary-layer functions. It is demonstrated that the constructed asymptotic formula provides for vanishing of the solution of the averaged problem for remainder term.
4 citations
TL;DR: In this paper, the authors derived a Timelike asymptotic series for many-particle matrix elements of products of almost local fields, which generalize and extend the Araki-Haag series of quasilocal operators.
Abstract: Timelike asymptotic series for many‐particle matrix elements of products of almost local fields are derived which generalize and extend the Araki‐Haag series of quasilocal operators. An interpretation of the asymptotic leading terms in the form of contributions from disconnected intermediate particle states is given. A discussion of the dependence of the asymptotic leading terms on the smearing in the space variables is presented.
4 citations
4 citations
TL;DR: In this paper, the periodic Ateb-functions were applied to construct single-frequency asymptotic approximations of solutions of problems for the nonlinear nonautonomous wave equation.
Abstract: Applying the periodic Ateb-functions we construct single-frequency asymptotic approximations of solutions of problems for the nonlinear nonautonomous wave equation.
4 citations
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TL;DR: The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation in this article, where a scalar theory is considered, both as a simple example and for its own sake.
Abstract: The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation A scalar theory is considered, both as a simple example and for its own sake This theory is summarized, then the relevant boundary problem is seen to be the full initial-value problem It is shown that, with any given system of gravitating bodies, one may associate a one-parameter family of similar systems, the parameter measuring the gravitational field-strength After a specific change of units, the derivation of asymptotic expansions becomes straightforward Two hypotheses could be made as to which time variable has to be used in the expansion The first one leads to an "asymptotic" post-Newtonian approximation (PNA) with instantaneous propagation, differing from the standard PNA in that, in the asymptotic PNA, all fields are expanded The second hypothese could lead to an "asymptotic" post-Minkowskian approximation (PMA) allowing to describe propagation effects, but it is not compatible with the Newtonian limit It is shown that the standard PNA is not compatible with the application of the usual method of asymptotic expansions as envisaged here
4 citations