Asymptotic Analysis

Fedoryuk, M. V.

doi:10.1007/978-3-642-58016-1

Cited by 193 publications

(161 citation statements)

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“…Formalism of the WKB method (see [2] with extensive reference list) can be tracked down to the work of A. Sommerfeld and J.Runge [4], published in 1911. In our work we will discuss modification of this formalism and advantages of such modification.…”

Section: Appendixmentioning

confidence: 99%

Reflection and refraction of sound on smoothed boundaries.

Maltsev¹

2012

Proceedings of Meetings on Acoustics

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Asymptotic solutions for the system of Euler equations for small motions of compressive fluid are received for two liquid half spaces divided by smoothed transition of sound velocity and density from one half space to another. Vertical Green function is integrated by Fast Field Program for different examples of media, producing field of sound pressure and particle velocities. Also new asymptotic expressions for Airy and Bessel functions are derived.

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Section: Appendixmentioning

confidence: 99%

Reflection and refraction of sound on smoothed boundaries.

Maltsev¹

2012

Proceedings of Meetings on Acoustics

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“…The rightmost integral in (G.1) is amenable to asymptotic analysis for v 1 using Laplace's method [9]. The minimum If m 2 1 + 2bd 1 < 4, which is a stronger condition than (11.11), then w is a critical point of f in (G.2), in the vicinity of which the quadratic approximation f ≈ f…”

Section: Z(y)mentioning

confidence: 99%

Tracing Diffusion in Porous Media with Fractal Properties

Vladimirov¹,

Klimenko²

2010

Multiscale Model. Simul.

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Abstract. This work is concerned with conditional averaging methods which can be used for modeling of transport in porous media with volume reactions in the fluid phase and surface reactions at the fluid/solid interface. The model under consideration takes into account convection, diffusion within the pores and on larger scales, and homogeneous and heterogeneous reactions. Near the interface with fractal properties, the fluid flow is slow, and diffusion, as a transport mechanism, dominates over convection. Following the conditional moment closure paradigm, we employ a diffusion tracer as a reference scalar field that makes the conditional averaging sensitive to the proximity of a point to the interface. The resulting conditionally averaged reactive transport equations are governed by the probability density function (PDF) of the diffusion tracer, and this makes the study of its behavior an important problem. We consider a hitting time stochastic interpretation of the diffusion tracer, establish integral equations relating it to a subsidiary distance tracer, and obtain distance-diffusion inequalities. Assuming that the fluid/solid interface and pores themselves possess fractal properties which are quantified, in particular, by a variant of the Minkowski-Bouligand fractal dimension, we investigate the interplay between the interface and network scenarios of fractality in the scaling laws of the diffusion tracer PDF. We also discuss and employ several hypotheses, including a lognormal cascade hypothesis on the behavior of the diffusion tracer at different length scales.

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“…In order to show that I = Ryyi/R^ we look at the quotient of Ryyi/R^ by the relations I and show that it is trivial. Proceeding in two steps we first show that (3) (9j9k9£) 2 = e mod I for all j,k,£ € {1,... ,m}.…”

Section: Rh^:=m(x)/dm{x) Is Naturally Isomorphic To ^(Xc)mentioning

confidence: 99%

“…two) deleted points is isomorphic to a curve of the family (^a)aec 3 (^sp. (^a)a€C 4 )• Each hyperelliptic curve of genus g with one WeierstraB point (resp.…”

Section: Hyperelliptic Curves With Liouville-formmentioning

confidence: 99%