UID:
almahu_9949199166602882
Format:
408 p. 7 illus.
,
online resource.
Edition:
1st ed. 1991.
ISBN:
9781475704358
Series Statement:
Nato Science Series B:, Physics, 284
Content:
An asymptotic expansion is a series that provides a sequence of increasingly accurate approximations to a function in a particular limit. The formal definition, given by Poincare (1886, Acta Math. 8:295), is as follows. Given a function,.
Note:
Asymptotology and Borel Summation -- Asymptotics, Superasymptotics, Hyperasymptotics -- Computation of Transcendental Effects in Growth Problems: Linear Solvability Conditions and Nonlinear Methods- The Example of the Geometric Model -- The Geometric Model of Crystal Growth -- The Geometric Model of Crystal Growth: An Overview -- Numerical Analysis of the Geometric Model for Dendritic Growth of Crystals -- Dendritic Crystal Growth -- Dendritic Crystal Growth-Overview -- An Experimental Assessment of Continuum Models of Dendritic Growth -- A New Formulation for Dendritic Crystal Growth in Two Dimensions -- Directional Solidification of Solids -- Directional Growth of Dilute Mixtures and Lamellar Eutectics -- A Flat Interface and Its Unfolding Bifurcations -- Flow in a Hele-Shaw Cell (Also known as VISCOUS FINGERING) -- Viscous Displacement in a Hele-Shaw Cell -- Saffman-Taylor Viscous Fingering in a Wedge -- Saffman-Taylor Problem in a Sector Geometry -- The Rapidly Forced Pendulum -- Exponentially Small Estimate for Separatrix Splittings -- Exponentially Small Phenomena in the Rapidly Forced Pendulum -- Proof of An Asymptotic Symmetry of the Rapidly Forced Pendulum -- Ordinary Differential Equations -- Exponentially Small Oscillations in the Solution of an Ordinary Differential Equation -- Singular Perturbations of Solitons -- Reflection Coefficient Beyond All Orders for Singular Problems -- Laminar Flow in a Porous Channel -- Existence and Stability of Particle Channeling in Crystals on Time-Scales Beyond All Orders -- Solitary Water Waves in the Presence of Small Surface Tension -- Gravity-Capillary Free Surface Flows -- Solitary Waves With Ripples Beyond All Orders -- Generalized Solitary Waves in a Stratified Fluid -- Problems in Optics -- Bending Losses in Optical Fibers -- Exponential Asymptotics and Spectral Theory for Curved Optical Waveguides -- Solitary Waves in Self-Induced Transparency -- Potpourri -- Exponential Asymptotics for Partial Differential Equations -- Problems of Existence of Nontopological Solitons (Breathers) for Nonlinear Klein-Gordon Equations -- Exponentially Small Residues Near Analytic Invariant Circles -- Asymptotics of Partial Differential and the Renormalization Group.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9781475704372
Additional Edition:
Printed edition: ISBN 9780306441127
Additional Edition:
Printed edition: ISBN 9781475704365
Language:
English
DOI:
10.1007/978-1-4757-0435-8
URL:
https://doi.org/10.1007/978-1-4757-0435-8
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