Segur / Tanveer / Levine Asymptotics beyond All Orders

Erscheinungsjahr 2012
ISBN: 978-1-4757-0435-8
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 284, 408 Seiten, eBook

Reihe: NATO Science Series: B

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,

Zielgruppe

Research

Autoren/Hrsg.

Segur, Harvey

Tanveer, Saleh

Levine, Herbert J.

Inhaltsverzeichnis

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 Asymptoticsand 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.