SEARCH Articles Figures Tables Activated complex asymptotics Activation-energy asymptotics Activation-energy asymptotics in ignition theory An Introduction to Asymptotic Approximations Analytic approximations asymptotic solutions Analytic geometry asymptotes Approach asymptotes Approximation errors asymptotic solutions Asymptote angles Asymptote high-frequency Asymptote horizontal Asymptote intersection Asymptote left-hand Asymptote right-hand Asymptote vertical Asymptotes, Bode plots Asymptotic Asymptotic Asymptotic Approximations and Expansions Asymptotic Behavior at Low-Frequency Asymptotic Behavior in the Transport Limited Regime Asymptotic Behavior of Exchange-Correlation Potentials Asymptotic Behavior of the Model Equations Asymptotic Cases of Langmuir Photoadsorption Isotherm Asymptotic Curie temperatur Asymptotic Effectiveness Factors for Arbitrary Kinetics Asymptotic Expansions and Sequences Asymptotic Hamiltonian Asymptotic Progress Model Asymptotic Solution for Asymptotic Solutions at the Moving Shock Front Asymptotic Thickness of an Island Asymptotic algorithms Asymptotic algorithms critical case Asymptotic analysis Asymptotic analysis equilibrium approach Asymptotic analysis for strongly temperature-dependent rates Asymptotic analysis function Asymptotic analysis integral time Asymptotic analysis susceptibilities Asymptotic analysis theories Asymptotic approximation Asymptotic approximation applications Asymptotic approximation boundary layers Asymptotic approximation boundary layers, singularly perturbed problems Asymptotic approximation defined Asymptotic approximation equations Asymptotic approximation expansion Asymptotic approximation first scale Asymptotic approximation general examples Asymptotic approximation initial value problem Asymptotic approximation matching techniques Asymptotic approximation nonlinear systems Asymptotic approximation on Bode diagrams Asymptotic approximation overview Asymptotic approximation regular terms Asymptotic approximation second scale Asymptotic behavior Asymptotic behavior analysis Asymptotic behavior elasticity Asymptotic behavior finite-size scaling Asymptotic behavior function Asymptotic behavior potentials Asymptotic behavior solutions Asymptotic behavior techniques Asymptotic behavior, momentum density Asymptotic behaviour Asymptotic behaviour of the sums Asymptotic boundary condition, incoming Asymptotic branch Asymptotic conditions Asymptotic conditions applications Asymptotic convergence Asymptotic cooling Asymptotic coordinates Asymptotic corrected functionals Asymptotic corrections Asymptotic decay in chaotic flows Asymptotic density model Asymptotic dependence Asymptotic directionality Asymptotic directions Asymptotic distribution, sampling Asymptotic energies, with confined Asymptotic enhancement factor Asymptotic equations for angular momenta Asymptotic exact input/output linearization Asymptotic expansion Asymptotic expansion coefficient Asymptotic expansion methods Asymptotic expansion scheme Asymptotic expansions domain perturbation Asymptotic expansions gauge function Asymptotic expansions general considerations Asymptotic expansions regular Asymptotic expansions singular Asymptotic expansions uniqueness Asymptotic expression Asymptotic flux shape Asymptotic form Asymptotic freedom Asymptotic front formation in reactive ion-exchange Asymptotic giant branch Asymptotic giant branch grains from Asymptotic giant branch stars Asymptotic giant branch stars evolution Asymptotic giant branch stars presolar grains Asymptotic giant branch stars stellar winds Asymptotic integration method Asymptotic integration method selected Asymptotic laws Asymptotic limits Asymptotic load Asymptotic magnitude Asymptotic method, defined Asymptotic method, semi Asymptotic methods Asymptotic methods domain perturbation method Asymptotic methods stretching Asymptotic modal methods Asymptotic normal form Asymptotic penetration Asymptotic phase Asymptotic potential Asymptotic power laws Asymptotic probability density Asymptotic properties derivative Asymptotic properties of H(q) Asymptotic properties of correlations between chain ends Fishers result Asymptotic properties theorem Asymptotic property Asymptotic property equilibria Asymptotic regime Asymptotic regions Asymptotic relationships Asymptotic representation Asymptotic scaling Asymptotic scattering Asymptotic scattering function Asymptotic scattering region Asymptotic self-similarity Asymptotic self-similarity group Asymptotic self-similarity nonideal systems Asymptotic sequence Asymptotic series Asymptotic series, defined Asymptotic shape Asymptotic solution Asymptotic solutions convergence Asymptotic solutions matched Asymptotic solutions order Asymptotic solutions regular Asymptotic state Asymptotic stochastic models Asymptotic theory Asymptotic wavefunctions Asymptotic yield stress Asymptotical phase Asymptotical solution Asymptotically Asymptotically Asymptotically Brownian chain with independent links Asymptotically Correct Asymptotically Correct Approximation Asymptotically autonomous system Asymptotically corrected Asymptotically corrected functionals Asymptotically orbitally stable Asymptotically orbitally stable periodic trajectory Asymptotically scattering Asymptotically stable Asymptotically stable globally Asymptotically stable solution Asymptotics Asymptotics Asymptotics and Perturbations B Asymptotic Expansions - General Considerations Bode diagram asymptote Boundary conditions asymptotic Boundary layer asymptotic limit Boundary layers asymptotic expansion Boundary layers asymptotic solutions Bubble asymptotic Chains with local correlations (asymptotically Brownian) Correction schemes asymptotic corrections Correlation functions asymptotic behavior Cross-section, asymptotic Damkohler-number asymptotics Direct correlation function asymptotic behavior Disease progress models asymptotic Disease progression asymptotic Dispersivity asymptotic Distribution functions asymptotic forms Distribution functions, asymptotic expansion Drag reduction asymptote, maximum E Use of the Asymptotic Results at Intermediate Pe (or Sc) Effectiveness factor asymptotic forms Electron density asymptotic behavior Exchange asymptotic behavior Exchange potential asymptotic behavior Exponentially asymptotically stable Fast time scales, asymptotic solution Formulation through asymptotic methods Fouling asymptotic Functional asymptotically corrected Generalized gradient approximation asymptotic corrections Heat transfer asymptote Helium asymptotic expansion Helium asymptotic giant branch Ignition theory, activation-energy asymptotics Improper HF Asymptotic Behaviour Induced dipole asymptotic form Integrals asymptotic forms Interaction energy general asymptotic form Intermediate asymptotics Leading order terms, asymptotic solutions Leungs asymptotic solutions for vapour pressure systems Local density approximation asymptotic corrections Low frequency asymptote Matched Asymptotic Expansions for Coupled Equations Matched asymptotic expansions Matched asymptotics Matching conditions, asymptotic solutions Method asymptotic analogies Method matched asymptotic expansions Method of the asymptotic limit Model asymptotic Modelling asymptotic approach Modelling asymptotic polystochastic Modelling asymptotic stochastic models Natural Attenuation of Asymptotic Gasoline-Range Hydrocarbons in Groundwater Nonlinear susceptibilities asymptotics Nonzero Asymptote Optimized effective potential asymptotic properties Orbitals asymptotic conditions Partial differential equations asymptotic solutions Phase space asymptotic Polarization moments asymptotical Porod asymptote Potentials asymptotic properties Potentials asymptotic structure Pure integrator asymptote Rays and asymptotic modal methods Reaction asymptotic behaviour at long times Reactivity asymptotic-period Renormalization and asymptotic form of Resonance Analysis Information from Asymptotic Wavefunctions Root locus asymptotes Schrodinger equation asymptotic behavior Secular terms, asymptotic solutions Selected asymptotic integration Slater potential asymptotic structure Slip velocity asymptotic Slow time scales asymptotic solutions Small parameters asymptotic solutions Stability asymptotic Stability asymptotic orbital Static reactivity asymptotic period Steady-state concentrations, asymptotic solutions Stochastic Models Based on Asymptotic Polystochastic Chains Stochastic Models Based on Asymptotic Polystochastic Processes Superparamagnetic particles asymptotics Surface hopping, asymptotic Taylor expansion, asymptotic solutions The Asymptotic Giant Branch The Asymptotic Laws of Freely-Ascending Convective Flows The Asymptotic Limit, Pr (or Sc) The Method of Matched Asymptotic Expansion The asymptotically exact equations Time scales asymptotic solutions Transition to Asymptotic Coordinates Vacuum, asymptotic structure Virial coefficients asymptotic behavior Virk s asymptote Virk’s maximum drag reduction asymptote Viscosity asymptotic critical behavior Wave equation asymptotic solution