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Perturbation Methods

TL;DR: This website becomes a very available place to look for countless perturbation methods sources and sources about the books from countries in the world are provided.
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Journal Article•DOI•
TL;DR: A powerful, easy-to-use analytic tool for nonlinear problems in general, namely the homotopy analysis method, is further improved and systematically described through a typical nonlinear problem, i.e. the algebraically decaying viscous boundary layer flow due to a moving sheet.

1,589 citations


Cites background from "Perturbation Methods"

  • ...Perturbation techniques [1,2] are currently the main stream....

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Journal Article•DOI•
TL;DR: A review of the fundamental and technological aspects of these subjects can be found in this article, where the focus is mainly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science.
Abstract: Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects

1,583 citations

Journal Article•DOI•
TL;DR: It is shown in a limited sense that so called Type II resetting occurs with models that obtain rhythmicity via a Hopf bifurcation and the differences between synapses that act rapidly and those that act slowly are shown.
Abstract: Type I membrane oscillators such as the Connor model (Connor et al. 1977) and the Morris-Lecar model (Morris and Lecar 1981) admit very low frequency oscillations near the critical applied current. Hansel et al. (1995) have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive. We use singular perturbation methods and averaging to show that this is a general property of Type I membrane models. We show in a limited sense that so called Type II resetting occurs with models that obtain rhythmicity via a Hopf bifurcation. We also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions.

994 citations

Journal Article•DOI•
K. U. Riemann1•
TL;DR: In this paper, the basic features of the plasma-sheath transition and their relation to the Bohm criterion are discussed and illustrated from a simple cold-ion fluid model, and a rigorous kinetic analysis of the vicinity of the sheath edge allows one to generalize Bohm's criterion accounting not only for arbitrary ion and electron distributions, but also for general boundary conditions at the wall.
Abstract: In the limit of a small Debye length ( lambda D to 0) the analysis of the plasma boundary layer leads to a two-scale problem of a collision free sheath and of a quasi-neutral presheath. Bohm's criterion expresses a necessary condition for the formation of a stationary sheath in front of a negative absorbing wall. The basic features of the plasma-sheath transition and their relation to the Bohm criterion are discussed and illustrated from a simple cold-ion fluid model. A rigorous kinetic analysis of the vicinity of the sheath edge allows one to generalize Bohm's criterion accounting not only for arbitrary ion and electron distributions, but also for general boundary conditions at the wall. It is shown that the generalized sheath condition is (apart from special exceptions) marginally fulfilled and related to a sheath edge field singularity. Due to this singularity, smooth matching of the presheath and sheath solutions requires an additional transition layer. Previous investigations concerning particular problems of the plasma-sheath transition are reviewed in the light of the general relations.

974 citations

Journal Article•DOI•
TL;DR: An extensive review of the literature in V&V in computational fluid dynamics (CFD) is presented, methods and procedures for assessing V &V are discussed, and a relatively new procedure for estimating experimental uncertainty is given that has proven more effective at estimating random and correlated bias errors in wind-tunnel experiments than traditional methods.

948 citations


Cites background from "Perturbation Methods"

  • ...Several textbooks, including [151,176, 223,256,341,343], also contain a number of analytical solutions that are useful for verification of CFD codes....

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  • ...These closed-form solutions are commonly represented by infinite series, complex integrals, and asymptotic expansions [110,137,151, 176,223,256,340,343]....

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  • ...[223] Nayfeh AH....

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