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Composite asymptotic expansions and scaling wall turbulence
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007In this article, the assumptions and reasoning that yield composite asymptotic expansions for wall turbulence are discussed. Particular attention is paid to the scaling quantities that are used to render the variables non-dimensional and of order one.
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Asymptotic Approximations and Extension of Time-Scales
SIAM Journal on Mathematical Analysis, 1980It is shown how to obtain $O(\varepsilon )$ (or any higher order)-approximations to the solutions of the differential equation \[\begin{gathered} \dot \phi = 1 + \sum\limits_{p = 1}^p {\varepsilon ^p X^p (\phi ,X),\quad \phi \in S^1, } \hfill \\ \dot x = \sum_{p = 1}^p {\varepsilon ^p Y^p (\phi ,X),\quad \begin{array}{*{20}c} {\varepsilon \in (0 ...
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Scaling of quasibrittle fracture: asymptotic analysis
International Journal of Fracture, 1997Fracture of quasibrittle materials such as concrete, rock, ice, tough ceramics and various fibrous or particulate composites, exhibits complex size effects. An asymptotic theory of scaling governing these size effects is presented, while its extension to fractal cracks is left to a companion paper (1) which follows.
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
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Scaling, Self-similarity, and Intermediate Asymptotics
1996Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using
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Multidisciplinary standards of care and recent progress in pancreatic ductal adenocarcinoma
Ca-A Cancer Journal for Clinicians, 2020Aaron J Grossberg +2 more
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Oral complications of cancer and cancer therapy
Ca-A Cancer Journal for Clinicians, 2012Joel B Epstein +2 more
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American Cancer Society Head and Neck Cancer Survivorship Care Guideline
Ca-A Cancer Journal for Clinicians, 2016Nader Sadeghi +2 more
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