Sheet Necking—I. Validity of Plane Stress Assumptions of the Long-Wavelength Approximation

1978 ◽  
pp. 111-126 ◽  
Author(s):  
J. W. Hutchinson ◽  
K. W. Neale ◽  
A. Needleman
Keyword(s):  
Plane Stress ◽  
Long Wavelength ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation

Peristaltic thrusting of a thermal-viscosity nanofluid through a resilient vertical pipe

2020 ◽  
Vol 75 (8) ◽  
pp. 727-738 ◽  
Author(s):  
Ramzy M. Abumandour ◽  
Islam M. Eldesoky ◽  
Mohamed H. Kamel ◽  
Mohamed M. Ahmed ◽  
Sara I. Abdelsalam
Keyword(s):  
Pressure Gradient ◽  
Hartmann Number ◽  
Amplitude Ratio ◽  
Variable Viscosity ◽  
Friction Forces ◽  
Long Wavelength ◽  
Viscosity Parameter ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Theoretical Results

AbstractIn the article, the effects of the thermal viscosity and magnetohydrodynamic on the peristalsis of nanofluid are analyzed. The dominant neutralization is deduced through long wavelength approximation. The analytical solution of velocity and temperature is extracted by using steady perturbation. The pressure gradient and friction forces are obtained. Numerical results are calculated and contrasted with the debated theoretical results. These results are calculated for various values of Hartmann number, variable viscosity parameter and amplitude ratio. It is observed that the pressure gradient is reduced with an increase in the thermal viscosity parameter and that the Hartmann number enhances the pressure difference.

Tensile Stability of Medial Arterial Tissues

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
Alan J. Levy ◽  
Xinyu Zhang
Keyword(s):  
Smooth Muscle ◽  
Constitutive Models ◽  
Constitutive Parameter ◽  
Axial Stretch ◽  
Long Wavelength ◽  
Arterial Tissue ◽  
Long Wavelength Approximation ◽  
Geometrical Imperfections ◽  
Wavelength Approximation ◽  
Nominal Load

Tensile stability of healthy medial arterial tissue and its constituents, subject to initial geometrical and/or material imperfections, is investigated based on the long wavelength approximation. The study employs existing constitutive models for elastin, collagen, and vascular smooth muscle which comprise the medial layer of large elastic (conducting) arteries. A composite constitutive model is presented based on the concept of the musculoelastic fascicle (MEF) which is taken to be the essential building block of medial arterial tissue. Nonlinear equations governing axial stretch and areal stretch imperfection growth quantities are obtained and solved numerically. Exact, closed-form results are presented for both initial and terminal rates of imperfection growth with nominal load. The results reveal that geometrical imperfections, in the form of area nonuniformities, and material imperfections, in the form of constitutive parameter nonuniformities, either decrease or increase only slightly with increasing nominal load; a result which is to be expected for healthy tissue. By way of contrast, an examination of a simple model for elastin with a degrading stiffness gives rise to unbounded imperfection growth rates at finite values of nominal load. The latter result indicates how initial geometrical and material imperfections in diseased tissues might behave, a topic of future study by the authors.

TRIVIALITY OF THE HIGGS FIELD

1989 ◽  
Vol 04 (05) ◽  
pp. 1037-1053 ◽  
Author(s):  
KERSON HUANG
Keyword(s):  
Monte Carlo ◽  
Perturbation Theory ◽  
Critical Review ◽  
Higgs Field ◽  
Higgs Sector ◽  
Long Wavelength ◽  
The Standard Model ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Function Potential

We give a critical review of the "triviality" of the λϕ4 theory, i.e., the vanishing of the renormalized self-coupling. Evidence from perturbation theory and Monte-Carlo simulations are cited. It is noted that (a) the theory is "trivial" but not entirely free, for there is spontaneous symmetry breaking; (b) perturbation theory is unreliable. Soluble examples with similar behavior are compared, in particular the Lee model and the 3D δ function potential. The latter case is especially important, for it shows that triviality is a symptom that the interaction is too singular, and suggests a cure. The import for the Higgs sector of the standard model is discussed. It is argued that, like the Fermi pseudopotential, the Higgs field is a long-wavelength approximation that should be used in lowest order perturbation theory only.

Slip and Heat Transfer Effects on Peristaltic Motion of a Carreau Fluid in an Asymmetric Channel

2010 ◽  
Vol 65 (12) ◽  
pp. 1121-1127 ◽  
Author(s):  
Tasawar Hayat ◽  
Najma Saleem ◽  
Awatif A. Hendi
Keyword(s):  
Heat Transfer ◽  
Peristaltic Flow ◽  
Asymmetric Channel ◽  
Peristaltic Motion ◽  
Carreau Fluid ◽  
Long Wavelength ◽  
Flow And Heat Transfer ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Pumping And Trapping

An analysis has been carried out for peristaltic flow and heat transfer of a Carreau fluid in an asymmetric channel with slip effect. The governing problem is solved under long wavelength approximation. The variations of pertinent dimensionless parameters on temperature are discussed. Pumping and trapping phenomena are studied.

Application of Rabinowitsch Fluid Model for the Mathematical Analysis of Peristaltic Flow in a Curved Channel

2015 ◽  
Vol 70 (7) ◽  
pp. 513-520 ◽  
Author(s):  
Ehnber Naheed Maraj ◽  
Sohail Nadeem
Keyword(s):  
Current Problem ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Shear Stresses ◽  
Curved Channel ◽  
Long Wavelength ◽  
Long Wavelength Approximation ◽  
Dimensional Parameters ◽  
Wavelength Approximation

AbstractThe present work is the mathematical investigation of peristaltic flow of Rabinowitsch fluid in a curved channel. The current problem is modeled and solutions for non-dimensional differential equation are obtained under low Reynolds number and long wavelength approximation. The effects of long lasting non-dimensional parameters on exact solution for velocity profile, pressure rise and shear stresses are studied graphically in the last section. Tables are also incorporated for shear stresses at the walls of the curved channel.

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