Self-similar optical waves in tapered power-law nonlinear materials with inter modal dispersion

Optik ◽  
2021 ◽  
Vol 229 ◽  
pp. 166301
Author(s):  
Kewei Wang ◽  
Jun-Rong He ◽  
Li Xue
Keyword(s):  
Power Law ◽  
Nonlinear Materials ◽  
Optical Waves ◽  
Modal Dispersion ◽  
Self Similar

Power-law decay and self-similar distributions in stadium-type billiards

2004 ◽  
Vol 193 (1-4) ◽  
pp. 96-127 ◽  
Author(s):  
Douglas N. Armstead ◽  
Brian R. Hunt ◽  
Edward Ott
Keyword(s):  
Power Law ◽  
Power Law Decay ◽  
Self Similar

Self-Similar Rational Models for Power-Law Processes

1994 ◽  
Vol 27 (1) ◽  
pp. 31-36
Author(s):  
Gregory J. Maskarinec ◽  
Banu Onaral
Keyword(s):  
Power Law ◽  
Rational Models ◽  
Self Similar

Modal dispersion of power-law profiles with tails

1980 ◽  
Vol 19 (14) ◽  
pp. 2439
Author(s):  
A. Weierholt
Keyword(s):  
Power Law ◽  
Modal Dispersion

Computational and Experimental Characterization of Indentation Creep

2003 ◽  
Vol 795 ◽  
Author(s):  
Ming Dao ◽  
Hidenari Takagi ◽  
Masami Fujiwara ◽  
Masahisa Otsuka
Keyword(s):  
Finite Element ◽  
Power Law ◽  
Constant Load ◽  
Dislocation Creep ◽  
Solid Solution Alloy ◽  
Indentation Creep ◽  
Creep Tests ◽  
Uniaxial Creep ◽  
Self Similar ◽  
Power Law Creep

ABSTRACT:Detailed finite-element computations and carefully designed indentation creep experiments were carried out in order to establish a robust and systematic method to accurately extract creep properties during indentation creep tests. Finite-element simulations confirmed that, for a power law creep material, the indentation creep strain field is indeed self-similar in a constant-load indentation creep test, except during short transient periods at the initial loading stage and when there is a deformation mechanism change. Self-similar indentation creep leads to a constitutive equation from which the power-law creep exponent, n, the activation energy for creep, Qc and so on can be evaluated robustly. Samples made from an Al-5.3mol%Mg solid solution alloy were tested at temperatures ranging from 573 K to 773 K. The results are in good agreement with those obtained from conventional uniaxial creep tests in the dislocation creep regime.

Lie Symmetry Analysis of Boundary Layer Stagnation-Point Flow and Heat Transfer of Non-Newtonian Power-Law Fluids Over a Nonlinearly Shrinking/Stretching Sheet with Thermal Radiation

2018 ◽  
Vol 19 (3-4) ◽  
pp. 415-426 ◽  
Author(s):  
G.C. Layek ◽  
Bidyut Mandal ◽  
Krishnendu Bhattacharyya ◽  
Astick Banerjee
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Power Law ◽  
Stretching Sheet ◽  
Symmetry Analysis ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Self Similar

AbstractA symmetry analysis of steady two-dimensional boundary layer stagnation-point flow and heat transfer of viscous incompressible non-Newtonian power-law fluids over a nonlinearly shrinking/stretching sheet with thermal radiation effect is presented. Lie group of continuous symmetry transformations is employed to the boundary layer flow and heat transfer equations, that gives scaling laws and self-similar equations for a special type of shrinking/stretching velocity ($c{x^{1/3}}$) and free-stream straining velocity ($a{x^{1/3}}$) along the axial direction to the sheet. The self-similar equations are solved numerically using very efficient shooting method. For the above nonlinear velocities, the unique self-similar solution is obtained for straining velocity being always less than the shrinking/stretching velocity for Newtonian and non-Newtonian power-law fluids. The thickness of velocity boundary layer becomes thinner with power-law index for shrinking as well as stretching sheet cases. Also, the thermal boundary layer thickness decreases with increasing values the Prandtl number and the radiation parameter.

Converging gravity currents over a permeable substrate

2015 ◽  
Vol 778 ◽  
pp. 669-690 ◽  
Author(s):  
Zhong Zheng ◽  
Sangwoo Shin ◽  
Howard A. Stone
Keyword(s):  
Power Law ◽  
Gravity Current ◽  
Gravity Currents ◽  
Numerical Predictions ◽  
Front Position ◽  
Dependent Position ◽  
Self Similar ◽  
Vertical Leakage ◽  
Similar Solutions ◽  
Lock Gate

We study the propagation of viscous gravity currents along a thin permeable substrate where slow vertical drainage is allowed from the boundary. In particular, we report the effect of this vertical fluid drainage on the second-kind self-similar solutions for the shape of the fluid–fluid interface in three contexts: (i) viscous axisymmetric gravity currents converging towards the centre of a cylindrical container; (ii) viscous gravity currents moving towards the origin in a horizontal Hele-Shaw channel with a power-law varying gap thickness in the horizontal direction; and (iii) viscous gravity currents propagating towards the origin of a porous medium with horizontal permeability and porosity gradients in power-law forms. For each of these cases with vertical leakage, we identify a regime diagram that characterizes whether the front reaches the origin or not; in particular, when the front does not reach the origin, we calculate the final location of the front. We have also conducted laboratory experiments with a cylindrical lock gate to generate a converging viscous gravity current where vertical fluid drainage is allowed from various perforated horizontal substrates. The time-dependent position of the propagating front is captured from the experiments, and the front position is found to agree well with the theoretical and numerical predictions when surface tension effects can be neglected.

scholarly journals Self-similar rupture of thin free films of power-law fluids

2015 ◽  
Vol 92 (2) ◽  
Author(s):  
Sumeet Suresh Thete ◽  
Christopher Anthony ◽  
Osman A. Basaran ◽  
Pankaj Doshi
Keyword(s):  
Power Law ◽  
Power Law Fluids ◽  
Self Similar ◽  
Free Films
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