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An important problem in lubrication is the squeezing of a thin liquid film between a rigid sphere and an elastic substrate under normal contact. Numerical solution of this problem typically uses iteration techniques. A difficulty with iteration schemes is that convergence becomes increasingly difficult under increasingly heavy loads. Here we devise a numerical scheme that does not involve iteration. Instead, a linear problem is solved at every time step. The scheme is fully automatic, stable and efficient. We illustrate this technique by solving a relaxation test in which a rigid spherical indenter is brought rapidly into normal contact with a thick elastic substrate lubricated by a liquid film. The sphere is then fixed in position as the pressure relaxes. We also carried out relaxation experiments on a lubricated soft PDMS (polydimethysiloxane) substrate under different conditions. These experiments are in excellent agreement with the numerical solution.
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Rytov’s EMT Applicability for Photonic Lattices
We address the properties of photonic lattices by Rytov’s EMT method. The symmetric solution of Rytov’s eigenvalue equations pertains to normal incidence angles with the asymmetric solution being relevant for off-normal illumination.
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- Award ID(s):
- 1809143
- PAR ID:
- 10352233
- Date Published:
- Journal Name:
- Technical Digest Series (Optica Publishing Group, 2021)
- Page Range / eLocation ID:
- JTh5A.138
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1364/FIO.2021.JTh5A.138
