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The wetting phenomenon at three-phase boundaries (solid, liquid, and gas) affects capillary-gravity wave scattering from barriers, but there is a lack of experimental data and comparison with simulations. The scattering is affected by surface tension and the contact lines at the three-phase boundary. When the solid surface conditions vary, the contact angle and the shape of the meniscus generated by the wetting effect change accordingly. It is possible to measure the influence of the wetting effect on the scattering by coating the barrier surface to be hydrophobic or hydrophilic. Our previous work focused on how the scattering is affected by the portion of the barrier immersed under the water surface with a pinned contact line. In this study, we will coat the barrier surface to experimentally measure how the wetting with different coatings affect the scattering. A comparison of the experimental measurements with numerical simulations of potential flow of the waves will be potentially included.
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Quantum scattering states in a nonlinear coherent medium
We present a comprehensive study of stationary states in a coherent medium with a quadratic or Kerr nonlinearity in the presence of localized potentials in one dimension for both positive and negative signs of the nonlinear term as well as for barriers and wells. The description is in terms of the nonlinear Schrödinger equation and hence applicable to a variety of systems, including interacting ultracold atoms in the mean field regime and light propagation in optical fibers. We determine the full landscape of solutions in terms of a potential step and build solutions for rectangular barrier and well potentials. It is shown that all the solutions can be expressed in terms of a Jacobi elliptic function with the inclusion of a complex-valued phase shift. Our solution method relies on the roots of a cubic polynomial associated with a hydrodynamic picture, which provides a simple classification of all the solutions, both bounded and unbounded, while the boundary conditions are intuitively visualized as intersections of phase space curves. We compare solutions for open boundary conditions with those for a barrier potential on a ring, and also show that numerically computed solutions for smooth barriers agree qualitatively with analytical solutions for rectangular barriers. A stability analysis of solutions based on the Bogoliubov equations for fluctuations shows that persistent instabilities are localized at sharp boundaries and are predicated by the relation of the mean density change across the boundary to the value of the derivative of the density at the edge. We examine the scattering of a wave packet by a barrier potential and show that at any instant the scattered states are well described by the stationary solutions we obtain, indicating applications of our results and methods to nonlinear scattering problems.
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- Award ID(s):
- 2011767
- PAR ID:
- 10476185
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review A
- Volume:
- 108
- Issue:
- 2
- ISSN:
- 2469-9926
- 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
- Journal Article:
- https://doi.org/10.1103/PhysRevA.108.023314
