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Full-Text Articles in Physics
Nonlinear Schrödinger Equation Solitons On Quantum Droplets, A. Ludu, A.S. Carstea
Nonlinear Schrödinger Equation Solitons On Quantum Droplets, A. Ludu, A.S. Carstea
Publications
Irrotational flow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrödinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic functions. In the quantum regime the algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which we expect to be relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops. In order to validate the model we match our theoretical energy spectra with experimental results on energy, angular momentum, and parity for …
Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy
Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy
All HMC Faculty Publications and Research
A thin layer of fluid flowing down a solid planar surface has a free surface height described by a nonlinear PDE derived via the lubrication approximation from the Navier Stokes equations. For thin films, surface tension plays an important role both in providing a significant driving force and in smoothing the free surface. Surfactant molecules on the free surface tend to reduce surface tension, setting up gradients that modify the shape of the free surface. In earlier work [12, 13J a traveling wave was found in which the free surface undergoes three sharp transitions, or internal layers, and the surfactant …
Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski
Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski
All HMC Faculty Publications and Research
The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerateparabolic, and admits traveling wave solutions in which the …