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Full-Text Articles in Physical Sciences and Mathematics
Nonlinear Ordinary Differential Equations In Fluid Dynamics, John D. Ramshaw
Nonlinear Ordinary Differential Equations In Fluid Dynamics, John D. Ramshaw
Physics Faculty Publications and Presentations
The equivalence between nonlinear ordinary differential equations (ODEs) and linear partial differential equations (PDEs) was recently revisited by Smith, who used the equivalence to transform the ODEs of Newtonian dynamics into equivalent PDEs, from which analytical solutions to several simple dynamical problems were derived. We show how this equivalence can be used to derive a variety of exact solutions to the PDEs describing advection in fluid dynamics in terms of solutions to the equivalent ODEs for the trajectories of Lagrangian fluid particles. The PDEs that we consider describe the time evolution of non-diffusive scalars, conserved densities, and Lagrangian surfaces advected …
Whispering-Gallery Acoustic Sensing: Characterization Of Mesoscopic Films And Scanning Probe Microscopy Applications, Andres H. La Rosa, Nan Li, Rodolfo Fernandez, Xiaohua Wang, Richard Nordstrom, S. K. Padigi
Whispering-Gallery Acoustic Sensing: Characterization Of Mesoscopic Films And Scanning Probe Microscopy Applications, Andres H. La Rosa, Nan Li, Rodolfo Fernandez, Xiaohua Wang, Richard Nordstrom, S. K. Padigi
Physics Faculty Publications and Presentations
Full understanding of the physics underlying the striking changes in viscoelasticity, relaxation time, and phase transitions that mesoscopic fluid-like films undergo at solid-liquid interfaces, or under confinement between two sliding solid boundaries, constitutes one of the major challenges in condensed matter physics. Their role in the imaging process of solid substrates by scanning probe microscopy (SPM) is also currently controversial. Aiming at improving the reliability and versatility of instrumentation dedicated to characterize mesoscopic films, a noninvasive whispering-gallery acoustic sensing (WGAS) technique is introduced; its application as feedback control in SPM is also demonstrated. To illustrate its working principle and potential …