Scholarly and Creative Works
2024
- Treinen, R. F., & Haug, J. (2024). Multi-scale spectral methods for bounded radially symmetric capillary surfaces. Electronic Transactions on Numerical Analysis, 60, 20–39.
2023
- Treinen, R. F. (2023). Spectral methods for capillary surfaces described by bounded generating curves. Applied Mathematics and Computation, 450.
- Treinen, R. F. (2023). Discussion of a uniqueness result in ``Equilibrium Configurations for a Floating Drop’’. Electronic Journal of Differential Equations, 32.
2022
- Treinen, R. F., & Trefethen, L. N. (2022). A droplet sitting on a surface. chebfun.org. Retrieved from http://www.chebfun.org/examples/ode-nonlin/Droplets.html
2020
- Treinen, R. F., & Ickes, H. E. (2020). The existence of an energy minimizing configuration for multiple solid objects floating in a bath of three liquids. Annali Di Matematica Pura Ed Applicata, 4(199), 821–831. https://doi.org/https://doi.org/10.1007/s10231-019-00902-4
2019
- Treinen, R. F., Blank, I., & Elcrat, A. (2019). Geometry of the triple junction between three fluids in equilibrium. Electron. J. Differential Equations, 2019, 1–35.
- Hu, Y., & Treinen, R. F. (2019). A one-step method for modeling longitudinal data with differential equations. British Journal of Mathematical and Statistical Psychology, 1.
2018
- Bagley, Z., & Treinen, R. (2018). On the Classification and Asymptotic Behavior of the Symmetric Capillary Surfaces. Experimental Mathematics, 1–15. Retrieved from http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1245641
- McCuan, J., & Treinen, R. F. (2018). On floating equilibria in a laterally finite container. SIAM Applied Mathematics, 78(1), 551–570.
2016
- Treinen, R. (2016). Examples of Non-Uniqueness of the Equilibrium States for a Floating Ball. Advances in Materials Physics and Chemistry, 6(07), 177.
2015
- Colter, L., & Treinen, R. (2015). Cylindrical liquid bridges. Involve, a Journal of Mathematics, 8(4), 695–705.
2013
- McCuan, J., & Treinen, R. (2013). Capillarity and Archimedes’ principle. Pacific Journal of Mathematics, 265(1), 123–150.
2012
- Treinen, R. (2012). Extended annular capillary surfaces. Journal of Mathematical Fluid Mechanics, 14(4), 619–632.
- Treinen, R. (2012). On the symmetry of solutions to some floating drop problems. SIAM Journal on Mathematical Analysis, 44(6), 3834–3847.
2011
- Elcrat, A., & Treinen, R. (2011). Floating drops and functions of bounded variation. Complex Analysis and Operator Theory, 5(1), 299–311.
2010
- Treinen, R. (2010). A general existence theorem for symmetric floating drops. Archiv Der Mathematik, 94(5), 477–488.
2005
- Elcrat, A., & Treinen, R. (2005). Numerical results for floating drops. Discrete Contin. Dyn. Syst, 241–249.
2004
- Elcrat, A., Kim, T.-E., & Treinen, R. (2004). Annular capillary surfaces. Archiv Der Mathematik, 82(5), 449–467.