Dr. Treinen received his Ph.D. from Wichita State University in 2004. He has been working on fluid mechanics and fluid dynamics problems, primarily studying the equilibrium state of fluids. The methods applied to these problems are somewhat diverse: techniques from partial and ordinary differential equations including free boundary regularity, numerical analysis, geometric measure theory, and the calculus of variations.
- L. Colter, R. Treinen, Cylindrical Liquid Bridges, Involve 8 (2015), no. 4, 695–705.
- J. McCuan, R. Treinen. Capillarity and Archimedes’ Principle. Pacific J Math. Vol. 265 (2013), No. 1, 123–150.
- Treinen, Capillarity and Archimedes’ Principle. Accepted in Pacific J Math (2012)
- Treinen On the symmetry of solutions to some floating drop problems. SIAM J. Math Anal. Vol. 44, No. 6, pp 3834-3847.
- Treinen. Extended annular capillary surfaces. Accepted for publication in J.Math. Fluid Mech., December 2012, Volume 14, Issue 4, pp 619-632.
- Elcrat; Treinen. Floating drops and functions of bounded variation. Complex Anal. Oper. Theory 5 (2011), no. 1, 299–311.
- Treinen. A general existence theorem for symmetric floating drops. Arch. Math. (Basel). 94 (2010), no. 5, 477–488.
- Elcrat; Treinen. Numerical results for floating drops. Discrete Contin. Dyn. Syst. 2005, suppl., 241--249.
- Elcrat; Kim; Treinen. Annular capillary surfaces. Arch. Math. (Basel)82 (2004), no. 5, 449--467.