Dr. Dai is an Associate Professor and the Graduate Program Director of the Department of Mathematics, College of Arts & Sciences. He is a mathematician that has a genuine interest in a wide range of real world problems. He studies mathematical problems that arise in physical, biological, and materials sciences. His research has been supported by NSF grants.
- Minimizers for the Cahn-Hilliard energy under strong anchoring conditions, S. Dai, B. Li, T. Luong. SIAM J. Appl. Math 80: 2299-2317 2020.
- Rigorous derivation of a mean field model for the Ostwald ripening of thin films, S. Dai, Communications in Mathematical Sciences 18: 293-320, 2020.
- Convergence of phase-field free energy and boundary force for molecular solvation, S. Dai, B. Li, J. Lu. Archive for Rational Mechanics and Analysis 227: 105-147, 2018.
- Weak solutions for the Cahn-Hilliard equation with degenerate mobility, S. Dai, Q. Du. Archive for Rational Mechanics and Analysis 219: 1161—1184, 2016.
- Motion of interfaces governed by the Cahn-Hilliard equation with highly disparate diffusion mobility, S. Dai, Q. Du. SIAM J. Appl. Math 72: 1818-1841, 2012.
Dr. Dai is research interest lie in nonlinear partial differential equations, applied analysis, and numerical analysis, with applications in physical, biological, and materials science. Specific areas include: network formation in amphiphilic mixtures with applications to lipid bilayer evolution and morphology in polymer electrolyte materials; phase-field variational models for molecular solvation; domain coarsening and self-similarity in materials science, phase transitions and thin films; free boundary problems.