Bounded and Unbounded Capillary Surfaces in a Cusp Domain
A capillary surface, a liquid surface at equilibrium, can be modelled mathematically by a nonlinear elliptic PDE called Laplace-Young equations. We first prove that the capillary surface can be bounded or unbounded at a cusp depending on the boundary condition and show asymptotic analyses results for the unbounded cases. Then based on the asymptotic analyses and finite element method, we construct an accurate computational methodology to approximate the unbounded capillary surfaces. Finally using this computational methodology, we investigate two open problems on the asymptotic behaviour of capillary surfaces in a cusp domain and propose conjectures.
This talk is based on the following papers: Yasunori Aoki and Hans De Sterck: Numerical Study of Unbounded Capillary Surfaces, Pacific Journal of Mathematics, Volume 267, Issue 1, 2014, Pages 1-34. Yasunori Aoki and David Siegel: Bounded and Unbounded Capillary Surfaces in a Cusp Domain, Pacific Journal of Mathematics, Volume 257, Issue 1, 2012, Pages 143-165.
March 23rd (Wednesday) 2:00-3:00pm
Mathematical and numerical challenges in Pharmacometrics.
Nonlinear mixed effect model has been shown to be an effective tool for the analysis of clinical trial data. As a result, pharmacometric analysis based on nonlinear mixed effect models, also known as population approach, has become an essential step of drug development. As the importance of pharmacometric analysis increases, more and more complex mathematical models are introduced and more complex challenges in mathematics and numerical computations start to arise.
In this talk we briefly describe the overview of pharmacometrics, then share the speaker’s experience of working in the field of pharmacometrics as an applied mathematician. We will base this talk around two published papers [1,2] and one manuscript/presentation , to present case examples on how applied mathematicians can potentially make differences to the field of pharmaceutical drug development.
 Yasunori Aoki, Rikard Nordgren, and Andrew C. Hooker. "Preconditioning of Nonlinear Mixed Effects Models for Stabilisation of Variance-Covariance Matrix Computations." The AAPS journal (2016): 1-14.  Yasunori Aoki, Monika Sundqvist, Andrew C. Hooker, and Peter Gennemark. “PopED lite: an optimal design software for preclinical pharmacokinetic and pharmacodynamic studies” Computer Methods and Programs in Biomedicine (2016), pp. 126-143.  Yasunori Aoki, Bengt Hamrén, Daniel Röshammar, Andrew C. Hooker “Averaged model based decision making for dose selection studies”, European Medicines Agency/European Federation of Pharmaceutical Industries and Associations workshop on the importance of dose finding and dose selection for the successful development, licensing and lifecycle management of medicinal products, http://www.ema.europa.eu/ema/index.jsp?curl=pages/news_and_events/events/2014/06/event_detail_000993.jsp&mid=WC0b01ac058004d5c3, December 2014.
Prof. Ken Hayami hayami[at]nii.ac.jp *Please replace [at] with @.