| Title: | Asymptotic Analysis of Steady Viscous Shocks in a 1-D Finite Nozzle in the Small Viscosity Limit |
| Time: | 10:30:00 - 11:30:00 |
| Place: | Room 501a, Academic Building No. 1, CUHK |
| Abstract: | In this talk, I present recent results on the asymptotic behavior of steady viscous 1-D shock solutions in finite nozzles under vanishing viscosity. While inviscid theory permits infinitely many transonic shock solutions with identical post-shock states but arbitrary shock positions, our analysis of the steady 1-D Navier-Stokes system reveals: 1. Viscous shock solutions exhibit L1-convergence as viscosity vanishes 2. The limiting shock solution's position depends critically on viscosity assumptions 3. Different viscous models yield distinct shock locations in the zero-viscosity limit These findings demonstrate fundamental differences between viscous and inviscid shock solutions, uncovering new phenomena that warrant further investigation. [Based on collaborations with Qin Zhao, Su Jiang, Piye Sun, and Ya-Guang Wang] |
| Title: | Inverse problems in phase field systems: uniqueness and algorithm |
| Time: | 15:00:00 - 16:00:00 |
| Place: | Room 2463 (Lift 25/26) |
| Abstract: | The phase field system is a nonlinear model that has significant applications in the field of materials science. In this talk, we are concerned with the uniqueness of determining the nonlinear energy potential in a phase-field system consisted of Cahn-Hilliard and Allen-Cahn equations. This system finds widespread applications in the development of alloys engineered to withstand extreme temperatures and pressures. The goal is to reconstruct the nonlinear energy potential through the measurements of concentration fields. We establish the local well-posedness of the phase-field system based on the implicit function theorem in Banach spaces. Both of the uniqueness results for recovering time-independent and time-dependent energy potential functions are provided through the higher order linearization technique. Numerical verifications based on the combination of semi-implicit Fourier scheme and neural network are presented in the end. |
| Title: | A cumulant approach to linear regression |
| Time: | 15:00:00 - 16:00:00 |
| Place: | Lecture Theatre F |
| Abstract: | Linear regression is a cornerstone of statistics. Despite its generality and flexibility, its interpretation can be subtle. In this talk I will describe a new perspective to linear regression through the lens of higher order cumulants and discuss how it offers new insights into a number of classical problems including the omitted variable bias. |
| Title: | Uniqueness of asymptotically conical Kähler-Ricci flow |
| Time: | 16:00:00 - 17:00:00 |
| Place: | Room 4504 (Lift 25/26) |
| Abstract: |
| Title: | Uniqueness of asymptotically conical Kähler-Ricci flow |
| Time: | 16:00:00 - 17:00:00 |
| Place: | Room 4504 (Lift 25/26) |
| Abstract: |