1. Time: October 21st (Tuesday) 10:00
Place: Natural Science Building #744
Speaker: Dr. Gyuyoung Hwang (Institute for Basic Science)

Title: Forward and inverse problems in coupled oscillator systems

Abstract:
When oscillators interact each other, they exhibit variety of phenomenon such as synchronization, chaotic motion, and kimera states. Such a system, called coupled oscillator system, is prevalent from neuronal oscillators and circadian rhythms to quantum optics and engineering. In this talk, we study the forward and inverse problem of the coupled oscillator systems. For the forward problem, we investigate the existence of periodic measure-valued solutions for a class of nonlocal continuity equations, which include the mean-field equations arising from the coupled systems of oscillators. We use a fixed point theorem for geodesically convex spaces constructed by optimal mass transport. On the other hand, in many real-life situations, we often lack the information of the exact model, in particular the interaction force between oscillators. Thus, in the next section, we study the inverse problem to search for the coupling function among oscillators using physics-informed neural networks.

2. Time: October 21st (Tuesday) 11:00
Place: Natural Science Building #744
Speaker: Prof. Jeongho Kim (Kyung Hee University)

Title: Asymptotic behavior of the Navier-Stokes-Korteweg system

Abstract:
Fluids with capillary effects appear in a wide range of contexts, including multiphase flow and quantum hydrodynamics. In this talk, I will introduce the compressible Navier–Stokes–Korteweg equations, which are extensions of the standard compressible fluid models that incorporate capillarity. Then, I will discuss the stability of viscous–dispersive shock profiles, and its composition with the rarefaction wave for the compressible Navier–Stokes–Korteweg system. These results are based on joint work with Prof. Moon-Jin Kang and Dr. Sungho Han (KAIST).