Jump To中央區塊/Main Content :::
:::

Seminars

Lecture Series

AS Conference 2025 Parallel Sessions:Mechanics, Wave Train, Scattering, and Future Applications

2025/07/02 (Wed.) 14:00~15:00
  • Date : 2025/07/02 (Wed.) 14:00~15:00
  • Location : Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
  • Speaker : Shih-Hsien Yu (AS)
  • Website : https://asconference2025.dia.as.edu.tw/
  • Abstract : In this talk we will briefly present various mechanical problems aroused from physics with important applications in science. Most of those mechanical problems are related to the basic equations such as heat equation, wave equation, Schrödinger equation, etc.; and one will give a simple review on the mathematical theories for those equations in terms of the notion “wave trains".

    Then, one will outline an ongoing mathematical development in AS for constructing a new methodology, “Laplace wave train and scattering", to represent the solutions of the basic equations for heterogeneous media. In this development, the key notions are the Green's function, phase length, reflection coefficient, transmission coefficient, and the space of path of interactions. By those notions one can obtain a combinatoric representation of the solutions for a mechanical problem. That is to represent the motions of mechanical problems for heterogeneous media in terms frequency of oscillations, wave numbers, and their amplitudes. One gave a rigorous way to transform a mechanical motion into observable data.

    In this talk, one will apply this development to represent seismic wave motions in layered media and discuss the possibility to use the development to learn the layered structures in seismology.
:::