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 10¤ëºtÁ¿ Colloquium, ¥xÆW¤j¾Ç¤j®ð¬ì¾Ç¨t ³¢ÂE°ò Á¿®y±Ð±Â Thursday, October 8, 15:10¡X16:00 ¼Æ¾Ç¨t3174 Title: Two-Dimensional Turbulence and Typhoon Vorticity Dynamics (¨â«×ªÅ¶¡¶Ã¬y»P»ä­·´õ«×°Ê¤O) Abstract:Earth¡¦s atmosphere and ocean, under the influence of rotation and density stratification, exhibit complex patterns of fluid motion over a wide range of space and time scales. The two-dimensional turbulence, which may be stemmed either from the fluid rotation or the fluid internal stratification, has been a paradigm for atmospheric oceanic fluid dynamics (AOFD). It is a remarkable fact that for any type of random initial state or external forcing, a two-dimensional fluid will rapidly organize itself into a system of coherent, interacting vortices swimming through a sea of passive filamentary structure produced from earlier vortex interactions. This discipline has also been instrumental in the development of single charge plasma physics, galaxy spiral, the Great Red spot, the ozone-hole problem and the typhoon dynamics. A brief review of 2D and 3D turbulence will be given. The mathematical nature of the 2D turbulence will be addressed. The nonlinear typhoon vorticity dynamics, such as merger dynamics, the eyewall rotation and mixing, the successive formation of tropical vortices and the concentric eyewall formation dynamics will be presented. These nonlinear vorticity dynamics are shown to bear great resemblance to the observations. ºtÁ¿°Q½×¨â«×ªÅ¶¡¶Ã¬y»P»ä­·´õ«×°Ê¤O¡C¦a²y¤j®ð®ü¬v¬yÅé¨ü¦a²y±ÛÂà»P±K«×¼h¤Æ¼vÅT¡A¨ä°Ê¤O¯S©Ê¬O¨â«×ªÅ¶¡¶Ã¬y¾Çªº¨å½d¡F¨â«×ªÅ¶¡¶Ã¬y«D½u©Ê¤Ø«×¥æ¤¬¬O©¹¤j¤Ø«×²¾°Ê¡A´õºx¦X¨Ö¦¨¤j´õºx¥H¤Î¤j¶qÀôÂ¶©PÃä²Óµ·´õ«×±a¡A¬O¨â«×ªÅ¶¡¶Ã¬y¯S©Ê¡C¤¶²Ð¥H¨â«×ªÅ¶¡¶Ã¬y¬ÛÃöªºª«²z²{¶H¡A¨Ã¥H¦¹Æ[ÂI±´°Qªº»ä­·´õ«×°Ê¤O¡A¤]·|°Q½×¼Æ¾Ç»P¦¹°Ê¤Oªº¬ÛÃö©Ê¡C Colloquium, ²H¦¿¤j¾Ç¼Æ¾Ç¨t ·¨©w´§±Ð±Â Thursday, October 8, 16:10¡X17:00 ¼Æ¾Ç¨t3174 Title: Some Recent Works on the Dynamics and Traveling Wave Solutions of Non-Monotone Three Species Food Web Models Abstract: Three species food web models are fundamental building blocks of large scale ecosystems. To clarify the local or global and short-term or long-term behavior of ecosystems, it is essential to understand the interacting dynamics of three species food web models. A monotone ecosystem whose interactions among n-species are all cooperative or competitive (n = 2) have been well studied in the past three decades by the theory of monotone dynamical systems. However, for a non-monotone system whose interactions are blended at least with one consumption (i.e. herbivory, predation or parasitism), most known results are constrained on two species cases since the classical Poincare-Bendixson Theorem can be applied. Hence recent attention has been attracted to the dynamics of a non-monotone ecosystem with at least three species. In this talk, we will first survey some recent progress on the non-diffusive predator-prey food web models. Then, with diffusion, the existence of traveling wave solutions by upper lower solutions/shooting method are investigated. Finally, some open problems of these topics are proposed. Colloquium, ¥æ³q¤j¾Ç³qÃÑ¤¤¤ß ³¯©ú¼ý±Ð±Â Thursday, October 15, 15:10¡X17:00 ¼Æ¾Ç¨t3174 Title: ¼Æ¾Ç»PÃÀ³N Abstract: Link Colloquium, °ê¥ß¥æ³q¤j¾ÇAI¾Ç°| ÃQ¿A¤H±Ð±Â Thursday, October 22, 15:10¡X16:00 ¼Æ¾Ç¨t3174 Title: °òÂ¦¼Æ¾Ç·§©À¦b²«×¾Ç²ßªºÀ³¥Î Abstract: ¥»¦¸ºtÁ¿¤¶²Ð¤@¨Ç°òÂ¦¼Æ¾Ç¤âªk¦b²«×¾Ç²ß¤¤ªºÀ³¥Î¡C¥D­nªº¥DÃD¦p¤U: * ¥Î¼Æ¾Ç¤Wªº¥­­±¡B¥ßÅé´X¦ó¨ÓÀ°§U³]­p¯«¸gºô¸ô¼Ò«¬ * ¥Î¤£ÅÜ¶qªº·§©À¡A³]­p¤Î°V½m¯«¸gºô¸ôµ²ºc * Neural ODE, ¥Î·L¤À¤èµ{°t¦X¯«¸gºô¸ô * ¼Æ¾Ç©w¸q¼Ò¦¡»P¯«¸gºô¸ôµ²ºcªº¬Û¦ü©Ê Colloquium, ¥æ³q¤j¾Ç¼Æ¾Ç¨t ªL«³亘§U²z±Ð±Â Thursday, October 29, 15:10¡X16:00 ¼Æ¾Ç¨t3174 Title: Monotonicity-Based Inversion of the Fractional Schrodinger Equation Abstract: We consider an inverse problem for the fractional Schrodinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal Dirichlet-to-Neumann maps. Based on the monotonicity relation, we can prove uniqueness for the nonlocal Calderon problem in a constructive manner. Secondly, we offer a reconstruction method for an unknown obstacles in a given domain. Our method is independent of the dimension and only requires the background solution of the fractional Schrodinger equation. Colloquium, °ê¥ß¤¤¥¡¤j¾Ç¼Æ¾Ç¨t ¶À·¬«n±Ð±Â Thursday, October 29, 16:10¡X17:00 ¼Æ¾Ç¨t3174 Title: Data Assimilation Technique with Long Short Term Memory Networks for Highway Traffic Flow Prediction Abstract: The development of accurate and reliable computational traffic flow prediction tools has always been an active research topic in transportation engineering and planning. Generally, the available predictive tools are divided into three categories, namely parametric methods, nonparametric methods, and PDE-based simulations. In particular, the machine learning methods (such as the k-nearest neighbor (K-NN) method and the long short term memory networks (LSTM)) are the nonparametric techniques, and the autoregressive integrated moving average (ARIMA) and its variants are one of the most representative parametric methods. In this work, we propose the data assimilation technique with the long short term memory networks (LSTM) for predicting the highway traffic flows. The proposed method is developed based on the framework of the Karman filtering (KF) algorithm, which consists of two key components: the prediction step and the correction step. The predicted value is obtained by performing numerical simulation and then corrected by Karman filtering with real data. As the numerical simulator, which is a kernel component of the predictive tool, we use an explicit Godunov¡¦s method to discretize the Lighthill-Whitham-Richards model, where the MacNicholas formulation is used as the fundamental relation between the velocity and density. Since the data at the upstream boundary point in the future period is not available. The pseudo-predicted values obtained by using LSTM are used for setting boundary conditions. In this study, we use Seasonal ARIMA (SARIMA), LSTM methods as baseline methods and compare them with our proposed method. The numerical results based on the real traffic for the Hsuehshan Tunnel extracted from the Freeway Bureau Ministry of Transportation and Communications (MOTC) database in Taiwan show that our method outperforms SARIMA and LSTM as well as the classical KF method. PDE Seminar, °ê¥ß¥xÆW¤j¾Ç¼Æ¾Ç¨t ¤ý®¶¨k±Ð±Â Friday, October 30, 11:10¡X12:00 ¼Æ¾Ç¨t3¼Ó·|Ä³«Ç Title: Non-Radiating Sources for the Elastic Waves in Anisotropic Inhomogeneous Media Abstract: In this talk, I would like to discuss the characterization of non-radiating volume and surface (faulting) sources for the elastic waves in anisotropic inhomogeneous media. Each type of the source can be decomposed into a radiating part and a non-radiating part. The radiating part can be unique determined by an explicit formula containing the near-field measurements. On the other hand, the non-radiating part does not induce scattered waves at a certain frequency. In other words, such non-radiating source can not be detected by measuring field at one single frequency in a region outside of the domain where the source is located. This is a recent joint work with Pu-Zhao Kow.

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 °ê¥ß¦¨¥\¤j¾Ç¼Æ¾Ç¨t 70101 ¥x«n¥«¤j¾Ç¸ô¤@¸¹ ¹q¸Ü¡J(06) 2757575 Âà 65100   ¶Ç¯u¡J(06) 2743191 em65100[at]email.ncku.edu.tw