陽明交通大學應用數學系

Abstract. We consider the hard-capacitated facility location problem with uniform facility cost (CFL-UFC). This problem arises as an indicator variation between the general CFL problem and the uncapacitated facility location (UFL) problem, and is related to the profound capacitated k-median problem (CKM). In this work, we present a rounding-based 4-approximation algorithm for this problem, built on a two-staged rounding scheme that incorporates a set of novel ideas and also techniques developed in the past for both facility location and capacitated covering problems. Our result
improves the decades-old LP-based ratio of 5 for this problem due to Levi et al. since 2004. We believe that the techniques developed in this work are of independent interests and may further lead to insights and implications for related problems.

Abstract
Pressure-induced drag and lift are key to the performance of wings, rotors and propellers; undulating fins and flapping wings generate forces that are key to locomotion in fish, birds and insects; time-varying fluid dynamic forces drive flutter and flow-induced vibrations of flexible structures in engineering and biology, and these same forces enable the extraction of energy from flow via devices such as wind-turbines. Pressure on a body immersed in a flow is however induced simultaneously by vortices, acceleration reaction (a.k.a. added mass) effects associated with body and/or flow acceleration, and viscous diffusion of momentum, and determining the relative contribution of these different mechanisms on surface pressure remains one of the most important and fundamental issues in fluid dynamics. I will describe the force partitioning method (FPM), a new data-enabled method that partitions pressure forces into components due to vorticity, acceleration reaction and viscous diffusion. FPM has been used to gain new insights into a variety of vortex dominated flows including dynamic stall in pitching foils, vortex-induced vibration of bluff-bodies, hydrodynamics of schooling fish and rough-wall boundary layers, and results from these analyses will be presented. Application of FPM to data generated from experiments will also be described. Finally, FPM has been extended to aeroacoustics, and applications of the aeroacoustic partitioning method (APM) to dissect aeroacoustic noise in engineering and biological flows will be presented.

Abstract. In this talk, we consider some nonlinear hyperbolic systems of balance laws near resonance. We focus on the classical solutions near or away from vacuum state (resonance ) to the compressible Euler equations for either isentropic or non-isentropic flows through non-uniform ducts. We establish the global existence of classical solutions for both cases. By the normalization of systems, maximum principle, generalized Lax transformation and the detail study of Riccati equations, we are able to obtain uniformly bounded C^1 norms of those solutions . The asymptotic behavior of solutions is also studied.

This series of projects are the joint works with Hsin-Yi Lee, Jay Chu, Ying-Chieh Lin, Shih-Wei Chou and Shih-Ming Wang.

Abstract. It is well known that the 2D Keller-Segel system has finite time blowup solutions if the initial density has total mass greater than and finite second moment. We have several constructive examples showing that the solution blows up with the only -mass concentration. We will exhibit a new blowup mechanism formed by a collision of two sub-collapses, resulting in a -mass concentrating solution. A similar phenomenon appears in the 2D mass critical NLS by the work of Martel-Raphael in 2018, where the construction relies on two specific features: a conformal invariance and a minimal mass blowup constraint. These properties are not available for parabolic equations such as the Keller-Segel system. We bring here for the first time a directly rigorous construction of such a multiple-collapsing blowup solution.

演講網址：meet.google.com/bfa-aykg-mjt

更多詳情請參考附件。

Abstract. West Nile virus (WNv) is a mosquito-borne disease caused by Flavivirus. To investigate the combined effects of vertical transmission, temperature-dependent incubation periods and environmental heterogeneity on the transmission of WNv, we develop a delay differential system with stage-structure and time-varying delays. We then derive the mosquito reproduction number and WNv reproduction number, respectively, and further show that these two numbers serve as threshold parameters that determine whether WNv will spread or not.

Numerical simulations support our analytic results and suggest that time-periodic delays and environmental heterogeneity can play important roles in the WNv dynamics

Abstract. We study diverse solutions to optimization problems and design fair scheduling of demands with different priorities on wireless networks The problem of finding several sufficiently-diverse, yet approximately-optimal solutions to an optimization problem can be described as follows: given an integer k, an approximation factor $\alpha$, and a diversity measure $\sigma$ on a set of solutions to an optimization problem P, find a set of k solutions to P that (a) are all $\alpha$ approximately-optimal for P and (b) maximize the diversity measure $\sigma$ over all such sets of k solutions. The optimization problems considered here are maximum matching, spanning tree, global min-cut, shortest path, and minimum weight bases of a matroid. Here, a solution is a set of edges, and the number of edges two given solutions differ in as the diversity measure of the pair. The diversity measure $\sigma$ of k solutions is the sum of the pairwise Hamming distance between the bit-vectors representing the k solutions. We propose the first polynomial-time algorithms that (except for the unweighted spanning tree), for these five graph problems, guarantee that their diversity is at least 1/4 times the optimal diversity under different $\alpha$.

This result is applied for minimum weight bases of a matroid, which means it gives us diverse $\alpha$-approximate minimum spanning trees, advancing a step towards achieving diverse $\alpha$-approximate TSP tours.