Annual Report 2005–06

研究 Research 55 傑 出 研 究 計 劃 Outstanding Research Project 數 學在生物科學中的應用是魏軍城教授的主要研究方向。發展生 物學研究的其中一個主要課題，是了解自然界多姿多采模式的 內在機制，例如海螺、魚及斑馬身上的點狀及紋狀。數學家圖靈早在一 九五二年就提出了用非線性偏微分方程來研究這些問題。但從前的研究 大多集中用線性的方法，而忽略了非線性的特點。 魏教授與他的合作者用數學上最前沿的非線性偏微分方程，徹底解決了 一維及二維圖靈非線性模式的內在機制問題，不僅開拓了一個新的數學 領域──凝聚解現象及其應用，而且第一次將深奧的數學應用在生物科 學裡。他的研究吸引了不同國家、不同領域的科學家的注意，也為純數 學的應用開闢了新領域。 Prof. Wei’s research on the application of ‘Nonlinear PDE Methods in Developmental Biology’ lies at the interface of mathematics and biological sciences — a fast growing research frontier. A key issue in developmental biology is mathematical understanding of how diverse patterns in nature, such as spots and stripes on sea-shells, fish and zebra, are produced. Using the basic idea from Turing (1952), these problems can be transformed into the study of system of partial differential equations (PDEs). In the last 20 years, there have been many studies on such systems, using the standard linear method which, however, can only predict linear patterns, that is, patterns near uniform state. By using rigorous and sophisticated nonlinear PDE methods, Prof. Wei and his collaborators developed a systematic approach in treating nonlinear patterns, which provides a complete understanding of nonlinear patterns in one or two spatial dimensions. Studies by Prof. Wei and his team of collaborators have opened up new dimensions in both pure and applied mathematics. 魏軍城教授 Prof. Wei Jun-cheng 生物數學的新進展 New Development in Mathematical Biology Research