International Conference on Multiscale Methods and Partial Differential Equations; August 26-27, 2005; Los Angeles, CA

多尺度方法与偏微分方程国际会议将于2005年8月26-27日在加州大学洛杉矶分校举行。本次会议的目的是将对多尺度问题和相关偏微分方程的理论、计算和实践方面感兴趣的研究人员、学生和实践者聚集在一起。会议将提供一个论坛来交流和激发来自不同学科的新思想，并制定新的具有挑战性的多尺度问题，这些问题将对应用产生影响。尽管在广泛的科学领域取得了相当大的进展，人们越来越认识到多尺度方法的重要性，但目前在多尺度方法、其严格的分析和应用方面存在着碎片化。迫切需要发展系统的多尺度分析和计算方法，以应用于广泛的实际问题。这一努力对偏微分方程理论提出了新的挑战。通过将分析人员、多尺度建模专家和计算科学家聚集在一起，我们可以确定多尺度数学中的关键问题以及来自不同学科的各种多尺度问题的共同主题。这为在这一领域取得重大进展提供了一个独特的机会。在过去的几十年里，计算科学的进步使计算能力提高了几个数量级。在小范围内对物理问题的建模和模拟已经相当成功。然而，解决涉及大范围空间或时间尺度的复杂物理问题仍然是许多科学学科面临的重大挑战。这些问题关系到我们的国家利益，影响着我们在环境科学、能源科学、生物科学、材料科学、信息科学等领域的政策和技术进步。多尺度分析、建模和仿真是一个新兴的研究领域，已经在许多科学学科中产生了重大影响。最近在多尺度分析、建模和仿真方面取得了许多令人兴奋的进展，但都是具体问题。到目前为止，大多数关于多尺度建模和计算的工作都是在一个单独的学科内发展起来的。特定领域的突破可能适用于更广泛的背景，但仍然是孤立的。因此，多尺度描述远没有达到其潜在的影响水平，包括在教育和工业领域。我们的多规模会议的主要目的之一是将这些孤立的努力和不同的发展结合起来。会议还将提供一个特别的机会，将应用数学家与多尺度建模和计算领域的专家联系起来。这将有助于弥合数学和其他应用学科之间在研究和知识转移方面的差距。

The International Conference on Multiscale Methods and Partial Differential Equations will be held at UCLA on August 26-27, 2005. The objective of this conference is to bring together researchers, students and practitioners with interest in the theoretical, computational and practical aspects of multiscale problems and related partial differential equations. The conference will provide a forum to exchange and stimulate new ideas from different disciplines, and to formulate new challenging multiscale problems that will have impact in applications. Despite considerable progress in a wide range of the sciences, and a growing awareness of the importance of multiscale approaches, currently there is fragmentation in multiscale methodology, its rigorous analysis and its applications. There is an urgent need to develop systematic multiscale analysis and computationalmethods that can be applied to a wide range of practical problems. This effort poses new challenge to the theory of partial differential equations. By bringing together analysts, experts in multiscale modeling,and computational scientists, we can identify the key issues in multiscale mathematics and common themes of various multiscale problems arising from different disciplines. This provides a unique opportunity to make significant advances in this area.Advances of computational sciences in the past few decades have resulted in an increase of several orders of magnitude in computing power. Modeling and simulations of physical problems in a narrow range of scales have been quite successful. However, to solve complex physical problems which involves a wide range of spatial or temporal scales remains to be a major challenge in many scientific disciplines. These problems are of vital importance to our nationalinterests, affecting our policy and technology advances in areas such as environmental science, energy, biology, materials science, and information science. Multiscale analysis, modeling, and simulation is an emerging new research area which has already made significant impact in many scientific disciplines. There have been many exciting recent, but problem specific, advances in multiscale analysis, modeling and simulation. Up to now, most work on multiscale modeling and computation has been developed within an individual discipline. Breakthroughs in specific domains could be applicable in a broader context, but remain isolated. As a result, multiscale descriptions are nowhere near their potential level of impact, including in education and industry. One of the main purposes of our multiscale conference is to integrate these isolated efforts and diverse developments. The conference will also provide a special opportunity to connect applied mathematicians with domain experts in multiscale modeling and computation. This will help bridge the gap in research and knowledge transfer between mathematics and other application disciplines.