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 computational methods 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 national interests, 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.
