Workshop on Dynamics and Bifurcations of Patterns in Dissipative Systems

在过去的几十年里，非线性科学的进步使数学家和物理学家更好地理解了在远离平衡的系统中观察到的各种结构。 宏观秩序的出现和时空对称性的自发打破是许多自然现象的共同特征。 事实上，我们世界上看到的每一个结构都可以被认为是一个复杂的非线性系统在非平衡条件下连续发生的一系列破坏性不稳定性的结果。 图案形成的跨学科领域寻求对来自流体力学，固态物理，非线性光学，化学和生物学等不同领域的系统中空间和时空图案的自发形成的共同理解。 虽然近年来在理解模式形成方面取得了很大进展，但仍然存在根本性的挑战。该奖项支持参加2003年春季在科罗拉多州立大学举行的耗散系统模式动力学和分叉研讨会的人员。 该研讨会的目标是汇集来自不同领域的理论家和实验学家，从应用数学到理论和实验物理，通过他们对非线性现象的兴趣统一起来，并寻求对复杂系统中模式形成和动力学的更深入理解。 该研讨会将促进专家，高级研究生和年轻研究人员之间的交流与合作，以确定耗散系统时空模式数学分析中的关键思想，新进展和开放性问题。 感兴趣的主题包括稳定性，分叉，模式的动力学，控制方程的简化，以及对称性的作用。 演讲和圆桌讨论将激发模式形成和分析方面的进一步理论和应用研究。模式科学的发展速度极快，被认为是物理学在新时代面临的六大挑战之一，这使得研讨会的目标变得紧迫。

Progress in nonlinear science achieved during the last decades has brought mathematicians and physicists a better understanding of the variety of structures observed in systems far from equilibrium. The emergence of macroscopic order and the spontaneous breaking of spatiotemporal symmetries are features common to many natural phenomena. Virtually every structure seen in our world can be considered the result of a long sequence of successive symmetry-breaking instabilities of a complex nonlinear system under nonequilibrium conditions. The interdisciplinary field of pattern formation seeks a common understanding of such spontaneous formation of spatial and spatiotemporal patterns in systems from areas as diverse as fluid mechanics, solid state physics, nonlinear optics, chemistry, and biology. While much progress towards understanding pattern formation has been made in recent years, fundamental challenges remain. This award supports participants in the Workshop on Dynamics and Bifurcations of Patterns in Dissipative Systems, held at Colorado State University in the spring of 2003. The goal of the workshop is to bring together theorists and experimentalists from different fields, from applied mathematics to theoretical and experimental physics, unified by their interest in nonlinear phenomena and in search of a deeper understanding of pattern formation and dynamics in complex systems. The workshop will stimulate communication and collaboration between experts, advanced graduate students, and young researchers in identifying key ideas, new advances, and open questions in the mathematical analysis of spatiotemporal patterns in dissipative systems. Topics of interest include stability, bifurcation, and dynamics of patterns, reduction of governing equations, and the role of symmetry. The presentations and roundtable discussions will stimulate further theoretical and applied investigations in pattern formation and analysis. The extremely rapid pace of developments in the science of patterns, identified as one of the six grand challenges for physics in a new era, lends urgency to the goals of the workshop.