Collaborative Research: RNMS: Kinetic Description of Emerging Challenges in Multiscale Problems of Natural Sciences

该奖项支持数学科学研究网络：？自然科学多尺度问题新挑战的动力学描述？（KI-net）。传统上，动力学描述在数学物理学的许多领域都扮演着核心角色。然而，在过去的二十年中，动力学描述已经成为定量描述各种现象的不可或缺的工具，从半导体，聚合物和等离子体，到细胞迁移，群集和神经元网络，以及交通，社会和经济网络。正是在这一背景下，知识创新网络将促进数学与其他科学学科之间的相互交流，特别侧重于以下三个领域：* 量子动力学及其在化学中的应用;* 网络动力学及其在社会科学中的应用;以及 * 生物过程的动力学模型。培养下一代的研究人员来应对新的挑战，并维持美国？在这一领域的国际舞台上发挥主导作用。拟议中的KI网将带来全方位的数学技术，以应对物理、生物和社会科学中新现象的动力学描述方面的重要科学挑战。最终目标是开发，分析和计算新的动力学描述与这些学科中的各种应用。KI-net将为实现这些目标提供一个独特的平台。它将围绕三个中心：马里兰州大学的科学计算数学建模中心（CSCAMM），UT奥斯汀的计算与工程科学研究所（ICES）以及威斯康星大学麦迪逊分校的数学系。在初始阶段，他们将通过一系列边缘互连12个节点，涉及25个核心参与者。KI-net Research Network主页：http://www2.cscamm.umd.edu/ki-net/。

This award supports a Research Network in Mathematical Sciences: ?Kinetic description of emerging challenges in multiscale problems of natural sciences? (KI-net). Kinetic descriptions have traditionally played a central role in many areas of mathematical physics. In the last two decades, however, kinetic descriptions have emerged as an indispensable tool for a quantitative description of diverse phenomena, ranging from semi-conductors, polymers and plasma, to cell migrations, swarming, and neuron networks, as well as traffic, social and economic networking. It is in this context that the KI-net will foster cross-fertilization between mathematics and other scientific disciplines, with particular focus on the following three areas:* Quantum dynamics with applications to chemistry;* Network dynamics with applications to social sciences; and* Kinetic models of biological processes.The principal objectives are to foster new kinetic-based national and international collaborations; to train a future generation of researchers to address new challenges, and to sustain the United-States? leading role on the international stage in this field. The proposed KI-net will bring the full range of mathematical techniques to bear on important scientific challenges in kinetic descriptions of new phenomena in physical, biological and social sciences. The ultimate goal is the development, analysis and computation of novel kinetic descriptions with various applications in these disciplines. KI-net will offer a unique platform to carry out these objectives. It will be centered around three hubs: the Center for Scientific Computation & Math Modeling (CSCAMM) in the University of Maryland, the Institute for Computational and Engineering Science (ICES) at UT Austin, and the Department of Mathematics at the University of Wisconsin-Madison. At the initial stage, they will inter-connect 12 nodes through a series of edges, involving 25 core participants. KI-net Research Network home page: http://www2.cscamm.umd.edu/ki-net/.