U.S.-Brazil Cooperative Research on Interacting Particle Systems and Hydrodynamic Limits

该奖项支持合作研究， 相互作用粒子系统的数学分析 由乔尔·莱博维茨领导的一组美国科学家 和五位巴西数学家： E.D. Andjel，P.A.法拉利，J.A. Galves和R.H. schonmann 圣保罗大学硕士瓦雷斯 2004年CNPq纯数学和应用数学研究所 里约热内卢。研究人员将继续和 在分析中加强为期五年的合作 相互作用的粒子系统及其流体动力学 极限，一个活跃的数学研究领域， 物理学后一种限制涉及相互作用的粒子 流体动力学偏微分方程组 有助于理解这些方程 这一合作卓有成效， 发表至少11篇关于互动的论文 粒子系统 这个领域的最初动机 源于随机力学，其目的是 使用概率模型研究时间 具有经典平衡态的系统的演化。 这样的模型自然地出现，例如，作为算法 用于吉布斯测度的蒙特卡罗模拟。 它 很快就发现同样的技术也可以 应用于生物学、生态学和行为学的模型， 以理工科为重 研究人员未来的工作将集中在 获得关于交互系统的更多信息， 包括将微观和宏观 波动，将先前的结果扩展到以下情况： 预计会出现不寻常缩放的大偏差， 将这些结果应用于更一般的设置， 例如，粒子在确定性动力学下运动， 相互作用的布朗运动或随机游动。

This award supports cooperative research in the mathematical analysis of interacting particle systems between a group of U.S. scientists headed by Joel Lebowitz of Rutgers University and five Brazilian mathematicians: E.D. Andjel, P.A. Ferrari, J.A. Galves and R.H. Schonmann of the Universidade de Sao Paulo and M.A. Vares of the Instituto de Matematica Pura e Aplicada (IMPA) of CNPq in Rio de Janeiro. The researchers will continue and strengthen a five year long collaboration in the analysis of interacting particle systems and their hydrodynamical limits, an active field of research in mathematics and physics. These latter limits relate interacting particle systems to hydrodynamical partial differential equations and are useful in understanding those equations. This collaboration has been very fruitful, resulting in the publication of at least eleven papers on interacting particle systems. The original motivation for this field arose from stochastic mechanics where the objective was to use probabilistic models in the study of the temporal evolution of systems with classical equilibrium states. Such models appear naturally, for example, as algorithms for making Monte Carlo simulations of Gibbs measures. It soon became clear that the same techniques could also be applied to models from biology, ecology, and the behavioral sciences. Future work by the researchers will center on obtaining more information about interacting systems, including relating microscopic and macroscopic fluctuations, extending previous results to the case where large deviations with unusual scalings are expected, and applying these results to more general settings, for example, particles moving under deterministic dynamics and interacting Brownian motions or random walks.