Computational Techniques From Geometry and Statistical Physics Applied To Fluid Mechanics and Interface Problems

Chorin0076510 研究人员和他的同事继续在界面建模，水平集方法和快速推进方法领域工作，并应用于塑料注射成型，地震走时计算，半导体制造和计算机视觉。 他们还继续发展统计预测方法的偏微分方程与欠分辨率和部分数据，与应用湍流，气候建模和多体问题。 这些主题的共同点是存在不确定性时的计算和分析 在许多重要的工程问题中，主要的困难是找到一个表面的确切位置或信号到达给定点的确切时间。 众所周知的例子发生在微芯片的制造中，在那里精确控制各种制造过程是很重要的，在机器人技术中，人们必须找到执行任务的最佳方式。 研究人员已经开发出解决这类问题的强有力的计算机方法;这些方法避免了在物理实验室中进行昂贵而漫长的试错。 他们继续改进这些工具，在制造业，地质学和计算机视觉中有新的应用。 科学中的许多问题缺乏足够的数据来完成一个完整的规范，或者是如此复杂，以至于无法完全解决。 例如天气和气候预报以及生物学问题。 研究人员仔细研究了在这种情况下人们能可靠地说的最多的是什么，并开发了计算机方法，以便在无法获得完整解决方案的问题中有效地找到最好的信息。 他们还在开发一些方法，当人们可以估计数据中的不确定性时，可以提前告诉答案中的不确定性。

Chorin0076510 The investigator an his colleague continue working in the area of interface modeling, level set methods and fast marching methods, with applications to plastic injection moulding, the computation of seismic travel times, semiconductor manufacturing and computer vision. They also continue to develop statistical prediction methods for partial differential equations with underresolution and partial data, with applications to turbulence, climate modeling, and many-body problems. The common thread of these topics is computation and analysis in the presence of uncertainty The main difficulty in many important problems of engineering is to find the exact location of a surface or the exact time a signal arrives at a given point. Well-known examples occur in the manufacture of microchips, where it is important to control exactly various manufacturing processes, and in robotics, where one has to find the optimal way to perform a task. The investigators have developed powerful computer methods for solving such problems; these methods obviate the need for costly and lengthy trial-and-error in a physical laboratory. They continue to improve these tools, with new applications in manufacturing, geology, and computer vision. Many problems in science lack sufficient data for a complete specification, or are so complex that they cannot be solved in full. Examples are weather and climate forecasting as well as problems in biology. The investigators have examined carefully what is the most one can reliably say in such situations, and have developed computer methods for finding effectively the best information one can in problems where a full solution is out of reach. They are also developing ways of telling in advance what the uncertainty in the answers will be when one can estimate the uncertainty in the data.