Acquisition of a Computational Mathematics Cluster

该奖项为购买128核计算数学集群提供资金，以支持圣地亚哥州立大学在数学方面的计算需求研究和教育项目。拟议的研究包括下列领域的项目。(1)耦合非线性导航装置建模。该项目由美国国家科学基金会资助，重点研究基于全球定位技术、耦合陀螺仪和加速度计的新一代导航传感器的理论和物理发展。由此产生的系统具有优越的灵敏度和抗干扰性。(2)流动网格上的反应扩散方程。火焰图案形成的非线性动力学将扩展到模拟温度和机械扰动的影响，应用分岔理论中的新方法。(3)高速内燃机仿真。一种日益流行的发动机设计，在载气中使用液体燃料液滴的细雾，将在非结构化网格上通过颗粒源电池方法进行建模。(4)海岸流模拟。为了预报蒙特利湾和其他沿海水域的洋流，将采用曲线坐标进行模拟。该模型最终将包括地质、化学和生物影响。该集群将支持研究生和本科生的研究项目，包括直接导致学生奖学金和随后就业的项目。大约20%的集群计算能力将全年用于本科生项目，包括(1)应用数学和统计学的高级论文研究项目；(2)数学建模、仿真和生物数学新课程的课堂和作业项目；(3)在现有的外部资助的奖学金项目下进行的本科生研究。作为全美授予学士学位的前十所大学之一，SDSU在为数学研究中被忽视的少数族裔提供这些机会方面占据了强势地位。为少数族裔提供S学位，以及14个不同的项目，以促进未被充分代表的群体参与科学。

This award provides funds for the purchase of a 128-core Computational Mathematics Cluster, to support computationally demanding research and educational projects in mathematics at San Diego State University. The proposed research encompasses projects in the following areas. (1) Modeling coupled nonlinear navigational devices. This NSF-funded project focuses on the theoretical and physical development of a new generation of navigational sensors based on a combination of global positioning technology and coupled gyroscopes and accelerometers. The resulting system offers superior sensitivity and resistance to interference. (2) Reaction-diffusion equations on fluxional grids. The nonlinear dynamics of flame pattern formation will be extended to model the effects of temperature and mechanical perturbations, applying new methods in bifurcation theory. (3) Simulation of high-speed combustion engines. An increasingly popular engine design, employing a fine mist of liquid fuel droplets in a carrier gas, will be modeled by particle-source-in-cell methods on unstructured grids. (4) Coastal current simulations. Simulations employing curvilinear coordinates will be carried out in order to forecast ocean currents in Monterey Bay and other coastal waters. The model will ultimately include geologic, chemical, and biological influences. The cluster will support graduate and undergraduate student research projects, including projects that have led directly to student fellowships and subsequent employment. Roughly 20% of the computing capacity of the requested cluster will be dedicated yearround to undergraduate projects, including (1) senior thesis research projects in applied mathematics and statistics; (2) in-class and homework projects for new courses in mathematical modeling, simulations, and biomathematics; (3) undergraduate research carried out under an existing, externally funded fellowship program. SDSU occupies a strong position for making these opportunities available to minorities underrepresented in mathematical research, as one of the top ten campuses in the nation granting bachelor?s degrees to ethnic minorities, and with 14 distinct programs to promote the participation of underrepresented groups in the sciences.