Novel Approaches for Problems with Uncertainties

本项目旨在为受输入数据不确定性影响的问题发展新的数学理论和数值方法。这种不确定性存在于大多数实际应用的数学模型中。对于这些问题，使用一组输入数据的单一确定性模拟是有限的。因此，处理随机性的新技术是必不可少的。这个项目中的问题是由铁磁性、结构声学和振动的具体应用驱动的。新的理论可以为认识铁磁材料和结构声学奠定基础。本课题所开发的新方法可能为随机液晶理论和其他界面问题的研究奠定基础。

This project aims to develop novel mathematical theories and numerical methods for problems affected by uncertainty in input data. This type of uncertainty exists in most mathematical models of real life applications. For these problems, a single deterministic simulation with one set of input data is of limited use. Therefore, novel techniques to deal with randomness are essential. The problems in this project are driven by specific applications from ferromagnetism, structural acoustics and vibration. The new theories may lay the foundation for understanding ferromagnetic materials and structural acoustics. The novel approaches to be developed in this project may form the basis for the study of stochastic liquid crystal theory and other interface problems.