Theory and Application of Computation in Statistical Physics

9978233 machta本基金支持统计物理学和理论计算机科学的交叉研究。该基金特别支持统计物理中聚类蒙特卡罗算法的开发和应用，以及从计算复杂性理论的角度分析统计物理中的模型。在第一个领域，PI将扩展先前的工作，开发一种新的侵入簇方法来模拟由晶格模型描述的材料的特性。其次，PI将把计算复杂性理论应用于相关的材料理论模型，如扩散有限聚集和入侵渗透。计算复杂性理论根据模拟问题所需的资源对问题进行分类。本基金支持计算机科学与材料理论结合的工作，并建议在两个相关领域进行研究。第一个领域将强调统计物理学中创新簇蒙特卡罗方法的发展和应用，以扩展当前材料相变计算建模的理论能力。第二个领域将强调将计算机科学中计算复杂性理论的发展应用于材料科学中的数学相关问题，如材料在扩散限制条件下的生长和多孔介质中的流体流动

9978233MachtaThis grant supports work at the interface of statistical physics and theoretical computer science. In particular this grant supports work involving the development and application of cluster Monte Carlo algorithms in statistical physics, and the analysis of models in statistical physics from the viewpoint of computational complexity theory. In the first area, the PI will extend previous work in developing a new invasive cluster approach to simulate the properties of materials described by lattice models. In the second, the PI will apply computational complexity theory, which classifies problems according to the resources required to simulate them, to related materials theory models such as diffusion limited aggregation and invasion percolation.%%%This grant supports work at the interface of computer science and materials theory, with research proposed in two related areas. The first area will emphasize the development and application of an innovative cluster Monte Carlo approach in statistical physics to expand current theoretical capabilities in computational modeling of phase transitions in materials. The second area will emphasize applying developments in computational complexity theory from computer science to mathematically related problems in materials science such as the growth of materials in diffusion limited conditions and fluid flow though porous media.***