多粒子随机系统中的多级粗粒化和纳米模式发现
Multilevel coarse graining and nano--pattern discovery in many particle stochastic systems
AI总结：
提出一种分层蒙特卡洛方法，通过耦合粗粒和微观状态空间，高效采样具有短程和长程相互作用的随机晶格系统的平衡性质，并显著降低计算成本。
摘要：
在这项工作中，我们提出了一种分层蒙特卡洛方法，用于采样具有竞争性短程和长程相互作用的随机晶格系统的平衡性质。每个蒙特卡洛步骤由两个或更多子步骤组成，有效耦合粗粒和微观状态空间。该方法可以设计为对目标分布进行精确采样或控制误差近似，提供不同分辨率级别以及微观级别的信息。在这两种策略中，与传统的马尔可夫链蒙特卡洛方法相比，该方法显著降低了计算成本。相变和模式形成问题的应用证实了所提出方法的效率。
英文摘要：
In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps efficiently coupling coarse and microscopic state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov Chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
