Assembling of a few particles into a cluster commonly occurs in many systems.However,it is still challenging to precisely control particle assembling,due to the various amorphous structures induced by thermal fluctuat...Assembling of a few particles into a cluster commonly occurs in many systems.However,it is still challenging to precisely control particle assembling,due to the various amorphous structures induced by thermal fluctuations during cluster formation.Although these structures may have very different degrees of aggregation,a quantitative method is lacking to describe them,and how these structures evolve remains unclear.Therefore a significant step towards precise control of particle self-assembly is to describe and analyze various aggregation structures during cluster formation quantitatively.In this work,we are motivated to propose a method to directly count and quantitatively compare different aggregated structures.We also present several case studies to evaluate how the aggregated structures during cluster formation are affected by external controlling factors,e.g.,different interaction ranges,interaction strengths,or anisotropy of attraction.展开更多
First passage time in Markov chains is defined as the first time that a chain passes a specified state or lumped states. This state or lumped states may indicate first passage time of an interesting, rare and amazing ...First passage time in Markov chains is defined as the first time that a chain passes a specified state or lumped states. This state or lumped states may indicate first passage time of an interesting, rare and amazing event. In this study, obtaining distribution of the first passage time relating to lumped states which are constructed by gathering the states through lumping method for a irreducible Markov chain whose state space is finite was deliberated. Thanks to lumping method the chain＇s Markov property has been preserved. Another benefit of lumping method in the way of practice is reduction of the state space thanks to gathering states together. As the obtained first passage distributions are continuous, it may be used in many fields such as reliability and risk analysis展开更多
文摘Assembling of a few particles into a cluster commonly occurs in many systems.However,it is still challenging to precisely control particle assembling,due to the various amorphous structures induced by thermal fluctuations during cluster formation.Although these structures may have very different degrees of aggregation,a quantitative method is lacking to describe them,and how these structures evolve remains unclear.Therefore a significant step towards precise control of particle self-assembly is to describe and analyze various aggregation structures during cluster formation quantitatively.In this work,we are motivated to propose a method to directly count and quantitatively compare different aggregated structures.We also present several case studies to evaluate how the aggregated structures during cluster formation are affected by external controlling factors,e.g.,different interaction ranges,interaction strengths,or anisotropy of attraction.
文摘First passage time in Markov chains is defined as the first time that a chain passes a specified state or lumped states. This state or lumped states may indicate first passage time of an interesting, rare and amazing event. In this study, obtaining distribution of the first passage time relating to lumped states which are constructed by gathering the states through lumping method for a irreducible Markov chain whose state space is finite was deliberated. Thanks to lumping method the chain＇s Markov property has been preserved. Another benefit of lumping method in the way of practice is reduction of the state space thanks to gathering states together. As the obtained first passage distributions are continuous, it may be used in many fields such as reliability and risk analysis
