Design And Realization Of Cluster Stability Model Based On Monte Carlo Method

System theory believes that openness,self-organization,complexity,integrity,relevance,hierarchical structure,dynamic balance,and timing are the common basic characteristics of all systems.In traditional geometry,people are always used to study and measure a geometric object in Euclidean space.Different from traditional geometry,fractal theory,as a new epistemology and methodology,has enlightening significance in many aspects: one is the similarity between the whole and the local form,which inspires people to understand the whole through recognizing parts;The new form between the whole and the part,order and disorder;the third is to reveal the picture of universal connection and unity in the world from a specific level.Clusters are widely present in nature and human society,involving many material movement processes and phenomena,such as catalysis,combustion,crystal growth,nucleation and solidification,phase change,sol,film formation,and sputtering.A cluster is a form of material between atoms,molecules and bulk materials,and it is a new level of material structure.The basic problem of cluster scientific research is how the cluster structure and properties change as the cluster evolves.Condensation and dispersion are the two basic processes in the development of clusters.Researchers have conducted a lot of and in-depth research on fractal agglomeration,and put forward many research models.However,in contrast to cluster dispersion,as the inverse process of aggregation,few researchers consider the dynamics of cluster splitting.Since small clusters can form large cluster structures through layerby-layer polymerization,the stability of large clusters cannot be ruled out under the action of various internal and external forces,and thus collapse into small structures.If the cluster collapses,what is the way to disperse it? How to determine the scattered site?What kind of property changes will occur after the clusters are dispersed? At present,research models in this area are very rare.In view of this,it is necessary to construct the stability model of fractal clusters as soon as possible.The Monte Carlo method uses random numbers(or more commonly pseudorandom numbers)to calculate and solve problems.When the number of trials is greater,the results obtained are more accurate.The computer can realize tens of millions of experiments in a short time,which can greatly reduce the actual experiment time,and the results are more accurate.Monte Carlo method has gradually become a powerful method in the study of random processes.This research attempts to study the dispersion and evolution of clusters from the perspective of system theory,using Monte Carlo simulation method to study the dispersion and evolution of clusters.It is hoped that fractal theory will be used to establish the internal connection between microscopic particles and mesoscopic clusters,while taking into account external factors such as gravity.The effect of the interaction on the evolution and development of clusters,thereby further enriching the existing theory of cluster stability.The main work and results of this paper are as follows:(1)The evolution model of fractal clusters is constructed based on the lattice simulation system.The model mainly involves the selection of clusters in the system,the selection of splitting methods,and the selection of simulation environment.Using the Python object-oriented programming language to structure the simulation program,a three-dimensional cluster stability model simulation program was developed,the simulation process was visualized,and the data related to the splitting process was recorded in real time.The program page is simple and can interact with users well.(2)Inspired by the idea of "dual cohesion" in the CCA cohesion model.This paper proposes a "two-part" dispersion model,that is,a successful split of a cluster will only produce two sub-clusters.The existing dispersion models are that when the cluster is subjected to the force of the external shear flow field,the cluster gradually deforms and finally collapses.In fact,the common forms of dispersion include crushing dispersion,fracturing dispersion,and erosive dispersion.The dispersion model established in this paper also organically unifies the above three dispersion forms,and the parameters that need to be controlled only need to consider the selection of the cluster splitting position and the calculation of the splitting probability.(3)This article explores the addition of the collision cohesion process to the stability model,that is,the random motion causes two clusters to collide,which leads to cohesion,so as to construct a coupling model of fractal dispersion and cohesion.In this case,this article considers the diffusion,collision,and aggregation of particles or clusters.The diffusion of particles or clusters is based on the theory of random processes.In this paper,the clusters' simulation results,fractal dimension and cluster concentration are shown in the clusters' dispersion process.(4)This paper also considers the influence of the gravity field and discusses the influence of random motion and gravity sedimentation on the evolution of clusters at the same time.The simulation results show that the clusters are affected by different effects in different periods.When the mass of the clusters is large in the early stage,it is mainly affected by gravity settlement,and the decrease of the clusters in the later stage is mainly affected by random motion.In summary,the cluster evolution model based on the Monte Carlo method constructed in this paper is not only suitable for describing cluster splitting methods under different conditions in static systems,but also for cluster research in complex scenarios.The experimental results verify the reliability and flexibility of the simulation software.The simulation software developed by this institute has a simple interface and strong interaction,which can provide certain technical support for subsequent research on the fractal dispersion of nanoparticles or colloidal systems.