粒子凝聚模拟软件开发与应用研究
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摘要
粒子凝聚是自然界常见现象,雪花的形成、晶体薄膜的生长、闪电的产生、土壤胶体凝聚等都是粒子凝聚过程。粒子凝聚是一个随机的非线性过程,在随机过程的背后往往存在自组织现象和自相似性。一些社会现象,如城市的增长等,也具有类似的特征。但是不同现象的粒子是如何凝聚的?不同条件下形成的凝聚体有什么样的特征?如何控制粒子凝聚?这些问题一直是科学家不断探索的问题,对这些问题的认识有助于了解这些自然和社会现象的形成和发展规律。由于实验方法研究粒子凝聚很难得到随机现象背后的规律性,因此利用计算机模拟粒子凝聚的结构和行为,正逐渐成为一种有力的研究手段。论文研究的目的是结合GIS中的一些方法,改进计算机粒子凝聚模拟算法和分析方法,开发一个粒子凝聚模拟软件,为粒子凝聚模拟应用提供技术平台。
本研究的主要工作和成果有以下六个方面：
1、粒子凝聚模型的算法研究与改进。论文研究了Eden模型、扩散限制凝聚模型(DLA)、反应限制凝聚模型(RLA)、电击穿模型(DBM)和团簇-团簇凝聚模型(CCA),包括扩散限制团簇凝聚模型(DLCA)、反应限制团簇凝聚模型(RLCA)等粒子凝聚模型的实现算法。针对已有算法存在的不足,提出了改进方法：1)已有的DLA算法在确认粒子周围是否被占据时,采用遍历查找的方法,速度较慢,本研究采用在已凝聚粒子上标记前后左右四个位置的占据情况,不再查找,加快了模拟速度。2)在DLCA算法中使用并查集方法对粒子进行查找和合并粘结处理,加快了DLCA模拟的速度。3)在DLCA模型中,目前的实现算法没有考虑粒子的同步运动,即在分析一个粒子移动时,假定其它粒子是静止的。本论文提出了粒子同步运动的连续碰撞检测DLCA算法,方法是先根据粒子运动方向和速度,估计粒子运动轨迹是否相交；如果在相同时间点有相交,则使用自适应技术检测粒子移动的步长；然后采用回退技术将检测出粒子在这种情况下的碰撞位置。使用这种连续检测粒子碰撞的方法,更符合粒子运动的实际情况。
2、凝聚体的分形特征分析,包括不同模型凝聚体的分维值比较、分维值的随机性分析、凝聚过程中分维值的变化、粘结概率对分形的影响和不同分维值计算方法的结果比较等。分析结果表明：1)Eden凝聚体的分维值接近整数,表明分形特征不明显；DLCA和DLA凝聚体的分形特征明显,DLCA凝聚体分维值比DLA凝聚体分维值小；DBM凝聚体分维值与被击穿的概率指数m相关,随着m的增大,分维值变小。2)DLA凝聚过程和DLCA凝聚过程中分维值都是波动的,但波动的幅度都不大。3)粘结概率对分形模型有影响,粘结概率越小,形成的凝聚体越密实,分维值越大。4)对同个凝聚体,用不同的分维值计算方法(盒计数法、回转半径法、SandBox法和密度-密度相关函数法)得到的分维值是有差异的,盒计数法和密度-密度相关函数法计算的分维值比较相近,回转半径法计算出来的分维值偏小,SandBox法计算出来的分维值较大。
3、凝聚体几何特征及与分形特征的关系研究。以往对凝聚体的特征研究主要以分形维数作为定量研究指标,而对其他的几何特征及其与分形维数的定量关系研究较少。论文针对目前孔隙度计算方法在计算各向异性凝聚体的孔隙度时存在的问题,提出利用外接凸多边形来代替原先的外接圆,并利用GIS中的凸包算法来获得外接凸多边形,计算出的孔隙度更符合实际情况。根据实际分析的需要,引入开放度和紧凑度的概念,并提出了计算方法。研究选取了不同模型凝聚体进行比较,分析结果表明：分维值大的凝聚体孔隙度和开放度小、紧凑度大,定量地反映了分维值与孔隙度、开放度、紧凑度的关系。
4、粒子凝聚模拟及可视化软件开发。本研究利用GDI+技术和OpenGL技术,开发了粒子凝聚模拟软件,软件包括粒子凝聚(二维和三维)模拟、凝聚体分形分析、凝聚体几何特征分析等模块。为了能更好地分析具有地理空间特征的粒子凝聚,在软件中还扩展了GIS功能,包括GIS基本功能、模拟结果与背景地图的叠置、研究对象的分形计算等。
5、粒子凝聚模拟及分形分析在土壤胶体凝聚的应用。本研究应用软件系统中的三维团簇凝聚模型模拟土壤胶体凝聚过程,显示随着粒子浓度或体积分数的增大,凝聚体分维值增大的规律；研究不同作用力下形成的凝聚体形态,这些作用力在形式上表现为粘结概率的影响,显示随着粘结概率由0.1变化到1时,凝聚体的分形维数值由2.48降低至1.87,即粘结概率越小,形成的凝聚体结构越致密；研究温度对凝聚的影响,显示温度对团聚体分形结构影响不大,只是影响凝聚的速度。
6、上海市中心城区城市扩展模拟及分形分析。本研究应用改进的Eden模型来模拟城市扩展,方法是根据影响城市发展的因素,确定建成区凝聚体外围栅格转化为城市的概率,再根据转化概率随机选取外围栅格作为新的城市栅格,通过确定性与随机性相结合方法模拟城市扩展。利用改进的Eden模型模拟了1947—1964年、1964—1979年和1979—1993年的城市扩展,通过与实际的建成区范围进行比较,显示模拟结果能够反映城市发展趋势。研究上海市中心城区四个时期建成区形态的分维值,发现除了1947年外,不同时期的城市建成区形态都具有比较明显的分形特征,分维值基本一致(1.7左右)。研究还发现对分形特征明显的城市建成区凝聚体来说,分维值越大,紧凑度也越大。
Common nature phenomenon of the formation of snowflakes, crystal film growth, lightning and soil colloid aggregation are particle aggregation process which is a rando nonlinear one. There is phenomenon of self-organization and self-similarity behind the random process. But how do the particles unite? What are the characteristics of the aggregates formed under different conditions? How to control particle cohesion? The understanding of these problems, which scientists continue to explore, helps to understand these natural and social phenomena of the formation and evelopment of law. The experimental method simulating particle cohesion is difficult to get regularity behind random phenomena, thus the use of computer simulating the structure and behavior of particle cohesion is becoming a powerful tool. In this context, this paper attempts to study the theory, methods, and applications of particle cohesion problem through computer simulation.
The main scientific findings of this research include:
1) This research has achieved and improved algorithm of variety models of particle cohesion. The algorithms of model of Eden, Diffusion-limited aggregation (DLA), Reaction-limted aggredation (RLA), Dielectric Breakdown Model(DBM) and Cluster-cluster aggregation (CCA),including Diffusion-limited aggregation cluster (DLCA) and Reaction-limted aggregation cluster (RLCA) have been achieved and cohesion results of a variety of models and qualitative analysis have been given. There are three improved methods for shortcomings of the existing algorithms.1) In exisitng DLA algorithms, the traversal find was used and slower in particles around the occupied ones, can not meet the particles aggregation requirements.This study used the mark four locations around the aggregated particles, speeding up the simulation speed.2)The union-find sets have been used in DLCA algorithm for finding and merging particles and the other nodes in the culster are removed, retaining only the root node of the clusters after bonding of the culsters. So the run speed has been enhanced.3) The continuous collision detection, which has been presented in the DLCA algorithm, makes simulation more accord with Colloidal Brownian motion laws.
2) The fractal characteristics of particle aggregation simulating by different aggregation model have been analyzed. The random statistical analyses on fractal dimension of aggregation have been studied for DLA and DLCA simulation. The study compared with different methods of fractal dimension calculation.1) The research results show that Eden aggregation have no distinct fractal structure because its fractal dimension is approximately2, that the fractal dimensions of DLCA aggregation are smaller than those of DLA. The fractal dimensions of DBM are associated with the breakdown probability index m, as m increases, the fractal dimensions are smaller.2) The dimensional values of the DLA and DLCA aggregation process are fluctuating and the magnitude of the fluctuations is not large, indicating that the particle aggregaiton process is random, but has incomplete self-similarity and scale invariance.3) The bond probability affect the fractal model, as the smaller of bond probability, the aggregates are more dense, the greater fractal dimension.4) The same aggregates with different fractal dimension calculation method including box counting method, radius of gyration method, SandBox and density-density corrlation function, the fractal value is different. The calculated value by box counting method is similar by using density-density correlation function one, and the calculated value of radius of gyration method is less and greater by SandBox.
3) The quantitative relationship between geometric charcteristics and fractal dimension value of aggregates has been discussed. In the past research people made fractal dimension as quantitative indicator of research for aggregates characteristics, and other geometric features, such as porosity, openness and compactness, and their quantitative relationship with fractal dimension were less studied. The geometric characteristics of porosity, openness and compactness have been defined and the calculated methods have been brought forward. The different aggregations of various models have been studied and the results show that the greater the fractal value, the porosity and openness is the less and the compactness is the greater. These results have clarified the quantitative relationship between geometric charcteristics and fractal value.
4) Based on the technology of GDI+and OpenGL in.Net IDE, the architecture of the2D and3D system of particle cohesion simulation and software prototype system have been prsented. The functions of various levels and their inner-relationship have been clarified. The architecture is further described in two aspects:Platform Function and Platform Interface. It provids holistic framework and top-level guidance for studying technologies and implementing platform. Under the guidance of the overall architecture, the algorithms of particles aggregation simulation, the analysis of fractal and geometric characteristics have been implemented using computer program and the software platform of particles aggregate simulation has been constructed. The system also extends GIS functions, including basic functions of GIS, the DLA aggregations loading on map and fractal calculations of urban elements.
5) The conceptual framework and methods presented in this research have been successfully applied to soil colloid aggregation simulation. The process of soil colloidal aggregation has been simulated by the three-dimensional cluster aggrgation model in software systems. The fractal dimension values of aggregation under various concentrations, the morphology of the aggregates formed in the different biasing force have been studied and the influence on aggregates of temperature also has been discussed. Soil colloidal particle simulation of three-dimensional cluster aggregation is an application example of software platform of the particle cohesion simulation system. These specific application cases have been developed to further verify the feasibility and applicability of the proposed methods and system.The application demonstrate that the fractal method renders a powerful mean for correlative applied research.
6) The urban expansion simulation and fractal analysis in this research have been successfully applied to Shanghai downtown urban, China. In this study, the improved Eden model is used to simulate urban expansion. Based on the factors influencing urban development, the probabilities of periphery grids of bulit-up areas translating to city are detemined. According to the probabilty the peripheral grids are randomly selected as a new city. The improved Eden model is used to simulate urban expansion of from1947to1964, from1964to1979and from1979to1993, and compared with the actual range of built-up areas, the simulation results can reflect developed trends of urban morphology. The value of fractal dimension of built-up area in downtown of Shanghai four times is calculated. In addition to1947, the urban built-up area forms at different times have obvious fractal characteristics consistent with the fractal dimension about1.7. The study also finds a significant fractal urban built-up area, the greater the fractal dimension, the greater compactness.
本研究的主要工作和成果有以下六个方面：
1、粒子凝聚模型的算法研究与改进。论文研究了Eden模型、扩散限制凝聚模型(DLA)、反应限制凝聚模型(RLA)、电击穿模型(DBM)和团簇-团簇凝聚模型(CCA),包括扩散限制团簇凝聚模型(DLCA)、反应限制团簇凝聚模型(RLCA)等粒子凝聚模型的实现算法。针对已有算法存在的不足,提出了改进方法：1)已有的DLA算法在确认粒子周围是否被占据时,采用遍历查找的方法,速度较慢,本研究采用在已凝聚粒子上标记前后左右四个位置的占据情况,不再查找,加快了模拟速度。2)在DLCA算法中使用并查集方法对粒子进行查找和合并粘结处理,加快了DLCA模拟的速度。3)在DLCA模型中,目前的实现算法没有考虑粒子的同步运动,即在分析一个粒子移动时,假定其它粒子是静止的。本论文提出了粒子同步运动的连续碰撞检测DLCA算法,方法是先根据粒子运动方向和速度,估计粒子运动轨迹是否相交；如果在相同时间点有相交,则使用自适应技术检测粒子移动的步长；然后采用回退技术将检测出粒子在这种情况下的碰撞位置。使用这种连续检测粒子碰撞的方法,更符合粒子运动的实际情况。
2、凝聚体的分形特征分析,包括不同模型凝聚体的分维值比较、分维值的随机性分析、凝聚过程中分维值的变化、粘结概率对分形的影响和不同分维值计算方法的结果比较等。分析结果表明：1)Eden凝聚体的分维值接近整数,表明分形特征不明显；DLCA和DLA凝聚体的分形特征明显,DLCA凝聚体分维值比DLA凝聚体分维值小；DBM凝聚体分维值与被击穿的概率指数m相关,随着m的增大,分维值变小。2)DLA凝聚过程和DLCA凝聚过程中分维值都是波动的,但波动的幅度都不大。3)粘结概率对分形模型有影响,粘结概率越小,形成的凝聚体越密实,分维值越大。4)对同个凝聚体,用不同的分维值计算方法(盒计数法、回转半径法、SandBox法和密度-密度相关函数法)得到的分维值是有差异的,盒计数法和密度-密度相关函数法计算的分维值比较相近,回转半径法计算出来的分维值偏小,SandBox法计算出来的分维值较大。
3、凝聚体几何特征及与分形特征的关系研究。以往对凝聚体的特征研究主要以分形维数作为定量研究指标,而对其他的几何特征及其与分形维数的定量关系研究较少。论文针对目前孔隙度计算方法在计算各向异性凝聚体的孔隙度时存在的问题,提出利用外接凸多边形来代替原先的外接圆,并利用GIS中的凸包算法来获得外接凸多边形,计算出的孔隙度更符合实际情况。根据实际分析的需要,引入开放度和紧凑度的概念,并提出了计算方法。研究选取了不同模型凝聚体进行比较,分析结果表明：分维值大的凝聚体孔隙度和开放度小、紧凑度大,定量地反映了分维值与孔隙度、开放度、紧凑度的关系。
4、粒子凝聚模拟及可视化软件开发。本研究利用GDI+技术和OpenGL技术,开发了粒子凝聚模拟软件,软件包括粒子凝聚(二维和三维)模拟、凝聚体分形分析、凝聚体几何特征分析等模块。为了能更好地分析具有地理空间特征的粒子凝聚,在软件中还扩展了GIS功能,包括GIS基本功能、模拟结果与背景地图的叠置、研究对象的分形计算等。
5、粒子凝聚模拟及分形分析在土壤胶体凝聚的应用。本研究应用软件系统中的三维团簇凝聚模型模拟土壤胶体凝聚过程,显示随着粒子浓度或体积分数的增大,凝聚体分维值增大的规律；研究不同作用力下形成的凝聚体形态,这些作用力在形式上表现为粘结概率的影响,显示随着粘结概率由0.1变化到1时,凝聚体的分形维数值由2.48降低至1.87,即粘结概率越小,形成的凝聚体结构越致密；研究温度对凝聚的影响,显示温度对团聚体分形结构影响不大,只是影响凝聚的速度。
6、上海市中心城区城市扩展模拟及分形分析。本研究应用改进的Eden模型来模拟城市扩展,方法是根据影响城市发展的因素,确定建成区凝聚体外围栅格转化为城市的概率,再根据转化概率随机选取外围栅格作为新的城市栅格,通过确定性与随机性相结合方法模拟城市扩展。利用改进的Eden模型模拟了1947—1964年、1964—1979年和1979—1993年的城市扩展,通过与实际的建成区范围进行比较,显示模拟结果能够反映城市发展趋势。研究上海市中心城区四个时期建成区形态的分维值,发现除了1947年外,不同时期的城市建成区形态都具有比较明显的分形特征,分维值基本一致(1.7左右)。研究还发现对分形特征明显的城市建成区凝聚体来说,分维值越大,紧凑度也越大。
Common nature phenomenon of the formation of snowflakes, crystal film growth, lightning and soil colloid aggregation are particle aggregation process which is a rando nonlinear one. There is phenomenon of self-organization and self-similarity behind the random process. But how do the particles unite? What are the characteristics of the aggregates formed under different conditions? How to control particle cohesion? The understanding of these problems, which scientists continue to explore, helps to understand these natural and social phenomena of the formation and evelopment of law. The experimental method simulating particle cohesion is difficult to get regularity behind random phenomena, thus the use of computer simulating the structure and behavior of particle cohesion is becoming a powerful tool. In this context, this paper attempts to study the theory, methods, and applications of particle cohesion problem through computer simulation.
The main scientific findings of this research include:
1) This research has achieved and improved algorithm of variety models of particle cohesion. The algorithms of model of Eden, Diffusion-limited aggregation (DLA), Reaction-limted aggredation (RLA), Dielectric Breakdown Model(DBM) and Cluster-cluster aggregation (CCA),including Diffusion-limited aggregation cluster (DLCA) and Reaction-limted aggregation cluster (RLCA) have been achieved and cohesion results of a variety of models and qualitative analysis have been given. There are three improved methods for shortcomings of the existing algorithms.1) In exisitng DLA algorithms, the traversal find was used and slower in particles around the occupied ones, can not meet the particles aggregation requirements.This study used the mark four locations around the aggregated particles, speeding up the simulation speed.2)The union-find sets have been used in DLCA algorithm for finding and merging particles and the other nodes in the culster are removed, retaining only the root node of the clusters after bonding of the culsters. So the run speed has been enhanced.3) The continuous collision detection, which has been presented in the DLCA algorithm, makes simulation more accord with Colloidal Brownian motion laws.
2) The fractal characteristics of particle aggregation simulating by different aggregation model have been analyzed. The random statistical analyses on fractal dimension of aggregation have been studied for DLA and DLCA simulation. The study compared with different methods of fractal dimension calculation.1) The research results show that Eden aggregation have no distinct fractal structure because its fractal dimension is approximately2, that the fractal dimensions of DLCA aggregation are smaller than those of DLA. The fractal dimensions of DBM are associated with the breakdown probability index m, as m increases, the fractal dimensions are smaller.2) The dimensional values of the DLA and DLCA aggregation process are fluctuating and the magnitude of the fluctuations is not large, indicating that the particle aggregaiton process is random, but has incomplete self-similarity and scale invariance.3) The bond probability affect the fractal model, as the smaller of bond probability, the aggregates are more dense, the greater fractal dimension.4) The same aggregates with different fractal dimension calculation method including box counting method, radius of gyration method, SandBox and density-density corrlation function, the fractal value is different. The calculated value by box counting method is similar by using density-density correlation function one, and the calculated value of radius of gyration method is less and greater by SandBox.
3) The quantitative relationship between geometric charcteristics and fractal dimension value of aggregates has been discussed. In the past research people made fractal dimension as quantitative indicator of research for aggregates characteristics, and other geometric features, such as porosity, openness and compactness, and their quantitative relationship with fractal dimension were less studied. The geometric characteristics of porosity, openness and compactness have been defined and the calculated methods have been brought forward. The different aggregations of various models have been studied and the results show that the greater the fractal value, the porosity and openness is the less and the compactness is the greater. These results have clarified the quantitative relationship between geometric charcteristics and fractal value.
4) Based on the technology of GDI+and OpenGL in.Net IDE, the architecture of the2D and3D system of particle cohesion simulation and software prototype system have been prsented. The functions of various levels and their inner-relationship have been clarified. The architecture is further described in two aspects:Platform Function and Platform Interface. It provids holistic framework and top-level guidance for studying technologies and implementing platform. Under the guidance of the overall architecture, the algorithms of particles aggregation simulation, the analysis of fractal and geometric characteristics have been implemented using computer program and the software platform of particles aggregate simulation has been constructed. The system also extends GIS functions, including basic functions of GIS, the DLA aggregations loading on map and fractal calculations of urban elements.
5) The conceptual framework and methods presented in this research have been successfully applied to soil colloid aggregation simulation. The process of soil colloidal aggregation has been simulated by the three-dimensional cluster aggrgation model in software systems. The fractal dimension values of aggregation under various concentrations, the morphology of the aggregates formed in the different biasing force have been studied and the influence on aggregates of temperature also has been discussed. Soil colloidal particle simulation of three-dimensional cluster aggregation is an application example of software platform of the particle cohesion simulation system. These specific application cases have been developed to further verify the feasibility and applicability of the proposed methods and system.The application demonstrate that the fractal method renders a powerful mean for correlative applied research.
6) The urban expansion simulation and fractal analysis in this research have been successfully applied to Shanghai downtown urban, China. In this study, the improved Eden model is used to simulate urban expansion. Based on the factors influencing urban development, the probabilities of periphery grids of bulit-up areas translating to city are detemined. According to the probabilty the peripheral grids are randomly selected as a new city. The improved Eden model is used to simulate urban expansion of from1947to1964, from1964to1979and from1979to1993, and compared with the actual range of built-up areas, the simulation results can reflect developed trends of urban morphology. The value of fractal dimension of built-up area in downtown of Shanghai four times is calculated. In addition to1947, the urban built-up area forms at different times have obvious fractal characteristics consistent with the fractal dimension about1.7. The study also finds a significant fractal urban built-up area, the greater the fractal dimension, the greater compactness.
引文
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