Copper fractal growth during recycling from waste printed circuit boards by slurry electrolysis

Superfine copper particles could be directly prepared from waste printed circuit boards by slurry electrolysis.Meanwhile,copper fractal growth could be observed.To better understand this phenomenon,the factors that affect copper dendrites in a point-cathode system were discussed in detail.These results showed that the fractal degree of copper dendrites increased as the increase of applied voltage and the decrease of copper sulfate and gelatin concentrations.Sodium lauryl sulfate and hydrochloric acid concentrations could not significantly impact the fractal degree of copper dendrites,while gelatin concentration could.The minimum copper fractal dimension was 1.069 when gelatin and copper sulfate concentration was 120 mg/L and 0.1 mol/L,respectively with an applied voltage of 11 V.Moreover,the results diffusion-limited aggregation model demonstrated that particle translational speed,particle numbers and binding probability significantly affected copper dendrite patterns.The scanning electron microscopy results indicated that the three additives greatly affected the refinement of the copper crystal.These findings contribute to enrich the theoretical study on metals recovery from e-waste by slurry electrolysis.

Fractal Growth of Giant Amphiphiles in Langmuir-Blodgett Films

Fractal structures have attracted considerable scientific interest,and fractal geometry is an effective tool to study the complicated structure and dynamic processes,such as dilation symmetry of disorder structure,percolation,gelation,and metal-insulator transition.Here,we summarized our findings of fractal growth of giant amphiphiles in Langmuir-Blodgett(LB)film.Giant amphiphiles composed of polyhedral oligomeric silsesquioxanes(POSS)derivatives and poly(ethylene oxide)(PEO),with structural diversities of POSS head modification,POSS head number,PEO chain length,are precisely synthesized.The effect of molecular structures and operation parameters on the fractal growth patterns are discussed,in addition,other fractal growth patterns in LB films and in Langmuir films are included,aiming to understand the basic molecular principle of fractal growth in LB system.

Formation process and fractal growth model of HCFC-141b refrigerant gas hydrate

The microscopic visualization experiment on the formation process of HCFC-141b refrigerant gas hydrate has been investigated, and the morphological photos of hydrate formation process have been obtained. The results show that gas hydrate originally nucleated on the interface of refrigerant HCFC-141b and water under the condition of supercooling, then the hydrate grows continually due to the inducement of formed nucleation and diffusion of refrigerant. The formation of gas hydrate presents an arboreous phenomenon. The fractal dimension of the hydrate formation morphology on different stages was calculated. The calculating results indicate that the initial stage of the hydrate formation belongs to fractal growth, and the dimension is about 1.52. Based on the fractal theory, an RIN-DLA (random inducement nucleation-diffusion limited aggregation) model for the HCFC-141b hydrate growth was developed. The hydrate growth process was simulated with the developed model, and the fractal dimension for the simulated morphology is well compared with that from the experiment.

Fractal Nature of Crack Growth under Different Temperature

We have studied numerically a simple crack growth model in a two-dimensional triangular lattice of bonds and nodes which incorporates the surface of a growing crack bond-breaking probability P-i similar to exp{(-V-i+E(i))phi(T)}, where E(i) is elastic energy stored in the i-th bond. Different energy temperature factors phi(T) are employed during crack formation and propagation process with a uniform dilation strain case and a shear case and with periodic boundary condition in the horizontal direction. Our results show that the patterns of the cracks generated are fractal structure and the effective fractal dimensionalities decrease with the increase of the temperature factor phi(T)(the absolute temperature T decreasing). In the paper we also discuss the relation between the effective fractal dimension D-eff (the radius R(g) of gyration) and the fractal dimensions D (the radius R of circular), and also give their modification values Omega about two kinds of methods in the lattice model.

Urban Growth Prediction Modelling Using Fractals and Theory of Chaos

Urban growth prediction has acquired an important consideration in urban sustainability. An effective approach of urban prediction can be a valuable tool in urban decision making and planning. A large urban development has been occurred during last decade in the touristic village of Pogonia Etoloakarnanias, Greece, where an urban growth of 57.5% has been recorded from 2003 to 2011. The prediction of new urban settlements was achieved using fractals and theory of chaos. More specifically, it was found that the urban growth is taken place within a Sierpinski carpet. Several shapes of Sierpinski carpets were tested in order to find the most appropriate, which produced an accuracy percentage of 70.6% for training set and 81.8% for validation set. This prediction method can be effectively applied in urban growth modelling, once cities are fractals and urban complexity can be successfully described through a Sierpinski tessellation.

近47年吐鲁番盆地人工绿洲精明增长的时空过程分析

以1976、1990、2000、2010、2023年5期Landsat遥感影像进行解译,借助数理统计模型、分形维数、紧凑度指数等方法,结合精明增长理论,构建了绿洲精明增长指标体系,测度并分析了近47年吐鲁番盆地人工绿洲的扩张及分布情况以及绿洲精明增长水平的时空表现。结果表明:(1)吐鲁番盆地绿洲规模空间扩张态势明显,呈现出明显的阶段性特征,绿洲面积由1976年的1259.33 km^(2)扩张至2023年的1810.27 km^(2);其扩展强度在经历缓慢下降—慢速增长—快速增长后转变为精明增长背景下的中低速增长。(2)吐鲁番盆地绿洲空间扩张方向具有分异性,扩张方向以西北、东北最为显著,空间重心迁移轨迹为西南—东北—西南,最大迁移距离为55.60 km。(3)在研究时间段内绿洲紧凑度维持在较高水平,土地利用率较高,但近10年呈现下降趋势;空间扩张模式呈现蔓延式—跳跃式—填充式的演变特征。(4)吐鲁番盆地的绿洲精明增长水平较低,精明得分由1976年的0.474下降至1990年的0.383,随后回升,2023年达到最大值0.517;从精明增长水平的空间差异看,以大河沿—塔尔朗流域下游、托克逊—白杨河流域下游为高水平的双核心趋势明显,呈现由中心向四周波动递减的态势。研究结果可为未来绿洲区的合理发展,防止绿洲无序蔓延扩张,保障干旱区绿洲土地资源的合理配置提供参考依据。

Directional region control of the thermal fractal diffusion of a space body

We present a directional region control （DRC） model of thermal diffusion fractal growth with active heat diffusion in three-dimensional space. This model can be applied to predict the space body heat fractal growth and study its directional region control. When the nonlinear interference term and the inner heat source term are generalized functions, the relationship between the particle aggregation probability and the interference terms can be obtained using the norm theory. We can then predict the aggregation form of particles in different regions. When the nonlinear interference terms in the model are expressed as a trigonometric function and its composite function, our simulations show that the DRC method of thermal fractal diffusion is effective and has reference value for the directional control of actual fractal growth systems.

基于分形理论的香根草根系护坡力学性能分析

为了定量评价香根草根系护坡效果,该研究以不同生长期的香根草为对象,基于植被生态学和分形理论获取根系形态参数指标,分析根系分形维数与生长期间演化规律。通过室内三轴试验研究不同含根量和根系分布方式对根土复合体抗剪强度的影响,分析根土复合体黏聚力和内摩擦角与根系分形维数间关系,并建立考虑香根草根系分形维数的边坡稳定性系数模型。结果表明:香根草根系数量和含根量与根系分形维数基本呈线性关系,而根系表面积与根系分形维数呈对数关系,三者均随根系分形维数增多而增大,但增幅均逐渐减小。含根量由0增加至1.0%时,根土复合体黏聚力、内摩擦角分别提高了72.0%和6.9%,含根量对黏聚力影响较大。不同根系分布方式对边坡稳定性影响能力由小到大依次为竖向、倾斜、相交和混合分布,同素土边坡相比,相交和混合分布根系的边坡稳定性系数分别提高了14.7%和15.8%,含根量为1.0%时,相交分布根系的边坡稳定性系数提高了28.4%。根系分形维数与边坡稳定性系数呈线性关系,利用根系分形维数能够评价边坡稳定性。研究结果可为香根草护坡工程提供参考。

Growth pattern of reed in Caogang Lake,Huanghuaihai Plain,China

The researches about reed growth were mainly concentrated on seasonal dynamics, investigation of reed resource, and comparison of different ecotypes of reed. By means of fractal geometric theory of non linear science, the fractal character of growth pattern of reed, for the purpose of quantitatively exploring the mechanism of reed growth was studied. The way to calculate fractal dimension of reed growth is box dimension (BD) and information dimension (ID). The results showed that the difference between two samplings in May and those among three samplings in June and later were not remarkable for both BD or ID. It was noted that the difference between samplings in and after May is significant. It was demonstrated that the fractal dimension of size distribution of reed ranged from 0 6235 to 0 8761 The distribution pattern could be statistically divided as two significant periods: the size of reed is quite well distributed at the beginning of reed growth (fractal dimension>0 8), but is irregular in the middle and later growth season (fractal dimension<0 7). These results are benefit to reach the goal of rational use of reed resources and to protect the biodiversity in wetland ecosystem.

Fractal characteristics of filamentous bacteria in activated sludge and its significance

On the basis of fractal theory, the fractal characteristics of filamentous bacteria in activated sludge are studied by image dissector system. The results show that the spatial distribution structure of filamentous bacteria in activated sludge has high self similarity in statistics and the filamentous bacteria have clear phenomenon of fractal growth. The critical fractal dimension values of filamentous bacteria bulking such as Eikelboom 021N, Eikelboom 1701, Sphaerotilus natans and Eikelboom 0041 are determined initially. The fractal dimensions can be taken as a parameter to describe filamentous bacteria of activated sludge quantitatively and bring to light the disorder in appearance and the rule in inherence of filamentous bacteria system.

Crack growth analysis for rock-like materials with ordered multiple pre-cracks under biaxial compression

The pre-burying iron sheets approach was used to prepare rock-like materials with ordered multiple pre-cracks. 60 specimens in total were prepared in these experiments. Through biaxial compression experiments, the influence of both the number of pre-cracks and pre-cracks angles to crack growth was analyzed. Meanwhile, species of rock bridge failure were summarized, namely, wing crack, secondary shear crack between horizontal pre-cracks and secondary shear crack between vertical pre-cracks. The wing crack plays a significant role in crack growth. Furthermore, fractal dimension was adopted to describe quantitatively the crack growth during the failure process. The results indicate that with the failure of specimens, corresponding fractal dimension for specimen monotonically increases, which indicates that the fractal dimension can be considered to the failure of the specimens quantitatively.

FRACTAL MORPHOLOGY IN DLA UNDER MULTIPARAMETER

Various fractal morphologies are obtained by introducing noise reduc-tion, tansential and radial probabilities into DLA (diffusion-limited aggregation)medel. As the noise is reduced, perimeter sites with extremely small values of lo-cal field gradient ar

湖南郴州柿竹园超大型钨多金属矿床的成矿复杂性研究

用非线性科学和复杂性理论对湖南郴州柿竹园超大型钨多金属矿床的成矿复杂性进行系统、深入的研究 ,以成矿作用与时空结构是一切矿产资源的本质与核心的自然哲学理念为根本立足点 ,从一种新的视角 ,就矿床的动力学属性、矿床的物质成分与结构、矿床的地质学场和成矿系统的演化四大相互联系的范畴 ,对矿产资源进行再认识 ,提出了矿床的新定义 ,并较深刻地揭示了矿床的动力学属性、成矿物质高度多样化和复杂性及其超常规模集成、矿田成矿分带的内部结构、矿床地质学场的时空分形结构、成矿系统时间演化的长期性和成矿过程的多期多阶段性以及成矿作用的发生和矿床形成的分形生长机制等方面的复杂性与动力学本质。项目成果将矿床学的研究提高到非线性科学和复杂性理论的层次 ,提供了如何应用这种理论和方法对矿床的成矿复杂性进行研究的实例 ,也是第一作者所提出的关于成矿系统复杂性的新成矿理论与方法论“成矿动力系统在混沌边缘分形生长”的具体化及其进一步深化。沿着这一研究方向的不断开拓将可使传统矿床学向精确科学跨越。

污泥热解过程中焦的表面孔隙结构分形生长

主要对污水污泥在高温热解和低温热解条件下热解焦炭的表面孔隙结构特性进行了研究。结果表明,污泥热解过程中随着挥发分的析出,污泥热解焦炭的孔隙结构逐渐发达。低温和高温热解过程中挥发分的析出,使得孔径为3.75 nm的孔得到了极大的发展。通过对污泥热解焦炭的N2吸附过程进行的分形分析发现,不同停留时间低温和高温热解焦炭的表面分形维数可以分为FD-1和FD-2。其中,FD-1主要表征了较大孔(>0.86 nm)的表面分形维数,FD-2则主要表征了超微孔(<0.86 nm)的表面分形维数。随着热解停留时间的延长,FD-1和FD-2逐渐增大并趋于稳定。与高温热解焦炭的超微孔表面分形维数相比低温热解焦炭出现了较大的增加,而较大孔的表面分形维数则相对低温热解焦炭未见有较大的改变。

PAM溶液中合成核/壳结构花生状碳酸钙粒子

在聚丙烯酰胺(PAM)溶液中,通过单一聚合物调控CaCO_3晶体生长,制备了核/壳结构的花生状CaCO_3粒子.采用扫描电子显微镜(SEM)、透射电子显微镜(TEM)及X射线粉末衍射(XRD)对合成样品的形貌、结构进行了表征.结果显示,花生状CaCO_3粒子的外壳由菱形的方解石组成,核由小粒子组成的短棒状粒子串组成,并形成由里向外的放射性状结构,核中间还具有较大体积的空腔.利用分形生长机理解释了粒子放射性结构的形成,并利用奥斯特瓦尔德熟化理论解释了核/壳结构的形成.

纳米镍粉内团聚的小角X射线散射的分形表征

采用小角X射线散射方法,对以水合肼溶液还原法制备的纳米金属镍粉的内团聚进行了两个方面的表征:1)内团聚的尺寸及其分布和比表面积等微观参数的测定;2)内团聚的分形维数测定。结果表明:纳米镍粉颗粒由相互嵌套包含的非均匀内团聚区域组成;这些内团聚实为一些离散镍分布非均匀区域,并由此导致局域非均匀电子分布而形成对X射线的小角散射;内团聚在1～100nm范围内遵循质量生长分形规律。

Ag和Ni离子注入聚合物的分形生长

在Ag和Ni离子注入聚合物样品结构分析中 ,首次观察到注入的离子在聚合物中分形生长现象 ,用透射电子显微镜和扫描电子显微镜在注入样品表面与横截面处均观察到了漂亮的离子注入分形生长图 .讨论了分形特点和分形生长的机理 。

芦苇生长格局分形特征的初步研究

应用非线性科学中的分形几何理论，以黄淮海平原封丘试区的芦苇为例，研究芦苇生长格局的分形特征。计算表明，芦苇大小分布的分形维数在0．6235—0．8761之间。统计分析表明，其分布格局可明显地分为两个时期：在芦苇生长的初期，其大小分布较为均匀（分维＞0.8），而在芦苇生长的中后期（6月底以后），大小分布差异较大（分维＜0.7）。

分形生长的新模型

为研究分形生长在实际工程中的应用问题,从分形产生的机理出发,突破传统的纯计算机模拟模型(如DLA、DMB和Eden模型等),应用第一原理分析了分形结构形成的过程,从普遍意义上提出了新的分形生长模型,并推导出分形生长结构的标度关系.最后介绍了分形生长结构具有的特点及其对实际工程的重要指导意义.

点阳极电沉积枝晶的分形生长

利用分形几何的原理模拟点阳极电沉积中枝晶的分形生长,分别研究阳极大小、射流速度、NiSO4浓度和温度等试验条件对点阳极射流电沉积中金属镍枝晶二维电沉积生长行为特性的影响,并从分形维数的角度对其进行分析。结果表明:点阳极射流电沉积中的枝晶也呈分形生长,其分形维数随着点阳极尺寸的增大而增加;射流速度的提高使枝晶簇根部的生长点明显增多,但在射流速度较低时,枝晶簇顶部的形貌较为致密;大量气泡的析出有利于产生分枝,此时气泡对枝晶生长的形貌起主导作用,使射流速度变化时的分形维数出现波折;电解质浓度的增大使枝晶簇的分形维数逐渐减小;且随着试验温度的提高,分形维数也随之增加。