Research on fractal characteristics of primary phase morphology in semi-solid A356 alloy

Semi-solid slurry of A356 alloy was prepared by low superheat pouring and slightly electromagnetic stirring, and the fractal characteristics of morphology in semi-solid primary phase was researched. The fractal dimensions of primary phase morphology in the semi-solid A356 alloy were calculated by the program written to calculate the fractal dimensions of box-counting in the image of solid phase morphology in semi-solid metal slurry. The results indicated that the morphology of primary phase in semi-solid A356 prepared by low superheat pouring and slightly electromagnetic stirring is characterized by fractal dimension, and the primary phase morphology obtained by the different processing parameters has different fractal dimensions. The morphology of primary phase at the different position of ingot has different fractal dimensions, which reflected the effect of solidified conditions at different positions in the same ingot on the morphology of semi-solid primary phase. Solidification of semi-solid alloy is a course of change in fractal dimension.

Use of digital image analysis combined with fractal theory to determine particle morphology and surface texture of quartz sands

The particle morphology and surface texture play a major role in influencing mechanical and hydraulic behaviors of sandy soils. This paper presents the use of digital image analysis combined with fractal theory as a tool to quantify the particle morphology and surface texture of two types of quartz sands widely used in the region of Vitória, Espírito Santo, southeast of Brazil. The two investigated sands are sampled from different locations. The purpose of this paper is to present a simple, straightforward,reliable and reproducible methodology that can identify representative sandy soil texture parameters.The test results of the soil samples of the two sands separated by sieving into six size fractions are presented and discussed. The main advantages of the adopted methodology are its simplicity, reliability of the results, and relatively low cost. The results show that sands from the coastal spit(BS) have a greater degree of roundness and a smoother surface texture than river sands(RS). The values obtained in the test are statistically analyzed, and again it is confirmed that the BS sand has a slightly greater degree of sphericity than that of the RS sand. Moreover, the RS sand with rough surface texture has larger specific surface area values than the similar BS sand, which agree with the obtained roughness fractal dimensions. The consistent experimental results demonstrate that image analysis combined with fractal theory is an accurate and efficient method to quantify the differences in particle morphology and surface texture of quartz sands.

Fractal Characteristics and Microstructure Evolution of Magnetron Sputtering Cu Thin Films

How to describe surface morphology characteristic and microstructure evolution are the hottest researches of current thin film researches. But in traditional characterization of surface morphology, the roughness parameters are scale related. And the microstructure evolution of thin film during post-treatment is usually not considered in detail, To give a better understanding of the roughness of thin films topography, fractal method is carried out. In addition, microstrueture evolution of thin films is analyzed based on the crystallography and energy theory. Cu thin films are deposited on Si （100） substrates by magnetron sputtering, and then annealed at different temperatures. Surface topography is characterized by atomic force microscope （AFM）. Triangular prism surface area （TPSA） algorithm is used to calculate the fractal dimension of the AFM images. Apparent scale effect exists between the surface morphology roughness and film thickness. Relationship between the fractal dimension and roughness is analyzed by linear regression method and linear relationship exists between fractal dimension and surface roughness root mean square （RMS）. Fractal dimension can be characterized as a scale independence parameter to represent the complex degree and roughness level of surface. With the increase of annealing temperature, surface roughness and fractal dimension decrease. But when the annealing temperature exceeds the recrystallization temperature, due to the agglomeration and coalescence of Cu grain, surface roughness and fractal dimension increase. Scale effect and changing regularity of grain growth and shape evolution for different film thickness under different annealing temperatures are analyzed. Based on minimum total free energy, regularity of grain growth and changing is proposed. The proposed research has some theory significance and applicative value of Cu interconnect process and development of MEMS.

Fractal Characteristics of Stagnic Anthrosols and the Relationship with Soil Micro-Structure

The Stagnic Anthrosols developed from quaternary yellow sedimentary parent material occupied an important position in Southwest China. Fractal dimensions of particle size and micro-aggregate size distributions of Stagnie Anthrosols and their relationship to soil micro-structure had been probed. Results showed that the soil particle size distributions were dominated by clay, the fractal dimensions of particle size distributions （Ds） were high and between 2.676-2.925, as the fractal dimensions of micro-aggregate size distributions （Da） were between 2.354-2.853. The fractal dimensions of particlesize distributions were preferably related with the ratio of coarse particles and fine particles （c/f20 ,m） and the micromorphological feature of skeleton grains. The evolution degree of micro-structure among horizons were reflected by the coefficient of variation of Ds within the profile. The fractal dimensions of micro-aggregate size distributions were related with the quantities, distributions of micro-aggregates and micro-pores. Results revealed that the soil micro-structures could be quantified by fractal dimensions preliminarily.

Similarity Analytic Solutions of a 3D-Fractal Nanofluid Uncoupled System Optimized by a Fractal Symmetric Tangent Function

The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these strategies is the similarity technique.Similarity technique is a generalization of the symmetric strategy,which depends only on the other approaches employed,which can be formulated by altering diversities.One of these methods is the fractal theory.In this investigation,we present a new method studying the similarity analytic solution(SAS)of a 3D-fractal nanofluid system(FNFS).The dynamic evolution is completely given by the concept of differential subordination and majorization.Subordination andmajorization relationships are the sets of observable individualities.Game theory can simplify the conditions under which particular sets combine.We offer an explicit construction for the complex possible velocity,energy and thermal functions of two-dimensional fluid flow(the complex variable is suggested in the open unit disk,where the disk is selected at a constant temperature and concentration with uniform velocity).We establish that whenever the 3D-fractal nanofluid systemis approximated by a fractal function,the solution has the same property,so a class of fractal tangent function gives SAS.Finally,we demonstrate some simulations and examples that give the consequences of this methodology.

Fractal Features of Urban Morphology and Simulation of Urban Boundary

Using fractal dimension to reflect and simulate urban morphology are two applications of fractal theory in city geography. As the only consistent description of a fractal, fractal dimension plays an important role in describing the basic features of fractals. Just like other fractals, our cities have similar characteristics. Fractal dimension to some extent is regarded as an indicator of urban expansion, and it may change with urban morphology in different time and space. Based on the Geographic Information System (GIS), taking Wuhan city as a test area, the fractal dimensions of different land use were calculated, and a linear regression equation was established to analyze the relationship between fractal dimension and residential areas. Then the author used fractal dimension to simulate the urban boundary which is an important part of urban mor-phology. A mid-point subdivision fractal generator is needed in the simulation process, and the shape of the generator is determined by fractal dimension. According to the fractal theory, fractal boundaries in different scales have self-similarity and they have the same fractal dimensions. Based on this fact, the simulation method the author used could quantitatively keep the similarity of configuration of the urban boundaries.

Effect of pouring temperature on fractal dimension of primary phase morphology in semi-solid A356 alloy

The fractal dimensions of primary phase morphology in semi-solid A356 alloy prepared by low superheat pouring and slightly electromagnetic stirring were calculated,and the effect of pouring temperature on fractal dimension of primary phase morphology in semi-solid A356 alloy was researched.The results indicate that it is feasible to prepare semisolid A356 alloy slurry by low superheat pouring and slightly electromagnetic stirring,and there is an important effect of pouring temperature on the morphology and the grain size of the primary phase in semi-solid A356 alloy,in which the reduction of pouring temperature can obviously improve grain size and shape factor of primary phase in semi-solid A356 alloy under the condition of a certain stirring power.The primary phase morphology of semi-solid A356 alloy prepared by low superheat pouring and slightly electromagnetic stirring can be characterized by fractal dimension,and the primary phase morphology obtained by the different processing parameters has the different fractal dimensions.Solidification of semi-solid alloy is a course of change in fractal dimension.

Fractal Evolving Theory and Growing Model of Olefin Polymerization Process

The surface morphology of Ti-Mg supported catalyst and the polyethylene particles are studied using scanning electron microscope(SEM) technology.The results show that either the catalyst's surface or polymer particle's surface is irregular and has fractal characteristics,which can be described by fractal parameter.The more interesting discovery is that the surface fractal dimension values of the polymer particles vary periodically with the polymerization time.We call this phenomenon fractal evolution,which can be divided into the 'revolution' stage and the 'evolution' stage,And then we present polymerization fractal growing model(PFGM),and successfully describe and /or predict the whole evolving process of the polyethylene particle morphology under the different slurry polymerization(including pre-polymerization) conditions without H2.

Study of Pitting Morphology Fractal Characteristic of Corroded Surface of 304 Stainless Steel in FeCl_3 Environment

Experiments were performed to study the pitting corrosion morphology of 304 stainless steel exposed to FeCl 3 environments and SEM micrographs of the pitting corrosion morphology were obtained. The image processing technique combining with the fractal method was employed to analyze these pitting corrosion images and the self-similarity of pits morphology was observed. It indicates that fractal characteristics exist in pitting corrosion of 304 stainless steel. The self-similarity and complexity of the pitting morphology phenomenon were described in terms of fractal dimension which can also be an important parameter related to characterize pitting morphology qualitatively and quantitatively.

Visual Evaluation of the Morphologic Structure of Nonwovens Using Image Analysis and Fractal Geometry

Nonwovens are fiber materials which are based on nonwoven technologies. For the complexity and randomness of nonwovens morphologic structures, it is difficult to express them effectively using classical method. Fractal geometry gives us a new idea and a powerful tool to study on irregularity of geometric objects. Therefore, we studied on the pore size, pore shape, pore size distribution and fiber orientation distribution of real nonwovens using fractal geometry combined with computer image analysis to evaluate nonwovens’ morphologic structures.

Morphology and fractal characteristic of deposits formed during fiber bundle media filtration

The scanning electronic microscope and automated image analyzer are adopted to investigate the morphology of deposits formed during fiber bundle media filtration, which results in the discovery of the self—similarity of the deposits. Then in this paper it is proposed that the deposits are a fractal structure. Moreover, the fractal dimension value is related to the filter performance. The higher the fractal dimension value, the higher the filtration efficiency, and the longer filtration cycle, but the development of the head loss is also faster.

Application of fractal theory to study morphology of manganese sulfide inclusion in resulfurized free-cutting steels

The morphology and distribution of manganese sulfide(MnS)inclusions have a significant influence on the comprehensive performance,which is an important research field for resulfurized steels.Based on the experiments of non-aqueous electrolyte and scanning electron microscope observation,the fractal theory was employed to study the three-dimensional morphologies of MnS inclusions.The results showed that the edge fractal dimension of MnS inclusions was between 1.59 and 1.88.In addition,similar morphology of MnS inclusions had a close fractal dimension.The MnS edge fractal dimension is highly positively correlated with the morphological parameters.The multifractal spectrums of MnS inclusions on two-dimensional plane of as-cast and as-rolled resulfurized free-cutting steels were calculated.The large-size MnS inclusions belong to large probability subset,while the small-size MnS inclusions belong to small probability subset.The multifractal spectrum can truly and effectively reflect the difference and non-uniformity of distribution of MnS inclusions on 2D plane.On the premise of similar content of MnS,with the refinement of MnS inclusions,the multifractal spectrum width and the multifractal spectrum symmetry parameter were decreased.The multifractal spectrum provides a new method for studying the second phase in materials.

Experimental-based study of gear vibration characteristics incorporating the fractal topography of tooth surface

Microscopic roughness is inevitable on the gear meshing surface,which is also a key parameter affecting the dynamic response.The surface roughness exhibits self‐affine characteristics across multiscales.To explore the influence of surface fractal topography on the vibration amplitude of the gear system under different rotational speeds and loads,an experimental setup of spur gear transmission is devised.The fractal dimension and fractal roughness of the meshing surface are calculated by the power spectral density method.The relationships between gear response and fractal parameters are revealed experimentally.Results indicate that a rougher tooth surface,that is,a smaller fractal dimension or larger fractal roughness,corresponds to an intense vibration amplitude.The sensitivity of dynamic response to the tooth surface topography varies at different rotational speeds and loads.Under low speed and light load conditions,the fractal dimension and fractal roughness have a more obvious influence on the dynamic response of the gear transmission system.With the increase of speed and load,the macroworking conditions gradually become the main factor attributed to vibration amplitude.

Application of Opening and Closing Morphology in Deep Learning-Based Brain Image Registration

In order to improve the registration accuracy of brain magnetic resonance images(MRI),some deep learning registration methods use segmentation images for training model.How-ever,the segmentation values are constant for each label,which leads to the gradient variation con-centrating on the boundary.Thus,the dense deformation field(DDF)is gathered on the boundary and there even appears folding phenomenon.In order to fully leverage the label information,the morphological opening and closing information maps are introduced to enlarge the non-zero gradi-ent regions and improve the accuracy of DDF estimation.The opening information maps supervise the registration model to focus on smaller,narrow brain regions.The closing information maps supervise the registration model to pay more attention to the complex boundary region.Then,opening and closing morphology networks(OC_Net)are designed to automatically generate open-ing and closing information maps to realize the end-to-end training process.Finally,a new registra-tion architecture,VM_(seg+oc),is proposed by combining OC_Net and VoxelMorph.Experimental results show that the registration accuracy of VM_(seg+oc) is significantly improved on LPBA40 and OASIS1 datasets.Especially,VM_(seg+oc) can well improve registration accuracy in smaller brain regions and narrow regions.

Fractal analysis of polyethylene catalysts surface morphologies based on wavelet transform modulus maxima method

Surface morphologies of supported polyethylene (PE) catalysts are investigated by an approach combining fractal with wavelet. The multiscale edge (detail) pictures of catalyst surface are extracted by wavelet transform modulus maxima (WTMM) method. And, the distribution of edge points on the edge image at every scale is studied with fractal and multifractal method. Furthermore, the singularity intensity distribution of edge points in the PE catalyst is analyzed by multifractal spectrum based on WTMM. The results reveal that the fractal dimension values and multifractal spectrums of edge images at small scales have a good relation with the activity and surface morphology of PE catalyst. Meanwhile the catalyst exhibiting the higher activity shows the wider singular strength span of multifractal spectrum based on WTMM, as well as the more edge points with the higher singular intensity. The research on catalyst surface morphology with hybrid fractal and wavelet method exerts the superiorities of wavelet and fractal theories and offers a thought for studying solid surfaces morphologies.

地热储层岩体粗糙裂隙的热流耦合效应研究

为了解决地热开采涉及复杂的多物理场耦合问题,提高开采效率,本文针对开采过程中的渗流-传热问题以离散元软件3DEC构建岩体粗糙裂隙热-流耦合数值模型。考虑不同三维形貌特征的岩体裂隙,模拟水力开度为19.17μm在不同流速时的水-岩温度变化规律。结果表明:由于裂隙形貌的阻滞作用,粗糙面出水口温度下降较慢,出水口温度有所上升,模型达到稳态所需的时间随流速和对流换热系数的增大而减小。裂隙形貌对流体和岩体温度分布均有影响,粗糙裂隙面的冷锋形态和裂隙面的形貌密切相关。光滑裂隙热突破快于粗糙裂隙,增加裂隙面的粗糙度有助于延长热突破时间。粗糙裂隙面相对于光滑裂隙面的总热量提取率略有提升,流速和对流换热系数的增加显著提高总热量提取率。通过本文研究可以为地热能系统的设计提供重要参数和指导,能够提高地热能开发利用效率。

开街 近代广州西关空间史笔记

西关地区是传统时代晚期广州城近郊最发达的地区,民国时期被纳入城市行政区。西关的变迁具有传统城市近代化与传统空间城市化的双重转型特征,也是民国广州通过马路街道建设实现城市空间转型的集中代表地区。文章以街道为主角,以空间权属内涵及其开发营造方式为切入点,围绕“开街”在形塑近代城市中的作用,提出了近代西关空间演变的阐释路径,显示了一种融合不同尺度,贯通形态、功能、习俗、制度与观念的空间史研究风格。文章同时也尝试对城市形态学与建筑类型学的研究方法、里坊制与街巷制问题、传统空间的公共性问题等若干宏观议题给出探索性的思考和评论。

Morphological and semi-quantitative characteristics of diesel soot agglomerates emitted from commercial vehicles and a dynamometer

Diesel soot aggregates emitted from a model dynamometer and 11 on-road vehicles were segregated by a micro-orifice uniform deposit impactor （MOUDI）. The elemental contents and morphological parameters of the aggregates were then examined by scanning electron microscopy coupled with an energy dispersive spectrometer （SEM-EDS）, and combined with a fractional Brownian motion （fBm） processor. Two mode-size distributions of aggregates collected from diesel vehicles were confirmed. Mean mass concentration of 339 mg/m3 （dC/dlogdp） existed in the dominant mode （180-320 nm）. A relatively high proportion of these aggregates appeared in PM 1, accentuating the relevance regarding adverse health effects. Furthermore, the fBm processor directly parameterized the SEM images of fractal like aggregates and successfully quantified surface texture to extract Hurst coefficients （H） of the aggregates. For aggregates from vehicles equipped with a universal cylinder number, the H value was independent of engine operational conditions. A small H value existed in emitted aggregates from vehicles with a large number of cylinders. This study found that aggregate fractal dimension related to H was in the range of 1.641-1.775, which is in agreement with values reported by previous TEM-based experiments. According to EDS analysis, carbon content ranged in a high level of 30%-50% by weight for diesel soot aggregates. The presence of Na and Mg elements in these sampled aggregates indicated the likelihood that some engine enhancers composed of biofuel or surfactants were commonly used in on-road vehicles in Taiwan. In particular, the morphological H combined with carbon content detection can be useful for characterizing chain-like or cluster diesel soot aggregates in the atmosphere.

施氮量对滴灌水稻根系形态构型和分形特征的影响

旨在探明水稻在膜下滴灌下根系形态、构型、氮利用效率变化及其与分形维数的关系。于2021—2022年,以氮高效品种(T-43)和氮低效品种(垦-26)为材料,设置滴灌(drip irrigation,DI)、淹灌(flooding irrigation,FI)2种方式与4种施氮水平(0、150、300和450 kg hm^(–2))的盆栽试验。基于盒维数法结合根系图像分形分析程序计算根系形态的分形维数和分形丰度,研究滴灌及施氮对水稻产量、氮素利用效率、根系形态、构型、分形维数、分形丰度的影响。结果表明,(1)在相同施氮水平下,与淹灌相比,滴灌处理下T-43和垦-26细根百分比、根长密度(root length density,RLD)β值、氮肥农学利用效率(nitrogen agronomic efficiency,NAE)显著提高(分别为6.8%~14.5%和9.9%~17.2%、0.65%~5.45%和0.32%~3.43%、12.1%~22.4%和12.2%~20.5%);>0.5 mm RLD、0~40 cm土层表面积密度(surface area density,SAD)和根体积密度(RLD)、分形维数(fractal dimension,FD)、分形丰度(fractal abundance,FA)显著降低,造成产量降低(3.8%~37.4%和7.6%~48.3%)。(2)滴灌模式下,施氮显著提高了水稻根系FD和FA,T-43在施氮量为300 kg hm^(–2)时,FD和FA最高(分别为1.55和14.07);垦-26在施氮量为450 kg hm^(–2)时最高(分别为1.62和14.78)。(3)相关分析表明,FD、FA与直径0.1~0.3 mm RLD、0~10 cm土层根长和根质量密度、产量、氮素稻谷生产效率呈显著正相关,与30~40 cm土层表面积密度呈显著负相关。因此,在滴灌条件下,氮高效品种“T-43”配施300 kg hm^(–2)氮肥,能够增加细根根长密度比例,优化表层根系形态分布,提高根系分形维数和丰度,进而实现滴灌水稻产量和氮肥利用效率协同提高。

Bed roughness adjustments determined from fractal measurements of river-bed morphology

The flow resistance in rivers is an old and partly unsolved problem. In this study, the bed surface fractal dimension（BSFD） is used to describe the bed morphology, and combined with the bed roughness, a general model experiment is developed. The results show that there is a positive relationship between the BSFD and the bed roughness, which can be further applied to estimate the roughness changes in rivers. These findings will also guide further studies of the mobile-bed flow resistance.