Fractal-based algorithmic design of Chinese ice-ray lattices

Chinese ice-ray lattices are perhaps one of the earliest and controlled designs of asymmetric and complex patterns applied as a traditional motif in windows.Suc...     

Characterization of bottom sediments in lakes using hydroacoustic methods and comparison with laboratory measurements

The acoustical properties of bottom sediments in two lakes were shown to be strongly correlated with clay content, organic C and total N concentrations, and other important sediment properties. The fractal dimension of the bottom echo was more strongly correlated with sediment physical and chemical properties than energy-based measures. The fractal dimension was also related to rates of PO₄-P and NH₄-N release from intact sediment cores and sediment oxygen demand. Measurements made at 430-kHz were more sensitive to differences in sediment properties than 201- or 38-kHz. Hydroacoustic measurements allow rapid assessment of properties important in lake restoration and water resource management.     

Digital representation methods: The case of algorithmic design

Architectural representation encompasses the means used to describe architectural entities. This discipline has long been under constant change due to architects' ever-present desire for innovation. Algorithmic design (AD) is currently making its way into the plethora of representation methods that integrate the architect's day-to-day work tools. However, it provides its fair share of controversy and hardship as it goes. This paper assesses whether AD is suitable as a representation method for architectural design by making a systematic analysis of this medium as a contemporary representation method. Specifically, we investigate (1) its birth and evolution as a means of representation, (2) the characteristics that make it simultaneously appealing and off-putting to the architectural community, (3) the influence of technological evolution and education on its proliferation, and (4) its capacity to represent design problems in comparison to the currently predominant means of digital architectural representation, that is, computer-aided drafting and building information modeling.     

Application of fractal dimensions to study the structure of flocs formed in lime softening process

The use of fractal dimensions to study the internal structure and settling of flocs formed in lime softening process was investigated. Fractal dimensions of flocs were measured directly on floc images and indirectly from their settling velocity. An optical microscope with a motorized stage was used to measure the fractal dimensions of lime softening flocs directly on their images in 2 and 3D space. The directly determined fractal dimensions of the lime softening flocs were 1.11-1.25 for floc boundary, 1.82-1.99 for cross-sectional area and 2.6-2.99 for floc volume. The fractal dimension determined indirectly from the flocs settling rates was 1.87 that was different from the 3D fractal dimension determined directly on floc images. This discrepancy is due to the following incorrect assumptions used for fractal dimensions determined from floc settling rates: linear relationship between square settling velocity and floc size (Stokes’ Law), Euclidean relationship between floc size and volume, constant fractal dimensions and one primary particle size describing entire population of flocs. Floc settling model incorporating variable floc fractal dimensions as well as variable primary particle size was found to describe the settling velocity of large (>50 μm) lime softening flocs better than Stokes’ Law. Settling velocities of smaller flocs (<50 μm) could still be quite well predicted by Stokes’ Law. The variation of fractal dimensions with lime floc size in this study indicated that two mechanisms are involved in the formation of these flocs: cluster-cluster aggregation for small flocs (<50 μm) and diffusion-limited aggregation for large flocs (>50 μm). Therefore, the relationship between the floc fractal dimension and floc size appears to be determined by floc formation mechanisms.     

分形理论在新-老混凝土粘结强度研究中的应用

介绍了对混凝土断裂面进行分形研究的重要性、分形理论及混凝土断裂面分析中几种主要的分数维测量方法.利用自行研制的分维仪对试验后的老混凝土断裂面进行测试,并应用分形几何这一理论工具对测试结果进行分析,得到了老混凝土断裂面的分数维与新-老混凝土界面粘结强度的关系.结果发现:用分数维来表征老混凝土表面的粗糙度,其预测结果精度较高;在粗糙度较高(分数维D较大)的老混凝土表面上浇注较高强度的新混凝土,获得的新-老混凝土界面粘结强度较高.     

Predicting the settling velocity of flocs formed in water treatment using multiple fractal dimensions

Here we introduce a distribution of floc fractal dimensions as opposed to a single fractal dimension value into the floc settling velocity model developed in earlier studies. The distribution of fractal dimensions for a single floc size was assumed to cover a range from 1.9 to 3.0. This range was selected based on the theoretically determined fractal dimensions for diffusion-limited and cluster-cluster aggregation. These two aggregation mechanisms are involved in the formation of the lime softening flocs analyzed in this study. Fractal dimensions were generated under the assumption that a floc can have any value of normally distributed fractal dimensions ranging from 1.9-3.0. A range of settling velocities for a single floc size was calculated based on the distribution of fractal dimensions. The assumption of multiple fractal dimensions for a single floc size resulted in a non-unique relationship between the floc size and the floc settling velocity, i.e., several different settling velocities were calculated for one floc size. The settling velocities calculated according to the model ranged from 0 to 10 mm/s (average 2.22 mm/s) for the majority of flocs in the size range of 1-250 μm (average 125 μm). The experimentally measured settling velocities of flocs ranged from 0.1 to 7.1 mm/s (average 2.37 mm/s) for the flocs with equivalent diameters from 10 μm to 260 μm (average 124 μm). Experimentally determined floc settling velocities were predicted well by the floc settling model incorporating distributions of floc fractal dimensions calculated based on the knowledge of the mechanisms of aggregation, i.e., cluster-cluster aggregation and diffusion-limited aggregation.     

Floc morphology and size distributions of cohesive sediment in steady-state flow

Fractal dimensions of particle populations of cohesive sediment were examined during deposition experiments in an annular flume at four conditions of steady-state flow (0.058, 0.123, 0.212 and 0.323Pa). Light microscopy and an image analysis system were used to determine area, longest axis and perimeter of suspended solids. Four fractal dimensions (D, D(1), D(2), D(k)) were calculated from the slopes of regression lines of the relevant variables on double log plots. The fractal dimension D, which relates the projected area (A) to the perimeter (P) of the particle (P proportional, variant A(D/2)), increased from 1.25+/-0.005 at a shear stress of 0.058Pa to a maximum of 1.36+/-0.003 at 0.121Pa then decreased to 1.34+/-0.001 at 0.323Pa. The change in D indicated that particle boundaries became more convoluted and the shape of larger particles was more irregular at higher levels of shear stress. At the highest shear stress, the observed decrease in D resulted from floc breakage due to increased particle collisions. The fractal dimension D(1), which relates the longest axis (l) to the perimeter of the particle (P proportional to l(D1)), increased from 1.00+/-0.006 at a shear stress of 0.058Pa to a maximum of 1.25+/-0.003 at 0.325Pa. The fractal dimension D(2), which relates the longest axis with the projected area of the particle (A proportional to l(D(2)), increased from 1.35+/-0.014 at a shear stress of 0.058Pa to a maximum of 1.81+/-0.005 at 0.323Pa. The observed increases in D(1) and D(2) indicate that particles became more elongated with increasing shear stress. Values of the fractal dimension D(k), resulting from the Korcak's empirical law for particle population, decreased from 3.68+/-0.002 at a shear stress of 0.058Pa to 1.33+/-0.001 at 0.323Pa and indicate that the particle size distribution changed from a population of similar sized particles at low shear to larger flocculated particles at higher levels of shear. The results show that small particle clusters (micro-flocs) are the formational units of larger flocs in the water column and the stability of larger flocs is a function of the shear stress at steady state.     

土木工程专业程序设计及算法语言教学改革调查与剖析

针对目前高校土木工程专业程序设计及算法语言教学中存在的通病,通过对东南大学土木工程专业一年级本科生的问卷调查,结合教学过程中的体会与经验,提出了适用于程序设计及算法语言的教学改革措施,且在教学实践中加以应用,效果良好。     

Application of fractal theory to unsaturated soil mechanics

The mechanical properties of unsaturated soils are a function of the saturation degree or matric suction, and can be obtained based on currently available procedures. However, each procedure has its limitations and consequently, care should be taken in the selection of a proper procedure. The fractal approach seems to be a potentially useful tool to describe hierarchical systems and is suitable to model the structure and hydraulic properties of unsaturated soils. In this paper, the soil-water characteristics, unsaturated hydraulic conductivity function, unsaturated shear strength, swelling deformation and compression were derived from the fractal model for the pore-size distribution, and were expressed by only two independent physical parameters, the fractal dimension and the air entry value. The predictions of the proposed soil-water characteristics, unsaturated hydraulic conductivity, unsaturated shear strength, swelling deformation and compression were in good agreement with published experimental data. Comparisons between the experimental results of unsaturated hydraulic conductivity and the predictions of the both fractal model and the van Genuchten-Mualem model were also performed, and it was found that the predictions of the fractal model were better than that of the van Genuchten-Mualem model. __________ Translated from Chinese Journal of Geotechnical Engineering, 2006, 28(5): 635–638 [译自: 岩土工程学报]     

Characteristics of aggregates formed by electroflocculation of a colloidal suspension

Electroflocculation (EF) is becoming recognized as an alternative process to conventional coagulation/flocculation, although both are somewhat different. The electrical current applied in EF to generate the active coagulant species creates a unique chemical/physical environment which affects coagulation mechanisms and subsequent aggregate formation. The chemical and physical characteristics of an electroflocculated kaolin suspension and the morphology/fractal dimension of the resulting aggregates were examined. An EF cell was operated in batch mode and comprised of two concentric electrodes-a stainless steel cathode (outer electrode) and an aluminum anode (inner electrode). The cell was run at constant current between 0.05 and 0.3A, velocity gradients were 0-30s(-1). The results show that the simultaneous hydrolysis occurring has a profound effect on the final pH and consequently on the coagulation mechanisms as indicated by differences in zeta potential measured. Moreover, the electrical field induced by passage of a current has an apparent effect on particle transport. A linear correlation between floc size and current was observed and lower fractal dimensions were obtained for larger floc sizes. The fractal dimensions of the flocs obtained in EF are on average lower than those reported for conventional coagulation.     

Coagulation dynamics of fractal flocs induced by enmeshment and electrostatic patch mechanisms

The size and structure of flocs during floc formation were monitored for various coagulation mechanisms. Two distinctive mechanisms, namely, enmeshment and electrostatic patch, govern the dynamics of kaolin particles coagulation by polyaluminum chloride (PACl). They were investigated by small angle static light scattering (SASLS) and solid-state ²⁷Al NMR. In addition, a novel wet SEM (WSEM) was used in-situ to image the morphology of the aggregate in aqueous solution. Synthetic suspended particles were coagulated by two PACl products, a commercial product (PACl) and one laboratory product (PACl-E). The PACl-E contained more than 60% Al₁₃ while the PACl contained only 7% Al₁₃, with large percentage of colloidal Al. For coagulation by PACl at neutral pH and high dosage where the strong repulsion between particles occurs, the enmeshment ruled by reaction-limited aggregation (RLA) results in larger sweep flocs as well as higher fractal dimensional structure. For coagulation by PACl-E at alkaline pH and low dosage, the flocs were coagulated predominately by electrostatic patch with Al₁₃ aggregates. At such condition, it is likely that diffusion-limited aggregation (DLA) predominately rule PACl-E coagulation. The fractal dimension (D_s) values of PACl and PACl-E flocs formed at enmeshment and electrostatic patch increased with dosage, respectively. When breakage of flocs occurs, the breakage rate of PACl-E flocs is slower than that of sweep flocs. By WSEM imaging, the adsorption of spherical Al precipitates onto the particles was observed to form sweep flocs with a rough and ragged contour, while the PACl-E flocs were formed with a smooth and glossy structure.     

Characteristic analysis on temporal evolution of floc size and structure in low-shear flow

A series of flocculation tests were performed to investigate the effect of low-shear rates (G = 3-16 s⁻¹) on flocculation of kaolin suspension by polyaluminum chloride (PACl), with the goal of understanding floc growth mechanisms. Results were reported in terms of floc average size (d_p) and boundary fractal dimension (D_pf), derived from a non-intrusive optical sampling and digital image analysis technique. As expected, the rate of floc aggregation increased with increasing G, resulting in faster changes in aggregate size and structure in the initial stage of flocculation. Nevertheless, steady state was attained faster for D_pf than for d_p at the same shear rates, possibly due to the self-similarity of fractal aggregates. An interesting finding was that at G = 3 s⁻¹, an obvious plateau was observed for the average-size evolution at steady state; for shear rates of 6 and 7 s⁻¹, the flocs exhibited some decrease after reaching the peak of size, mainly as a result of floc settling at steady state; and for G = 11-16 s⁻¹, a decrease in floc size was possibly attributed to the irreversibility of PACl-floc breakage. The process of floc growth was described using a fractal growth model, which defined flocculation as the result of the combined processes of aggregation and restructuring. The conceptual model could effectively characterize temporal changes in floc size and structure, and found that fragmentation followed by reformation seemed to be more effective in forming larger and more compact aggregates than the restructuring process due to erosion and reformation, which may provide useful insights for the design of flocculation reactors.     

Three-dimensional double-rough-walled modeling of fluid flow through self-affine shear fractures

This study proposes a double-rough-walled fracture model to represent the natural geometries of rough fractures.The rough surface is generated using a modified successive random additions(SRA) algorithm and the aperture distribution during shearing is calculated using a mechanistic model.The shear-flow simulations are performed by directly solving the Navier-Stokes(NS) equations.The results show that the double-rough-walled fracture model can improve the accuracy of fluid flow simulations by approximately 14.99%-19.77%,compared with the commonly used single-rough-walled fracture model.The ratio of flow rate to hydraulic gradient increases by one order of magnitude for fluids in a linear flow regime with increment of shear displacement from 2.2 mm to 2.6 mm.By solving the NS equations,the inertial effect is taken into account and the significant eddies are simulated and numerically visualized,which are not easy to be captured in conventional experiments.The anisotropy of fluid flow in the linear regime during shearing is robustly enhanced as the shearing advances;however,it is either increased or decreased for fluids in the nonlinear flow regime,depending on the geometry of shear-induced void spaces between the two rough walls of the fracture.The present study provides a method to represent the real geometry of fractures during shearing and to simulate fluid flow by directly solving the NS equations,which can be potentially utilized in many applications such as heat and mass transfer,contaminant transport,and coupled hydro-thermo-mechanical processes within rock fractures/fracture networks.     

The effect of variable yield strength and variable fractal dimension on flocculation of cohesive sediment

A new formulation for floc yield strength of cohesive sediment is theoretically derived and incorporated into a flocculation model based on variable fractal dimension. The new flocculation model is validated with existing data on the temporal evolution of floc size measured in the laboratory. Comparing with existing flocculation models using a constant yield strength, it is found that new flocculation model based on variable yield strength and variable fractal dimension is superior in predicting the temporal evolution of floc size. It is also demonstrated that the present model results are very similar to that using an empirical formulation of variable yield strength suggested by Sonntag and Russel (1987. Structure and breakup of floccs subjected to fluid stressses. II. Theory. J. Colloid Interface Sci. 115(2), 378-389) when the empirical coefficient is specified according to our theoretical value. Hence, it is concluded that the new variable yield strength formulation derived in this study and the variable fractal dimension are effective in improving the prediction of flocculation process.     

基于改进蚁群算法的钢结构优化设计

在介绍蚁群优化算法的原理、基本框架的基础上,提出了一种改进的蚁群算法——分层蚁群算法,并将该算法应用到钢结构优化设计中,最后通过一个算例验证了该方法的效率和有效性,结果表明该方法科学可行,具有很好的应用前景。     

从“师法自然”到“算法自然”——分形法则在建筑设计中的运用

分形几何及其理论是重新认识建筑现象和评价建筑设计方法的新工具。本文以分形理论在建筑设计中的几个运用案例分析为出发点,探讨了从感性的"师法自然"到理性地运用分形理论的"算法自然"的必要性。     

混沌理论在建筑设计中的应用

首先明确了混沌理论的含义,然后分析其理论来源及历史,之后从混沌理论内在随机性和初值的敏感性等的本质特征出发,简述在建筑与城市中的体现应用,最后简要指出其在建筑设计方面的意义。     

结构抗震设计理论的进展

介绍了结构抗震设计理论的发展过程,指出了基于位移的抗震设计理论和基于性能的抗震设计理论的提出背景,详细介绍了这两种抗震设计理论的发展情况及研究内容,以及随机振动理论在结构抗震设计中的应用进展。     

浅析大学校园景观空间设计

通过对大学校园建设现状的分析,提出了校园景观空间设计的不足,强调了校园景观空间设计的重要性,并提出了在校园景观空间设计中应当了解和注意的关键问题。