The fractal dimension of Islamic and Persian four-folding gardens

Since Benoit Mandelbrot (1924–2010) coined the term “fractal” in 1975, mathematical theories of fractal geometry have deeply influenced the fields of landscape perception, architecture, and technology. Indeed, their ability to describe complex forms nested within each other, and repeated towards infinity, has allowed the modeling of chaotic phenomena such as weather patterns or plant growth. Some human-designed patterns such as the ones developed by Islamic cultures have been found to follow similar principles of hierarchy, symmetry, and repetition. However, the application of these principles in the design of gardens is an underexplored field. This paper presents a comparative exploration of the four-fold garden design model—the chahár-bágh—typical of Persian and Islamic garden design by analyzing two case studies: Taj Mahal and Isfahan’s city plan. This four-fold pattern is known to not only have a religious reading but to be also linked with ideals of fair distribution. Using an innovative compositional fractal analysis inspired by architecture, our results demonstrate that these gardens contain a high level of self-replication and scale invariance and that they exhibit a high fractal dimension. The novel application of this method of analysis to historical landscape plans allows us to assess to what extent fractal concepts were already in use before the European Renaissance and Mandelbrot’s explorations, and to speculate on their symbolism in the context of Islamic and Persian garden design. Specifically, we conclude that the fractal characteristics of these gardens might be intended as a representation of the infinite divine but also of principles of fairness and equality. Moving forward, this approach could be applied to design spaces, namely in the infrastructural design of the urban fabric, which are both meaningful and environmentally just.

The Impacts of Matrix Compositions on Nanopore Structure and Fractal Characteristics of Lacustrine Shales from the Changling Fault Depression, Songliao Basin, China

The Lower Cretaceous Shahezi shales are the targets for lacustrine shale gas exploration in Changling Fault Depression (CFD), Southern Songliao Basin. In this study, the Shahezi shales were investigated to further understand the impacts of rock compositions, including organic matters and minerals on pore structure and fractal characteristics. An integrated experiment procedure, including total organic carbon (TOC) content, X-ray diffraction (XRD), field emission-scanning electron microscope (FE-SEM), low pressure nitrogen physisorption (LPNP), and mercury intrusion capillary pressure (MICP), was conducted. Seven lithofacies can be identified according to on a mineralogy-based classification scheme for shales. Inorganic mineral hosted pores are the most abundant pore type, while relatively few organic matter (OM) pores are observed in FE-SEM images of the Shahezi shales. Multimodal pore size distribution characteristics were shown in pore width ranges of 0.5–0.9 nm, 3–6 nm, and 10–40 nm. The primary controlling factors for pore structure in Shahezi shales are clay minerals rather than OM. Organic-medium mixed shale (OMMS) has the highest total pore volumes (0.0353 mL/g), followed by organic-rich mixed shale (ORMS) (0.02369 mL/g), while the organic-poor shale (OPS) has the lowest pore volumes of 0.0122 mL/g. Fractal dimensions D1 and D2 (at relative pressures of 0–0.5 and 0.5–1 of LPNP isotherms) were obtained using the Frenkel–Halsey–Hill (FHH) method, with D1 ranging from 2.0336 to 2.5957, and D2 between 2.5779 and 2.8821. Fractal dimensions are associated with specific lithofacies, because each lithofacies has a distinctive composition. Organic-medium argillaceous shale (OMAS), rich in clay, have comparatively high fractal dimension D1. In addition, organic-medium argillaceous shale (ORAS), rich in TOC, have comparatively high fractal dimension D2. OPS shale contains more siliceous and less TOC, with the lowest D1 and D2. Factor analysis indicates that clay contents is the most significant factor controlling the fractal dimensions of the lacustrine Shahezi shale.

Using magnetic powder to enhance coagulation membrane filtration for treating micro-polluted surface water

The magnetic enhanced coagulation membrane filtration (MECMF) process was introduced into micro-polluted surface water treatment. The process was conducted by adding magnetic powder (MP) for enhancing coagulation. By contrasting the water quality parameters including dissolved organic carbon (DOC), UV254 and turbidity of permeates of MECMF and coagulation/flocculation membrane filtration (CFMF), results showed that the removal efficiency in the MECMF process was higher than those in the CFMF process. According to normalized flux and resistance analysis, membrane flux declined relatively slow and irreversible fouling resistance was lesser in the MECMF process. By analyzing the three-dimensional fluorescence of permeates and raw water, it was clearly shown that the permeate quality of the MECMF process was superior to that of the CFMF process apparently, which highlighted the removal of protein-like substances was more effectively in MECMF. Furthermore, the addition of MP could provide Lorentz and magnetic dipole forces between colloidal matters during coagulation, leading to the increase of collision frequency and efficiency and the formation of large size flocs with high fractal dimension. Large and high fractal dimension flocs could form a porous cake layer, which could increase water permeability. On the basic of the above findings, it was suggested that magnetic-enhanced coagulation that promoted flocs to develop could regulate cake layer structure and mitigate membrane fouling to some extent.

The interaction of an Hii region with a fractal molecular cloud

We describe an algorithm for constructing fractal molecular clouds that obeys prescribed mass and velocity scaling relations.The algorithm involves a random seed, so that many different realisations corresponding to the same fractal dimension and the same scaling relations can be generated. It first generates all the details of the density field, and then position the SPH particles, so that the same simulation can be repeated with different numbers of particles to explore convergence. It can also be used to initialise finite-difference simulations. We then present preliminary numerical simulations of Hii regions expanding into such clouds, and explore the resulting patterns of star formation. If the cloud has low fractal dimension, it already contains many small self-gravitating condensations, and the principal mechanism of star formation is radiatively driven implosion. This results in star formation occurring quite early, throughout the cloud. The stars resulting from the collapse and fragmentation of a single condensation are often distributed in a filament pointing radially away from the source of ionising radiation; as the remainder of the condensation is dispersed, these stars tend to get left behind in the Hii region. If the cloud has high fractal dimension, the cloud does not initially contain dense condensations, and star formation is therefore delayed until the expanding Hii region has swept up a sufficiently massive shell. The shell then becomes gravitationally unstable and breaks up into protostars. In this collect-and-collapse mode, the protostars are distributed in tangential arcs, they tend to be somewhat more massive, and as the expansion of the shell stalls they move ahead of the ionisation front.

Surface Characteristics of the Engineered Polymeric Media for Filtration and Adsorption in Urban Runoff

Urban runoff is one of the major sources that contaminates water supplies because it contains toxic compounds such as heavy metals and PAHs (poly aromatic hydrocarbons) as well as suspended solids, organic compounds, and nutrients. The eingineered polymetric media in this research were developed as filtering media in the storm water treatment equipment. The media used in this study can remove contaminants in urban runoff via adsorption and filtration. The engineered media composed of polypropylene and anion surfactant were foamed to have buoyacy and then shattered by mechanical device for efficient filtration. Surface characteristics of the engineered media were determined by using a scanning electron microscope and a microscope. Results indicated that surface area of the engineered media were increased from less than 0.05m2/g for the neither foamed nor shattered media to 7.82m2/g for the foamed and shattered media. Specific gravity of the media that were foamed and shattered was 0.108~0.154 whereas the non-treated media had specific gravity of 0.914. Fractal dimension of media was measured for the irregularity of the media shape and the media that had high fractal dimension value was performed high filtration efficiency of suspended solids in runoff.

STATISTICAL ANALYSIS OF CLUSTER STRUCTURES FORMED BY DIPOLE-DIPOLE INTERACTIONS

We developed a statistical model of the cluster formation of ferromagnetic particles and analysed the cluster structures. We investigated the effect of the control parameter λ, that is, the ratio of magnetic dipole moment energy to thermal energy, and external magnetic fields on the fractal dimensions of three-dimensional ferromagnetic clusters. We found that the fractal dimension of clusters, D, changes from 5/3 to 2 as λ increases in the absence of a magnetic field. We also found that when clusters are subjected to a magnetic field, the fractal dimension decreases and the transition region from high fractal dimension to D=1 becomes shorter as λ increases.

Crystal Chemistry of Colloids Obtained by Hydrolysis of Fe(III) in the Presence of SiO4 Ligands

ABSTRACTThe crystal chemistry of a number of Fe-Si systems (Si/Fe 0-4, pH 3-10) was investigated by combining local scale spectroscopic methods (EXAFS, FTIR and NMR) and at the semi local scale (SAXS). The Fe clusters within the precipitates have two growth regimes depending on the Si/Fe ratio: the growth is three and two dimensional for Si/Fe fl and Si/Fe ≤ 1 respectively. The presence of Fe-O-Si bonds within the precipitated phases has been demonstrated. Their formation and relative proportion was found to be very dependent on the pH and Si concentration The size of silica domains within the precipitates was shown to increase with increasing Si/Fe and/or decreasing pH. The high fractal dimension (Df) of the aggregates is attributed to the presence of the SiO4 ligands, but the evolution of Df linearly depends on the polymerization state of iron.