Fractal Architecture Research Articles

Small-angle neutron scattering (SANS) and spin-echo SANS measurements reveal the logarithmic fractal structure of the large-scale chromatin organization in HeLa nuclei

This paper reports on the two-scale fractal structure of chromatin organization in the nucleus of the HeLa cell. Two neutron scattering methods, small-angle neutron scattering (SANS) and spin-echo SANS, are used to unambiguously identify the large-scale structure as being a logarithmic fractal with the correlation function γ(r) ∼ ln(r/ξ). The smaller-scale structural level is shown to be a volume fractal with dimension D F = 2.41. By definition, the volume fractal is self-similar at different scales, while the logarithmic fractal is hierarchically changed upon scaling. As a result, the logarithmic fractal is more compact than the volume fractal but still has a rather high surface area, which provides accessibility at all length scales. Apparently such bi-fractal chromatin organization is the result of an evolutionary process of optimizing the compactness and accessibility of gene packing. As they are in a water solution, the HeLa nuclei tend to agglomerate over time. The large-scale logarithmic fractal structure of chromatin provides the HeLa nucleus with the possibility of penetrating deeply into the adjacent nucleus during the agglomeration process. The interpenetration phenomenon of the HeLa nuclei shows that the chromatin-free space of one nucleus is not negligible but is as large as the volume occupied by chromatin itself. It is speculated that it is the logarithmic fractal architecture of chromatin that provides a comfortable compartment for this most important function of the cell.

건축 패턴의 복잡성 정도의 선호도에 대한 사례 연구 -프랙탈 건축의 자기유사적 패턴을 중심으로-

건축 패턴의 복잡성 정도의 선호도에 대한 사례 연구 -프랙탈 건축의 자기유사적 패턴을 중심으로-

Fractal granular BiVO4 microspheres as high performance anode material for Li-ion battery

A fractal architecture where self-grown nanoparticles aggregates together to form a larger microstructures with high surface area and improved surface to volume ratio is promising approach to engineer high performance battery materials. Herein, we have engineered BiVO4 micro-spheres with fractal granularity using cost-effective surfactant-assisted hydrothermal method. The fractal architecture of BiVO4 is composed of nanoparticles of sizes in the range of 20–40 nm and grown into large micro-spheres of around 1–2 μm. The unique design of BiVO4 micro-spheres offers high reversible capacity of 590 mAh/g at 0.1 A/g and delivers excellent cycling stability of around 96% over 200 cycles. Thus, we have provided an innovative approach to design fractal granular micro-nanostructures for the development of high performance battery materials.

A formula for the settling velocity of cohesive sediment flocs in water

Abstract A simple formula is developed to relate the size and settling velocity of cohesive sediment flocs in both the viscous and inertial settling ranges. This formula maintains the same basic structure as the existing formula but is amended to incorporate the fact that the flocculated sediment has an internal fractal architecture and is composed of different-sized primary particles. The input parameters needed for calculating the settling velocity include the median size and size distribution of the primary particles, the fractal dimension of the floc, the density of the sediment, and two calibrated coefficients that incorporate the effects of floc shape, permeability, and flow separation on drag. The proposed formula is compared with four data sets of settling velocity–floc size collected from the published literature, and a good agreement between the model and these data can be found.

Modeling and Thermal Analysis of a CCP Collector System Based on Fractal Architecture: Receiver Proposal

Solar concentrator technology has been researches in different fields in order to enhancement efficiency and energy storage of these systems. Some changes in fluid and numerous components of the collectors has been proposed in recent years. In this context, this paper present results associates to the modeling and thermal analysis of a concentrating system based on parabolic through collector with receiver piper, designed with fractal geometry with the aim of improve system heat transfer. Founded on thermal modeling of heat transfer phenomena as radiation, convection and conduction, physical and mathematical relations between fractal geometrical parameters and transfer heat coefficient were established to find the influence of a chaotic structure on thermal behavior. Proposed designs were simulated through Solid works ® Flow Simulation tool. Was possible obtain maximum temperatures in air with fractal and cylindrical pipes of de 89°C, 86°C y 81°C respectively. The gap between fractal geometry results and cylindrical geometry is 10°C around.

Revealing rangeomorph species characters using spatial analyses

Rangeomorphs dominate the Ediacaran Avalonian macrofossil assemblages of Charnwood Forest, UK (∼562 Ma). However, their unfamiliar fractal architecture makes distinguishing phylogenetically reliable characters from intraspecific features difficult. Fortunately, spatial analysis of large in-situ populations offers an independent means of assessing their taxonomy. Populations of a single biological species are likely to exhibit similar spatial distributions due to their shared responses to the biological and ecological processes acting upon them. As such, spatial analyses can be used to interrogate which are the most taxonomically deductive characters in similar species. We used random labelling analyses to investigate the presence or absence of characters of Primocandelabrum boyntoni, P. aethelfalaedia, and P. aelfwynnia on the Bed ‘B’. The resultant spatial distributions were compared to observed characters using goodness-of-fit tests to determine which characters were associated with unique populations, and which were found across multiple populations. We found that P. boyntoni and P. aelfwynnia had statistically indistinguishable character distributions, suggesting that they represent a single biological species, and that they exhibited significantly different distributions to P. aethelfalaedia, suggesting that there are two (rather than three) species of Primocandelabrum present on the B surface. Furthermore, we found that the distribution of concealed versus unconcealed 1st order branches across all specimens exhibited significantly different density-dependant behaviour, with unconcealed branching occurring in areas of higher density populations and concealed branching occurring in the lower density areas of Primocandelabrum. We speculate that unconcealed branches may have been a response to the reduced availability of resources in higher density areas, implying rangeomorphs were capable of ecophenotypic responses.

Layer-by-layer assembled gold nanoparticles/lower-generation (Gn≤3) polyamidoamine dendrimers-grafted reduced graphene oxide nanohybrids with 3D fractal architecture for fast, ultra-trace, and label-free electrochemical gene nanobiosensors

Three layer-by-layer (LBL) assembled gold nanoparticles (AuNPs)/lower-generation (Gn≤3) polyamidoamine dendrimer (PD) with reduced graphene oxide (rGO) as the core/mercaptopropinoic acid (MPA)/Au were successfully fabricated and employed as electrochemical gene nanobiosensing platforms with three-dimensional (3D) fractal nanoarchitecture for fast, ultra-trace determination of label-free DNA hybridization. Three Gn≤3PD were initially grafted to graphite oxide (GO) via the covalent functionalization between amino terminals of PD and carboxyl terminals of GO where a concomitant reduction of GO, which were covalently linked onto MPA that was self-assembled onto Au substrate, and finally AuNPs were encapsulated onto GG1PD by strong physicochemical interaction between AuNPs and -OH of rGO in GG1PD, Their morphologies, structures, electrochemical properties, and gene nanobiosensing performances were characterized and evaluated. AuNPs/GG2PD-based probe displayed the best excellent structural stability, lowest mobility on solid surface with the increasing charge resistance, widest linear range (1.1 × 10−6 – 1 × 10−18), and the lowest limit of detection (1.87 × 10−19 M) in comparison with both AuNPs/GG1PD-based and AuNPs/GG3PD-based probes. This work will provide a new candidate for the development of metal nanoparticles functionalized PD with inorganic nonmetallic nanomaterials as cores with 3D fractal nanoarchitecture and promising electrochemical gene nanobiosensing platforms based on dendrimer-nanoinorganic hybrids with 3D nanoarchitectures and LBL assembly for fast and ultra-trace detection of label-free DNA hybridization with potential application in bioanalysis and medical diagnosis of genetic diseases.

Space-Filling Supercapacitor Carpets: Highly scalable fractal architecture for energy storage

Revamping ground-breaking ideas from fractal geometry, we propose an alternative micro-supercapacitor configuration realized by laser-induced graphene (LIG) foams produced via laser pyrolysis of inexpensive commercial polymers. The Space-Filling Supercapacitor Carpet (SFSC) architecture introduces the concept of nested electrodes based on the pre-fractal Peano space-filling curve, arranged in a symmetrical equilateral setup that incorporates multiple parallel capacitor cells sharing common electrodes for maximum efficiency and optimal length-to-area distribution. We elucidate on the theoretical foundations of the SFSC architecture, and we introduce innovations (high-resolution vector-mode printing) in the LIG method that allow for the realization of flexible and scalable devices based on low iterations of the Peano algorithm. SFSCs exhibit distributed capacitance properties, leading to capacitance, energy, and power ratings proportional to the number of nested electrodes (up to 4.3 mF, 0.4 μWh, and 0.2 mW for the largest tested model of low iteration using aqueous electrolytes), with competitively high energy and power densities. This can pave the road for full scalability in energy storage, reaching beyond the scale of micro-supercapacitors for incorporating into larger and more demanding applications.

DNA knots occur in intracellular chromatin.

In vivo DNA molecules are narrowly folded within chromatin fibers and self-interacting chromatin domains. Therefore, intra-molecular DNA entanglements (knots) might occur via DNA strand passage activity of topoisomerase II. Here, we assessed the presence of such DNA knots in a variety of yeast circular minichromosomes. We found that small steady state fractions of DNA knots are common in intracellular chromatin. These knots occur irrespective of DNA replication and cell proliferation, though their abundance is reduced during DNA transcription. We found also that in vivo DNA knotting probability does not scale proportionately with chromatin length: it reaches a value of ∼0.025 in domains of ∼20 nucleosomes but tends to level off in longer chromatin fibers. These figures suggest that, while high flexibility of nucleosomal fibers and clustering of nearby nucleosomes facilitate DNA knotting locally, some mechanism minimizes the scaling of DNA knot formation throughout intracellular chromatin. We postulate that regulation of topoisomerase II activity and the fractal architecture of chromatin might be crucial to prevent a potentially massive and harmful self-entanglement of DNA molecules in vivo.

Fractal-like concepts for evaluation of toxic metals adsorption efficiency of feldspar-biomass composites

Effective treatment of metals polluted water may be achieved using low-cost materials synergistically modified to obtain composite adsorbents. Thus, feldspar–biomass composites have been prepared via calcination of feldspar (FLC) and Carica papaya seeds or pine cone seeds to yield Carica papaya-FLC (CPF) and pine-cone-FLC (PCF) composite adsorbents, respectively. The composites physicochemical properties and effectiveness for Pb(II), Cd(II) and Cu(II) removal in aqueous solutions were examined. Results showed that calcination did not promote any structural modification in the basic FLC lattice. Though CPF and PCF exhibited lower specific surface area when compared with the FLC, their cation exchange capacities were enhanced. Unlike on the FLC, the metals adsorption on CPF and PCF were higher (>40%) for Cu(II) and Cd(II), pH independent and faster. The study showed that adsorption process on a system with varying types of surface sites and with varying affinity for an adsorbent can best be described by the fractal-like kinetic and equilibrium adsorption isotherm models (fractal pseudo-second order kinetic model and fractal Brouers–Sotolongo adsorption model) compared with the classical models (pseudo-first order and pseudo-second order kinetic models, Langmuir and Freundlich adsorption isotherm models). These adsorption processes were thermodynamically spontaneous, feasible and endothermic; however the modification significantly reduced their energy requirements. The Brouers–Sotolongo model showed that modification of FLC increased the width of the sorption energy distribution on the composites indicating the heterogeneity of the surface adsorption sites. Though no single classical theory of sorption can presently be put forward to explain the overall adsorptive process, metals adsorption on these feldspar-biomass composites are heterogeneous and complex processes with fractal architecture.

RENORMALIZATION ANALYSIS OF A COMPOSITE ULTRASONIC TRANSDUCER WITH A FRACTAL ARCHITECTURE

To ensure the safe operation of many safety critical structures such as nuclear plants, aircraft and oil pipelines, non-destructive imaging is employed using piezoelectric ultrasonic transducers. These sensors typically operate at a single frequency due to the restrictions imposed on their resonant behavior by the use of a single length scale in the design. To allow these transducers to transmit and receive more complex signals it would seem logical to use a range of length scales in the design so that a wide range of resonating frequencies will result. In this paper, we derive a mathematical model to predict the dynamics of an ultrasound transducer that achieves this range of length scales by adopting a fractal architecture. In fact, the device is modeled as a graph where the nodes represent segments of the piezoelectric and polymer materials. The electrical and mechanical fields that are contained within this graph are then expressed in terms of a finite element basis. The structure of the resulting discretized equations yields to a renormalization methodology which is used to derive expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities. A comparison with a standard design shows some benefits of these fractal designs.

Mechanical History Dependence in Carbon Black Suspensions for Flow Batteries: A Rheo-Impedance Study.

We studied the effects of shear and its history on suspensions of carbon black (CB) in lithium ion battery electrolyte via simultaneous rheometry and electrical impedance spectroscopy. Ketjen black (KB) suspensions showed shear thinning and rheopexy and exhibited a yield stress. Shear step experiments revealed a two time scale response. The immediate effect of decreasing the shear rate is an increase in both viscosity and electronic conductivity. In a much slower secondary response, both quantities change in the opposite direction, leading to a reversal of the initial change in the conductivity. Stepwise increases in the shear rate lead to similar responses in the opposite direction. This remarkable behavior is consistent with a picture in which agglomerating KB particles can stick directly on contact, forming open structures, and then slowly interpenetrate and densify. The fact that spherical CB particles show the opposite slow response suggests that the fractal structure of the KB primary units plays an important role. A theoretical scheme was used to analyze the shear and time-dependent viscosity and conductivity. Describing the agglomerates as effective hard spheres with a fractal architecture and using an effective medium approximation for the conductivity, we found the changes in the derived suspension structure to be in agreement with our qualitative mechanistic picture. This behavior of KB in flow has consequences for the properties of the gel network that is formed immediately after the cessation of shear: both the yield stress and the electronic conductivity increase with the previously applied shear rate. Our findings thus have clear implications for the operation and filling strategies of semisolid flow batteries.

Recognition of the role of nature in the formation of fractal architecture

Abstract After a long period of one-way consumerist attitude toward nature, there have been some alternate perspectives on the systemic relationship between humans and nature, which have been again brought up during the past few decades. Since the late twentieth century, fractal architecture has been one of the most important themes discussed in architecture and it is based on the chaos and complexity theories. Critics often criticize this architecture due to its lack of architectural values, practicality, and attention to economy, culture, and history. The current study aims to clarify the scientific theories that are the theoretical foundations of this approach in contemporary architecture. By categorizing the practical examples of this architectural approach, they are analyzed in terms of their relationship with nature using the logical reasoning method to achieve a favorable architecture. In fact, the gap between this architecture and nature’s behavior is shown.

A fractal growth model: Exploring the connection pattern of hubs in complex networks

Fractal is ubiquitous in many real-world networks. Previous researches showed that the strong disassortativity between the hub-nodes on all length scales was the key principle that gave rise to the fractal architecture of networks. Although fractal property emerged in some models, there were few researches about the fractal growth model and quantitative analyses about the strength of the disassortativity for fractal model. In this paper, we proposed a novel inverse renormalization method, named Box-based Preferential Attachment (BPA), to build the fractal growth models in which the Preferential Attachment was performed at box level. The proposed models provided a new framework that demonstrated small-world-fractal transition. Also, we firstly demonstrated the statistical characteristic of connection patterns of the hubs in fractal networks. The experimental results showed that, given proper growing scale and added edges, the proposed models could clearly show pure small-world or pure fractal or both of them. It also showed that the hub connection ratio showed normal distribution in many real-world networks. At last, the comparisons of connection pattern between the proposed models and the biological and technical networks were performed. The results gave useful reference for exploring the growth principle and for modeling the connection patterns for real-world networks.

Cadaveric study of branching pattern of left coronary artery

Abstract Background and aim: The branching pattern of vascular system has been the subject of much discussion and debate since it was first suggested that these systems have fractal architecture. Coronary arteries of human heart and their branching pattern have been the subject of particular attention among researchers. Hence, this study of branching pattern ofleft coronary artery (LCA) has been undertaken to highlight the variations of branches of left coronary arterial system. Material and methods: The study material consisted of 50 heart specimens obtained from the cadavers of Anatomy and Forensic departments which were studied by the conventional dissection method. Results: Left posterior aortic sinus gave origin to left coronary artery in all specimens with 90% ostium being below the level of sinotubular junction (STJ). Nearly 50% specimens were of the length ranging between 6-lOmm.Left coronary artery bifurcated into its two main branches in 62%, trifurcated in 32% and quadfurcated in 6%. Among the 16 trifurcating specimens, in five specimens the diagonal artery was seen at the junction of its two main branches, in 11 specimens the diagonal artery was found arising from the anterior interventricular artery and an additional branch the "Median Artery" was seen at the junction. Conclusion : Recent technical advances in the study of coronary arteries make it necessary for all angiographers and cardiac surgeons to be familiar with the variants of left coronary artery branching pattern.

Experimental evidence of how the fractal structure controls the hydrodynamic resistance on granular aggregates moving through water

Summary A comprehensive set of experiments was carried out to investigate the effect of the fractal architecture of granular aggregates on the free-fall acceleration through a still water column. Test aggregates were first generated numerically with a method that allowed to control the fractal dimension d and, next, three stochastic replicates were lithographically fabricated for each of six values of d ranging between 1.9 and 2.7. The recorded position, velocity and acceleration served to analyze their dynamics in the Reynolds and Galilei number space, and to calculate the momentum rate of change and the intensity of drag (viscous and impact) and inertial forces (added mass and Basset–Bousinnesq). Analysis of these forces highlighted a strong dependence on d ; additionally, integration of these forces in the particle momentum equation allowed to identify an additional resistance R x that showed a strong correlation with d . A correlation analysis of R x with various scaling laws combining velocity and acceleration suggested that R x could be described by a nonlinear drag force and a force intermediate between drag and inertia. It was therefore concluded that irregular granular fractal aggregates accelerating in water are subject to highly complex and nonlinear hydrodynamic effects caused by surface roughness and volume porosity, and that these effects have tight connection with the internal and external fractal characteristics of the aggregates.

Analysis of the effect of organic matter content on the architecture and sinking of sediment aggregates

Analysis of 52 data sets totaling 1226 points of the size and settling velocity of suspended sediment collected in various ecosystems worldwide allowed the establishment of relations between sediment density and fractal parameters for a wide range of organic matter contents. While the fractal dimension showed some nonlinearities against sediment density and organic matter content for sizes smaller than 1 mm and larger than 10 mm, more than 50% of the average settling velocities were nearly invariant and ranged only between 1 and 4 mm/s regardless of size spanning nearly 4 orders of magnitude and organic matter fraction ranging between about 0 and 1. Analyses suggested that settling invariance was the result of a trade-off between the aggregate bulk (excess) density and its fractal architecture. An analysis of the governing quantities of the aggregate fractal scaling (i.e., the primary particle size and fractal dimension as well as its rate of change over the aggregate size) explained how these ultimately affected the settling rate. • The fractal dimension of biomineral aggregates is affected by the organic matter. • This effect is nonlinear with the content and quality of organic matter. • Size- and density-dependent fractal scaling can be used to describe biomineral aggregates. • The settling rate of biomineral aggregates is nearly invariant with the aggregate properties.

One‐Step Multicomponent Self‐Assembly of a First‐Generation Sierpiński Triangle: From Fractal Design to Chemical Reality

AbstractA novel terpyridine‐based architecture that mimics a first‐generation Sierpiński triangle has been synthesized by multicomponent assembly and features tpyCdIItpy connectivity (tpy=terpyridine). The key terpyridine ligands were synthesized by the Suzuki cross‐coupling reaction. Mixing two different terpyridine‐based ligands and CdII in a precise stoichiometric ratio (1:1:3) produced the desired fractal architecture in near‐quantitative yield. Characterization was accomplished by NMR spectroscopy, mass spectrometry, and transmission electron microscopy.

One-step multicomponent self-assembly of a first-generation Sierpiński triangle: from fractal design to chemical reality.

A novel terpyridine-based architecture that mimics a first-generation Sierpiński triangle has been synthesized by multicomponent assembly and features tpy-Cd(II)-tpy connectivity (tpy=terpyridine). The key terpyridine ligands were synthesized by the Suzuki cross-coupling reaction. Mixing two different terpyridine-based ligands and Cd(II) in a precise stoichiometric ratio (1:1:3) produced the desired fractal architecture in near-quantitative yield. Characterization was accomplished by NMR spectroscopy, mass spectrometry, and transmission electron microscopy.

A novel wick structure of vapor chamber based on the fractal architecture of leaf vein

A new pattern of wick in vapor chamber is designed and analyzed in this study. The wick is a kind of leaf-vein-like fractal architecture with polygon loops which are composed of many Y-shaped bifurcations, for this reason that the condensable area is enlarged efficiently. The polygonal loops play a unique role in avoiding blocking. And the sucking capacity is introduced to evaluate the wick performance. The permeability in both the length and height direction as well as the resistance in length direction are calculated, and compared with the parallel structure. It shows the permeability in both directions is far greater than that of the parallel structure under the same power source condition. Not only that, the resistance is far less than that of the parallel structure as the reasonable width ratio was chose. The analytical results indicate that the leaf-vein-like fractal architecture has better performance than the parallel structure.