Three-dimensional Fractal Structure Research Articles

Highly efficient droplet generation device based on a three-dimensional fractal structure

In this paper, a three-dimensional axisymmetric fractal structure device was proposed for massive production of monodisperse droplets. Its channel number could increase to nm for an m-stage fractal device with n-channel distributors. A fractal device with 36 channels was constructed, and the droplet generation experiment was carried out. The experiment showed that the coefficient of variations (CVs) of the generated droplets were all lower than 4.0% at four different flow rates. Additionally, the relationship between the mass flow rate and fractal structure variation was examined through theoretical and data regression analysis. To elaborate the overall structure deviation, the accumulated deviation was introduced, the formula of accumulated deviation and droplet size was given. The results showed that the droplet products were highly monodisperse. The droplet size deviation was within 2% when the accumulated deviation of dispersed- and continuous-phase distributors was less than 4% and 10%, respectively.

МАТЕМАТИЧНА МОДЕЛЬ РОЗПІЗНАВАННЯ ФРАКТАЛЬНИХ СТРУКТУР З ВИКОРИСТАННЯМ ТЕХНОЛОГІЇ НЕЙРОННИХ МЕРЕЖ

The article goes about the methods of training a neural network to recognize fractal structures with the rotation of iteration elements by means of an improved randomized system of iteration functions. Parameters of fractal structures are used to calculate complex parameters of physical phenomena. They are an effective tool in scientific works and used to calculate quantitative indicators in technical tasks. The calculation of these parameters is a very difficult mathematical problem. This is caused by the fact that it is very difficult to describe the mathematical model of the fractal image, it is difficult to determine the parameters of the iterative functions. The neural network learning will allow you to quickly determine the parameters of the first iterations of the fractal based on the finished fractal image and basing on them to determine the parameters of the iterative functions. The improved system of randomized iterative functions (SRIF) will allow to describe the mathematical process and to develop the software for generating fractal structures with the possibility of rotating elements of iterations. In its turn, this will make it possible to form an array of data for training a neural network. The trained neural network will be able to determine the parameters of the figures of the first iterations by means of which it will be possible to build a system of iterative functions. It will help to reproduce a fractal structure qualitatively. This approach can be used for three-dimensional fractal structures. After setting the parameters of the first iterations of the fractal, it will be possible to determine the geometric structure which is the basis of the fractal structure. In the future, this approach may be included in the system for recognizing objects under fractal structures, for example, under masking nets.

Simulation analysis of micromixer with three-dimensional fractal structure with electric field effect

Simulation analysis of micromixer with three-dimensional fractal structure with electric field effect

A New Method for a Fractal-Type Temperature Sensor Using Cellular Oscillatory Networks

A new fractal temperature sensor structure using simple cellular oscillatory networks is proposed. The frequency of the cellular oscillatory networks is analyzed in terms of threshold voltage and mobility, and then expressed as a function of temperature. In order to validate this new method, sensor networks with 405 inverters is used in the network, but it can be expanded infinitely in two-dimensional or even three-dimensional fractal structure. Through simulations, we found that local temperature change yields an instant global frequency drift in the fractal structure. For analysis, we used VLSI simulations with specifically BSIM4 model parameters (level54 using HSPICE). Compared with other temperature sensors, this structure significantly increased operating sensing range, − 50 °C to + 150 °C, with maximum 6 μW power consumption. With standard 100 nm CMOS MOSFET devices, less than ± 1.8 °C (0.9%) sensing accuracy, with 1 V supply voltage was achieved.

Three-dimensional fractal structure with double negative and density-near-zero properties on a subwavelength scale

We constructed a three-dimensional fractal acoustic metamaterial using the combination of zigzag channels and Menger fractal structures that had high structural symmetry and could extend into 3D space easily. Reflection and transmission coefficients were numerically calculated and experimentally measured, and the results matched well with each other. Using the finite element method and the S-parameter retrieval method, the band structures, the equivalent frequency surface and the effective parameters of the acoustic metamaterial were calculated. The results showed that the 3D acoustic metamaterial had double negative property in the normalized frequency range of 0.205–0.269 and density-near-zero property in the normalized frequency vicinity of 0.356. A plate lens model and a quarter-bending model were constructed to demonstrate the double negative property and the density-near-zero property of the acoustic metamaterial, respectively. These results showed that the 3D acoustic metamaterial could achieve excellent acoustic properties and would be promising to construct the 3D double negative structure and control acoustic waves on a subwavelength scale within a single unit.

Bio-inspired plasmonic leaf for enhanced light-matter interactions

Abstract The mathematical concept of fractals is widely applied to photonics as planar structures ranging from terahertz resonators, optical antennas, to photodetectors. Here, instead of a direct mathematical abstract, we design a plasmonic leaf with fractal geometry from the outline of a leaf from Wargrave Pink. The enhanced light-matter interactions are observed numerically from the improvement in both absorption and near-field intensification. To demonstrate the effect experimentally, a three-dimensional fractal structure is realised through direct laser writing, which significantly improves the photothermal conversion. By virtue of the self-similarity in geometry, the artificial leaf improves the absorption of a 10-nm-thick gold film with 14 × temperature increment compared to flat Au film. Not limited to the proof-of-concept photothermal experiment demonstrated here, the fractal structure with improved light-matter interactions can be utilised in a variety of applications ranging from non-linear harmonic generation, plasmonic-enhanced fluorescence, to hot electron generation for photocatalysis.

Self-assembly of fractal liquid crystal colloids

Nematic liquid crystals are anisotropic fluids that self-assemble into vector fields, which are governed by geometrical and topological laws. Consequently, particulate or droplet inclusions self-assemble in nematic domains through a balance of topological defects. Here, we use double emulsions of water droplets inside radial nematic liquid crystal droplets to form various structures, ranging from linear chains to three-dimensional fractal structures. The system is modeled as a formation of satellite droplets, distributed around a larger, central core droplet and we extend the problem to explain the formation of fractal structures. We show that a distribution of droplet sizes plays a key role in determining the symmetry properties of the resulting geometric structures. The results are relevant to a variety of inclusions, ranging from colloids suspensions to multi-emulsion systems. Such systems have potential applications for novel switchable photonic structures as well as providing wider insights into the packing of self-assembled structures.

Self-interacting polymer chains terminally anchored to adsorbing surfaces of three-dimensional fractal lattices

We have studied the adsorption problem of self-attracting linear polymers, modeled by self-avoiding walks (SAWs), situated on three-dimensional fractal structures, exemplified by 3d Sierpinski gasket (SG) family of fractals as containers of a poor solvent. Members of SG family are enumerated by an integer b (b≥2), and it is assumed that one side of each SG fractal is an impenetrable adsorbing surface. We calculate the critical exponents γ1,γ11, and γs, which are related to the numbers of all possible SAWs with one, both, and no ends anchored to the adsorbing boundary, respectively. By applying the exact renormalization group (RG) method (for the first three members of the SG fractal family, b=2,3, and 4), we have obtained specific values of these exponents, for θ-chain and globular polymer phase. We discuss their mutual relations and relations with corresponding values pertinent to extended polymer chain phase.

Spontaneous Fabrication of Three-Dimensional Multiscale Fractal Structures Using Hele-Shaw Cell

Several biosystems such as leaf veins, respiratory system, blood circulation, and some plant xylem involving multiscale fractal topologies are being mimic for their inherent natural optimization. Three-dimensional fractal structures spanning multiple scales are difficult to fabricate. In this paper, we demonstrate a new method to fabricate structures spanning meso- and microscale in a relatively easy and inexpensive manner. A well-known Saffman–Taylor instability is exploited for the same in a lifted Hele-Shaw cell. In this cell, a thin layer of liquid is squeezed between two plates being lifted angularly leaving behind the fractal rearrangement of fluid which is proposed to be solidified later. We demonstrate and characterize fractal structures fabricated using two different fluids and corresponding methods of solidification. The first one is ceramic suspension in a photopolymer and another is polystyrene solution with photopolymerization and solvent vaporization as methods of solidification, respectively. The fabrication process is completed in period of a few seconds.

334 セルオートマトンによるフラクタル構造のモデル化とその音響特性に関する考察

In the present study, acoustic characteristics of fractal structures are modeled and studied using Cellular Automata (CA). CA is a discrete system which consists of finite state variables arranged on uniform grid (cell). The dynamics of CA is expressed by temporary updating the states of cells according to the local interaction rules, defined among a cell and its neighbors. In this paper, the influence of the fractal shaped structures to the property of wave propagation phenomena in free field is investigated. Local rules are provided for the construction of three-dimensional fractal structures as well as representation of wave propagation phenomena.

Non-resonant Electromagnetic Scattering Properties of Menger's Sponge Composed of Isotropic Paraelectric Material

Menger's sponge (MS) is a kind of three-dimensional fractal structure. To analyze non-resonant electromagnetic properties of MS composed of isotropic paraelectric material, a novel, high-speed computation method employing simple recursion equations in terms of scattering amplitudes for two MS's with adjacent stage numbers, which are the parameters describing structural differences of MS's, is formulated. Within the scope of non-resonant electromagnetic phenomena, scattering patterns, forward and backward scattering amplitudes, and total cross sections of MS are investigated as a function of stage number and incident plane waves, and behaviors typical to fractal structures are extracted from the numerical results of the above equations. In addition, scattering properties at infinite stage number are discussed..

Strong localization of microwave in photonic fractals with Menger-sponge structure

Photonic fractal with self-similar structure of dielectric medium can strongly localize the electromagnetic wave energy in the three-dimensional fractal structure. We have fabricated Menger-sponge fractal structures of epoxy by using stereolithography. Titania–silica particles were dispersed into the epoxy to increase the dielectric constant and decrease the dielectric loss. The samples have square holes of 1, 3, 9 and 27 mm in edge length through the cubic body of 81 mm. Four types of Menger-sponge samples with fractal stages 1–4 were subjected for measurement of microwave responses. The both reflection and transmission amplitudes were attenuated simultaneously at frequencies of 9.5, 10.5, 12.0 and 13.5 GHz for each sample with fractal stages 1, 2, 3 and 4, respectively. The electromagnetic field amplitudes in the air holes measured by inserting a mono-pole antenna probe confirmed the strong localization of the electromagnetic wave in the central air cavity. The localized mode frequency can be calculated using the sample size, number of stage, and the effective dielectric constant. The localization efficiency increased according to the fractal stage number.

On the total number of distinct self-interacting self-avoiding walks on three-dimensional fractal structures

We have studied self-interacting self-avoiding walks (SAWs) situated on three-dimensional fractal structures, represented by a 3D Sierpinski gasket (SG) family of fractals. To this end, we have applied the exact renormalization group method (for the first three members of the SG fractal family, b = 2, 3 and 4) to calculate the critical exponents γE, γθ and γG (associated with the total number of distinct SAWs in extended phase, θ-chain and globular-collapsed polymer phase, respectively). To extend the obtained sequence of exact values for γE, we have applied the Monte Carlo renormalization group method for fractals with 2 ≤ b ≤ 40. Our results demonstrate that the critical exponent γE, as a function of b, monotonically increases and is always larger than the corresponding three-dimensional Euclidean value. On the other hand, γθ (for the values b = 2, 3 and 4), being smaller than the corresponding Euclidean value, decreases with b.

Reduction of cathode carbon deposit by buffer gas outflow

The problem of the cathode carbon deposit arising from the carbon vapor developed by conventional arc discharge plasma during fullerene synthesis is addressed. This carbon deposit significantly reduces fullerene productivity, wastes valuable energy and graphite material, and presents a major obstacle in achieving desirable productivity and scalability. A study of the deposit microstructure and its mechanical and physical properties revealed that the deposit is of a three-dimensional fractal structure having a rigid and microporous structure. Analysis reveals that the graphite evaporation rate determines carbon deposit formation, soot content, fullerene yield, and vapor quality, as well as defines the deposit formation. The buffer gas outflow approach utilizes the injection of a buffer gas into the hot plasma zone, provides quick evacuation of the produced carbon vapor away from the plasma zone, allows usage of large currents and bigger electrodes without a significant reduction of fullerene yield, and reduces the carbon deposit by more then 99%. Based on this work, the elimination of the cathode deposit is a major step in the development of efficient, productive and scalable fullerene and nanotube technology.

Structures and their influence factors of three‐dimensional fractal cadmium layer formed by electrodeposition

AbstractThree‐dimensional fractal structure of the electrodeposited cadmium layer was investigated. The results suggested that the fractal growth begin with nanometer scale aggregate within which the atoms arrange in hexagonal close‐packed lattice (the normal cadmium lattice). The fractal structure is correlated to the current density. The higher the current density is, the larger the size of fractal growth will be. Fractal structures can emerge in both the complete diffusion‐limited process and the combination‐limited process of the electrochemical reaction and diffusion. The fractal structure obtained from the simple hydrated ion electrolyte is different from that obtained from the complex ion electrolyte, which indicates they grow in different modes. The fractal dimensionality of deposit from the simple hydrated ion electrolyte is 2.592, smaller than that (2.608) from the complex ion electrolyte.

Multifractal analysis of cluster distribution in two dimensions

view Abstract Citations (15) References (72) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Multifractal Analysis of Cluster Distribution in Two Dimensions Borgani, Stefano ; Plionis, Manolis ; Valdarnini, Riccardo Abstract We perform a multifractal analysis on samples of galaxy clusters, obtained by cutting the Lick catalog at different values of the galaxy surface density, as well as on the Lick galaxy distribution. This kind of analysis is particularly relevant in order to properly test the scaling behavior of the cluster distribution and how it changes when peaks of different height are selected. We find that the highest selected peaks possess well-defined scaling properties up to the angular scale θ~6^deg^ - 7^deg^, corresponding to ~20 h^-1^ Mpc at the characteristic depth of our samples. remarkably similar to the correlation length of rich galaxy systems. This finding suggests a relation between scale-invariance of the cluster distribution and nonlinear clustering. The resulting spectrum of multifractal dimensions D_q_ indicates that the rich cluster distribution is essentially space- filling in the underdense regions (D_q_~ 2 for q <~ 1), while the overdense regions (corresponding to q ~> 1) are characterized by a dimension D_q_~ 1. On the contrary, the distributions of clusters corresponding to lower peaks show no definite scaling properties. In fact, although the dimensionality of these distributions is always near to one at sufficiently small angular scales, they have a dimension around two at larger scales θ ~> 7^deg^ (thus indicating homogeneity) without evidence of scale range where the dimensions take a constant value. A similar result holds also for the distribution of Lick galaxies, which reaches homogeneity already at the scale θ~ 2.5^deg^. We suggest that the absence of scaling for the distributions of clusters identified as lower peaks and of galaxies could well be due to projection effects that homogenize the three-dimensional clustering and, thus, are more severe in distorting the spatial scaling properties of less clustered structures. Our results indicate that well-defined scaling properties are associated in our projected samples only with the nonlinear clustering of high peaks and a corresponding dimension D ~ 1 is preferred. In order to properly test the effects of projection on the sky and of luminosity selection, we generate a three-dimensional fractal structure with an a priori known multifractal spectrum. We then assign luminosities to the points of this set drawn from a Schechter-like luminosity function, and then project onto a sphere, to generate apparent magnitude limited samples. We find that the resulting multifractal spectrum for these synthetic angular samples turns out to be distorted with respect to the original (three-dimensional) one. In particular, overdense regions are smoothed by projection, thus increasing D_q_ for q > 2, while underdense regions are filled, thus lowering the values of the negative-order dimensions. Despite this variation of the multifractal dimensions, the three-dimensional scale-invariance is however preserved. This result suggests that the break seen in D_q_(θ) (for high values of q) of the highest peak distribution is real and not due to projection or luminosity selection effects. Thus, the presence of a characteristic scale in the angular distribution of rich clusters strongly argues against a pure fractal picture extending with the same dimension over all the considered scales. Publication: The Astrophysical Journal Pub Date: February 1993 DOI: 10.1086/172255 Bibcode: 1993ApJ...404...21B Keywords: Fractals; Galactic Clusters; Two Dimensional Models; Universe; Astronomical Catalogs; Computational Astrophysics; Astrophysics; GALAXIES: CLUSTERING; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; METHODS: NUMERICAL full text sources ADS |