Self-similar Properties Research Articles

Wideband Square Sierpinski Fractal Microstrip Patch Antenna for Various Wireless Applications

In this paper, a square Sierpinski fractal microstrip patch antenna over a rectangular-shaped partial ground plane is introduced. A self-similar property of fractal geometry is used based on the iteration algorithm that reaches up to four iterations. It is simulated by High-Frequency Structure Simulator (HFSS) software package version.14. A square slot is used to enhance antenna performance such as bandwidth and reflection coefficient S11. This antenna has been designed on an FR4 substrate with a compact size of (34×34) mm2, 1.5mm substrate thickness h, a permittivity of 4.3 and 0.02 loss tangent. Microstrip line feed is implemented to excite the proposed antenna. This antenna is designed for wide bandwidth (2.7-5.7) GHz, and it has two resonant frequencies at 3.2GHz and 4.8GHz with an impedance bandwidth of 3GHz. Four parameters are optimized in order to achieve wider bandwidth such as length of ground Lg, the width of feed line Wf, square slot area, and feed point position X. Also, the surface current distribution at various frequencies is presented. Simulation results indicate a good reflection coefficient S11 values equal to -17.7 dB and -43.1dB at two resonant frequencies (3.2, 4.8) GHz and radiation efficiency about 75% with a peak gain of 3.72dB. This antenna is suitable for various wireless applications such as S-band applications like radar and some communication satellite such as (wireless LAN, Bluetooth, GPS, microwave devices/communications and mobile phone), also it can be used in the lower portion of C-band.

Is there always a conservation law behind the emergence of fractal and multifractal?

One of the most basic ingredients of fractal or multifractal is its scale-invariance or self-similar property albeit they appear seemingly disordered or apparently bewildering. In this article, we give several examples of deterministic, random and stochastic fractals as well as multifractals to show that there is always at least one conservation law behind all these systems. On the other hand, it is well-known and it has been shown here too that fractals and multifractals are self-similar which is also some form of symmetry that sends the object to itself. This is reminiscent to Noether’s first theorem that states that for every continuous symmetry of an action, there exists a conserved quantity. Finding the connection between conserved quantity in fractal and multifractal with scale-invariance of self-similarity can actually be coined as an equivalent counterpart of the Noether’s first theorem.

Local fluctuations of critical Mandelbrot cascades

Nous etudions les cascades de Mandelbrot generalisees a la temperature (critique) de freezing. Il est connu qu’apres une mise a l’echelle appropriee, une telle suite de cascades multiplicatives converge faiblement vers une certaine mesure aleatoire continue. La question est alors de savoir a quel point la mesure limite $\mu$ fluctue. Pour tout point $x$ donne, et en notant $B_{n}(x)$ la boule de rayon $2^{-n}$ centree en $x$, nous presentons des bornes superieures et inferieures optimales pour $\mu(B_{n}(x))$ lorsque $n\to\infty$.

Continuous cascades in the wavelet space as models for synthetic turbulence.

We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized "wave forms" with multiplicative intensity in the spirit of the Richardson cascade picture of turbulence. We establish the convergence and the minimum regularity of our construction. We show that its continuous wavelet transform is characterized by stochastic self-similarity and multifractal scaling properties. This model constitutes a stationary, "grid free" extension of W cascades introduced in the past by Arneodo, Bacry, and Muzy using a wavelet orthogonal basis. Moreover, our approach generically provides multifractal random functions that are not invariant by time reversal and therefore is able to account for skewed multifractal models and for the so-called "leverage effect." In that respect, it can be well suited to providing synthetic turbulence models or to reproducing the main observed features of asset price fluctuations in financial markets.

Towards Infinite Tilings with Symmetric Boundaries

Large-time coarsening and the associated scaling and statistically self-similar properties are used to construct infinite tilings. This is realized using a Cahn–Hilliard equation and special boundaries on each tile. Within a compromise between computational effort and the goal to reduce recurrences, an infinite tiling has been created and software which zooms in and out evolve forward and backward in time as well as traverse the infinite tiling horizontally and vertically. We also analyze the scaling behavior and the statistically self-similar properties and describe the numerical approach, which is based on finite elements and an energy-stable time discretization.

Models of fluid flowing in non-conventional media: New numerical analysis

The concept of differentiation with power law reset has not been investigated much in the literature, as some researchers believe the concept was wrongly introduced, it is unable to describe fractal sharps. It is important to note that, this concept of differentiation is not to describe or display fractal sharps but to describe a flow within a medium with self-similar properties. For instance, the description of flow within a non-conventional media which does not obey the classical Fick's laws of diffusion, Darcy's law and Fourier's law cannot be handle accurately with conventional mechanical law of rate of change. In this paper, we pointed out the use of the non-conventional differential operator with fractal dimension and it possible applicability in several field of sciences, technology and engineering dealing with non-conventional flow. Due to the wider applicability of this concept and the complexities of solving analytically those partial differential equations generated from this operator, we introduced in this paper a new numerical scheme that will be able to handle this class of differential equations. We presented in general the conditions of stability and convergence of the numerical scheme. We applied to some well-known diffusion and subsurface flow models and the stability analysis and numerical simulations for each cases are presented.

From rock microstructure to macromechanical properties based on fractal dimensions

Basic rock mechanical parameters, that is, the uniaxial compressive strength σc and elastic modulus E, have close relationships with the fractal dimension and inhomogeneity. Scanning electronic microscopy and fractal dimension calculations are applied to four different rock types (mudstone, sandstone, limestone, and basalt) in order to investigate the relationships between the rock mechanical properties, fractal dimensions, and homogeneity. The results show that the fractal dimension of each rock type fluctuates as the scanning electronic microscopy magnification increases. Rocks with different uniaxial compressive strength and elastic modulus values possess different self-similarity properties, and when the uniaxial compressive strength or elastic modulus increases, the fractal dimension of the rock microstructure decreases. The rock homogeneity is consistent with the fractal dimension, that is, the higher the homogeneity is, the larger the fractal dimension. Generally, homogeneity refers to the macroscale, and fractal dimension refers to the microscale. Overall, this research provides an innovative and effective approach for researching the mechanical behavior of rocks through a combination of uniaxial compression tests, homogeneity, and fractal dimensions.

On the extension and security of key schedule of GOST

A type of simple key schedule especially suitable for lightweight block ciphers is defined as straightforward key schedule in this study. As a typical example, GOST-type key schedule, which is an extension of the key schedules of Russian Standard GOST and its newly modified version GOST2, is introduced and classified. GOST2 is designed based on the GOST encryption structure with different but the same type of key schedule to overcome the weakness of GOST against self-similarity properties-based attacks. However, it has been shown in Fast Software Encryption 2017, the simple change in the key schedule is insufficient to offer 256-bit security. By constructing an evaluation framework combining self-similarity properties and meet-in-the-middle attack, properties of GOST-type key schedules are evaluated, and candidate key schedules are provided in this work. These candidate key schedules are able to provide much better security for GOST and GOST2 ciphers than their original key schedules, and the pre-existing self-similarity properties-based attacks of full round GOST and GOST2 can be avoided. The designers of GOST and GOST2 should have been more cautious choosing the parameters of key schedules. The evaluation framework proposed can be used for reference in the design of other Feistel ciphers with straightforward key schedules.

Maximizing Nonlocal Self-Similarity Prior for Single Image Super-Resolution

Prior knowledge plays an important role in the process of image super-resolution reconstruction, which can constrain the solution space efficiently. In this paper, we utilized the fact that clear image exhibits stronger self-similarity property than other degradated version to present a new prior called maximizing nonlocal self-similarity for single image super-resolution. For describing the prior with mathematical language, a joint Gaussian mixture model was trained with LR and HR patch pairs extracted from the input LR image and its lower scale, and the prior can be described as a specific Gaussian distribution by derivation. In our algorithm, a large scale of sophisticated training and time-consuming nearest neighbor searching is not necessary, and the cost function of this algorithm shows closed form solution. The experiments conducted on BSD500 and other popular images demonstrate that the proposed method outperforms traditional methods and is competitive with the current state-of-the-art algorithms in terms of both quantitative metrics and visual quality.

Multiphase flow in tight sandstone: An improved application for 3D intermingled fractal model

Abstract Multiphase displacement in tight sandstone is fundamental and critical for tight oil production. Micropores dominate the pore space in tight sandstone. Microscopic mineral components in micropores substantially influence the multiphase displacement behavior. Pore size distribution exhibits a self-similar or fractal property, similar to inorganic mineral grains. Utilizing fractal theory eases the rebuilding of the flowing space and calculation of relative permeability. As an improvement of previous work, we successfully extended the 3D intermingled fractal model (3D IFM). The extended 3D IFM can evaluate multiphase flow behavior in tight sandstone, considering fractal characteristics of pore size distribution and mineral grain distribution. The fractal information of pores and mineral properties are obtained by scalable scanning electron microscopy (SEM) and energy dispersive spectroscopy(EDS) images, respectively. This method is useful and reliable for calculating relative permeability and residual saturation. The method is also successfully used to evaluate the influence of oil-water viscosity ratio, mineral components and formation depth on multiphase displacement behavior, proving its convenience and potential in rapidly evaluating multiphase displacement behavior in tight sandstone.

A Coarse-to-Fine Method for Infrared Small Target Detection

Infrared small target detection in a complex background is a challenging problem. A complex background generally contains structured edges, unstructured clutter, and noise, which completely have different properties. It is very difficult to separate small target from these interferences by exploiting one property. To solve this problem, we propose a coarse-to-fine method to gradually detect small target. In the coarse phase, nonlocal self-similarity property of the structured edges is exploited so as to separate the structured edges from the other components, such as the random noise, the unstructured clutter, and also the small target. In the fine phase, we utilize the local contrast prior of the small target in a local region so as to distinguish the small target from the unstructured clutter and noise. Multiscale information is further introduced to accommodate the changing size of the small target. This progressive detection pipeline utilizes the nonlocal, local, and multiscale information in a single image, which facilitates gradually differentiating the small target from the structured edges, unstructured clutter, and noise. Extensive experimental results demonstrate that the proposed method outperforms the state-of-the-art methods.

Investigation of the motion of a magnet along conductive inclined plane by means of a robotic set

The article presents the results of an experimental study on the motion of a neodymium magnet on an inclined duralumin plate. During experiments, the time of motion was measured, and the steady-state velocity of the magnet motion was determined. To measure the time, a robotic set was used, which made it possible to measure the time of the motion with an accuracy of 0.001 s. It is demonstrated that the velocity of the motion of a magnet in the case when its direction is perpendicular to the magnetic moment (vector directed from the south pole of the magnet to the north) and both vectors lie in the plane parallel to the plate is 3.3 times larger than in the case when these vectors are parallel. The article gives a qualitative explanation of this phenomenon. In the non-stationary formulation, the problem of the motion of a conductor in a homogeneous magnetic field is solved. It is demonstrated that in the approximation when the self-induction effects can be neglected, the solution has the self-similarity property (that is, the solution contains no parameters other than the variable coordinate and time). The dependence of the coordinate of the conductor on the travel time turned out to be similar to that for a magnet.

Бактерівські оцінки параметра Хюрста дробового броунівського руху

In the paper consistent estimates of the Hurst parameter of fractional Brownian motion are obtained and confidence intervals of the obtained estimates are constructed. In many applications related to data processing, it is necessary to estimate the Hurst parameter. Among such tasks is the task of signal processing and analysis, when the signal can be considered as the imposition of a useful signal and background noise. Background noise is usually a combination of stochastic and fractal components. Numerical indicators of these properties are, respectively, the Hurst index, the stability index, the coefficients of the relationship of increments, which generalize the autocorrelation function. Obviously, the estimation of the Hurst index is a priority in the analysis of self-similar processes. Currently, there are many methods for estimating the Hurst parameter, but they are all focused on individual cases of processes where the property of self-similarity is combined with either long-term dependence (fractional Brownian motion), or with heavy tails. RS-analysis, disperse-time analysis and deviation analysis are most often used in estimating the Hurst parameter. A common feature of these methods is that they are all based on the use of statistical properties of second-order samples (variance, standard deviation, correlation coefficients).

A CLASS OF SELF-SIMILAR NETWORKS

Large graphs, also known as networks, are often used to represent different natural or human made structures. In many of these networks the phenomenon of self-similarity was detected. Here we present a deterministic method for construction of a class of self-similar networks. The elements of this class are obtained by a vertex-transitive graphs, and an iterative construction procedure implemented on these graphs. This procedure provides the property of self-similarity in the obtained network.

Self-assembly of Au nano-islands with tuneable organized disorder for highly sensitive SERS

A thermophoretically driven Au aerosol deposition process is used for the self-assembly of thin films consisting of plasmonic nano-islands (NIs) with a controllable and highly reproducible degree of disorder resulting in long-range periodicity with self-similar properties and stochastically distributed hot-spots, benefitting their applications as SERS substrates.

MPLS Network Parameters Analysis when Changing the Topology

One of the main tasks in network design is to evaluate the probability-time characteristics of the functioning of information and communication networks. Considering that the traffic of modern networks possesses the properties of self-similarity, we observe the difficulties while using the traditional mathematical apparatus of public serve theory. This paper presents us the results of jitter simulation estimating the delay, the probability of traffic loss when traffic processing in MPLS network. It was taken the real multimedia traffic and an on-off flow with a distribution of Pareto periods on and off as the researched flows. As the result, we discovered that when the network load increases or network size increases, jitter usually decreases, while the delay and loss probability increase.

Image Integration with Local Linear Model Using Demosaicing Algorithm

Recovering picture from corrupted observations necessary for several real-world applications. During this paper, we propose a unified framework to perform progressive image recovery supported hybrid graph Laplacian regularized regression. We first construct a multiscale illustration of the target image by Laplacian pyramid, then more and more recover the degraded image within the scale area from coarse to fine so the sharp edges and texture will be eventually recovered. On one hand, among every scale, a graph Laplacian regularization model represented by implicit kernel is learned, that at the same time minimizes the smallest amount sq. error on the measured samples and preserves the geometrical structure of the image information area. In this procedure, the intrinsic manifold structure is expressly considered exploitation each measured and unmeasured samples, and the nonlocal selfsimilarity property is used as a fruitful resource for abstracting aprioriknowledge of the photographs. On the other hand, between 2 sequential scales, the projected model is extended to a projected high-dimensional feature area through explicit kernel mapping to explain the interscale correlation, in which the native structure regularity is learned and propagated from coarser to finer scales. During this manner, the projected algorithmic rule gradually recovers additional and additional image details and edges, which couldn't be recovered in previous scale. We have a tendency to take a look at our algorithm on one typical image recovery task: impulse noise removal. Experimental results on benchmark take a look at pictures demonstrate that the projected technique achieves higher performance than progressive algorithms

Generalized Rauzy tilings and bounded remainder sets

Rauzy introduced a fractal set associted with the toric shift by the vector (β − 1 , β − 2 ), where β is the real root of the equation β 3 = β 2 + β + 1. He show that this fractal can be partitioned into three fractal sets that are bounded remaider sets with respect to the considered toric shift. Later, the introduced set was named as the Rauzy fractal. Further, many generalizations of Rauzy fractal are discovered. There are many applications of the generalized Rauzy fractals to problems in number theory, dynamical systems and combinatorics. Zhuravlev propose an infinite sequence of tilings of the original Rauzy fractal and show that these tilings also consist of bounded remainder sets. In this paper we consider the problem of constructing similar tilings for the generalized Rauzy fractals associated with algebraic Pisot units. We introduce an infinite sequence of tilings of the d −1-dimensional Rauzy fractals associated with the algebraic Pisot units of the degree d into fractal sets of d types. Each subsequent tiling is a subdivision of the previous one. Some results describing the self-similarity properties of the introduced tilings are proved. Also, it is proved that the introduced tilings are so called generalized exchanding tilings with respect to some toric shift. In particular, the action of this shift on the tiling is reduced to exchanging of d central tiles. As a corollary, we obtain that the Rauzy tiling of an arbitrary order consist of bounded remainder sets with respect to the considered toric shift. In addition, some self-similarity property of the orbit of considered toric shift is established.

On a gateway between continuous and discrete Bessel and Laguerre processes

By providing instances of approximation of linear diffusions by birth-death processes, Feller [Fel50] has offered an original path from the discrete world to the continuous one. In this paper, by identifying an intertwining relationship between squared Bessel processes and some linear birth-death processes, we show that this connection is in fact more intimate and goes in the two directions. As by-products, we identify some properties enjoyed by the birth-death family that are inherited from squared Bessel processes. For instance, these include a discrete self-similarity property and a discrete analogue of the beta-gamma algebra. We proceed by explaining that the same gateway identity also holds for the corresponding ergodic Laguerre semi-groups. It follows again that the continuous and discrete versions are more closely related than thought before, and this enables to pass information from one semi-group to the other one.

Quasi-periodic Geometry for Architectural Acoustics

The discovery of quasi-periodic atomic order in the crystalline state has uncovered an exciting new class of symmetries that has never been explored before. Because of their non-periodic translational order and self-similar properties, quasi-periodic structures offer unique opportunities for investigating questions related to their acoustical behavior. Their unique long-range non-periodic formations have the ability to diffuse and orchestrate the flow of sound energy in many unique ways; offering intriguing potential for innovating a new wave of optimized sound diffusers. One key limitation with available periodic diffusers is that their repeating logic creates repetitive energy loops, which significantly reduce their ability to uniformly disperse sound energy. Quasi-periodic geometry can mitigate such limitation. By encapsulating an infinite variety of distinct profiles in all directions, quasi-periodic surfaces can eliminate the formation of bundled or looped reflections; considerably enhancing the ability of the diffuser to uniformly disperse sound energy. To investigate this hypothesis, an experimental approach is used to simulate sound reflection patterns of the quasi-periodic surface profiles using a ray tracing method. Both qualitative and quantitative analyses are used to interpret the simulated results. The international Standards (ISO) metrics are used to validate the proposed approach and verify the results. Results show that the diffusion quality of the tested quasi-periodic surface is superior to the diffusion performance of the tested periodic surface.