Self-similar Characteristics Research Articles

Slow light by dual-periodic self-similar dielectric multilayered films.

We demonstrate the emergence of slow-light in dual-periodic dielectric one-dimensional photonic crystals with self-similar features at different length scales. Specifically, using numerical modelling, we explore self-similar photonic crystals which are formed as effective combinations of dual periodic stacks of dielectric layers and show that the emergent photonic band diagram can be widely designed by different structural parameters. The width and the position of bandgaps can be designed to work over a wide range of bands and frequencies. The proposed design also leads to the emergence of flat bands and major slow-light regimes, with possible group refractive index of light as large as 103 and in a range of bands.

Self-similarity feature based few-shot learning via hierarchical relation network

Self-similarity feature based few-shot learning via hierarchical relation network

Self-similar propagation and flame acceleration of hydrogen-rich syngas turbulent expanding flames

In order to investigate the flame self-similar propagation and flame acceleration characteristics of hydrogen-rich syngas turbulent expanding flames, the turbulent combustion experimental studies of H2/CO/air mixtures with XH2 = 55%-95%, φ = 0.6–1.0, P = 1 bar-3 bar, u’=0.809–2.533 were conducted in a fan-stirred turbulent combustion chamber with an inner diameter of 380 mm. Results show that the normalized flame propagation speed ST/SL and turbulent flame Reynolds number ReT,flame could be represented by power-law correlations. With the increase of hydrogen fraction from 55% to 95%, the power exponent decreases from 0.413 to 0.301. The increase of hydrogen fraction makes the flame acceleration weaker because that the enhancing of laminar flame speed is more obvious than the differential-diffusion effect by decreasing Le. With the decrease of equivalence ratio from 1.0 to 0.6, the power exponent increases from 0.304 to 0.411 in this study. The relative high power exponent under low equivalence ratio is due to the coupling between differential-diffusion and the flame stretch on the local wrinkled flame structures. In addition, the influence of turbulence and flame intrinsic instabilities on flame acceleration propagation process of hydrogen-enriched syngas were studied. The acceleration exponent was extracted to quantitatively investigate the flame self-acceleration propagation in the transition stage, and the relationships between acceleration exponent and turbulence intensity (u’), Kovasznay number (Kz), turbulence integral length scale (LT), flame thickness (δ), thermal expansion ratio (ρu/ρb), effective Lewis number (Leeff) were analyzed

Look-alike Landau levels in locally biased twisted bilayer graphene

Large lattice constant of Moire superlattice formed in twisted bilayer graphene enables observing Landau levels splitting into Hofstadter butterflies. This is expected for homogeneous bias conditions but its robustness against spatial potential fluctuations is left open question. We study the energy structure of twisted bilayer system in dependence of both, homogeneous magnetic field and bias voltage applied in its central region. Although translational symmetry is broken, the energy states localized outside the biased region still form Landau levels revealing self-similarity feature. Moreover, besides generic Landau levels appearing when both layers are biased with the same voltage, the second look-alike energy branch can be developed by states largely localized in central biased region. Otherwise, for counter-biasing of layers, only generic branch exists but with lowest Landau levels flanked by either, hole-like and electron-like states localized at the top or at the bottom layer of central biased part of twisted bilayer system.

A mechanics model based on information entropy for identifying influencers in complex networks.

The network, with some or all characteristics of scale-free, self-similarity, self-organization, attractor and small world, is defined as a complex network. The identification of significant spreaders is an indispensable research direction in complex networks, which aims to discover nodes that play a crucial role in the structure and function of the network. Since influencers are essential for studying the security of the network and controlling the propagation process of the network, their assessment methods are of great significance and practical value to solve many problems. However, how to effectively combine global information with local information is still an open problem. To solve this problem, the generalized mechanics model is further improved in this paper. A generalized mechanics model based on information entropy is proposed to discover crucial spreaders in complex networks. The influence of each neighbor node on local information is quantified by information entropy, and the interaction between each node on global information is considered by calculating the shortest distance. Extensive tests on eleven real networks indicate the proposed approach is much faster and more precise than traditional ways and state-of-the-art benchmarks. At the same time, it is effective to use our approach to identify influencers in complex networks.

Escape Criteria for Generating Fractals of Complex Functions Using DK-Iterative Scheme

Fractals are essential in representing the natural environment due to their important characteristic of self similarity. The dynamical behavior of fractals mostly depends on escape criteria using different iterative techniques. In this article, we establish an escape criteria using DK-iteration as well as complex sine function (sin(zm)+c;m≥2,c∈C) and complex exponential function (ezm+c;m≥2,c∈C). We use this to analyze the dynamical behavior of specific fractals namely Julia set and Mandelbrot set. This is achieved by generalizing the existing algorithms, which led to the visualization of beautiful fractals for m=2,3 and 4. Moreover, the image generation time in seconds using different values of input parameters is also computed.

Interelectrode microwave glow discharge in atmospheric-pressure argon flow

The spatio-temporal structure and plasma parameters of a new type of glow discharge—atmospheric-pressure interelectrode microwave discharge in gas flow—were studied experimentally and numerically. A multi-electrode coaxial-type cold plasma torch developed for large-area surface treatment was used as a gas discharge device. The torch was supplied with microwave power (2.45 GHz, ∼100 W) via a coaxial cable by a typical wave-guide plasmatron. Self-sustained glow discharges were excited between the round ends of the rod-like electrodes and inner wall of the cylindrical discharge chamber near the outlet. The filamentation of the discharge channel in the near-electrode regions was detected by high-speed video filming. The dendritic self-similar (fractal) character of the filaments’ structure was revealed and analyzed. The branching factor and fractal dimension of this structure were estimated as 3 and 1.1–1.3, respectively. Using discharge gas temperature T g = 1200 ± 100 K, as determined from the emission spectroscopy measurements, the following discharge plasma parameters were obtained from numerical calculations: electron temperature eV and concentration – m−3, conductivity current density A m−2, and electric field strength V m−1.

Hyperspectral Image Denoising via Robust Subspace Estimation and Group Sparsity Constraint

Hyperspectral cameras capture electromagnetic information within hundreds of narrow spectral bands, producing hyperspectral images (HSIs) with the capability to accurately characterize the attribute information of objects. However, mixed noise induced by instrument and atmospheric effects hinders the interpretations and applications of the HSIs. In this paper, we propose a novel subspace representation based mixed noise removal method for hyperspectral images via Robust Subspace Estimation and weighted Group Sparsity constraint (RoSEGS). An outlier detection method is proposed to effectively detect sparse noise and replace the sparse noise with new estimates. A subspace estimation strategy, which is robust to mixed noise, is proposed. The subspace is first estimated after sparse noise detection and then optimized iteratively. In addition to the introduction of a state-of-the-art denoiser based on the plug-and-play technique to exploit self-similarity characteristics of the eigen-images, we impose a weighted group sparse regularization on the eigen-images to better promote the group sparsity of the spatial differences between the eigen-images, which further improves the denoising performance. We performed extensive experiments on two simulated and two real HSIs to fully demonstrate the effectiveness of the proposed method in comparison with seven state-of-the-art competitors.

Combining Phase Congruency and Self-Similarity Features for Multimodal Remote Sensing Image Matching

The structural features using self-similarity have become more popular for multimodal remote sensing image matching. However, mostly because of significant geometric distortions and nonlinear intensity differences between images, these methods produce a limited matching performance when directly applied to multimodal remote sensing images. To address that, we propose a novel feature descriptor named pyramid features of orientated self-similarity (POSS) for multimodal remote sensing image matching, which integrates phase congruency (PC) into the self-similarity model for better encoding structural information. Unlike these conventional self-similarity-based descriptors, the POSS is constructed by using PC instead of image intensity in a pyramid manner and thus has better discriminability and robustness to modality variations. In addition, we design a uniform multimoment of PC (UMMPC) detector for feature detection, which can improve the number, distribution, and repeatability of feature points. Experimental results demonstrate its superior applicability of the proposed method over the state-of-the-art methods, showing much better matching performance.

Global Context-Based Self-Similarity Feature Augmentation and Bidirectional Feature Fusion for Surface Defect Detection

Global Context-Based Self-Similarity Feature Augmentation and Bidirectional Feature Fusion for Surface Defect Detection

Frequency-dependent P-wave anelasticity due to multiscale (fractal) heterogeneities in rocks

Understanding the effect that multiscale heterogeneities have on the wave responses of rocks at different frequencies is essential in the interpretation of seismic data. In fact, the behaviors of ultrasonic and seismic waves differ because the experiments involve different spatial scales. Then, a solution is to apply a theory that establishes a relation between the wave properties at different frequency bands considering a size range of heterogeneities. To investigate this problem, we have measured the compressional wave (P-wave) anelasticity (velocity and attenuation) of tight reservoir rocks at ultrasonic, sonic and seismic frequencies. The wave behavior as a function of porosity or clay content shows a consistent trend. With increasing confining pressure, the effect of porosity on attenuation decreases, while that of clay content gradually becomes important. To interpret the data, we propose a double-fractal poroelasticity model by incorporating the self-similarity characteristics of cracks and clay minerals. The comparison between the experimental data and model results reveals the fractality of the clay inclusions and cracks, with radii range of [10−6, 10−1.5] m and [10−6, 10−3.1] m, respectively, which is responsible for the anelastic behavior of the waves on a wide frequency band.

Wavelet-based approach for diagnosing attention deficit hyperactivity disorder (ADHD)

Attention deficit hyperactivity disorder (ADHD) is a common cognitive disorder affecting children. ADHD can interfere with educational, social, and emotional development, so early detection is essential for obtaining proper care. Standard ADHD diagnostic protocols rely heavily on subjective assessments of perceived behavior. An objective diagnostic measure would be a welcome development and potentially aid in accurately and efficiently diagnosing ADHD. Analysis of pupillary dynamics has been proposed as a promising alternative method of detecting affected individuals effectively. This study proposes a method based on the self-similarity of pupillary dynamics and assesses its strength as a potential diagnostic biomarker. Localized discriminatory features are developed in the wavelet domain and selected via a rolling window method to build classifiers. The application on a task-based pupil diameter time series dataset of children aged 10–12 years shows that the proposed method achieves greater than 78% accuracy in detecting ADHD. Comparing with a recent approach that constructs features in the original data domain, the proposed wavelet-based classifier achieves more accurate ADHD classification with fewer features. The findings suggest that the proposed diagnostic procedure involving interpretable wavelet-based self-similarity features of pupil diameter data can potentially aid in improving the efficacy of ADHD diagnosis.

Comparison of the mean flow and turbulence characteristics of a single offset jet and a dual offset jet

This study compares the mean flow characteristics of a dual offset jet, comprising two 2-dimensional or plane turbulent offset jets, to a single offset jet. An in-house computational model is used to solve the incompressible form of the governing equations which are based on the standard k−ϵ Reynolds Averaged Navier–Stokes turbulence model. The offset ratio, defined as the vertical distance from the solid wall to the jet centreline divided by the nozzle width, of the upper jet is varied from 7 to 13, while the same for the lower jet is equal to 3. The jets’ inlet Reynolds number is 10,000 with a turbulence intensity of 5%. The mean flow results reveal that the presence of the second offset jet greatly influences the flow patterns compared to those of the single offset jet, although at some distance downstream of the inlet, the flow fields of both jet configurations resemble that of a classical wall jet. A single recirculation zone is formed underneath the single offset jet, whereas the flow field of the dual offset jet comprises two recirculation zones, one below the lower jet and the other between the two jets. In the pre-impingement region, the dual offset jet experiences a more rapid decay of the jet half width as compared to the single offset jet; however, the rate of growth of the jet half width for the single offset jet is faster than the dual offset jet. The self-similar solutions confirm that the dual offset jet begins to preserve self-similar characteristics for the mean flow field at a downstream distance greater than that for the single offset jet. For a given offset ratio, the total momentum flux for the single offset jet is found to be greater than that for the dual offset jet. Furthermore, the turbulent Reynolds stresses in the neighbourhood of the merging point are greater for the dual offset jet, but near the reattachment point, they are greater for the single offset jet. No self-similar characteristic of turbulence Reynolds stresses is obtained for both the jets. The turbulent kinetic energy budget reveals the highest value of the production term in the outer shear layer of the lower offset jet for the dual offset jet, which is greater than that for the single offset jet.

The Wall-Jet Region of a Turbulent Jet Impinging on Smooth and Rough Plates

The study reports direct numerical simulations of a turbulent jet impinging onto smooth and rough surfaces at Reynolds number Re = 10,000 (based on the jet mean bulk velocity and diameter). Surface roughness is included in the simulations using an immersed boundary method. The deflection of the flow after jet impingement generates a radial wall-jet that develops parallel to the mean plate surface. The wall-jet is structured into an inner and an outer layer that, in the limit of infinite local Reynolds number, resemble a turbulent boundary layer and a free-shear flow. The investigation assesses the self-similar character of the mean radial velocity and Reynolds stresses profiles scaled by inner and outer layer units for varying size of the roughness topography. Namely the usual viscous units u_tau and delta _nu are used as inner layer scales, while the maximum radial velocity u_m and its wall-normal location z_m are used as outer layer scales. It is shown that the self-similarity of the mean radial velocity profiles scaled by outer layer units is marginally affected by the span of roughness topographies investigated, as outer layer velocity and length reference scales do not show a significantly modified behavior when surface roughness is considered. On the other hand, the mean radial velocity profiles scaled by inner layer units show a considerable scatter, as the roughness sub-layer determined by the considered roughness topographies extends up to the outer layer of the wall-jet. Nevertheless, the similar character of the velocity profiles appears to be conserved despite the profound impact of surface roughness.

Self-similar solutions of shallow water equations with porosity

Simulated free surface transients in periodic urban layouts have been reported to be self-similar in the space-time domain when averaged on the scale of the building period. Such self-similarity is incompatible with the head loss model formulae used in most porosity-based shallow water models. Verifying it experimentally is thus of salient importance. New dam-break flow laboratory experiments are reported, where two different configurations of idealized periodic buildings layouts are explored. A space-time analysis of the experimental water level fields validates the self-similar character of the flow. Simulating the experiment using the two-dimensional shallow water model also yields self-similar period-averaged flow solutions. Then, the Single Porosity (SP), Integral Porosity (IP) and Dual Integral Porosity (DIP) models are applied. Although all three models behave in a similar fashion when the storage and connectivity porosities are close to each other, the DIP model is the one that upscales best the refined 2D solution.

Self-similar characteristics of underexpanded, cryogenic hydrogen and methane jets

Underexpanded, cryogenic hydrogen and methane jets were measured using laser Raman scattering diagnostic. The jets were released from 1 mm to 1.25 mm orifices for the stagnation pressure ranges of 2–6 bar and temperature ranges of 37–46 K (hydrogen) and 112–189 K (methane). Raman signals are inherently small, thus a denoising algorithm was developed to substantially reduce the noise hindering the statistical analysis of the data. The time-averaged concentration and temperature data were plotted to show a hyperbolic decay law along the jet centerline and a Gaussian distribution in the radial direction. The concentration fluctuations of the cryogenic jets are similar to those of warm jets, the centerline RMS mass fraction decays similarly to the mean mass fraction, and the highest radial concentration fluctuations appear in the shear layer. Thus, the self-similar characteristics of the cryogenic jets are comparable with room-temperature jets for the present test conditions.

Effect of particle shape on packing fraction and velocity profiles at outlet of a silo

Many studies on how the particle shape affects the discharge flow mainly focus on discharge rates and avalanche statistics. In this study, the effect of the particle shape on the packing fraction and velocities of particles in the silo discharge flow are investigated by using the discrete element method. The time-averaged packing fraction and velocity profiles through the aperture are systematically measured for superelliptical particles with different blockinesses. Increasing the particle blockiness is found to increase resistance to flow and reduce the flow rate. At an identical outlet size, larger particle blockiness leads to lower velocity and packing fraction at the outlet. The packing fraction profiles display evidently the self-similar feature that can be appropriately adjusted by fractional power law. The velocity profiles for particles with different shapes obey a uniform self-similar law that is in accord with previous experimental results, which is compatible with the hypothesis of free fall arch. To further investigate the origin of flow behaviors, the packing fraction and velocity field in the region above the orifice are computed. Based on these observations, the flow rate of superelliptical particles is calculated and in agreement with the simulated data.

Research on Satellite Network Traffic Prediction Based on Improved GRU Neural Network.

The current satellite network traffic forecasting methods cannot fully exploit the long correlation between satellite traffic sequences, which leads to large network traffic forecasting errors and low forecasting accuracy. To solve these problems, we propose a satellite network traffic forecasting method with an improved gate recurrent unit (GRU). This method combines the attention mechanism with GRU neural network, fully mines the characteristics of self-similarity and long correlation among traffic data sequences, pays attention to the importance of traffic data and hidden state, learns the time-dependent characteristics of input sequences, and mines the interdependent characteristics of data sequences to improve the prediction accuracy. Particle Swarm Optimization (PSO) algorithm is used to obtain the best network model Hyperparameter and improve the prediction efficiency. Simulation results show that the proposed method has the best fitting effect with real traffic data, and the errors are reduced by 26.9%, 37.2%, and 57.8% compared with the GRU, Support Vector Machine (SVM), and Fractional Autoregressive Integration Moving Average (FARIMA) models, respectively.

EEGDnet: Fusing non-local and local self-similarity for EEG signal denoising with transformer

Electroencephalogram (EEG) has shown a useful approach to produce a brain–computer interface (BCI). One-dimensional (1-D) EEG signal is yet easily disturbed by certain artifacts (a.k.a. noise) due to the high temporal resolution. Thus, it is crucial to remove the noise in received EEG signal. Recently, deep learning-based EEG signal denoising approaches have achieved impressive performance compared with traditional ones. It is well known that the characteristics of self-similarity (including non-local and local ones) of data (e.g., natural images and time-domain signals) are widely leveraged for denoising. However, existing deep learning-based EEG signal denoising methods ignore either the non-local self-similarity (e.g., 1-D convolutional neural network) or local one (e.g., fully connected network and recurrent neural network). To address this issue, we propose a novel 1-D EEG signal denoising network with 2-D transformer, namely EEGDnet. Specifically, we comprehensively take into account the non-local and local self-similarity of EEG signal through the transformer module. By fusing non-local self-similarity in self-attention blocks and local self-similarity in feed forward blocks, the negative impact caused by noises and outliers can be reduced significantly. Extensive experiments show that, compared with other state-of-the-art models, EEGDnet achieves much better performance in terms of both quantitative and qualitative metrics. Specifically, EEGDnet can achieve 18% and 11% improvements in correlation coefficients when removing ocular artifacts and muscle artifacts, respectively.

A one dimensional ubiquitiform damage model for quasi-brittle materials

Considering the self-similar characteristic of irregular pore network of materials during the damage evolution process, a pore ubiquitiform model (PUM) is developed to characterize the multiscale pore or microcrack network of quasi-brittle materials, and then based on the PUM, the ubiquitiform damage model (UDM) is proposed to describe the damage evolution process of quasi-brittle materials under quasi-static uniaxial tensile loading. The values of porosity and pore specific surface area estimated from the PUM and the stress-deformation curves including the softening curve calculated from the UDM are in good agreement with previous experimental data, respectively. It can be found that, the PUM can be adopted to characterize the self-similar multiscale pore network and estimate the porosity and pore specific surface area, and the UDM can describe the damage evolution process of quasi-brittle materials under quasi-static uniaxial tensile loading. Meanwhile, the UDM can characterize the self-similar characteristic of pore network during the damage evolution process of quasi-brittle materials through the evolving ubiquitiform complexity.