Symmetry

34 pages, 3749 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Thinking Outside the Box: Numerical Relativity with Particles

by Stephan Rosswog, Peter Diener and Francesco Torsello

Symmetry 2022, 14(6), 1280; https://doi.org/10.3390/sym14061280 - 20 Jun 2022

Cited by 10 | Viewed by 6799

The observation of gravitational waves from compact objects has now become an active part of observational astronomy. For a sound interpretation, one needs to compare such observations against detailed Numerical Relativity simulations, which are essential tools to explore the dynamics and physics of [...] Read more.

The observation of gravitational waves from compact objects has now become an active part of observational astronomy. For a sound interpretation, one needs to compare such observations against detailed Numerical Relativity simulations, which are essential tools to explore the dynamics and physics of compact binary mergers. To date, essentially all simulation codes that solve the full set of Einstein’s equations are performed in the framework of Eulerian hydrodynamics. The exception is our recently developed Numerical Relativity code SPHINCS_BSSN which solves the commonly used BSSN formulation of the Einstein equations on a structured mesh and the matter equations via Lagrangian particles. We show here, for the first time, SPHINCS_BSSN neutron star merger simulations with piecewise polytropic approximations to four nuclear matter equations of state. In this set of neutron star merger simulations, we focus on perfectly symmetric binary systems that are irrotational and have 1.3

M_{⊙}

masses. We introduce some further methodological refinements (a new way of steering dissipation, an improved particle–mesh mapping), and we explore the impact of the exponent that enters in the calculation of the thermal pressure contribution. We find that it leaves a noticeable imprint on the gravitational wave amplitude (calculated via both quadrupole approximation and the

Ψ_{4}

formalism) and has a noticeable impact on the amount of dynamic ejecta. Consistent with earlier findings, we only find a few times

10^{- 3}

M_{⊙}

as dynamic ejecta in the studied equal mass binary systems, with softer equations of state (which are more prone to shock formation) ejecting larger amounts of matter. In all of the cases, we see a credible high-velocity (∼

0.5 \dots 0.7 c

) ejecta component of ∼

10^{- 4}

M_{⊙}

that is launched at contact from the interface between the two neutron stars. Such a high-velocity component has been suggested to produce an early, blue precursor to the main kilonova emission, and it could also potentially cause a kilonova afterglow. Full article

(This article belongs to the Special Issue Relativistic Hydrodynamics and Symmetry: Theory, Methods and Applications)

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13 pages, 449 KiB

Open AccessArticle

Stability of Euler Methods for Fuzzy Differential Equation

by Cuilian You, Yan Cheng and Hongyan Ma

Symmetry 2022, 14(6), 1279; https://doi.org/10.3390/sym14061279 - 20 Jun 2022

Cited by 3 | Viewed by 1716

Abstract

The Liu process is a fuzzy process whose membership function is a symmetric function on an expected value. The object of this paper was a fuzzy differential equation driven by Liu process. Since the existing fuzzy Euler solving methods (explicit Euler scheme, semi-implicit [...] Read more.

The Liu process is a fuzzy process whose membership function is a symmetric function on an expected value. The object of this paper was a fuzzy differential equation driven by Liu process. Since the existing fuzzy Euler solving methods (explicit Euler scheme, semi-implicit Euler scheme, and implicit Euler scheme) have the same convergence, to compare them, we presented four stabilities, i.e., asymptotical stability, mean square stability, exponential stability, and A stability. By choosing special fuzzy differential equation as a test equation, we deduced that mean square stability is equivalent to exponential stability. Furthermore, an explicit fuzzy Euler scheme and semi-implicit fuzzy Euler scheme showed asymptotical stability and mean square stability, while an explicit fuzzy Euler scheme failed to meet A stability but that an implicit fuzzy Euler scheme is A stable, and whether semi-implicit fuzzy Euler scheme is A stable depends on the values of

α

and

λ

. Full article

(This article belongs to the Special Issue Fuzzy Set Theory and Uncertainty Theory)

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24 pages, 10313 KiB

Open AccessReview

Discrete and Continuous Symmetries of Stratified Flows Past a Sphere

by Yuli D. Chashechkin

Symmetry 2022, 14(6), 1278; https://doi.org/10.3390/sym14061278 - 20 Jun 2022

Cited by 4 | Viewed by 2071

Abstract

This study presents the detailed experimental results of fine structures and dynamics in a stratified flow past a sphere, which is towed with constant velocity in a transparent basin. We developed experimental procedures based on the complete solutions of the truncated fundamental fluid [...] Read more.

This study presents the detailed experimental results of fine structures and dynamics in a stratified flow past a sphere, which is towed with constant velocity in a transparent basin. We developed experimental procedures based on the complete solutions of the truncated fundamental fluid equations. These complete solutions describe the waves and fine accompanying ligaments, as well as the vortices and other flow structures. To visualize the flow, a variety of classical schlieren and electrolytic precipitation procedures were used. Ligaments appear in the schlieren images of the flow as fine interfaces and fibers. They strengthen the influence of the relatively weak density gradient in a continuously stratified fluid (CSF). The symmetry in the wake is discrete at small Froude numbers with the domination of buoyancy effects. At increased velocity and high Froude numbers, when the inertial and non-linear effects turn out to be significant, an axial symmetry becomes continuous. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

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29 pages, 550 KiB

Open AccessArticle

An Ensemble Framework to Forest Optimization Based Reduct Searching

by Jin Wang, Yuxin Liu, Jianjun Chen and Xibei Yang

Symmetry 2022, 14(6), 1277; https://doi.org/10.3390/sym14061277 - 20 Jun 2022

Cited by 4 | Viewed by 1709

Abstract

Essentially, the solution to an attribute reduction problem can be viewed as a reduct searching process. Currently, among various searching strategies, meta-heuristic searching has received extensive attention. As a new emerging meta-heuristic approach, the forest optimization algorithm (FOA) is introduced to the problem [...] Read more.

Essentially, the solution to an attribute reduction problem can be viewed as a reduct searching process. Currently, among various searching strategies, meta-heuristic searching has received extensive attention. As a new emerging meta-heuristic approach, the forest optimization algorithm (FOA) is introduced to the problem solving of attribute reduction in this study. To further improve the classification performance of selected attributes in reduct, an ensemble framework is also developed: firstly, multiple reducts are obtained by FOA and data perturbation, and the structure of those multiple reducts is symmetrical, which indicates that no order exists among those reducts; secondly, multiple reducts are used to execute voting classification over testing samples. Finally, comprehensive experiments on over 20 UCI datasets clearly validated the effectiveness of our framework: it is not only beneficial to output reducts with superior classification accuracies and classification stabilities but also suitable for data pre-processing with noise. This improvement work we have performed makes the FOA obtain better benefits in the data processing of life, health, medical and other fields. Full article

(This article belongs to the Special Issue Recent Advances in Granular Computing for Intelligent Data Analysis)

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12 pages, 21891 KiB

Open AccessArticle

On the Error Estimation of the FEM for the Nikol’skij-Lizorkin Problem with Degeneracy in the Lebesgue Space

by Viktor Rukavishnikov and Elena Rukavishnikova

Symmetry 2022, 14(6), 1276; https://doi.org/10.3390/sym14061276 - 20 Jun 2022

Viewed by 1388

Abstract

In this manuscript, the Nikol’skii-Lizorkin problem with degeneracy on the entire boundary of the domain is considered. The degeneracy is caused by the behavior of the coefficients and right-hand sides of the problem on the boundary. The triangulation of the domain with a [...] Read more.

In this manuscript, the Nikol’skii-Lizorkin problem with degeneracy on the entire boundary of the domain is considered. The degeneracy is caused by the behavior of the coefficients and right-hand sides of the problem on the boundary. The triangulation of the domain with a special compression to the boundary of the domain is carried out and the finite element method is constructed. An estimate for the rate of convergence of an approximate solution to an exact solution with the second order in the mesh step in the

L_{2} (Ω)

space norm is proved. Numerical experiments have confirmed the established estimate of the convergence rate. Full article

(This article belongs to the Special Issue Mesh Methods—Numerical Analysis and Experiments II)

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21 pages, 23878 KiB

Open AccessArticle

Distributed Integrated Synthetic Adaptive Multi-Objective Reactive Power Optimization

by Jiayin Song, Chao Lu, Qiang Ma, Hongwei Zhou, Qi Yue, Qinglin Zhu, Yue Zhao, Yiming Fan and Qiqi Huang

Symmetry 2022, 14(6), 1275; https://doi.org/10.3390/sym14061275 - 20 Jun 2022

Cited by 1 | Viewed by 1631

Abstract

Reactive power is the core problem of voltage stability and economical operation in power systems. Aiming at the problem that multi-objective normalization reactive power optimization function is dependent on weight, an integrated synthesis of adaptive multi-objective particle swarm optimization (ISAMOPSO) is proposed to [...] Read more.

Reactive power is the core problem of voltage stability and economical operation in power systems. Aiming at the problem that multi-objective normalization reactive power optimization function is dependent on weight, an integrated synthesis of adaptive multi-objective particle swarm optimization (ISAMOPSO) is proposed to achieve weight adaptive. Through seven test functions and three algorithm comparison experiments, it is proved that the ISAMOPSO algorithm has stronger global search capability and better convergence. Considering the optimal access position and capacity of distributed generation (DG), the ISAMOPSO algorithm is used for three-objective reactive power optimization. Finally, the results indicate that the ISAMOPSO algorithm can not only provide a variety of optimization schemes to meet different needs, but also realize dynamic reactive power optimization, which further proves that the algorithm can provide effective technical support for solving reactive power optimization problems in practical engineering. Full article

(This article belongs to the Special Issue Adaptive Filtering and Machine Learning)

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13 pages, 306 KiB

Open AccessArticle

Analysis of Solutions to a Parabolic System with Absorption

by Haihua Lu, Jiayuan Wu and Wenjun Liu

Symmetry 2022, 14(6), 1274; https://doi.org/10.3390/sym14061274 - 20 Jun 2022

Cited by 2 | Viewed by 1470

Abstract

In this paper, we investigate the blow-up rate and global existence of solutions to a parabolic system with absorption under the homogeneous Dirichlet boundary. By using the comparison principle and super-sub solution method, we obtain some sufficient conditions for the global existence and [...] Read more.

In this paper, we investigate the blow-up rate and global existence of solutions to a parabolic system with absorption under the homogeneous Dirichlet boundary. By using the comparison principle and super-sub solution method, we obtain some sufficient conditions for the global existence and blow-up in finite time of solutions and establish some estimates of the upper and lower bounds of the blow-up rates. For the special case, if the domain is symmetric, for example, if it is a ball, the results of this paper also hold. Full article

(This article belongs to the Special Issue Symmetry and Biomathematics: Recent Developments and Challenges)

19 pages, 285 KiB

Open AccessArticle

The Solvability of a System of Quaternion Matrix Equations Involving ϕ-Skew-Hermicity

by Zhuo-Heng He, Xiao-Na Zhang, Yun-Fan Zhao and Shao-Wen Yu

Symmetry 2022, 14(6), 1273; https://doi.org/10.3390/sym14061273 - 20 Jun 2022

Cited by 3 | Viewed by 1451

Abstract

Let

H

be the real quaternion algebra and

H^{m \times n}

denote the set of all

m \times n

matrices over

H

. For

A \in H^{m \times n},

we denote by

A_{ϕ}

the

n \times m

matrix obtained [...] Read more.

Let

H

be the real quaternion algebra and

H^{m \times n}

denote the set of all

m \times n

matrices over

H

. For

A \in H^{m \times n},

we denote by

A_{ϕ}

the

n \times m

matrix obtained by applying

ϕ

entrywise to the transposed matrix

A^{T},

where

ϕ

is a non-standard involution of

H

.

A \in H^{n \times n}

is said to be

ϕ

-skew-Hermicity if

A = - A_{ϕ}

. In this paper, we provide some necessary and sufficient conditions for the existence of a

ϕ

-skew-Hermitian solution to the system of quaternion matrix equations with four unknowns

A_{i} X_{i} {(A_{i})}_{ϕ} + B_{i} X_{i + 1} {(B_{i})}_{ϕ} = C_{i}, (i = 1, 2, 3), A_{4} X_{4} {(A_{4})}_{ϕ} = C_{4}

. Full article

(This article belongs to the Special Issue Selected Papers from the 2021 International Conference on Matrix Inequalities and Matrix Equations)

9 pages, 1139 KiB

Open AccessArticle

A Residual Voltage Data-Driven Prediction Method for Voltage Sag Based on Data Fusion

by Chen Zheng, Shuangyin Dai, Bo Zhang, Qionglin Li, Shuming Liu, Yuzheng Tang, Yi Wang, Yifan Wu and Yi Zhang

Symmetry 2022, 14(6), 1272; https://doi.org/10.3390/sym14061272 - 20 Jun 2022

Cited by 2 | Viewed by 1723

Abstract

Voltage sag is the most serious power quality problem in the three-phase symmetrical power system. The influence of multiple factors on the voltage sag level and low computational efficiency also pose challenges to the prediction of residual voltage amplitude of voltage sag. This [...] Read more.

Voltage sag is the most serious power quality problem in the three-phase symmetrical power system. The influence of multiple factors on the voltage sag level and low computational efficiency also pose challenges to the prediction of residual voltage amplitude of voltage sag. This paper proposes a voltage sag amplitude prediction method based on data fusion. First, the multi-dimensional factors that influence voltage sag residual voltage are analyzed. Second, these factors are used as input, and a model for predicting voltage sag residual voltage based on data fusion is constructed. Last, the model is trained and debugged to enable it to predict the voltage sag residual voltage. The accuracy and feasibility of the method are verified by using the actual power grid data from East China. Full article

(This article belongs to the Special Issue Advanced Technologies in Power Quality and Power Disturbance Data Application)

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14 pages, 1864 KiB

Open AccessArticle

Free-Space Continuous-Variable Quantum Key Distribution with Imperfect Detector against Uniform Fast-Fading Channels

by Lu Fan, Yiming Bian, Yichen Zhang and Song Yu

Symmetry 2022, 14(6), 1271; https://doi.org/10.3390/sym14061271 - 20 Jun 2022

Viewed by 1849

Abstract

Free-space continuous-variable quantum key distribution based on atmospheric laser communications is expected to play an important role in the global continuous-variable quantum key distribution network. The practical homodyne detector model is applied in free-space continuous-variable quantum key distribution which models the imperfect characteristics [...] Read more.

Free-space continuous-variable quantum key distribution based on atmospheric laser communications is expected to play an important role in the global continuous-variable quantum key distribution network. The practical homodyne detector model is applied in free-space continuous-variable quantum key distribution which models the imperfect characteristics including the detection efficiency and the electronic noise. In the conventional model, we must calibrate them simultaneously. In the modified model, only one of the imperfections needs to be calibrated to simplify the calibration process of the practical experiments, also known as one-time calibration. The feasibility of the modified detector model against the fast-fading channel is proved. The results of the symmetry operations are considered when presenting detailed security analysis. Some remarkable features of the uniform fast-fading channel were found from the simulation results. The performances of the conventional model and the modified model are similar but the modified model has the advantage of achieving one-time calibration. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Cryptography)

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10 pages, 298 KiB

Open AccessArticle

Spectral Distribution and Numerical Methods for Rational Eigenvalue Problems

by Xiaoping Chen, Wei Wei, Xueying Shi and An Luo

Symmetry 2022, 14(6), 1270; https://doi.org/10.3390/sym14061270 - 20 Jun 2022

Cited by 1 | Viewed by 1589

Abstract

Rational eigenvalue problems (REPs) have important applications in engineering applications and have attracted more and more attention in recent years. Based on the theory of low-rank modification, we discuss the spectral properties and distribution of the symmetric rational eigenvalue problems, and present two [...] Read more.

Rational eigenvalue problems (REPs) have important applications in engineering applications and have attracted more and more attention in recent years. Based on the theory of low-rank modification, we discuss the spectral properties and distribution of the symmetric rational eigenvalue problems, and present two numerical iteration methods for the above REPs. Numerical experiments demonstrate the effectiveness of our proposed methods. Full article

(This article belongs to the Special Issue Selected Papers from the 2021 International Conference on Matrix Inequalities and Matrix Equations)

12 pages, 926 KiB

Open AccessArticle

Differential Response to Cytotoxic Drugs Explains the Dynamics of Leukemic Cell Death: Insights from Experiments and Mathematical Modeling

by Ekaterina Guzev, Svetlana Bunimovich-Mendrazitsky and Michael A. Firer

Symmetry 2022, 14(6), 1269; https://doi.org/10.3390/sym14061269 - 20 Jun 2022

Cited by 2 | Viewed by 2215

Abstract

This study presents a framework whereby cancer chemotherapy could be improved through collaboration between mathematicians and experimentalists. Following on from our recently published model, we use A20 murine leukemic cells transfected with monomeric red fluorescent proteins cells (mCherry) to compare the simulated and [...] Read more.

This study presents a framework whereby cancer chemotherapy could be improved through collaboration between mathematicians and experimentalists. Following on from our recently published model, we use A20 murine leukemic cells transfected with monomeric red fluorescent proteins cells (mCherry) to compare the simulated and experimental cytotoxicity of two Federal Drug Administration (FDA)-approved anticancer drugs, Cytarabine (Cyt) and Ibrutinib (Ibr) in an in vitro model system of Chronic Lymphocytic Leukemia (CLL). Maximum growth inhibition with Cyt (95%) was reached at an 8-fold lower drug concentration (6.25 μM) than for Ibr (97%, 50 μM). For the proposed ordinary differential equations (ODE) model, a multistep strategy was used to estimate the parameters relevant to the analysis of in vitro experiments testing the effects of different drug concentrations. The simulation results demonstrate that our model correctly predicts the effects of drugs on leukemic cells. To assess the closeness of the fit between the simulations and experimental data, RMSEs for both drugs were calculated (both RMSEs < 0.1). The numerical solutions of the model show a symmetrical dynamical evolution for two drugs with different modes of action. Simulations of the combinatorial effect of Cyt and Ibr showed that their synergism enhanced the cytotoxic effect by 40%. We suggest that this model could predict a more personalized drug dose based on the growth rate of an individual’s cancer cells. Full article

(This article belongs to the Special Issue Mathematical Models: Methods and Applications)

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14 pages, 3938 KiB

Open AccessArticle

Optimization for an Indoor 6G Simultaneous Wireless Information and Power Transfer System

by Chien-Ching Chiu, Wei Chien, Po-Hsiang Chen, Yu-Ting Cheng, Hao Jiang and En-Lin Chen

Symmetry 2022, 14(6), 1268; https://doi.org/10.3390/sym14061268 - 19 Jun 2022

Cited by 1 | Viewed by 2023

Abstract

Antenna beamforming for Simultaneous Wireless Information and Power Transfer (SWIPT) and Wireless Power Transfer (WPT) in an indoor 6G communication system is presented in this paper. The objective function is to maximize the total harvesting power for the SWIPT and WPT nodes with [...] Read more.

Antenna beamforming for Simultaneous Wireless Information and Power Transfer (SWIPT) and Wireless Power Transfer (WPT) in an indoor 6G communication system is presented in this paper. The objective function is to maximize the total harvesting power for the SWIPT and WPT nodes with the constraints of the bit error rate and minimum harvesting power. In the study, the power-splitting ratio between harvesting power and decoding information can be adjusted for the SWIPT node. Due to the non-convex problem, we use Self-Adaptive Dynamic Differential Evolution (SADDE) to optimize the designed multi-objective function. We use a symmetric antenna array to study three situations of distance—closer, farther, and similar—between the transmitting antenna and the individual SWIPT and WPT nodes in this paper. Experimental results show that the overall harvesting efficiency is improved, especially in the case of SWIPT nodes closer to the transmitter. The total harvesting power can be improved by 86.7% in the total short-distance case, and by 7.87% in the total long-distance case. Full article

(This article belongs to the Special Issue Selected Papers from IIKII 2022 Conferences)

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17 pages, 856 KiB

Open AccessArticle

An Innovative Framework for Coincidental Correctness Impacting on Fault Localization

by Heling Cao, Lei Li and Yigui Sun

Symmetry 2022, 14(6), 1267; https://doi.org/10.3390/sym14061267 - 19 Jun 2022

Viewed by 1582

Abstract

An important research aspect of Spectrum-Based Fault Localization (SBFL) is the influence factors of the effectiveness of suspiciousness formulas from the perspective of symmetry. Coincidental correctness is one of the most important factors impacting the effectiveness of suspiciousness formulas. The influence of fault [...] Read more.

An important research aspect of Spectrum-Based Fault Localization (SBFL) is the influence factors of the effectiveness of suspiciousness formulas from the perspective of symmetry. Coincidental correctness is one of the most important factors impacting the effectiveness of suspiciousness formulas. The influence of fault localization by coincidental correctness has attracted a large amount of research in the perspective of empirical study; however, it can hardly be considered as sufficiently comprehensive when there are a large number of the symmetrical suspiciousness formulas. Therefore, we first develop an innovative theoretical framework with function derivation investigating suspiciousness formulas impacted by coincidental correctness. We define three types of relations between formulas affected by coincidental correctness: namely, improved type, invariant type and uncertain type. We investigated 30 suspiciousness formulas using this framework and group them into three categories. Furthermore, we conduct an empirical study to verify the effectiveness of SBFL affected by coincidental correctness on four relatively large C programs. We proved that coincidental correctness has a positive effect on 23 out of these 30 formulas, no effect on 5 of them, and the effect on the remaining 2 of them depend on certain conditions. The experimental results show that the effectiveness of some suspiciousness formulas can be enhanced and that of some suspiciousness formulas remain unchanged. Full article

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16 pages, 355 KiB

Open AccessArticle

On the Topological Indices of Commuting Graphs for Finite Non-Abelian Groups

by Fawad Ali, Bilal A. Rather, Nahid Fatima, Muhammad Sarfraz, Asad Ullah, Khalid Abdulkhaliq M. Alharbi and Rahim Dad

Symmetry 2022, 14(6), 1266; https://doi.org/10.3390/sym14061266 - 19 Jun 2022

Cited by 17 | Viewed by 2273

Abstract

A topological index is a number generated from a molecular structure (i.e., a graph) that indicates the essential structural properties of the proposed molecule. Indeed, it is an algebraic quantity connected with the chemical structure that correlates it with various physical characteristics. It [...] Read more.

A topological index is a number generated from a molecular structure (i.e., a graph) that indicates the essential structural properties of the proposed molecule. Indeed, it is an algebraic quantity connected with the chemical structure that correlates it with various physical characteristics. It is possible to determine several different properties, such as chemical activity, thermodynamic properties, physicochemical activity, and biological activity, using several topological indices, such as the geometric-arithmetic index, arithmetic-geometric index, Randić index, and the atom-bond connectivity indices. Consider

G

as a group and H as a non-empty subset of

G

. The commuting graph

C (G, H)

, has H as the vertex set, where

h_{1}, h_{2} \in H

are edge connected whenever

h_{1}

and

h_{2}

commute in

G

. This article examines the topological characteristics of commuting graphs having an algebraic structure by computing their atomic-bond connectivity index, the Wiener index and its reciprocal, the harmonic index, geometric-arithmetic index, Randić index, Harary index, and the Schultz molecular topological index. Moreover, we study the Hosoya properties, such as the Hosoya polynomial and the reciprocal statuses of the Hosoya polynomial of the commuting graphs of finite subgroups of

SL (2, C)

. Finally, we compute the Z-index of the commuting graphs of the binary dihedral groups. Full article

(This article belongs to the Special Issue Topological Indices and Symmetry in Complex Networks)

31 pages, 5655 KiB

Open AccessArticle

New Approach to Cross-Correlation Reflectometry Diagnostics of Nonlocality of Plasma Turbulence

by Alexander B. Kukushkin and Andrei A. Kulichenko

Symmetry 2022, 14(6), 1265; https://doi.org/10.3390/sym14061265 - 19 Jun 2022

Cited by 3 | Viewed by 1574

Abstract

One of the most important properties of stochastic nonlinear processes, including the turbulence of the hydrodynamic motion of continuous media, is distant spatial correlations. To describe them, an approach was proposed by Shlesinger and colleagues based on a linear integro-differential equation with a [...] Read more.

One of the most important properties of stochastic nonlinear processes, including the turbulence of the hydrodynamic motion of continuous media, is distant spatial correlations. To describe them, an approach was proposed by Shlesinger and colleagues based on a linear integro-differential equation with a slowly decaying kernel, which corresponds to superdiffusion (nonlocal) transfer in the regime of Lévy walks (Lévy flights when the finite velocity of the carriers is taken into account). In this paper, we formulate a similar approach that makes it possible to formulate the problem of determining these properties from the scattering spectra of electromagnetic (EM) waves and cross-correlation reflectometry. A universal description of the relationship between the observed symmetric quasi-coherent component in the spectrum of scattered EM waves in plasmas and a process of the Mandelstam–Brillouin scattering type is obtained. It is shown that the nonlocality of spatial correlations of density fluctuations in a turbulent medium is due to long-free-path carriers of the medium’s perturbations, for which the free path distribution function is described by the Lévy distribution. The effectiveness of the proposed method is shown by the example of the interpretation of the data of cross-correlation reflectometry of EM waves in the radio-frequency range for the diagnosis of turbulent plasma in magnetic confinement devices for axisymmetric toroidal thermonuclear plasma. Full article

(This article belongs to the Special Issue Symmetry in Physics of Plasma Technologies)

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22 pages, 856 KiB

Open AccessArticle

Dynamic Event-Triggered Integral Sliding Mode Adaptive Optimal Tracking Control for Uncertain Nonlinear Systems

by Wei Tan, Wenwu Yu and He Wang

Symmetry 2022, 14(6), 1264; https://doi.org/10.3390/sym14061264 - 18 Jun 2022

Cited by 4 | Viewed by 1885

Abstract

In this paper, we study the event-triggered integral sliding mode optimal tracking problem of nonlinear systems with matched and unmatched disturbances. The goal is to design an adaptive dynamic programming-based sliding-mode controller, which stabilizes the closed-loop system and guarantees the optimal performance of [...] Read more.

In this paper, we study the event-triggered integral sliding mode optimal tracking problem of nonlinear systems with matched and unmatched disturbances. The goal is to design an adaptive dynamic programming-based sliding-mode controller, which stabilizes the closed-loop system and guarantees the optimal performance of the sliding-mode dynamics. First, in order to remove the effects of the matched uncertainties, an event-triggered sliding mode controller is designed to force the state of the systems on the sliding mode surface without Zeno behavior. Second, another event-triggered controller is designed to suppress unmatched disturbances with a nearly optimal performance while also guaranteeing Zeno-free behavior. Finally, the benefits of the proposed algorithm are shown in comparison to several traditional triggering and learning-based mechanisms. Full article

(This article belongs to the Special Issue Recent Advances in Sliding Mode Control/Observer and Its Applications)

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29 pages, 9539 KiB

Open AccessArticle

Numerical Model Validation for Detection of Surface Displacements over Twin Tunnels from Metro Line 1 in the Historical Area of Seville (Spain)

by Maziyar Bahri, Emilio J. Mascort-Albea, Rocío Romero-Hernández, Mohammadreza Koopialipoor, Cristina Soriano-Cuesta and Antonio Jaramillo-Morilla

Symmetry 2022, 14(6), 1263; https://doi.org/10.3390/sym14061263 - 18 Jun 2022

Cited by 8 | Viewed by 2317

Abstract

In order to solve connectivity problems in metropolitan areas, the development of underground metro lines constitutes an unquestionable requirement. However, the construction work thereof encounters unfavourable circumstances when surface excavations must be carried out that cross historical areas of the city, due to [...] Read more.

In order to solve connectivity problems in metropolitan areas, the development of underground metro lines constitutes an unquestionable requirement. However, the construction work thereof encounters unfavourable circumstances when surface excavations must be carried out that cross historical areas of the city, due to the need to control surface movements. The design of the metro in the city of Seville (Spain) from 2004 to 2006 provides a representative example of this situation and triggered major upheavals that exerted repercussions on historical buildings. For these reasons, the excavation stages of Line 1 of this metro have been simulated by numerical methods using FLAC3D software and validated with the results provided by the real conditions. Consequently, various surface settlements have been evaluated by taking not only variates of the main parameters that characterise the soil of Seville, but also of the various load situations and excavation conditions. Notable results have been achieved through calibration of 54 variants of the same model corresponding to Line 1, and their comparison with the real results obtained in nine critical areas of the itinerary. The results obtained have made it possible to determine the effects of excavation on the subsoil of the city of Seville with great accuracy, since the percentage error of calculated vertical surface movements varies from 0.1% to 5.3%. Full article

(This article belongs to the Special Issue Applied Mechanics, Engineering and Modeling)

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12 pages, 9104 KiB

Open AccessFeature PaperArticle

A Scent of Peppermint—A Microwave Spectroscopy Analysis on the Composition of Peppermint Oil

by Anna Krin, María Mar Quesada Moreno, Cristóbal Pérez and Melanie Schnell

Symmetry 2022, 14(6), 1262; https://doi.org/10.3390/sym14061262 - 18 Jun 2022

Cited by 3 | Viewed by 6064

Abstract

Essential oils have a vast number of applications in different areas of our daily life. Detailed chiral analysis and structural characterization of their constituents remains an important subject in analytical chemistry. Here, we report on a broadband rotational spectroscopy study of peppermint oil [...] Read more.

Essential oils have a vast number of applications in different areas of our daily life. Detailed chiral analysis and structural characterization of their constituents remains an important subject in analytical chemistry. Here, we report on a broadband rotational spectroscopy study of peppermint oil in the frequency range 2–8 GHz. We focus on an unambiguous determination of the excess enantiomers of the oil constituents menthone and isomenthone in the oil by applying chirality-sensitive rotational spectroscopy, the so-called microwave three-wave mixing (M3WM) technique. Additionally, a new menthol conformer, not previously characterized, was experimentally observed, and the gas-phase structures of the two conformers of menthol and menthone were determined experimentally based on the assignment of their

^{13} C

-isotopologues in natural abundance. Full article

(This article belongs to the Special Issue Asymmetric Molecules and Chirality Recognition)

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15 pages, 1939 KiB

Open AccessArticle

Stress Point Monitoring Algorithm for Structure of Steel Cylinder Concrete Pipes in Large Buildings

by Huabin Yang and Suo Jiang

Symmetry 2022, 14(6), 1261; https://doi.org/10.3390/sym14061261 - 18 Jun 2022

Viewed by 1699

Abstract

The internal structure of steel cylinder concrete pipe in large buildings is complex. Traditionally, the safety monitoring method is unable to accurately monitor the situation of every stress point in the structure. Therefore, the wireless sensor network with practical value in the field [...] Read more.

The internal structure of steel cylinder concrete pipe in large buildings is complex. Traditionally, the safety monitoring method is unable to accurately monitor the situation of every stress point in the structure. Therefore, the wireless sensor network with practical value in the field of building safety monitoring was introduced. A monitoring algorithm for stress points in pipeline structure was put forward. The distribution law of circumferential prestress produced by prestress steel wire on the pipe core concrete was analyzed. According to the influencing factors, the mechanical performance of tube concrete pipe structure was discussed, and the method of calculating prestress of pipe structure was constructed. Combined with sensor network nodes, a series of basic hypothesis information was set. Moreover, the force between node and stress point was analyzed by virtual potential field. Based on the force analysis for the centroid of the sensing area, the monitoring of the stress point in pipeline structures was completed. After that, a rectangular area to be monitored was selected and the force points were established randomly. According to the relationship between network coverage rate and monitoring efficiency, we found that the proposed algorithm had good network immunity. According to the different number of nodes, sensing radii and perception angles, the influence of index on the monitoring accuracy was discussed. Experimental results show that the accuracy of the proposed algorithm is sensitive to the change of node parameter. When the number of nodes, sensing radius and sensing angle change, the maximum fluctuation range of monitoring accuracy is 0.08–0.99. From the application effect of the algorithm, we can see that the detection effect of the algorithm has obvious advantage. Full article

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9 pages, 248 KiB

Open AccessArticle

Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus

by Vuk Stojiljković, Slobodan Radojević, Eyüp Çetin, Vesna Šešum Čavić and Stojan Radenović

Symmetry 2022, 14(6), 1260; https://doi.org/10.3390/sym14061260 - 18 Jun 2022

Cited by 5 | Viewed by 2008

Abstract

Sharp bounds for

\frac{cosh (x)}{x}, \frac{sinh (x)}{x}

, and

\frac{sin (x)}{x}

were obtained, as well as one new bound for

\frac{e^{x} + arctan (x)}{\sqrt{x}}

. A new situation to [...] Read more.

Sharp bounds for

\frac{cosh (x)}{x}, \frac{sinh (x)}{x}

, and

\frac{sin (x)}{x}

were obtained, as well as one new bound for

\frac{e^{x} + arctan (x)}{\sqrt{x}}

. A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann–Liovuille fractional integral and in terms of the standard integral. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis)

10 pages, 776 KiB

Open AccessArticle

Motor Skills Training Program Reinforces Crossing the Body’s Midline in Children with Developmental Coordination Disorder

by Orifjon Saidmamatov, Paula Rodrigues and Olga Vasconcelos

Symmetry 2022, 14(6), 1259; https://doi.org/10.3390/sym14061259 - 17 Jun 2022

Cited by 2 | Viewed by 3481

Abstract

Midline crossing problems have been associated with children with atypical development. When compared to typical development (TD) children, they are less likely to cross the midline into contralateral space with their preferred hand. A motor skills training program is the most beneficial intervention [...] Read more.

Midline crossing problems have been associated with children with atypical development. When compared to typical development (TD) children, they are less likely to cross the midline into contralateral space with their preferred hand. A motor skills training program is the most beneficial intervention for children with developmental coordination disorder (DCD). However, there is not enough information on how this intervention will affect crossing the midline. The goal of this study was to find out midline crossing behavior after an intervention program for children with DCD. The Movement Assessment Battery for Children (MABC-2) was used to assess motor coordination, and Bishop’s card-reaching task measured the ability of children to cross the midline. The study included 48 right-handed children, 28 with TD and 20 with DCD (5.17 ± 0.70 years) from four preschools in the Khorezm region (Uzbekistan). Participants identified as having DCD were placed in an experimental group (EG: n = 15), receiving ten weeks of a motor skills training program, and a control group (CG: n = 5). Concerning midline crossing behavior before intervention, DCD children showed more contralateral and less midline right-hand use compared to TD children. After intervention, a significant group × position interaction was found between the EG and CG at positions 1 and 4, and between the EG and TD group at position 4. Concerning the midline reaching, fewer right-hand reaches were made by the EG group compared to the other two groups. The same could be seen at position 1 when compared to the CG group. It can be concluded that, after intervention, DCD children in the EG showed fewer right-hand reaches in the contralateral space, but they improved their right-hand reaches in the midline, showing a similar behavior to TD children. Full article

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9 pages, 386 KiB

Open AccessArticle

The Surviving Rate of IC-Planar Graphs

by Xiaoxue Hu, Jiacheng Hu and Jiangxu Kong

Symmetry 2022, 14(6), 1258; https://doi.org/10.3390/sym14061258 - 17 Jun 2022

Viewed by 1514

Abstract

Let k and n be two positive integers. Firefighting is a discrete dynamical process of preventing the spread of fire. Let G be a connected graph G with n vertices. Assuming a fire starts at one of the vertices of G, the [...] Read more.

Let k and n be two positive integers. Firefighting is a discrete dynamical process of preventing the spread of fire. Let G be a connected graph G with n vertices. Assuming a fire starts at one of the vertices of G, the firefighters choose k unburned vertices at each step, and then the fire spreads to all unprotected neighbors of the burning vertices. The process continues until the fire stops spreading. The goal is to protect as many vertices as possible. When a fire breaks out randomly at a vertex of G, its k-surviving rate,

ρ_{k} (G)

, is the expected number of saved vertices. A graph is IC-planar if it has a drawing in which each edge cross once and their endpoints are disjoint. In this paper, we prove that

ρ_{4} (G) > \frac{1}{124}

for every IC-planar graph G. This is proven by the discharging method and the locally symmetric of the graph. Full article

(This article belongs to the Special Issue Symmetry in Graph and Hypergraph Theory)

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12 pages, 1076 KiB

Open AccessArticle

Subjective and Objective Evaluation of the Symmetry of Maxillary Incisors among Residents of Southwest Poland

by Paulina Chrapla, Anna Paradowska-Stolarz and Katarzyna Skoskiewicz-Malinowska

Symmetry 2022, 14(6), 1257; https://doi.org/10.3390/sym14061257 - 17 Jun 2022

Cited by 13 | Viewed by 2553

Abstract

Dental aesthetics is an essential factor affecting people’s psychosocial wellbeing. One of the most critical components of an aesthetic smile is symmetry within the dentition. Dentists and orthodontists, unlike laypersons, are critical in assessing dental aesthetics. This study aimed to evaluate the accuracy [...] Read more.

Dental aesthetics is an essential factor affecting people’s psychosocial wellbeing. One of the most critical components of an aesthetic smile is symmetry within the dentition. Dentists and orthodontists, unlike laypersons, are critical in assessing dental aesthetics. This study aimed to evaluate the accuracy of patients’ assessment of the symmetry of their maxillary incisors and some factors that influence it. The study was conducted on 83 participants aged from 11 to 39 years. First, the participants filled out a questionnaire to obtain patients’ opinions of the symmetry of their upper incisors. This stage was followed by an intraoral examination, during which we used a digital caliper to measure the width of four maxillary incisors. The data were entered into STATISTICA v. 13.3. The following conclusions were drawn from the study. First, the respondents were generally able to determine the asymmetry of the incisors. Second, among the maxillary incisors, the participants defined the symmetry of maxillary central incisors more accurately than the maxillary lateral incisors. The cut-off value for incisor asymmetry noticeable to a layperson is 0.2 mm for maxillary medial incisors and 0.55 for maxillary lateral incisors. Third, we found no dependence of the accuracy of the assessment of incisor asymmetry on the age of the subjects; however, in our study group, the age range (spread) was not significant, so further studies are recommended. Finally, results concerning the relationship with gender showed that males assess the level of symmetry of their maxillary incisors more accurately than females. Full article

(This article belongs to the Special Issue Dentofacial Asymmetry — Challenges and Perspectives)

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14 pages, 4322 KiB

Open AccessArticle

Digital Integration of LiDAR System Implemented in a Low-Cost FPGA

by Jiajian Huang, Shengyao Ran, Wei Wei and Qun Yu

Symmetry 2022, 14(6), 1256; https://doi.org/10.3390/sym14061256 - 17 Jun 2022

Cited by 5 | Viewed by 4287

Abstract

With the development of artificial intelligence, LiDAR finds significant applications in robotics and autonomous driving. Aiming at increasing the compactness and the integration of 2-D LiDAR, this paper presents a highly digitally integrated 2-D LiDAR system implemented in a low-cost FPGA. The system [...] Read more.

With the development of artificial intelligence, LiDAR finds significant applications in robotics and autonomous driving. Aiming at increasing the compactness and the integration of 2-D LiDAR, this paper presents a highly digitally integrated 2-D LiDAR system implemented in a low-cost FPGA. The system is made of off-the-shelf components to limit the cost to USD 100. A laser transceiver with a symmetrical transmitting and receiving lens emits and collects laser pulses to range distance using the time-of-flight (ToF) method. As a key component in ToF, the FPGA-based time-to-digital converter (TDC) is adopted for counting the round-trip time of pulses, which is implemented in a low-cost FPGA of ZYNQ7010 with limited resources. The symmetrical structure of the delay line is used to design a more efficient TDC. The FPGA-TDC enables flexibility of design and integration with more functional logics and is microcontroller-free. All the digital logics including data processing and controlling are integrated into an FPGA with the TDC logics to realize fully digital integration and compact dimensions. The utilization of the whole architecture in the FPGA is about 15%. The experimental results demonstrated that the ranging accuracy of the LiDAR is about 2 cm, which is suitable for consumer electronics. Full article

(This article belongs to the Special Issue New Advances in New-Generation Communication and Symmetry)

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17 pages, 293 KiB

Open AccessArticle

Study of Weak Solutions for a Class of Degenerate Parabolic Variational Inequalities with Variable Exponent

by Yudong Sun and Huan Wang

Symmetry 2022, 14(6), 1255; https://doi.org/10.3390/sym14061255 - 17 Jun 2022

Cited by 5 | Viewed by 1730

Abstract

The authors of this text study weak solutions to the variational inequalities with degenerate parabolic operators and symmetric structure in Sobolev spaces with variable exponent. The existence and uniqueness of the solutions are treated by using the penalty method and the reduction method [...] Read more.

The authors of this text study weak solutions to the variational inequalities with degenerate parabolic operators and symmetric structure in Sobolev spaces with variable exponent. The existence and uniqueness of the solutions are treated by using the penalty method and the reduction method in the weak sense. The authors also discuss the nonexistence and long-time behavior of solutions. Full article

(This article belongs to the Section Mathematics)

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18 pages, 3248 KiB

Open AccessArticle

ShChain_3D-ResNet: Sharding Blockchain with 3D-Residual Network (3D-ResNet) Deep Learning Model for Classifying DDoS Attack in Software Defined Network

by E. Fenil and P. Mohan Kumar

Symmetry 2022, 14(6), 1254; https://doi.org/10.3390/sym14061254 - 16 Jun 2022

Cited by 3 | Viewed by 2126

Abstract

The distributed denial of service (DDoS) vulnerabilities have rapidly extended and have been given different possibilities for even more advanced assaults on specific targets in recent times, thanks to the growth of innovative technology such as the Internet of Things (IoT) and Software-Defined [...] Read more.

The distributed denial of service (DDoS) vulnerabilities have rapidly extended and have been given different possibilities for even more advanced assaults on specific targets in recent times, thanks to the growth of innovative technology such as the Internet of Things (IoT) and Software-Defined Networking (SDN). The attack patterns route comprises unprotected and susceptible IoT systems that are internet-connected, as well as denial of service weaknesses in the SDN controllers, such as southbound connection exhaustion. (1) Background: The review does not go into detail about the symmetry blockchain approaches used to mitigate DDoS attacks, nor does it classify them in IoT; (2) To overcome the privacy issues, a novel deep learning-based privacy preservation method was proposed named ShChain_3D-ResNet. This novel method combines Sharding, blockchain and Residual Network for securing the SDN. Under this network, the proposed efficient attention module jointly learns attention to enforce the symmetry on weights for various channels in spatial dimension as well as attention weights of multiple frames in temporal dimension assistance of pre-training, updating, and dense convolution process; (3) Results: the proposed ShChain_3D-ResNet achieves 95.6% of accuracy, 97.3% of precision, 95.2% of recall, 94.4% of F1-score, 32.5 ms of encryption time and 35.2 ms of decryption time for dataset-1. Further, it achieves 97.3% accuracy, 95.3% precision, 96.1% recall, 98.2% F1-score, 32.1 ms of encryption time, and 36.2 ms of decryption time for dataset-2; (4) Conclusions: The Sharding strategy can increase ShChain performance while simultaneously utilizing Multi User (MU) resources for SDN. Full article

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18 pages, 4562 KiB

Open AccessArticle

A Hybrid Particle Swarm Optimization-Based Wavelet Threshold Denoising Algorithm for Acoustic Emission Signals

by Farrukh Hassan, Lukman Ab. Rahim, Ahmad Kamil Mahmood and Saad Adnan Abed

Symmetry 2022, 14(6), 1253; https://doi.org/10.3390/sym14061253 - 16 Jun 2022

Cited by 10 | Viewed by 2614

Abstract

Acoustic emission (AE) as a non-destructive monitoring method is used to identify small damage in various materials effectively. However, AE signals acquired during the monitoring of oil and gas steel pipelines are always contaminated with noise. A noisy signal can be a threat [...] Read more.

Acoustic emission (AE) as a non-destructive monitoring method is used to identify small damage in various materials effectively. However, AE signals acquired during the monitoring of oil and gas steel pipelines are always contaminated with noise. A noisy signal can be a threat to the reliability and accuracy of the findings. To address these shortcomings, this study offers a technique based on discrete wavelet transform to eliminate noise in these signals. The denoising performance is affected by several factors, including wavelet basis function, decomposition level, thresholding method, and the threshold selection criteria. Traditional threshold selection rules rely on statistical and empirical variables, which influence their performance in noise reduction under various conditions. To obtain the global best solution, a threshold selection approach is proposed by integrating particle swarm optimization and the late acceptance hill-climbing heuristic algorithms. By comparing five common approaches, the superiority of the suggested technique was validated by simulation results. The enhanced thresholding solution based on particle swarm optimization algorithm outperformed others in terms of signal-to-noise ratio and root-mean-square error of denoised AE signals, implying that it is more effective for the detection of AE sources in oil and gas steel pipelines. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Damage Detection, Wavelet Transformation and Applied Mechanics)

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14 pages, 337 KiB

Open AccessArticle

The Outer-Planar Anti-Ramsey Number of Matchings

by Changyuan Xiang, Yongxin Lan, Qinghua Yan and Changqing Xu

Symmetry 2022, 14(6), 1252; https://doi.org/10.3390/sym14061252 - 16 Jun 2022

Viewed by 1602

Abstract

A subgraph H of an edge-colored graph G is called rainbow if all of its edges have different colors. Let

a r (G, H)

denote the maximum positive integer t, such that there is a t-edge-colored graph G [...] Read more.

A subgraph H of an edge-colored graph G is called rainbow if all of its edges have different colors. Let

a r (G, H)

denote the maximum positive integer t, such that there is a t-edge-colored graph G without any rainbow subgraph H. We denote by

k K_{2}

a matching of size k and

O_{n}

the class of all maximal outer-planar graphs on n vertices, respectively. The outer-planar anti-Ramsey number of graph H, denoted by

a r (O_{n}, H)

, is defined as

max {a r (O_{n}, H) | O_{n} \in O_{n}}

. It seems nontrivial to determine the exact values for

a r (O_{n}, H)

because most maximal outer-planar graphs are asymmetry. In this paper, we obtain that

a r (O_{n}, k K_{2}) \leq n + 3 k - 8

for all

n \geq 2 k

and

k \geq 6

, which improves the existing upper bound for

a r (O_{n}, k K_{2})

, and prove that

a r (O_{n}, k K_{2}) = n + 2 k - 5

for

n = 2 k

and

k \geq 5

. We also obtain that

a r (O_{n}, 6 K_{2}) = n + 6

for all

n \geq 29

. Full article

(This article belongs to the Special Issue Symmetry in Graph and Hypergraph Theory)

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27 pages, 6261 KiB

Open AccessArticle

Symplectic Dynamics and Simultaneous Resonance Analysis of Memristor Circuit Based on Its van der Pol Oscillator

by Baonan Yang, Zhen Wang, Huaigu Tian and Jindong Liu

Symmetry 2022, 14(6), 1251; https://doi.org/10.3390/sym14061251 - 16 Jun 2022

Cited by 5 | Viewed by 2282

Abstract

A non-autonomous memristor circuit based on van der Pol oscillator with double periodically forcing term is presented and discussed. Firstly, the differences of the van der Pol oscillation of memristor model between Euler method and symplectic Euler method, four-order Runge–Kutta method (RK4) and [...] Read more.

A non-autonomous memristor circuit based on van der Pol oscillator with double periodically forcing term is presented and discussed. Firstly, the differences of the van der Pol oscillation of memristor model between Euler method and symplectic Euler method, four-order Runge–Kutta method (RK4) and four-order symplectic Runge–Kutta–Nyström method (SRKN4), symplectic Euler method and RK4 method, and symplectic Euler method and SRKN4 method in preserving structure are compared from theoretical and numerical simulations, the symmetry and structure preserving and numerical stability of symplectic scheme are demonstrated. Moreover, the analytic solution of the primary and subharmonic simultaneous resonance of this system is obtained by using the multi-scale method. Finally, based on the resonance relation of the system, the chaotic dynamics behaviors with different parameters are studied. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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