Traditional Perturbation Method Research Articles

Impact of relativistic positron beam on ion-acoustic solitary, periodic and breather waves in Earths' ionospheric region through the framework of KdV and modified KdV equation

Abstract This study explores the propagation characteristics of ion-acoustic periodic, soliton, and breather waves in electron-positron-ion (EPI) plasma with a relativistic positron beam. The Korteweg-de Vries (KdV) equation is obtained by applying the traditional reductive perturbation method (RPM) to the fundamental set of fluid equations. When the KdV model is unable to accurately represent the nonlinear system's evolution, a modified Korteweg-de Vries (mKdV) equation is constructed. In both models, Jacobi elliptic functions are used to derive periodic solutions, and a connection between periodic waves and soliton solutions is established. Hirota's bilinear method is used to generate breathers directly from the KdV type framework without utilizing the modified Schrodinger framework inferred from the KdV type framework, which is a prevalent method in studies of nonlinear waves. Numerical knowledge of various physical factors in the ionospheric region is incorporated into the model to elucidate wave propagation in the Earth's upper atmosphere.

An Innovative Approach in Inspecting a Damped Mathieu Cubic–Quintic Duffing Oscillator

Abstract Purpose The objective of the present study is to analyze a damped Mathieu–cubic quintic Duffing oscillator as a parametric nonlinear oscillatory dynamical system. This equation has multiple applications in diverse fields, including optics, quantum physics, and general relativity. There are multiple concerns related to periodic motion and the analysis of boundary-value problems with elliptic symmetries. The current effort aims to determine the frequency amplitude of parametric nonlinear issues. Method The non-perturbative approach (NPA) is employed to transform the nonlinear ordinary differential equation (ODE) into a linear equation. The derivation of the approximate solutions is achieved without relying on typical perturbation approaches, separate from the series expansion. Hence, the objective of this study is to depart from traditional perturbation methods and acquire approximated solutions for minor amplitude parametric components without imposing any limitations. Furthermore, the technique is extended to ascertain optimal solutions for the nonlinear large amplitude of fluctuation. Results The current approach allows for rapid estimation of the frequency-amplitude relationship in order to attain successive approximations of the solutions for parametric nonlinear fluctuations. A validation is obtained for the derived parametric equation, demonstrating a high level of agreement with the original equation. An analysis of stability behavior is conducted in multiple scenarios. In addition, the Floquet theory is used to examine the transition curves. Conclusion The current technique is characterized by its clear principles, making it practical, user-friendly, and capable of achieving exceptionally high numerical precision. The current approach is highly beneficial for addressing nonlinear parametric problems due to its ability to minimize algebraic complexity during implementation.

Relevant interval perturbation method for uncertainty analysis of structural–acoustic coupling model

The parameters in structural–acoustic coupling models are often coupled with each other, and the independence of the uncertain parameters is a necessary condition for using the traditional interval perturbation method. This article proposes a relevant interval perturbation method for the uncertainty analysis of a structural–acoustic coupling model with uncertain-but-bounded parameters. Aiming at the linear inequality constraint relationship in the uncertain parameters, this method introduces a sensitivity ranking mechanism for the uncertainty parameters, which overcomes the limitation of uncertain parameter independence in the traditional interval model, and effectively restrains the interval expansion phenomenon of the system response in the uncertainty analysis. Through numerical examples, it is demonstrated that the relevant interval perturbation analysis method can effectively solve a constrained problem when there are uncertain parameters, and the obtained response interval radius is smaller than that of the traditional method under constraint conditions.

Analytic Nuclear Gradients for Complete Active Space Linearized Pair-Density Functional Theory.

Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings, as well as the inherently multiconfigurational character of excited states. As such, one needs a multistate method that incorporates state interaction in order to accurately model the potential energy surface at all nuclear coordinates. The recently developed linearized pair-density functional theory (L-PDFT) is a multistate extension of multiconfiguration PDFT, and it has been shown to be a cost-effective post-MCSCF method (as compared to more traditional and expensive multireference many-body perturbation methods or multireference configuration interaction methods) that can accurately model potential energy surfaces in regions of strong nuclear-electronic coupling in addition to accurately predicting Franck-Condon vertical excitations. In this paper, we report the derivation of analytic gradients for L-PDFT and their implementation in the PySCF-forge software, and we illustrate the utility of these gradients for predicting ground- and excited-state equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.

A novel approach to evaluate dynamic performance for photovoltaic system using software platform

With the growing demand for renewable energy, solar photovoltaic (PV) systems have gained popularity as a reliable source of clean electricity. However, the performance of these systems can be limited by factors such as suboptimal maximum power point tracking (MPPT) algorithms. In order to improve the power generation efficiency of PV systems, it is important to evaluate the performance of dynamic MPPT algorithms that can adapt to varying operating conditions. Traditionally, such evaluations have been time consuming and expensive, often requiring extensive testing and measurement equipment. In this paper, we propose a novel approach to evaluate dynamic MPPT performance very quickly and simply using PSIM software. This approach enables accurate and efficient evaluation of MPPT performance under a wide range of operating conditions, while minimizing the cost and time involved in traditional testing methods. When applying the proposed method to a 3.7 kW inverter using the traditional perturbation and observation (P and O) method, we found that the highest average efficiency was 98.92% at an MPPT control period of 0.1s and a voltage perturbation of 1 V. This evaluation technique provides valuable insights into the design and optimization of more efficient MPPT control algorithms, leading to improved power generation efficiency and increased adoption of solar PV systems.

Existence of both compressional and rarefactive nonlinear solitary waves in a chain of dust particles

Not only the compressional dust acoustic solitary wave, but also the rarefactive one in a chain of the dust particles are verified by using the molecular dynamics simulation method. The compressional dust acoustic solitary wave is also obtained by using the traditional reductive perturbation method, while the rarefactive dust acoustic solitary wave solution is fitted by the numerical simulation results. The application scope of the traditional reductive perturbation method to derive compressional dust acoustic solitary waves in a chain of the dust particles is given. The application scope of the fitted results of the rarefactive dust acoustic solitary waves is also given.

An improved homotopy perturbation method for dynamic force reconstruction

In many engineering application, it is still a challenge in directly obtaining external force acting on structures. Moreover, many researchers attach more attention to indirect measurement technology using some response signals. This paper presents an improved homotopy perturbation method (IHPM) for dynamic load identification. This method can identify multi-source dynamic sine and triangle force. Firstly, the present method is proposed based on improved homotopy operator. Secondly, the sequence that the present method generates is proved to be a Cauchy sequence when ‖Aeα−I‖<1. Finally, the proposed method is applied to the dynamic load identification of hanging basket structure. Numerical simulations verify the stability and effectiveness of the newly developed method, and also validate that it is superior to the traditional homotopy perturbation method (HPM) and Tikhonov regularization method.

An Evaluated PMCHWT Solution of EM Scattering for Mutimedium Targets With Variant Permittivities

An evaluated PMCHWT is formulated in terms of the asymptotic waveform evaluation (AWE) technique to predict the scattering characteristics of multi-medium targets. At first the uncertain dielectric constant can vary within a certain range by setting it as the permittivity variable. Then the evaluated PMCHWT is constructed with these permittivity variables. Noted that the inversion of the impedance matrix is needed only once and the moment matching technique is used in the process of recursion. Moreover, the high-order derivatives are applied in order to obtain the greater convergence radius. Finally, the impedance matrix, right vector and the current density are expanded with the Taylor series. And the current density is approximated by the reduced order rational Padé function. Compared with the traditional perturbation method, greater radius of convergence can be obtained by using the proposed method. In addition, higher efficiency can be gotten than the general Monte Carlo (MC) method.

Configurational entropy as a probe of the stability condition of compact objects

We systematically extend the statement that the configurational entropy provides an alternative approach to studying gravitational stability of compact objects, carried out in the previous work of M. Gleiser and N. Jiang, Phys. Rev. D {\bf 92}, 044046 (2015). Inspired by that paper, we try to answer the crucial question: Is there any one-to-one correspondence between the minimum of the configurational entropy and the stability point for each realistic equation of state? In view of the above question, we focus on neutron stars, quark stars, as well as on the third family of compact stars (hybrid stars), where a possible phase transition may lead to the existence of twin stars (stars with equal mass but different radius). In each case, we use a large set of equations of state investigating the possibility to find correlations between the stability region obtained from the traditional perturbation methods to the one obtained by the minimum of configurational entropy. We found that the suggested prediction of the stability by the minimization of the configurational entropy, concerning neutron stars and quark stars, does not have, at least quantitatively, universal validity. However, in several cases it qualitatively predicts the existence of the stability point. In conclusion, the configurational entropy, can be considered as an additional tool which enters into the quiver for studying the stability of compact objects such as for example neutron and quark stars, but taking into account that the accuracy of the predictions depends on the specific character of each equation of state.

A symplectic homotopy perturbation method for random structural dynamics response analysis based on Birkhoffian systems

With the enhancement of the engineering structure complexity, numerical computation plays a prominent role in structural dynamics analysis. In theory, general mechanical systems can be transformed into Birkhoffian forms, whose matching symplectic numerical algorithms perform well in accuracy and stability. Besides, the influence of uncertainty cannot be ignored in practical engineering, but the research on uncertainty symplectic algorithms of Birkhoffian systems is still weak. This paper proposes a symplectic homotopy perturbation method (SHPM) for general Birkhoffian equations with random uncertainties. Different from the traditional perturbation method, the proposed method does not depend on small parameters. Based on the homotopy perturbation method, embedded parameters are introduced to establish the matrix and parameter perturbation equations of random Birkhoffian equations, respectively. Then the formulas for calculating the mean value and standard deviation of the response are derived with probability theory. Combined with Birkhoffian symplectic preserving algorithms, a symplectic homotopy perturbation method for the numerical solution of random Birkhoffian equations is proposed. Finally, numerical examples are given to verify the applicability and effectiveness of the proposed method and its superiority compared with the traditional non-symplectic method.

Peristaltic Transport of Carreau Coupled Stress Nanofluid with Cattaneo-Christov Heat Flux Model Inside a Symmetric Channel

The current analytical study is concerned with studying the impact of Cattaneo-Christov heat flux of an incompressible flow which obeys Carreau nanofluid inside a symmetric channel in the existence of the porous medium. The impacts of couple stress, heat generation absorption, joule heating, couple stress viscous dissipation with Soret as well as Dufour numbers are all presumed. Long wavelength and law Reynold’s number approximations are utilized for solving the governing system of equations. Furthermore, the traditional perturbation method together with the homotopy perturbation technique (HPM) are applied to obtain the resultant solutions of these equations. The different physical parameters on velocity, temperature and nanoparticles concentration distributions are illustrated through a set of graphs. It is found that the elevate in the slip velocity parameter dwindle the velocity. Meanwhile, the rise in the value of thermal relaxation time parameter led to decay the temperature of the fluid. Over and above, enhancing the nano Biot number value caused an enrichment in the concentration of nanofluid.

A New Nonlinear Photothermal Iterative Theory for Port-Wine Stain Detection.

The development of appropriate photothermal detection of skin diseases to meet complex clinical demands is an urgent challenge for the prevention and therapy of skin cancer. An extensive body of literature has ignored all high-order harmonics above the second order and their influences on low-order harmonics. In this paper, a new iterative numerical method is developed for solving the nonlinear thermal diffusion equation to improve nonlinear photothermal detection for the noninvasive assessment of the thickness of port-wine stain (PWS). First, based on the anatomical and structural properties of skin tissue of PWS, a nonlinear theoretical model for photothermal detection is established. Second, a corresponding nonlinear thermal diffusion equation is solved by using the new iterative numerical method and taking into account harmonics above the second-order and their effects on lower-order harmonics. Finally, the thickness and excitation light intensity of PWS samples are numerically simulated. The simulation results show that the numerical solution converges fasterand the physical meaning of the solution is clearerwith the new method than with the traditional perturbation method. The rate of change in each harmonic with the sample thickness for the new method is higher than that for the conventional perturbation method, suggesting that the proposed numerical method may provide greater detection sensitivity. The results of the study provide a theoretical basis for the clinical treatment of PWS.

Investigation of an arbitrary solitary wave and head on collision between two solitary waves in a strongly coupled complex plasma

By using the traditional perturbation method and recently proposed equation of state of the strongly coupled complex plasma: , the nonlinear wave in a monolayer complex plasma is studied. The trajectories of two solitary waves propagating in the opposite directions under different plasma parameters are given. It is shown that the solitary waves suffer a time delay after collision. The dependence of the phase shifts on the plasma parameters such as the screening parameter κ, coupling strength parameters Γ are given in the present paper for a monolayer complex plasma. Moreover, a traditional Sagdeev potential method is used to study an arbitrary amplitude nonlinear wave in a monolayer complex plasma. It is found that there is a limit of the propagation wave speed of the solitary wave in a monolayer complex plasma. The nonlinear wave speed is larger than the sound speed, while it is less than times of the sound speed for our given system parameters. The comparisons between the results obtained from the Sagdeev potential method and that from the reductive perturbation method are given for small amplitude waves. It is found that both are good agreements. Therefore, the arbitrary amplitude solitary waves solution in a monolayer complex plasma obtained by the Sagdeev potential method are correct.

Optimized Control Strategy for Photovoltaic Hydrogen Generation System with Particle Swarm Algorithm

Distributed generation is a vital component of the national economic sustainable development strategy and environmental protection, and also the inevitable way to optimize energy structure and promote energy diversification. The power generated by renewable energy is unstable, which easily causes voltage and frequency fluctuations and power quality problems. An adaptive online adjustment particle swarm optimization (AOA-PSO) algorithm for system optimization is proposed to solve the technical issues of large-scale wind and light abandonment. Firstly, a linear adjustment factor is introduced into the particle swarm optimization (PSO) algorithm to adaptively adjust the search range of the maximum power point voltage when the environment changes. In addition, the maximum power point tracking method of the photovoltaic generator set with direct duty cycle control is put forward based on the basic PSO algorithm. Secondly, the concept of recognition is introduced. The particles with strong recognition ability directly enter the next iteration, ensuring the search accuracy and speed of the PSO algorithm in the later stage. Finally, the effectiveness of the AOA-PSO algorithm is verified by simulation and compared with the traditional control algorithm. The results demonstrate that the method is effective. The system successfully tracks the maximum power point within 0.89 s, 1.2 s faster than the traditional perturbation and observation method (TPOM), and 0.8 s faster than the incremental admittance method (IAM). The average maximum power point is 274.73 W, which is 98.87 W higher than the TPOM and 109.98 W more elevated than the IAM. Besides, the power oscillation range near the maximum power point is small, and the power loss is slight. The method reported here provides some guidance for the practical development of the system.

K-Anonymization approach for privacy preservation using data perturbation techniques in data mining

Nowadays, privacy is a big issue for everyone because the internet generates and shares massive amounts of data every day. Because traditional privacy-preserving techniques do not protect sensitive data well enough, malicious attacks on sensitive data are possible. Traditional methods may have many drawbacks due to various attacks on sensitive data. Thus, data must be preserved before being shared with others. K-Anonymity protects privacy. By definition, anonymization means that a person is not identifiable, traceable, or reachable. Anonymization using k-anonymity protects data privacy and protects entire datasets. The traditional data perturbation method only works with numerical data, but the proposed method is designed to work with categorical data. The Proposed Framework perturbs data for multiple columns at once. The proposed framework's performance is evaluated in two ways. Initially, it keeps the data mining model accurate. Second, it protects the original data privacy while minimizing data loss. The main motivation for using k-anonymity is to remove or transfer personally identifiable information.

Reflection and transmission of an incident solitary wave at an interface of a binary complex plasma in a microgravity condition.

Theoretical results are given in the present paper, which can well explain the experimental observations performed under microgravity conditions in the PK-3 Plus Laboratory on board the International Space Station about the propagation of a solitary wave across an interface in a binary complex plasma. By using the traditional reductive perturbation method and the continuity conditions of both the electric potential and the momentum at the interface, we obtain the equivalent "initial conditions" for both the transmitted wave and the reflected waves from the incident wave. Then we obtain the numbers of the reflected and the transmitted solitary waves as well as all the wave amplitudes by using the inverse scattering method. The ripples of both reflection and transmission have also been given by using the Fourier series. The number of the reflected and the transmitted solitary waves produced by interface, as well as all the solitary wave amplitudes, depend on the system parameters such as the number density, electric charge, mass of the dust particles, and the effective temperature in both regions. The analytical results agree with observations in the experiments.

Research on MPPT control strategy of photovoltaic cells under multi-peak

Under the condition of partial shadow occlusion, the P-U curve of the photovoltaic array exhibits the characteristics of multi-peak output. The traditional maximum power point tracking (MPPT) algorithm is easy to fail, and the particle swarm algorithm, as multi-objective optimization algorithm, is characterized by its low volatility and fast convergence speed. It is applied to the optimization process of multi-peak photovoltaic cells. Aiming at the multi-peak output of the photovoltaic array, this paper builds a simulation model based on the standard particle swarm algorithm and the perturbation and observation method through MATLAB/Simulink. The simulation results show that compared with the traditional perturbation and observation method, the standard particle swarm algorithm can reduce fluctuations when the power is stable and can quickly track the output multi-peak maximum power point when the light intensity changes suddenly.

Research on control strategy of maximum power tracking variable step size perturbation & observation method for photovoltaic power generation system

There are three defects of traditional perturbation and observation method in the maximum power tracking control process of photovoltaic power generation systems, which are oscillation, misjudgment and poor tracking accuracy. Thus, a variable step perturbation and observation method based on power prediction is proposed for three-level DC/DC converters in this paper, which effectively solved oscillation, misjudgment, tracking accuracy problems, improving the tracking speed and precision of the algorithm, and the verification results of the maximum power tracking algorithm based on the three-level DC/DC converter structure has also been indicated.

BMOP: Bidirectional Universal Adversarial Learning for Binary OpCode Features

For malware detection, current state-of-the-art research concentrates on machine learning techniques. Binaryn-gram OpCode features are commonly used for malicious code identification and classification with high accuracy. Binary OpCode modification is much more difficult than modification of image pixels. Traditional adversarial perturbation methods could not be applied on OpCode directly. In this paper, we propose a bidirectional universal adversarial learning method for effective binary OpCode perturbation from both benign and malicious perspectives. Benign features are those OpCodes that represent benign behaviours, while malicious features are OpCodes for malicious behaviours. From a large dataset of benign and malicious binary applications, we select the most significant benign and malicious OpCode features based on the feature SHAP value in the trained machine learning model. We implement an OpCode modification method that insert benign OpCodes into executables as garbage codes without execution and modify malicious OpCodes by equivalent replacement preserving execution semantics. The experimental results show that the benign and malicious OpCode perturbation (BMOP) method could bypass malicious code detection models based on the SVM, XGBoost, and DNN algorithms.

Homotopy perturbation method with rank upgrading technique for the superior nonlinear oscillation

In the present work, the rank upgrade method is suggested to obtain a periodic approximate solution for some complicated nonlinear problems. The method depends on obtaining an equivalent simple equation having a polynomial of nonlinearity without using the Taylor expansion. The solution process is extremely simple, as simple as that by the traditional perturbation method. This approach yields a highly accurate in obtaining analyticity approximate solution for the superior nonlinear oscillation. The results are attractive and valid for both weakly and strongly nonlinear cases.