Iterative Perturbation Research Articles

Improvement to dynamic condensation of structural systems using an innovative virtual model reduction

Model reduction methods have primarily been used in the field of the structural dynamic analysis to reduce the computational time. However, it has progressively been extending to other engineering practices like the damage detection to extract the structural response by means of limited monitored degrees-of-freedom. This paper aims to improve the iterative dynamic condensation method, as a convenient method of the model reduction, for better assessment of the structural dynamic properties. The improvement consists of: (1) Capturing different modal frequencies by applying an iterative perturbation near the frequency obtained from the static condensation. The perturbation is evaluated in a manner that there is no need to solve eigenvalue problem successively; (2) Developing virtual dynamic condensation (VDC) procedure to generalize unique reduced stiffness and mass matrices, reflecting the influence of all modes of vibration, needed for a complete dynamic analysis. Finally, the accuracy of the proposed VDC method was proved by solving three examples.

Perturbation iteration transform method for solving fractional order integro-differential equation

In this study, the Perturbation Iteration transform method, namely PITM, is in short presented and implemented for solving a class of fractional integro-differential equations. The fractional derivative will be in the Atangana–Baleanu Caputo fractional derivative sense (ABC). The (PITM) is consists of merging Laplace transform method and the perturbation iteration algorithm (PIM). The proposed method furnish the solution in the form of a fastly convergent series. Some illustrative examples are presented to illustrate that the PITM is a powerful, efficient and accurate method and it can be enforced to other nonlinear problems.

New Perturbation–Iteration Algorithm for Nonlinear Heat Transfer of Fractional Order

Ordinary differential equations have recently been extended to fractional equations that are transformed using fractional differential equations. These fractional equations are believed to have high accuracy and low computational cost compared to ordinary differential equations. For the first time, this paper focuses on extending the nonlinear heat equations to a fractional order in a Caputo order. A new perturbation iteration algorithm (PIA) of the fractional order is applied to solve the nonlinear heat equations. Solving numerical problems that involve fractional differential equations can be challenging due to their inherent complexity and high computational cost. To overcome these challenges, there is a need to develop numerical schemes such as the PIA method. This method can provide approximate solutions to problems that involve classical fractional derivatives. The results obtained from this algorithm are compared with those obtained from the perturbation iteration method (PIM), the variational iteration method (VIM), and the Bezier curve method (BCM). All solutions are tested with numerical simulations. The study found that the new PIA algorithm performs better than the PIM, VIM, and BCM, achieving high accuracy and low computational cost. One significant advantage of this algorithm is that the solutions obtained have established that the fractional values of alpha, specifically α, significantly influencing the accuracy of the outcome and the associated computational cost.

Allosteric Cholesterol Site in Glycine Receptors Characterized through Molecular Simulations.

Glycine receptors are pentameric ligand-gated ion channels that conduct chloride ions across postsynaptic membranes to facilitate fast inhibitory neurotransmission. In addition to gating by the glycine agonist, interactions with lipids and other compounds in the surrounding membrane environment modulate their function, but molecular details of these interactions remain unclear, in particular, for cholesterol. Here, we report coarse-grained simulations in a model neuronal membrane for three zebrafish glycine receptor structures representing apparent resting, open, and desensitized states. We then converted the systems to all-atom models to examine detailed lipid interactions. Cholesterol bound to the receptor at an outer-leaflet intersubunit site, with a preference for the open and desensitized versus resting states, indicating that it can bias receptor function. Finally, we used short atomistic simulations and iterative amino acid perturbations to identify residues that may mediate allosteric gating transitions. Frequent cholesterol contacts in atomistic simulations clustered with residues identified by perturbation analysis and overlapped with mutations influencing channel function and pathology. Cholesterol binding at this site was also observed in a recently reported pig heteromeric glycine receptor. These results indicate state-dependent lipid interactions relevant to allosteric transitions of glycine receptors, including specific amino acid contacts applicable to biophysical modeling and pharmaceutical design.

A Novel Technique for Solving the Nonlinear Fractional-Order Smoking Model

In the study of biological systems, nonlinear models are commonly employed, although exact solutions are often unattainable. Therefore, it is imperative to develop techniques that offer approximate solutions. This study utilizes the Elzaki residual power series method (ERPSM) to analyze the fractional nonlinear smoking model concerning the Caputo derivative. The outcomes of the proposed technique exhibit good agreement with the Laplace decomposition method, demonstrating that our technique is an excellent alternative to various series solution methods. Our approach utilizes the simple limit principle at zero, making it the easiest way to extract series solutions, while variational iteration, Adomian decomposition, and homotopy perturbation methods require integration. Moreover, our technique is also superior to the residual method by eliminating the need for derivatives, as fractional integration and differentiation are particularly challenging in fractional contexts. Significantly, our technique is simpler than other series solution techniques by not relying on Adomian’s and He’s polynomials, thereby offering a more efficient way of solving nonlinear problems.

New Analytical and Numerical Solutions for Squeezing Flow between Parallel Plates under Slip

In this article, the effects of physical flow parameters on squeezed fluid between parallel plates are explored through the Darcy porous channel when fluid is moving as a result of the upper plate being squeezed towards the stretchable lower plate, such as velocity slip, thermal slip, solutal slip, thermal stratification parameter, solutal stratification parameter, squeezing number, Darcy number, Prandtl number, and Schmidt number. The governing equations are transformed into a nonlinear ordinary differential equation using the appropriate similarity transformations. The resulting equations are solved by using the perturbation iteration method (PIT) to produce a convergent analytical solution with high accuracy. The phenomena of the squeezing fluid as the plates are moving apart and when they are coming together are illustrated using the resulting analytical solutions. Plots are used to discuss the significant effects of physical parameters on velocity, temperature, and fluid concentration profiles. The skin friction coefficient and Nusselt Sherwood values have graphical interpretations that are listed. For strong velocity slip parameters, the results demonstrate the existence of a minimum velocity profile close to the plate and a growing velocity profile distant from the plate. Additionally, as the slip effects rise, the fluid temperature and concentration both considerably drop. The results of the fourth-order Runge-Kutta method (RK4M) and the presented analytical solutions provided are in excellent agreement.

Explanation-Guided Adversarial Example Attacks

Neural network-based classifiers are vulnerable to adversarial example attacks even in a black-box setting. Existing adversarial example generation technologies mainly rely on optimization-based attacks, which optimize the objective function by iterative input perturbation. While being able to craft adversarial examples, these techniques require big budgets. Latest transfer-based attacks, though being limited queries, also have a disadvantage of low attack success rate. In this paper, we propose an adversarial example attack method called MEAttack using the model-agnostic explanation technology, which can more efficiently generate adversarial examples in the black-box setting with limited queries. The core idea is to design a novel model-agnostic explanation method for target models, and generate adversarial examples based on model explanations. We experimentally demonstrate that MEAttack outperforms the state-of-the-art attack technology, i.e., AutoZOOM. The success rate of MEAttack is 4.54%-47.42% higher than AutoZOOM, and its query efficiency is reduced by 2.6-4.2 times. Experimental results show that MEAttack is efficient in terms of both attack success rate and query efficiency.

Probabilistic relative entropy in elasto‐plasticity using the iterative generalized stochastic stress‐based Finite Element Method

AbstractThe generalized iterative stochastic perturbation approach to the stress‐based Finite Element Method has been proposed in this work. This approach is completed using the complementary energy principle, Taylor expansion of the general order applicable to all random functions and parameters as well as nodal polynomial response bases determined with the use of the Least Squares Method. The main aim of this elaboration is the usage of such a probabilistic approach to determine Bhattacharyya relative entropy for some nonlinear engineering stress analysis with uncertainty. Mathematical apparatus with its numerical implementation has been used to study elastoplastic torsion of some prismatic bar with Gaussian material uncertainty and the corresponding reliability measures. This problem has been solved using the Constant Stress Triangular (CST) plane finite elements, the modified Newton–Raphson algorithm, whereas the first four probabilistic characteristics resulting from the iterative generalized stochastic perturbation method have been contrasted with these obtained with the crude Monte‐Carlo sampling and the semi‐analytical probabilistic approach.

Iterated Perturbation Theory for Mott Insulators in a Static Electric Field with Optical Phonons

This article aims to compare the so‐called iterated perturbation theory (IPT) and auxiliary master equation approach (AMEA) impurity solvers for a Mott insulating system driven out of equilibrium by a static electric field. Electronic heat bath and optical phonons are employed as dissipation mechanism of the current‐induced Joule heat that the excited electrons of the lattice experience as the result of the field's driving. Despite its simplicity, the IPT approach yields results that qualitatively are in good agreement with those obtained within the AMEA impurity solver, although fails to reproduce some correlation effects.

IG-Based Method for Voiceprint Universal Adversarial Perturbation Generation

In this paper, we propose an Iterative Greedy-Universal Adversarial Perturbations (IGUAP) approach based on an iterative greedy algorithm to create universal adversarial perturbations for acoustic prints. A thorough, objective account of the IG-UAP method is provided, outlining its framework and approach. The method leverages a greedy iteration approach to formulate an optimization problem for solving acoustic universal adversarial perturbations, with a new objective function designed to ensure that the attack has higher accuracy in terms of minimizing the perceptibility of adversarial perturbations and increasing the accuracy of successful attacks. The perturbation generation process is described in detail, and the resulting acoustic universal adversarial perturbation is evaluated in both target-attack and no-target-attack scenarios. Experimental analysis and testing were carried out using comparable techniques and dissimilar target models. The findings reveal that the acoustic generality adversarial perturbation produced by the IG-UAP method can obtain effective attack results even when the audio training data sample size is minimal, i.e., one for each category. Moreover, the human ear finds it difficult to detect the loss of original data information and the addition of adversarial perturbation (for the case of a target attack, the ASR values range from 82.4% to 90.2% for the small sample data set). The success rates for untargeted and targeted attacks average 85.8% and 84.9%, respectively.

Colossal Kerr nonlinearity without absorption in a five-level atomic medium

In this work, we present an analytical method to achieve giant Kerr nonlinearity without absorption in a five-level atomic medium. By using iterative perturbation technique on density matrix equations, we have derived the analytical expressions of nonlinear susceptibility and Kerr nonlinear coefficient in the presence of spontaneously generated coherence (SGC) and relative phase between applied laser fields. It shows that, this five-level atomic medium exhibits multiple electromagnetically induced transparency (EIT) at three different frequencies, at the same time, the Kerr nonlinear coefficient is enhanced around three transparent spectral regions; in each such EIT region appears a pair of positive–negative peaks of Kerr nonlinear coefficient. In particular, these nonlinear peaks are moved to the center of the EIT windows via SGC. This means that the Kerr nonlinear coefficient is enhanced with completely suppressed absorption at different transparency frequencies. Furthermore, the magnitude and the sign of the Kerr nonlinear coefficient are easily controlled according to the SGC strength, the coupling laser intensity, and the relative phase between applied laser fields. Such a giant nonlinear medium can be useful for photonic devices working in the resonant frequency region without absorption. As a typical application, this giant Kerr nonlinear material has been applied to an interferometer for the formation of optical bistability, and showed the appearance of OB at the resonant frequency with significantly reduced threshold intensity and OB width.

A new approach in handling one-dimensional time-fractional Schrödinger equations

<abstract> <p>Our aim of this paper was to present the accurate analytical approximate series solutions to the time-fractional Schrödinger equations via the Caputo fractional operator using the Laplace residual power series technique. Furthermore, three important and interesting applications were given, tested, and compared with four well-known methods (Adomian decomposition, homotopy perturbation, homotopy analysis, and variational iteration methods) to show that the proposed technique was simple, accurate, efficient, and applicable. When there was a pattern between the terms of the series, we could obtain the exact solutions; otherwise, we provided the approximate series solutions. Finally, graphical results were presented and analyzed. Mathematica software was used to calculate numerical and symbolic quantities.</p> </abstract>

Analytical Solutions of the Blasius Equation by Perturbation Iteration Method

The Blasius equation is treated by employing the Perturbation Iteration method. Analytical solutions are derived for different perturbation iteration algorithms. Solutions are contrasted with the numerical solution obtained by an adaptive step size Runge-Kutta algorithm. It is found that the series type perturbation iteration solution better represents the behavior inside the boundary layer whereas the exponentially decaying perturbation iteration solution better represents the real solution outside the boundary layer. A composite expansion uniting both solutions and valid over the whole region is constructed using the gamma interval functions. The composite analytical solution is indistinguishable from the numerical one and can replace the numerical solution in calculations.

New Numerical Iteration Schemes Based on Perturbation Iteration Algorithms

Perturbation–Iteration algorithms (PIA) have been developed recently to solve differential equations analytically. A continuous solution in terms of closed form functions as an approximation of the original equation can be found using the method. The method has been implemented to algebraic equations, ordinary and partial differential equations successfully. Based on the formalism developed previously, in this work, purely numerical versions of the perturbation–iteration algorithms are proposed for the first time for first-order nonlinear ordinary differential equations. The new algorithms are called as the Numerical Perturbation–Iteration Algorithms (NPIA) to distinguish them from the continuous analytical ones (PIA) and the method in general will be called the Numerical Perturbation–Iteration Method (NPIM). Iteration schemes based on one correction term in the perturbation solution and first-order derivatives in the Taylor series expansions (NPIA(1,1)), and one correction term in the perturbations and second-order derivatives in the series expansions (NPIA(1,2)) are derived. The numerical results are compared with the exact solutions and a very good match is observed. NPIA(1,2) produced slightly better results compared to NPIA(1,1) with total errors being at least [Formula: see text], [Formula: see text] being the step size for both methods. An improvement suggestion for NPIA(1,1) is proposed in the last section to eliminate unrealistic blow-up solutions which are encountered for some specific equations.

An evaluation of multispecies population dynamics models through numerical simulations using the new iterative method

This study explores the multispecies Lotka-Volterra population dynamics models, a captivating nonlinear mathematical framework with significant applications in natural sciences and environmental studies. The primary objective is to deliver precise solutions for these models using the New Iterative Method (NIM). Numerical simulations are conducted on three distinct types of nonlinear dynamic problems, comparing the accuracy of the NIM with that of the Perturbation Iteration Algorithm (PIA), existing exact solutions, and the traditional fourth-order Runge–Kutta method. A continuous step time of Δ = 0.001 was used for the Runge–Kutta method in all computations. Notably, the NIM's solutions for the nonlinear multispecies Lotka-Volterra models demonstrate very good accuracy, achieving convergence to the Runge–Kutta method's solutions within five iterations. The correctness of the NIM is found to be better than the other existing solutions. Its distinctive attribute lies in its computational efficiency, providing high accuracy without necessitating linearization, discretization, multipliers, or polynomials for nonlinear terms. This leads to simpler solution procedures while maintaining commendable accuracy. The findings underscore NIM's reliability and broad applicability in both linear and nonlinear models, highlighting its potential as an invaluable tool in numerical computation.

Perturbation Iteration Method Compared with Direct Method and Fuzzy Logic Strategy for Solving An Optimal Control Problem of An Uninfected Hepatitis B Virus Dynamics

This paper aims at solving the optimal control problem of the dynamic of HBV infection under treatment using the perturbation iteration method. This method serves as a tool to determine the approximate solutions of nonlinear equations for which exact solutions cannot be obtained. To test the efficacy of this method, the authors propose to compare the numerical simulation results with those of the direct method and fuzzy logic strategy. The newly used method for solving the above optimal control problem is very important since the findings compared to those obtained from the two other methods are in good agreement with experimental data and they demonstrate the response drugs to the dynamics of uninfected hepatocytes, infected hepatocytes, and free virions for a patient suffering from HBV. Since the perturbation iteration method provides satisfactory results which are close to other used numerical methods, it is an important numerical tool to determine the solution of an optimal control problem. In particular, it provides optimal trajectories in medicine, biology, and other related scientific fields. For instance, the response of treatment as control of the human body ensures the health of patients.

The reversibility of cancelable biometric templates based on iterative perturbation stochastic approximation strategy

Researchers have been proposing different matching frameworks for cancelable template design to improve the matching performance and security of biometric authentication systems. Despite the advantages provided by these systems, they are often vulnerable to different attacks due to their templates' invertible nature. This study utilized an iterative perturbation stochastic approximation procedure to analyze the irreversible order-based encoding approach used in cancelable biometric template transformation. The strategy begins by exploiting the scores corresponding to the encoded words, then a mixed variable-based iterative perturbation is used to generate independent random elements and consequently the corresponding template from the scores. The strategy exploits the vulnerability of three different cancelable systems it has tested, demonstrating that other techniques of similar nature fall short of the security standard for attack mitigation that cancelable biometric systems require. After analyzing the reasons that exploit the system's vulnerability, we use a parameterized thresholding non-uniform quantization as a countermeasure to boost the system's robustness while maintaining a balanced performance-security trade-off. As a result, the system can evade attacks without significantly hindering its matching performance. Finally, generality and computational complexity evaluations on different modalities and strategies validate the attack's efficacy and realism, respectively.

Semi-Analytical Assessment of Magneto-Hydrodynamic Nano-Fluid Flow Jeffrey- Hamel Problem

In this paper, analyzing the non-dimensional Magnesium-hydrodynamics problem Using nanoparticles in Jeffrey-Hamel flow (JHF) has been studied. The fundamental equations for this issue are reduced to a three-order ordinary differential equation. The current project investigated the effect of the angles between the plates, Reynolds number, nanoparticles volume fraction parameter, and magnetic number on the velocity distribution by using analytical technique known as a perturbation iteration scheme (PIS). The effect of these parameters is similar in the converging and diverging channels except magnetic number that it is different in the divergent channel. Furthermore, the resulting solutions with good convergence and high accuracy for the different values ​​of the physical parameters are in the form a power-series of the problem posed. The efficiency of this method is shown by comparison between for different cases between computed results with numerical solution and solutions by other methods.

A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces

Abstract In this paper, we propose and analyze a projected homotopy perturbation method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. To expedite convergence, the approach uses two search directions given by homotopy perturbation iteration, and the new iteration is calculated as the projection of the current iteration onto the intersection of stripes decided by above directions. The method allows to use L 1 {L^{1}} -like penalty terms, which is significant to reconstruct sparsity solutions. Under reasonable conditions, we establish the convergence and regularization properties of the method. Finally, two parameter identification problems are presented to indicate the effectiveness of capturing the property of the sparsity solutions and the acceleration effect of the proposed method.

Dynamic behaviors for the graphene nano/microelectromechanical system in a fractal space

The microelectromechanical devices have triggered rocketing interest in various advanced technologies, that is, sensors, material science, and energy harvesting, and now the devices tend to a nanoscale size, making the technology much more attractive in both academic and industrial communities. This paper takes a graphene nano/microelectromechanical system as an example to study its dynamical property, which is the foundation for the optimal design and reliable operation. As the system is inextricably complex with singularity and zero conditions in a fractal space, the iteration perturbation method is used to obtain the periodic solution of the system. The results show clearly the low-frequency property of the system and pull-in instability; furthermore, the fractal dimension affects greatly the system’s dynamical property.