Perturbation Method Research Articles

Аэродинамическое качество тонкого крыла с винглетами различной высоты

The paper considers the problem of asymmetrical airflow around a thin wing with winglets. There is studied the effect of winglets height on lifting force and aerodynamic quality of a thin wing. In frames of this theory, the problem is reduced to a system of three dual integral equations. To solve this system, a discrete form of equations which based on the discrete vortex method is presented. A method for calculating inductive drag, viscous friction, suction force and aerodynamic quality is described. There are presented the data obtained by using a mathematical model, which is based on a linearized theory of thin wing and a method of small perturbations. Conclusions about the effect of winglets on the lifting force and aerodynamic quality are made. Increasing the height of the winglets leads to a linear increase in lifting force. It is noted that at angles of attack up to 4°, winglets do not increase aerodynamic quality. At angles above 4°, increasing the height of the winglets increases aerodynamic quality of a thin wing.

Homotopy Perturbation Method for Analyzing the Effect of Viscous Dissipation on Steady Natural Convection Couette Flow with Convective Boundary Conditions

This research article presents an analytical study of convective flow in a vertical channel with convective boundary conditions. Because of the nonlinear nature of the governing energy and momentum equations, the homotopy perturbation method was employed. The effects of various physical parameters on temperature and velocity profiles are illustrated in Figures 2 to 9, and a comparison table is provided to validate the results. Notably, both temperature and velocity distributions increased with higher viscous dissipation. Furthermore, the velocity profile decreased with an increase in the Biot number, while the temperature profile adjacent to the plate increased as the Biot number grew. Shear stress also exhibited an upward trend with rising viscous dissipation. Finally, an increase in the Grashof number and Biot number is found to elevate the skin friction on both plates. The mean temperature is higher when air is used as the working fluid compared to mercury. To validate this study, the temperature and velocity results were compared with previously published work, showing excellent agreement. This confirms the efficiency of the Homotopy Perturbation Method in solving coupled and nonlinear system of differential equations. Additionally, it was observed that both temperature and velocity increase with a rise in the Prandtl number, attributed to the dominance of momentum diffusivity over thermal diffusivity.

Periapsis precession in general stationary and axisymmetric spacetimes

This work studies the periapsis shift in the equatorial plane of arbitrary stationary and axisymmetric spacetimes. Two perturbative methods are systematically developed. The first works for small eccentricity but very general orbit size and the second, which is post-Newtonian and includes two variants, is more accurate for orbits of large size but allows general eccentricity. Results from these methods are shown to be equivalent under small eccentricity and large size limits. The periapsis shift of Kerr–Newman, Kerr–Sen and Kerr–Taub-NUT spacetimes is computed to high orders. The electric charge and NUT charge are shown to contribute to the leading order but with opposite signs. The frame-dragging term and high-order effect of spacetime spin are given. The electric and NUT charges of the Earth, Sun and Sgr A* are constrained using the Mercury, satellite and S2 precession data. Periapsis shifts of other spacetimes are obtained too.

Radiative effects on 2D unsteady MHD Al2O3‐water nanofluid flow between squeezing plates: A comparative study using AGM and HPM in Python

AbstractThis research uses Python programming to explore the influence of magnetic field strength on a two‐dimensional squeezing nanofluid flow confined between two parallel plates. The primary objective is to examine an aluminum oxide nanofluid's velocity and heat transfer characteristics which are governed by dimensionless parameters such as the Prandtl number and friction coefficient. The non‐dimensionalized differential equations are solved employing two analytical techniques: the Akbari‐Ganji Method and the Homotopy Perturbation Method, both implemented through Python programming. Using Python programming to solve these equations represents a novel approach that offers accurate and efficient results. The study's findings reveal that as the Prandtl number increases, the temperature and thermal properties of the nanofluid flow also increase while the concentration decreases. Additionally, the Nusselt number experiences a decline. The implementation of Python programming in this research showcases the versatility of the language in solving complex mathematical problems, particularly in fluid dynamics. Python's ability to provide accurate solutions efficiently enhances its potential for further applications and advancements in this area.

Molecular Interactions and Responsive Locations of CO2-Responsive Surfactants in an Oil-Water-Surfactant System: Molecular Dynamics Simulation and Free Energy Perturbation.

Understanding the mechanism of a CO2-responsive surfactant is essential for enhancing its industrial applications. Conventional experimental methods face challenges in pinpointing the exact location of proton transfer within the system and in accurately describing the impact of intermolecular and intramolecular interactions on the CO2 responsiveness of such substances. To address this gap, this study employs molecular dynamics simulations and free energy perturbation methods to investigate the proton transfer process between a CO2-responsive cationic surfactant N'-dodecyl-N,N-dimethylacetamidinium (DMAAH+) and its counterion bicarbonate ion at the oil-water interface and micelle surface and in the bulk aqueous phase. Molecular dynamics simulations identified potential locations for the proton transfer process within the system and elucidated the types of interactions contributing to changes in Gibbs free energy. Subsequently, free energy perturbation was employed to calculate Gibbs free energy changes associated with proton transfer at different locations. The respective contributions of various intramolecular and intermolecular interactions were then compared and analyzed. It has been revealed that the deprotonation process is not thermodynamically spontaneous at all three responsive locations. The proton transfer occurs more frequently at the oil-water interface than at the micelle surface and is less common in the bulk aqueous phase. The findings enhance our understanding of the fundamental mechanisms governing the responsiveness of CO2-responsive surfactants and provide valuable insights for their practical application in industrial processes.

Stability Analysis in Cosmological Models Using Perturbative Methods in f(R,T) Theory

This study examines the stability of cosmological models through perturbation theory, focusing on different formulations of the deceleration parameter (DP). By analysing the eigenvalues of perturbations, we identify key insights into the models’ long-term dynamics and stability. The results reveal the presence of stable and marginally stable modes, indicating how perturbations evolve and dissipate over cosmic time. These findings provide a deeper understanding of cosmic evolution, the formation of large-scale structures, and the behaviour of perturbations, offering significant contributions to cosmological research and theoretical modelling of the Universe.

Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields.

This work presents a perturbational decomposition method for simulating quantum evolution under the one-dimensional Ising model with both longitudinal and transverse fields. By treating the transverse field terms as perturbations in the expansion, our approach is particularly effective in systems with moderate longitudinal fields and weak to moderate transverse fields relative to the coupling strength. Through systematic numerical exploration, we characterize parameter regimes and evolution time windows where the decomposition achieves measurable improvements over conventional Trotter decomposition methods. The developed perturbational approach and its characterized parameter space may provide practical guidance for choosing appropriate simulation strategies in different parameter regimes of the one-dimensional Ising model.

Perturbation Methods in Solving the Problem of Two Bodies of Variable Masses with Application of Computer Algebra

The classical many-body problem is not integrable, so perturbation theory based on an exact solution to the two-body problem is usually applied to investigate the dynamics of planetary systems. However, in the case of variable masses, the two-body problem is not integrable, in general, and application of perturbation theory is required to investigate it, as well. In the present paper, we use the perturbation theory to derive the differential equations determining the orbital elements of the relative motion of one body around the other. Two models of the perturbed aperiodic motion on conic and quasi-conic sections are considered and compared. Special attention is paid to the practically important case of small eccentricities, when the perturbing forces may be replaced by the corresponding power series expansions. The differential equations of the perturbed motion are averaged over the mean anomaly, and the evolutionary equations describing the behavior of the orbital elements over long periods of time are obtained for two models. Comparing the corresponding solutions to the evolutionary equations, we have shown that both models demonstrate similar behavior with regard to the secular perturbations of the orbital elements. However, the second model, based on the aperiodic motion on a quasi-conic section, is more appropriate for generalization to the many-body problem with variable masses. All the relevant symbolic and numerical calculations are performed with the computer algebra system Wolfram Mathematica.

CO adsorption on CeO2(111): A CCSD(T) benchmark study using an embedded-cluster model.

A benchmark model that combines an embedded-cluster approach for ionic surfaces with wavefunction-based methods to predict the vibrational frequencies of molecules adsorbed on surfaces is presented. As a representative case, the adsorption of CO on the lowest index non-polar and most stable facet of CeO2, that is, (111) was studied. The CO harmonic vibrational frequencies were not scaled semiempirically but explicitly corrected for anharmonic effects, which amount to about 25 cm-1 with all tested methods. The second-order Møller-Plesset perturbation method (MP2) tends to underestimate the CO harmonic frequency by about 40-45 cm-1 in comparison with the results obtained with the coupled-cluster singles and doubles with perturbational treatment of triple excitation method [CCSD(T)] and independently from the basis set used. The best estimate for the CO vibrational frequency (low-coverage case) differs by 12 cm-1 with the experimental value obtained by infrared reflexion absorption spectroscopy of 1 monolayer CO adsorbed on the oxidized CeO2(111) surface. In addition, a conservative estimate of the adsorption energy of about -0.22 ± -0.07eV obtained at the CCSD(T) level confirms the physisorption character of the adsorption of CO on the CeO2(111) surface.

Semiconductor Transistor-Based Detection of Epithelial-Mesenchymal Transition via Weak Acid-Induced Proton Perturbation.

Developing new detection methods for the epithelial-mesenchymal transition (EMT), where epithelial cells acquire mesenchymal traits, is crucial for understanding tissue development, cancer invasion, and metastasis. Conventional in vitro EMT evaluation methods like permeability measurements are time-consuming and low-throughput, while the transepithelial electrical resistance measurements struggle to differentiate between cell membrane damage and tight junction (TJ) loss and are affected by cell proliferation. In this study, we developed a pH perturbation method to detect TJ barrier disruption during epithelial EMT by sensing proton leakage induced by a weak acid using a pH-responsive semiconductor. Mardin-Darby canine kidney (MDCK) epithelial cell sheets cultured on an ion-sensitive field effect transistor's gate insulator were induced into EMT by exposure to the cytokine transforming growth factor-β1 (TGF-β). Our pH perturbation method successfully detected EMT in MDCK sheets at a TGF-β concentration one-tenth of that required for conventional methods. The high sensitivity and selectivity arise from using minimal protons as indicators of TJ barrier disruption. TGF-β-induced EMT detection results using our method align with EMT-related gene and protein expression data. In drug screening with EMT inhibitors, this novel method showed similar trends to conventional ones. The pH perturbation method enables highly sensitive, real-time EMT detection, contributing to elucidating biological phenomena and pharmaceutical development.

The onset of Magneto–Darcy–Rayleigh–Bénard convection under local thermal non-equilibrium with two-layer system

The investigation focuses on the consequences of various thermal distributions examined in the context of Magneto–Darcy–Rayleigh–Bénard (MDRB) convection onset under local thermal non-equilibrium (LTNE). The system under consideration consists of a two-layer configuration, with an incompressible fluid and horizontally positioned adiabatic peripheries. An analytical solution to the resultant problem is accomplished using the regular perturbation method. Concerning the six thermal distributions, we examine variables such as the ratio of heat expansion in the solid phase, the ratio of heat diffusivities in the solid phase, and the inter-phase heat diffusivity ratio, which exhibits a propensity towards LTNE. Furthermore, we investigate the consequences of modifying the values of constraints, namely, the ratio of heat expansion in the fluid phase, the ratio of heat diffusivities in the fluid phase, the porous parameter, the heat ratio, and the Chandrasekhar number. The empirical observations indicate that the model (iii) exhibits a significantly higher degree of instability when compared to other distributions. Conversely, model (v) demonstrates a notable level of stability. Moreover, it is intriguing that the system governed by the model (vi) exhibits higher stability than the model (iv) thermal distribution within the context of a composite system.

Analysis of unsteady heat and mass transfer in rotating MHD convection flow over a porous vertical plate

The aim of this research paper is to investigate the rotational flow of an unsteady magnetohydrodynamic heat and mass transfer flow due to convection over a vertical porous semi-infinite plate. The plate undergoes continuous circular motion, maintaining a constant velocity. To achieve this, we worked on both numerical methods and analytical techniques, particularly utilizing perturbation methods to solve the governing partial differential equations. Consequently, we derive an expression for the Nusselt and Sherwood numbers. We delve into the analysis of the velocity profile, temperature distribution, and concentration variation, exploring their behaviour under different physical parameters, including the magnetic field parameter, Grashof num-ber, Soret number and Schmidt number, as well as the Prandtl number. Our findings reveal that the velocity increases with rising values of Grashof, modified Grashof and Soret numbers, whereas it decreases with declining values of the magnetic field parameter, Prandtl number and Schmidt number. Additionally, as rotation gradually intensifies, the fluid velocity closely follows the boundary and becomes negligible as it moves away from it. To facilitate a comprehensive examination of the fluid flow and heat and mass transfer characteristics, we employ graphical representations. Furthermore, this paper offers an in-depth discussion of the underlying physical aspects and their implications.

The Formation of Ion-Acoustic Solitary Waves in a Plasma Having Nonextensive Electrons and Positrons

In this plasma model, consisting of ions, electrons and positrons have been theoretically investigated when both the electrons and positrons are obeying q-nonextensive velocity distribution. The reductive perturbation method is used to obtain a Korteweg-de Vries(KdV) equation describing the basic set of normalized fluid equations. The ion-acoustic solitary waves model are depended on nonextensive parameter, electron to positron temperature ratio, ion to electron temperature ratio and streaming velocity are investigated numerically. It has been found that solely fast ion-acoustic modes can produce the coexistence of small amplitude rarefactive solitons.

Image Watermark Embedding Method Based on Security Service Secure

To solve the problem of privacy leakage and response latency in outsourced image watermark embedding in cloud computing, an efficient and privacy-preserving watermark embedding method for outsourced digital images was proposed by introducing edge computing technology. We had proposed a perturbing encryption method with homomorphism to ensure the information security and the correctness of discrete wavelet transformation in the encrypted domain. In addition, the framework was designed to guarantee the safety of singular value decomposition that edge server could not recover the original image matrix. The experimental results show that the proposed method is superior to similar secure watermarking schemes in terms of encryption/decryption time and ciphertext expansion. The proposed method enables the watermarking operation to be performed in an unsafe outsourced environment while achieving a watermarking effect similar to the plaintext equivalent

Influence of the homotopy stability perturbation on physical variations of non-local opto-electronic semiconductor materials

In the current work, we investigate a novel technique specialized in stability perturbation theory to analyze the primary variations such as thermal, carrier, elastic, and mechanical waves in photothermal theory. The interface of the non-local semiconductor material is utilized to study the stability analysis. The problem is established using a 1D opto-electronic-thermoelastic deformation in the context of the photo-thermoelasticity (PTE) framework. The Laplace transform method is used to convert the system from the time domain into the frequency domain, and the boundary conditions for the thermal, elastic, and plasma waves are applied to the interface of the medium. The homotopy perturbation method was used as an innovative approach to analyze the stability of the non-local silicon’s primary physical fields. The numerical inversion method is applied, yielding many graphs focusing on important numerical factors such as non-local effects, thermo-energy, and thermo-electric coupling parameters. Investigating dual solutions between stable and unstable regions for critical parameters like thermo-electric and thermo-energy coupling factors demonstrates that the homotopy perturbation technique can effectively analyze the stability analysis. The comparison between silicon and germanium is illustrated graphically. Utilizing the homotopy perturbation technique, we can effectively examine the stability of the primary physical variations with the effect of some values for eigenvalues approaches.Graphical abstract

A Fast and Accurate Method for dq Impedance Modeling of Power Electronics Systems Based on Finite Differences

This paper presents a finite-difference-based method for numerically deriving the DQ impedance model of power electronics-based power systems, specifically tailored for stability analysis. The proposed method offers a computationally efficient alternative to traditional approaches by directly applying finite-difference approximations to the large-signal dynamic system, without relying on repetitive time-domain simulations or small-signal analytical models. This method eliminates the need for additional models or complex procedures to compute the steady-state solution, streamlining the impedance modeling process. The accuracy, efficiency, and precision of the proposed method are evaluated through comparative studies with analytical and time-domain perturbation methods. Results demonstrate that the proposed approach provides accuracy comparable to analytical models while significantly reducing computational effort, outperforming perturbation methods in both speed and precision. These findings highlight the practical value of the proposed method for real-time and large-scale system analysis, making it a robust tool for power systems stability assessment.

Anti-windup higher derivative Newton-based extremum seeking under input saturation

The physical constraint of actuators in practical systems, such as actuator magnitude saturation, can significantly impact the behaviour of control systems. To address this issue, a fast learning mechanism is introduced in this paper for constrained input in higher derivatives Newton-based extremum seeking. The approach employs a constrained optimisation method with an anti-windup loop based on a wide range of penalty functions to adapt the search and prevent the violation of constraints, thereby avoiding windup of integral action in a controller. The practical asymptotic stability of the proposed algorithm is proven through a modified singular perturbation method, and its effectiveness is validated through simulations.

Spectral representation of cosmological correlators

Cosmological correlation functions are significantly more complex than their flat-space analogues, such as tree-level scattering amplitudes. While these amplitudes have simple analytic structure and clear factorisation properties, cosmological correlators often feature branch cuts and lack neat expressions. In this paper, we develop off-shell perturbative methods to study and compute cosmological correlators. We show that such approach not only makes the origin of the correlator singularity structure and factorisation manifest, but also renders practical analytical computations more tractable. Using a spectral representation of massive cosmological propagators that encodes particle production through a suitable iϵ prescription, we remove the need to ever perform nested time integrals as they only appear in a factorised form. This approach explicitly shows that complex correlators are constructed by gluing lower-point off-shell correlators, while performing the spectral integral sets the exchanged particles on shell. Notably, in the complex mass plane instead of energy, computing spectral integrals amounts to collecting towers of poles as the simple building blocks are meromorphic functions. We demonstrate this by deriving a new, simple, and partially resummed representation for the four-point function of conformally coupled scalars mediated by tree-level massive scalar exchange in de Sitter. Additionally, we establish cosmological largest-time equations that relate different channels on in-in branches via analytic continuation, analogous to crossing symmetry in flat space. These universal relations provide simple consistency checks and suggest that dispersive methods hold promise for developing cosmological recursion relations, further connecting techniques from modern scattering amplitudes to cosmology.

Perturbation Method and Regularization of the Lagrange Principle in Nonlinear Constrained Optimization Problems

Perturbation Method and Regularization of the Lagrange Principle in Nonlinear Constrained Optimization Problems

Lie algebraic approach to the Hellmann Hamiltonian by considering perturbation method

Lie algebraic approach to the Hellmann Hamiltonian by considering perturbation method