Asymptotic Method Research Articles

Topological defects on the q-deformed superstatistics of modified shifted morse potential for carbon monoxide molecule

The application of topological defects to the study of different molecular potential models has been a focus of interest in recent times due to its significant role in shaping the behavior and interactions of molecular systems. In lieu of this, the asymptotic iteration method is employed to obtain the eigensolutions of the Schrödinger equation of the modified shifted Morse potential model with topological defect. Vibrational energies for carbon monoxide have been presented numerically for various topological defects and the results are compared with experimental data. With the help of the energy expression of modified shifted Morse potential, the q-deformed partition function and other superstatistical function expressions of modified shifted Morse potential for carbon monoxide within the modified Dirac delta distribution are obtained, using the Euler–MacLaurin’s formula. For various temperature values considered, the superstatistical plots show a high level of dependence on the topological defect parameter and deformation parameter. The superstatistical functions for a deformation parameter of zero correspond to the conventional thermodynamic functions. Our results also agree with the available results in the literature.

Nonlinear optimal control of variable speed wind turbines using optimal homotopy asymptotic method

This paper presents a new nonlinear optimal controller for wind energy conversion systems. This study utilizes a new strategy to solve the Hamilton–Jacobi–Bellman (HJB) equation and design a nonlinear optimal controller for wind turbines. The optimal homotopy asymptotic method (OHAM) is applied to derive the solution of the HJB equation corresponding to variable-speed wind turbines. The OHAM controller ensures proper tracking and achieves maximum wind power extraction while preventing excessive loads on the drive train. The proposed control strategy can provide fast convergence and rapid transient responses with high precision and small control input. The OHAM strategy requires a few iterations and can adjust the convergence domain and the convergence rate. The proposed OHAM controller is compared and evaluated with some existing control strategies. The obtained results indicate that OHAM achieves a suitable compromise between maximizing aerodynamic power capture and minimizing low-speed shaft oscillation.

Asymptotic Method for Solving the Problem of Scattering of Electromagnetic Fields by a Set of Small Impedance Particles

Asymptotic Method for Solving the Problem of Scattering of Electromagnetic Fields by a Set of Small Impedance Particles

A scaling fractional asymptotical regularization method for linear inverse problems

A scaling fractional asymptotical regularization method for linear inverse problems

Point and interval estimation for one-shot devices under Weibull distribution with dependent failure modes using copulas

A one-shot device is a unit that performs its intended function only once. Actual lifetimes of such kind of devices cannot be observed. One can only observe if a failure occurred before or after a certain inspection time so the data is either left- or right-censored. Since one-shot devices are highly reliable products, accelerated life testing is commonly used to induce early failures. There are often more than one dependent failure modes causing the device to fail. Copula models have become one of the most popular tools for modeling dependence. In this paper, we provide statistical inference for modeling the dependence structure between failure modes in one-shot devices under constant stress accelerated life testing using copulas with Weibull marginals. The point estimates of the unknown parameters for the Weibull distribution along with the dependence parameter estimate are obtained using two estimation methods; the maximum likelihood estimation and the inference function for margins. Also, interval estimates are constructed using the asymptotic and bootstrap methods. The basic bootstrap and the studentized-t bootstrap intervals are obtained. Moreover, the survival probabilities are predicted under normal conditions. Numerical analysis including simulated data and a real life data are conducted to study the performance of the estimates.

Investigation of Thermal Management Capacity of Casson Electrolytes in Porous Electrodes in Lithium‐Ion Battery Applications

ABSTRACTThe study of the Casson electrolyte in lithium‐ion batteries (LIBs) is important because of their complexities due to tougher operational conditions and other challenges during charging–discharging challenges with their improved thermal management capacity and enhanced safety. This further optimizes the thermal management avoiding chances of hot spots or thermal runaway, thereby making LIBs safer. In this investigation, convective loads for non‐Newtonian fluid as electrolyte Casson‐type boundary layer flow related to plate and flat surfaces in non‐Darcy permeable porous electrodes have been deliberated. We have employed the Optimal Homopotic Asymptotic Method technique to solve the equation of the system. The effects and influences of Casson factors, permeability, flow constraints, Prandtl values related to flow and thermal dissipation, and boundary layer profiles have been studied. From the results, it is concluded that thermal parameters and porousness have affected the system, and the upsurge in the porousness actually decreases heat transport effects and proportions. The results of this study are relevant to the development of more effective porous electrodes for achieving high performance with long cycle life. These studies help improve the utilization of mass and heat transfer properties, as affected by the non‐Newtonian behavior of the electrolyte, to help in the design of next‐generation LIBs with higher energy density along with fast charge/discharge rates.

NONLINEAR VIBRATION OF A BEAM SUBJECTED TO MECHANICAL IMPACT AND WINKLER-PASTERNAK FOUNDATION

The simultaneous effects of mechanical impact and Winkler-Pasternak foundation on the dynamic response of an Euler-Bernoulli beam are studied. By means of the Galerkin-Bubnov procedure, the governing equation with partial derivatives is reduced to an ordinary differential equation. This nonlinear equation is solved by means of the Optimal Homotopy Asymptotic Method (OHAM).

Enhancing navigation performance in unknown environments using spiking neural networks and reinforcement learning with asymptotic gradient method

Achieving accurate and generalized autonomous navigation in unknown environments poses a significant challenge in robotics and artificial intelligence. Animals exhibits superlative navigation capabilities by combining the representation of internal neurals and sensory cues of self-motion and external information. This paper proposes a brain-inspired navigation method based upon the spiking neural networks (SNN) and reinforcement learning, integrated with a lidar system that serves as the local environment explorer, by which realizes high performance of obstacle avoidance and target arrival in mapless circumstances. An asymptotic gradient method is introduced to optimize the backpropagation during training, which facilitates the improvement of model robustness. The results of our experiments conducted on the Gazebo platform showcase how our approach effectively improves navigation performance in various intricate environments. Our approach yielded a higher success navigation rate ranging from 2% to 5%, depending on the SNN timesteps. Considering the inherent lower computational cost of SNN, this work contributes to advancing the fusion of SNN and reinforcement learning techniques for energy-efficient autonomous navigation tasks in real-world mapless scenarios.

Quantum pseudo-harmonic oscillator potential in non-Euclidean space: application to diatomic molecules

Abstract The present work analyzes a physical system with a quantum pseudo-harmonic oscillator in three-dimensional constant curvature spaces within the framework of non-relativistic theory. We present expressions for the energy equation and radial wavefunctions that depend on the curvature parameter k, using the functional analysis approach and the asymptotic iteration method. Additionally, we calculate the energy eigenvalues for diatomic molecules N2, H2, and ScH as a function of the constant curvature k. Using the Hellmann-Feynmann theorem, we derive expressions for the curvature-dependent expectation values of r-2 and p2, which we detail for the diatomic molecule system in this work. Furthermore, we perform a comparative analysis of the results for non-Euclidean space (spherical and hyperbolic spaces with constant curvature) and Euclidean space.

Modeling of Functionally Graded Material Shells

In this research, we propose an algorithm to study the buckling of thin Functionally Graded Material (FGM) shells, utilizing a novel implementation of the asymptotic numerical method (ANM). Our approach integrates a three-step process: representation of variables and loading conditions through a truncated Taylor series, discretization using the finite element method (FEM), and advancement via a continuation method. This method is particularly effective for tracking the solution curve through systematic matrix inversion and tolerance adjustments. By applying this robust algorithm within the framework of Kirchhoff-Love theory, we analyze how the properties of FGM shells vary smoothly from metal at the base to ceramic at the surface, crucial for applications in aeronautics and civil engineering where stability under load is paramount. The results are validated against the Abaqus industrial code, demonstrating the accuracy of our model. Furthermore, we detail the impact of the volume fraction index on the load-displacement behavior and structural deformations, providing valuable insights for enhancing the design and safety of these critical structures.

Stochastic Dynamic Response of Delaminated Flexbeam Like Structures

In this work, the free vibration characteristics of flexbeam like structures, typically used in helicopter main or tail rotor blades, are investigated. The tapering effect in these laminated composite structures is introduced by terminating plies, which act as potential delamination sites. Delamination and uncertainties in material properties at various scales influence their dynamic behavior. The variational asymptotic method (VAM) is used as a mathematical framework to develop a model of a tapered composite beam with delamination. Subsequently, the modal characteristics are obtained by coupling the VAM model with the reduced 1D finite element beam model. Stochastic natural frequencies are investigated by combining the source uncertainties in the delaminated structure. Following a detailed validation study, the model capability is demonstrated on flexbeams typically used in helicopter rotor blades.

Bending theory and numerical simulation of open-web sandwich plate based on Fourier integral transform and mechanical asymptotic method

Bending theory and numerical simulation of open-web sandwich plate based on Fourier integral transform and mechanical asymptotic method

Asymptotic BLSCP models in uncertain and asymmetric environments-Take the charging station location problem.

The rapid development of the field of vehicles exposes many problems of charging station, the most common is the uncertainty and asymmetry of its task volume, so the flexibility of location and scale design is crucial. This paper proposes the asymptotic BLSCP model, suitable for uncertain and asymmetric environments, which balances facility workload and minimizes cost through the forward or backward asymptotic methods of candidate center locations and flexible allocation of jurisdictions. Additionally, the findings suggest these methods possess considerable potential for application and generalization.

THE COMBINED LAPLACE TRANSFORM AND OPTIMAL HOMOTOPY ASYMPTOTIC METHOD FOR SOLVING WAVE AND HEAT EQUATIONS

The goal of this research paper is to present a new hybrid method based on Laplace transform and optimal homotopy asymptotic method (LT-OHAM) for solving partial differential equations. In particular, we focus our attention to a number of standard partial differential equations (wave and heat), and present in detail our hybrid method for obtaining their solutions. Numerical experiments are considered to confirm the validity of this method. Comparisons are made with exact solutions. The results are in good agreement with the exact results.

Thermo-Magnetic properties of non-relativistic particles under the effect of energy-dependent Hellmann potential

This manuscript presents an analysis of the thermal and magnetic properties of particles moving in two dimensions under the influence of an external magnetic field and Aharanov-Bohm flux, considering an energy-dependent Hellmann potential. The energy eigenvalue is obtained using the asymptotic iteration method. Next, we model the system as a canonical ensemble and derive the partition function to acquire analytical expressions for the Helmholtz free energy, entropy, mean energy, and specific heat. We observe that an increase in the external magnetic field and AB flux generally increases the energy eigenvalues, with a stronger effect at lower flux values, while energy eigenvalues decrease with an increase in the screening parameter. Additionally, Helmholtz free energy and entropy functions are sensitive to temperature, particularly in the low-temperature regime, while specific heat exhibits a Schottky anomaly. We also compute the magnetisation and susceptibility functions, finding that both magnetisation and susceptibility increase with the external magnetic field strength and the AB flux.

Dynamic Behaviours of Non-Uniform Rayleigh Beam under Variable-Magnitude Accelerating Masses and Resting on Non-Uniform Bi-parametric Foundation with General Boundary Conditions

This paper investigates the dynamic behaviours of non-uniform Rayleigh beam under variable-magnitude accelerating masses and resting on non-uniform bi-parametric foundation with general boundary conditions. The problem is governed by a fourth-order partia l differential equation, generalised Galerkin’s method use to reduces the fourth-order partial differential equation to sequence second-order ordinary differential equations. Two cases are examined: moving force (neglecting inertia term) and moving mass (considering inertia). In order to solve the moving force problem, the transverse displacement response is obtained by variation of parameters. In order to solve the moving mass problem, the Runge-Kutta of fourth order is used to obtain the approximate solution because the commonly used Struble asymptotic method was unable to simplify the coupled second order ordinary differential equation due to the variability of the load magnitude. Analytical and numerical solutions (Runge-Kutta) are compared for validation of accuracy of the Runge-kutta scheme and found compared favourably. The results are presented in plotted curves, illustrating the effects of shear modulus, rotatory inertia correction factor results show increased shear moduli and rotatory inertia decrease response amplitudes, and critical speed for moving mass is lower than for moving force, leading to earlier resonance. Resonance conditions for the dynamical system are also established.

The use case of an asymptotic matching method in physics: large-angle pendulum

Abstract This paper examines the calculation of the period of a simple pendulum in the case of extremely large amplitude movements. The calculation is carried out using the method of asymptotic matching, which allows obtaining analytical solutions for the pendulum period that contrast very well with the values found through numerical integration. This analysis can be of great use to undergraduate and graduate students in physical sciences, as it provides mathematical tools that are highly useful in the fields of physical and mathematical sciences. These tools can be applied to a range of more complex problems in areas such as quantum mechanics, fluid mechanics, and related fields.

Radiation Effect on MHD Free Convective Flow Past a Semi-Infinite Porous Vertical Plate Through Porous Medium

The study of MHD heat and mass transfer dissipative free convective flow past a semi-infinite porous vertical plate through porous medium in presence of thermal radiation is considered. The novelty of the present work is to examine radiation effect (Rosseland Approximation) on the flow transport characteristics. The equations governing the flow of heat and mass transfer are solved by asymptotic series expansion method to evaluate the expressions for velocity, temperature, concentration fields, skin-friction, rate of heat and mass transfer. The influence of various physical parameters on the flow is discussed through graphs and in tabular form. It is found that an increase in radiation parameter to decrease the velocity and temperature. Further, it is seen that the skin -friction at the plate decreased with increasing values of radiation parameter.

An Enhanced Lagrangian‐Eulerian Method for a Class of Balance Laws: Numerical Analysis via a Weak Asymptotic Method With Applications

ABSTRACTIn this work, we designed and implemented an enhanced Lagrangian‐Eulerian numerical method for solving a wide range of nonlinear balance laws, including systems of hyperbolic equations with source terms. We developed both fully discrete and semi‐discrete formulations, and extended the concept of No‐Flow curves to this general class of nonlinear balance laws. We conducted a numerical convergence study using weak asymptotic analysis, which involved investigating the existence, uniqueness, and regularity of entropy‐weak solutions computed with our scheme. The proposed method is Riemann‐solver‐free. To evaluate the shock‐capturing capabilities of the enhanced Lagrangian‐Eulerian numerical scheme, we carried out numerical experiments that demonstrate its ability to accurately resolve the key features of balance law models and hyperbolic problems. A representative set of numerical examples is provided to illustrate the accuracy and robustness of the proposed method.

Perturbation Theory Methods for the Semiconductor Plasma Diode Simulation

A technique for solving a nonlinear singularly perturbed boundary value problem of predicting the state of an electron-hole plasma in the active region of p-i-n (plasma) diodes is considered. The problem is formulated for system of equations of the electron and hole currents continuity and the Poisson's equation. The solution to the problem is sought by the asymptotic method of boundary corrections. It is shown that boundary corrections play a key role in forming the electric field in the active region of the diode. Under certain conditions, boundary corrections demonstrate non-monotonic behavior. The presence of boundary corrections makes it possible to solve problems of heat distribution in the semiconductor device under study, problems of the influence of external electromagnetic fields on electron-hole plasma, etc. A series of computer experiments were conducted.