Mathematical Parameters Calculation of Double Exponential Function by a New Numerical Method

Background: Lightning electromagnetic pulse (LEMP) and high-altitude electromagnetic pulse (HEMP) are widely described by three physical parameters (rise time tr, full-width at half-maximum pulse width tw, and maximum electric field strength E0). These pulse shapes are often given by a double exponential form concerning four mathematical parameters, namely α, β, k and Ep. Objective: The transformation from physical parameters into mathematical parameters is necessary in waveform simulation and is traditionally accomplished by linear fit functions regarding the two groups of parameters. However, traditional methods commonly rely on data analysis and calculation. In order to obtain more concise and clear mathematical parameters. Methods: In this paper, a numerical method to calculate the mathematical parameters by solving nonlinear equations with three key constraints is proposed. Firstly, we establish the nonlinear system of equations regarding four variables, namely t1, t2, α and β. Then, three constraints are given to converge the solutions of the equations. Lastly, selecting the minimal value of the convergent solution of each equation. Results: Results: Comparing the solutions obtained by our proposed method to the iterated ones, the overall relative error is less than 2×10-8. Conclusion: The results show that our proposed method not only simplifies the transformation from physical parameters to mathematical parameters, but also keeps the solutions highly accurate.

Exploration of Temperature-Dependent Thermal Conductivity and Diffusion Coefficient for Thermal and Mass Transportation in Sutterby Nanofluid Model over a Stretching Cylinder

This declaration ponders the impacts of Joule warm, separation, and warming radiation for the progression of MHD Sutterby nanofluid past over an all-inclusive chamber. The wonder of warmth and mass conduction is demonstrated under warm conductivity relying upon temperature and dispersion coefficients individually. Besides, the conventional Fourier and Fick laws have been applied in the outflows of warm and mass transport. The control model comprising of a progression of coupled incomplete differential conditions is changed over into a standard arrangement of nonlinear coupled differential conditions by reasonable likeness changes. The subsequent arrangement of articulations is systematically treated through an ideal homotopic method. The impacts of various dimensionless stream boundaries on the speed, temperature, and focus fields are delineated through diagrams. The range of some parameters involved is assumed for the convergent solution as 0 < R e < 10 , 0 < P r < 6.5 , 0 < E c < 40 , 0 < R d < 1.5 , 0 < S 1 < 0.5 , 0 < S 2 < 0.5 , 0 < L e < 0.5 , 0 < N t < 2.5 , and 0 < N b < 2.0 . The patterns of skin friction coefficient, local Nusselt, and Sherwood numbers are examined via bar charts. The principle consequence of the proposed study is that the decay of the speed for the Sutterby liquid boundary, the deterioration of the variable warm conductivity, the temperature, and the radiation increase the framework temperature. The delineation boundaries show the opposite conduct for the temperature and fixation outskirts layers.

Application of discretization error estimators in stepped column buckling problems

In order to reduce the discretization error, in this paper, Richardson’s Extrapolation and Convergence Error Estimator were used to investigating the buckling problem convergence. The main objective was to verify the convergence order of the stepped column problem and to define a consistent moment of inertia at the point of variation of the cross-section. The variable of interest was the critical buckling load obtained by the Finite Difference Method. The convergent solution obtained errors less than 10-8, and this work showed that the best solution is not defined by excessive mesh refinement, but by the solution convergence analysis.

Strong Convergence on the Aggregate Constraint-Shifting Homotopy Method for Solving General Nonconvex Programming

In the paper, the aggregate constraint-shifting homotopy method for solving general nonconvex nonlinear programming is considered. The aggregation is only about inequality constraint functions. Without any cone condition for the constraint functions, the existence and convergence of the globally convergent solution to the K-K-T system are obtained for both feasible and infeasible starting points under much weaker conditions.

APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

Acceleration Method for Evolutionary Optimization of Variable Cycle Engine

Variable cycle engine (VCE) is considered as one of the best options for advanced military or commercial supersonic propulsion system. Variable geometries enable the engine to adjust performance over the entire the flight envelope but add complexity to the engine. Evolutionary algorithms (EAs) have been widely used in the design of VCE. The initial guesses of the engine model are generally set using design point information during evolutionary optimization. However, the design point information is not suitable for all situations. Without suitable initial guesses, the Newton-Raphson solver will not be able to reach the solution quickly, or even get a convergent solution. In this paper, a new method is proposed to obtain suitable initial guesses of VCE model during evolutionary optimization. Differential evolution (DE) algorithm is used to verify our method through a series of optimization cases of a double bypass VCE. The result indicates that the method can significantly reduce the VCE model call number during evolutionary optimization, which means a dramatic reduction in terms of evolution time. And the robustness of the optimization is not affected by the method. The method can also be used in the evolutionary optimization of other engines.

Optimal control of rapid cooperative spacecraft rendezvous with multiple specific-direction thrusts

Focusing on the long-distance rapid cooperative rendezvous of two spacecraft under finite continuous thrust, this paper proposes a practical strategy for space operation using multiple specific-direction thrusts. Based on the orbital dynamic theory and Pontryagin’s maximum principle, the dynamic equations and optimal control equations for radial, circumferential, and normal thrust are determined. The optimization method is a hybrid algorithm. The initial costate variables for the fuel-optimal rapid cooperative rendezvous problem are obtained using quantum particle swarm optimization and subsequently set as the initial values in the sequence quadratic programming to search for the exact convergent solution. The elliptical and near-circular mission orbital rendezvous for spacecraft with multiple specific-direction thrusts are simulated and optimized. Numerical examples verifying the proposed method are provided. The results facilitate easier realization of rapid spacecraft maneuvering under continuous thrust conditions.

Globally convergent method for designing twice spline contractual function

To design a quadratic spline contractual function in the case of discretely unknown nodes, a modified constraint shifting homotopy algorithm for solving principal–agent problems is constructed in the paper. Then the existence of globally convergent solution to KKT systems for the principal–agent problem with spline contractual function is proved under a much weaker condition. The proposed algorithm only requires that any initial point is in the shifted feasible set but not necessarily in the original feasible set.