The Optimal Auxiliary Functions Method

2021 ◽  
pp. 11-16
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu ◽  
Bogdan Marinca
Keyword(s):  
Auxiliary Functions

Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

2021 ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu ◽  
Bogdan Marinca
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Auxiliary Functions

scholarly journals Construction of Analytic Solution to Axisymmetric Flow and Heat Transfer on a Moving Cylinder

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1335
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stokes Equations ◽  
Nonlinear Differential Equations ◽  
Axisymmetric Flow ◽  
Control Parameters ◽  
Auxiliary Functions ◽  
Flow And Heat Transfer ◽  
Moving Cylinder ◽  
Convergence Control

Based on a new kind of analytical approach, namely the Optimal Auxiliary Functions Method (OAFM), a new analytical procedure is proposed to solve the problem of the annular axisymmetric stagnation flow and heat transfer on a moving cylinder with finite radius. As a novelty, explicit analytical solutions were obtained for the considered complex problem. First, the Navier–Stokes equations were simplified by means of similarity transformations that depended on different parameters and some combinations of these parameters, and the problem under study was reduced to six nonlinear ordinary differential equations with six unknowns. The OAFM proves to be a powerful tool for finding an accurate analytical solution for nonlinear problems, ensuring a fast convergence after the first iteration, even if the small or large parameters are absent, since the determination of the convergence-control parameters is independent of the magnitude of the coefficients that appear in the nonlinear differential equations. Concerning the main novelties of the proposed approach, it is worth mentioning the presence of some auxiliary functions, the involvement of the convergence-control parameters, the construction of the first iteration and much freedom to select the procedure for determining the optimal values of the convergence-control parameters.

scholarly journals A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-30 ◽  
Author(s):  
Dongyan Shi ◽  
Yunke Zhao ◽  
Qingshan Wang ◽  
Xiaoyan Teng ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Analysis Model ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Auxiliary Functions ◽  
Arbitrary Boundary Conditions ◽  
Closed Shells

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

scholarly journals Use of lined-up auxiliary functions in the evaluation of overlap integrals over integer and non-integer n Slater type orbitals

2019 ◽  
Vol 12 ◽  
pp. 298-301
Author(s):  
Israfil I. Guseinov ◽  
Zekayi Andıç ◽  
Bahtiyar A. Mamedov ◽  
Nurşen Seçkin Görgün
Keyword(s):  
Slater Type Orbitals ◽  
Overlap Integrals ◽  
Slater Type ◽  
Auxiliary Functions

scholarly journals A design of stretcher with auxiliary functions of lateral positioning and transferring for immobilized patients

2021 ◽  
Vol 336 ◽  
pp. 02014
Author(s):  
Ying Xiong ◽  
Xuehua Tang ◽  
Congcong Shi ◽  
Yang Yang
Keyword(s):  
Inverse Kinematics ◽  
Forward Kinematics ◽  
Motion Simulation ◽  
Practical Application ◽  
Auxiliary Functions ◽  
Rigid Rods ◽  
Hospital Bed ◽  
Motion Process ◽  
Lateral Positioning ◽  
Position State

For now, many hospitals that require nurses to move patients by hand from stretchers to a hospital bed, so a design of stretcher with auxiliary functions of lateral positioning and transferring for immobilized patients, which is a mechanical mechanism consisted of rigid rods, joints and sliders, was designed to help the nurses to move patients between beds and reduce their workload. Driven by motors, the rigid rods can be rotated, stretched or shortened so that the entire stretcher bed board can archive to a proper posture and position. In this paper, the following objectives will be achieved: (i) Create a schematic of the mechanism and describe the principles and functions (ii) the calculation of inverse kinematics, forward kinematics, dynamics (including energy), and PD control in the mechanism (iii) The motion process of simulating the mechanism using MATLAB (iv) Using MATLAB to create the plots of angle, torque, and position state (v) Using SolidWorks to construct the prototype and to implement the motion simulation of the mechanism (vi) Describe the practical application and future Extensions of this mechanism.

Photosynthetic and Auxiliary Functions of Arabidopsis Thaliana — In Vivo and In Vitro Studies

1998 ◽  
pp. 2079-2082
Author(s):  
Hanna Norén ◽  
Bertil Andersson ◽  
Per Svensson
Keyword(s):  
Arabidopsis Thaliana ◽  
In Vitro Studies ◽  
Auxiliary Functions

Piecewise Optimal Auxiliary Functions Method

2021 ◽  
pp. 417-434
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu ◽  
Bogdan Marinca
Keyword(s):  
Auxiliary Functions
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