Reverse pulse voltammetry and polarography: a general analytical solution

1994 ◽  
Vol 72 (12) ◽  
pp. 2369-2377 ◽  
Author(s):  
Luis Camacho ◽  
Juan José Ruiz ◽  
Carmen Serna ◽  
Angela Molina ◽  
Francisco Martínez-Ortiz
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Arbitrary Power ◽  
Plane Electrode ◽  
General Analytical Solution ◽  
Reverse Pulse ◽  
Pulse Voltammetry

A rigorous analytical solution to reverse pulse techniques for a plane electrode expanding with an arbitrary power of time is presented. Our results include the plane approximation for SMDE as well as the expanding plane electrode model for DME. In the case of SMDE, our results have been contrasted with those obtained by numerical solution of the problem, obtaining identical results. Finally, we have compared our treatment with previous solutions in literature.

A General Method for the Fatigue-Resistant Design of Mechanical Components—Part 2: Analytical

1975 ◽  
Vol 97 (3) ◽  
pp. 970-975
Author(s):  
D. T. Vaughan ◽  
L. D. Mitchell
Keyword(s):  
Analytical Solution ◽  
Fatigue Fracture ◽  
Fracture Criterion ◽  
Fatigue Loading ◽  
General Analytical Solution ◽  
Failure Theory ◽  
Straight Line ◽  
Mechanical Components ◽  
General Method

This paper develops the general analytical solution to the design of mechanical components under fatigue loading. Its only limitation is that the overloading lines must be a straight line on the σa−σm diagram. The designer is free to select his own failure theory for the material he intends to use as well as to select his own fatigue fracture criterion.

scholarly journals Analytical and Experimental Analyses of Nonlinear Vibrations in a Rotary Inverted Pendulum

2021 ◽  
Author(s):  
Mohammadjavad Rahimi dolatabad ◽  
Abdolreza Pasharavesh ◽  
Amir Ali Akbar Khayyat
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Multiple Scales ◽  
Nonlinear Oscillations ◽  
Wide Frequency Range ◽  
Perturbative Method ◽  
Full State Feedback ◽  
Rotary Inverted Pendulum

Abstract Gaining insight into possible vibratory responses of dynamical systems around their stable equilibria is an essential step, which must be taken before their design and application. The results of such a study can significantly help prevent instability in closed-loop stabilized systems through avoiding the excitation of the system in the neighborhood of its resonance. This paper investigates nonlinear oscillations of a Rotary Inverted Pendulum (RIP) with a full-state feedback controller. Lagrange’s equations are employed to derive an accurate 2-DoF mathematical model, whose parameter values are extracted by both the measurement and 3D modeling of the real system components. Although the governing equations of a 2-DoF nonlinear system are difficult to solve, performing an analytical solution is of great importance, mostly because, compared to the numerical solution, the analytical solution can function as an accurate pattern. Additionally, the analytical solution is generally more appealing to engineers because their computational costs are less than those of the numerical solution. In this study, the perturbative method of multiple scales is used to obtain an analytical solution to the coupled nonlinear motion equations of the closed-loop system. Moreover, the parameters of the controller are determined, using the results of this solution. The findings reveal the existence of hardening- and softening-type resonances at the first and second vibrational modes, respectively. This led to a wide frequency range with moderately large-amplitude vibrations, which must be avoided when adjusting a time-varying set-point for the system. The analytical results of the nonlinear vibration of the RIP are verified by experimental measurements, and a very good agreement is observed between the results of both approaches.

The Effect of Biot Number on a One-Dimensional General Conduction Solution

2021 ◽  
Author(s):  
Robert L. McMasters ◽  
Filippo de Monte ◽  
James V. Beck
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Biot Number ◽  
Analytical Solutions ◽  
Heat Fluxes ◽  
Graphical Form ◽  
Large Temperature ◽  
Convection Coefficient ◽  
General Analytical Solution

Abstract Analytical solutions for thermal conduction problems are extremely important, particularly for verification of numerical codes. Temperatures and heat fluxes can be calculated very precisely, normally to eight or ten significant figures, even in situations involving large temperature gradients. It can be convenient to have a general analytical solution for a transient conduction problem in rectangular coordinates. The general solution is based on the principle that the three primary types of boundary conditions (prescribed temperature, prescribed heat flux, and convective) can all be handled using convective boundary conditions. A large convection coefficient closely approximates a prescribed temperature boundary condition and a very low convection coefficient closely approximates an insulated boundary condition. Since a dimensionless solution is used in this research, the effect of various values of dimensionless convection coefficients, or Biot number, are explored. An understandable concern with a general analytical solution is the effect of the choice of convection coefficients on the precision of the solution, since the primary motivation for using analytical solutions is the precision offered. An investigation is made in this study to determine the effects of the choices of large and small convection coefficients on the precision of the analytical solutions generated by the general convective formulation. Results are provided, in tablular and graphical form, to illustrate the effects of the choices of convection coefficients on the precision of the general analytical solution.

scholarly journals Comparative Study of Analytic Solution and Numerical Solution of Baseband Symbol Signal Based on Optimal Generic Function

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Mingxin Liu ◽  
Wei Xue ◽  
Sergey B. Makarov ◽  
Junwei Qi ◽  
Beiming Li
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Solution Process ◽  
Development Trend ◽  
Partial Solution ◽  
Research Process ◽  
Constraint Condition ◽  
Energy Limit ◽  
Function Model ◽  
Boundary Constraints

In this paper, the optimal mathematical generic function model is established using the minimum out-of-band energy radiation criterion. Firstly, the energy limit conditions, boundary constraints, and peak-to-average ratio constraints are applied to the generic function model; thus, the analytical solutions are obtained under different parameters. Secondly, a single symbol signal energy constraint condition and boundary constraint condition are added to the generic function model; thus, the numerical solution of the different parameters is obtained. In the process of solving the analytical solution, the partial solution process is simplified to solve the analytical solution, and there are also digital truncation problems. In addition, the corresponding order of the Lagrange differential equation increases by a multiple of 2 when the parameter n increases, which makes the solution extremely complicated or even impossible to solve. The numerical solution is in line with the current development trend of digital communication, and there is no need to simplify the solution process in the process of solving the numerical solution. When the parameter n and the Fourier series m take different values, the obtained symbol signals can also meet the needs of different communication occasions. The relevant data of the above research process were solved by a MATLAB software simulation, which proves the correctness of the method and the superiority of the numerical method.

General analytical solution for photoacoustic effect with multilayers

2008 ◽  
Vol 92 (1) ◽  
pp. 014103 ◽  
Author(s):  
Hanping Hu ◽  
Wei Zhang ◽  
Jun Xu ◽  
Yi Dong
Keyword(s):  
Analytical Solution ◽  
Photoacoustic Effect ◽  
General Analytical Solution
Sign in / Sign up

Export Citation Format

Share Document