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

2021 ◽  
Vol 14 ◽  
Author(s):  
Yongli Wei ◽  
Peng Li ◽  
Baofeng Cao ◽  
Xiaoqiang Li ◽  
Xiong Zhang ◽  
...  
Keyword(s):  
Numerical Method ◽  
Electromagnetic Pulse ◽  
Physical Parameters ◽  
Exponential Form ◽  
Double Exponential ◽  
Linear Fit ◽  
Waveform Simulation ◽  
Convergent Solution ◽  
Double Exponential Function ◽  
Parameters Calculation

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.

Regulation of calcium current by voltage and cytoplasmic calcium in canine gastric smooth muscle

1992 ◽  
Vol 262 (3) ◽  
pp. C691-C700 ◽  
Author(s):  
F. Vogalis ◽  
N. G. Publicover ◽  
K. M. Sanders
Keyword(s):  
Time Course ◽  
Fast Component ◽  
Patch Clamp Technique ◽  
Similar Time ◽  
Whole Cell Patch Clamp ◽  
Gastric Smooth Muscle ◽  
Double Exponential ◽  
Circular Layer ◽  
Double Exponential Function ◽  
Ca2 Channels

The regulation of Ca2+ current by intracellular Ca2+ was studied in isolated myocytes from the circular layer of canine gastric antrum. Ca2+ current was measured with the whole cell patch-clamp technique, and changes in cytoplasmic Ca2+ ([Ca2+]i) were simultaneously measured with indo-1 fluorescence. Ca2+ currents were activated by depolarization and inactivated despite maintained depolarization. Ca2+ current inactivation was fit with a double exponential function. Using Ba2+ or Na+ as charge carriers removed the fast component of inactivation, whereas enhanced intracellular buffering of Ca2+ did not remove the fast component. Ca2+ currents were associated with a rise in [Ca2+]i. The decrease in [Ca2+]i following repolarization was exponential, and during the relaxation of [Ca2+]i, Ca2+ current was inactivated. The inward current recovered with a similar time course as the decrease in [Ca2+]i, suggesting that [Ca2+]i regulates the basal availability of Ca2+ channels. These data support the hypothesis that, although [Ca2+]i may influence the resting level of inactivation, it is the "submembrane" compartment of [Ca2+]i that regulates the development of inactivation.

scholarly journals The Parameter Estimation of Double Exponential Pulse Based on a Least Infinity Norm Fitting Method

2021 ◽  
Vol 2083 (4) ◽  
pp. 042002
Author(s):  
Yuewu Shi ◽  
Wei Wang ◽  
Zhizhen Zhu ◽  
Xin Nie
Keyword(s):  
Estimation Error ◽  
Estimation Method ◽  
Maximum Amplitude ◽  
Least Square Method ◽  
Least Square ◽  
Physical Parameters ◽  
Infinity Norm ◽  
Fitting Method ◽  
Double Exponential ◽  
Exponential Pulse

Abstract This paper presents an estimation method of double exponential pulse (DEP) between the physical parameters rise time (t r), full width at half maximum amplitude (t FWHM) and the mathematical parameters α, β. A newly fitting method based on the least infinity norm criterion is proposed to deal with the estimation problem of DEP. The calculation process and equation of parameters of this method is proposed based on an m-th-order polynomial fitting model. This estimation method is compared with the least square method by the same data and fitting function. The results show that the maximum estimation error of parameters of double exponential pulse obtained by the least infinity norm method is 1.5 %.

Implementation of DTM as a numerical study for the Casson fluid flow past an exponentially variable stretching sheet with thermal radiation

2021 ◽  
pp. 2150111
Author(s):  
Khadijah M. Abualnaja
Keyword(s):  
Fluid Flow ◽  
Thermal Radiation ◽  
Numerical Method ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Transformation Method ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Special Cases

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement.

scholarly journals Effect of Dry-Wet Circulation on Moisture Absorption of Autoclaved Aerated Concrete

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Xiao He ◽  
Jian Yin ◽  
Jiewen Yang ◽  
Qiao Liang ◽  
Songyun Wu
Keyword(s):  
Moisture Absorption ◽  
Autoclaved Aerated Concrete ◽  
Double Exponential ◽  
Temperature And Humidity ◽  
Cracking Performance ◽  
Absorption Performance ◽  
Aerated Concrete ◽  
Spss Software ◽  
C 30 ◽  
Double Exponential Function

Moisture absorbability is the characteristic of autoclaved aerated concrete that differs from other wall materials. For autoclaved aerated concrete, dry-wet circulation is the main actual service environment and can directly affect moisture absorbability, which influences cracking performance of structure. In this study, autoclaved aerated concrete with dry-wet circulation times of 0, 30, 60, 150, and 270 is selected. The experiment is performed under the condition of temperatures 20°C, 30°C, 40°C, and 50°C and relative humidities (RH) of 40%, 60%, and 80%. The temperature and humidity have significant effects on moisture absorption. When the dry-wet circulation times are increased, the moisture absorption performance improves; when comparing the specimen at the dry-wet circulation of 0 times with the specimen of dry-wet circulation of 270 times, the amount of moisture absorption content increased by 85.7%, at the temperature of 50°C and RH of 80%. Origin software is chosen to fit the moisture absorption kinetics model. SPSS software is used to analyse the linear regression and variance. The results of hygroscopic kinetics showed that the fitting effect of the double exponential function was optimal, and the temperature and humidity were closely correlated with the specimens under dry-wet circulation, for R2 greater than 0.941.

TEMPORAL PROPERTIES OF PHOTOREFRACTIVE MATERIALS

1996 ◽  
Vol 05 (01) ◽  
pp. 9-24 ◽  
Author(s):  
D. STATMAN ◽  
G.C. GILBREATH
Keyword(s):  
Exponential Function ◽  
Modulation Depth ◽  
Rate Equations ◽  
Temporal Properties ◽  
High Modulation ◽  
Beam Coupling ◽  
Double Exponential ◽  
Photorefractive Materials ◽  
Double Exponential Function

Photorefractive two-beam coupling is examined experimentally for the case of high modulation depth. It is seen that the dynamics of signal growth and decay are best described by a double exponential function. The properties of this function with respect to interaction angle and modulation depth are studied. It is suggested that the equations governing photorefractive dynamics may be reduced to a pair of coupled bilinear rate equations which adequately describe photorefractive dynamics for high modulation depth.

The Hardness Changing Regularity of Quenched-Steel in Tempering Process and Its Double-Exponential Model

2010 ◽  
Vol 146-147 ◽  
pp. 1578-1582
Author(s):  
Cong Sheng Guo ◽  
Shu Ming Long ◽  
Hai Wa Bo ◽  
Hong Bin Tan
Keyword(s):  
Phase Transformation ◽  
Exponential Function ◽  
Optimization Design ◽  
Hardness Test ◽  
Exponential Model ◽  
Physical Metallurgy ◽  
Double Exponential ◽  
Quenched Steel ◽  
Double Exponential Function ◽  
Tempering Process

The transformation of tempering for quenched steel corresponded to complicated process of phase transformation, and mechanical properties of quenched-and-tempered steel were related to the phase transformation. In practice, hardness test was adopted to judge whether the properties of tempered-parts qualified because of its facility. Numerous researches indicated that, there existed correlativity expressed by different function forms between tempering hardness of quenched-steel and its tempering parameters. However, considering physical metallurgy of tempering process, the adoption of double-exponential function would help to describe regularity of hardness changing more exactly for quenched-steel during tempering process. Additionally, results of hardness tests for isothermal tempering and molding/simulation researches have shown that, the model of double-exponential function, which can reflect decline law of tempering hardness for quenched-steel, would provide basis for optimization design of tempering parameters, performance prediction of tempered-parts, and energy-saving heat-treatment on tempering process.

A Three-Dimensional Numerical Method for Turbomachinery Blading

1992 ◽  
Author(s):  
C. W. Gu ◽  
J. Z. Xu ◽  
J. Y. Du
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Stream Function ◽  
Three Dimensional ◽  
Computational Results ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Stream Functions ◽  
Derivatives Of ◽  
Convergent Solution

By inversing one of the stream functions and their principal equations in a three–dimensional flow the equations with the second–order partial derivatives of both the coordinate and another stream function are derived. The corresponding boundary conditions are easily specified. Based on these equations and the boundary conditions the convergent solution for turbomachinery blading is obtained. The computational results show that the method is simple and effective.

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