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.

Optimization and Application of Spacing Parameter for Loosening Blasting with 24-m-High Bench in Barun Open-Pit Mine

In view of the near slope blasting in Barun open-pit mine, which has merged sublevel mining, the operation safety conditions of middle-sized and large equipment in the second phase expansion are poor and need urgent improvement. To increase the efficiency of expansion and reduce costs, a 24-m-high bench and large spacing parameter for loosening blasting are proposed. The analysis of the physical mechanism of the stress wave attenuation in the rock indicates that the cylindrical charge is equivalent to several spherical charges. Considering the pressure attenuation, reflection, transmission, and superposition of the spherical charge after the equivalence, a double exponential function correction equation of the stress wave attenuation is obtained based on the Mises strength criterion. The stress of any point in the rock medium with various spacing parameter is obtained by calculation. ANSYS/LS-DYNA was used to simulate and study the stress distribution of a 24-m-high bench with various spacing parameter. Meanwhile, the accuracy of the correction equation was verified. The parameters of the high-bench blasting with good effect and low cost were determined to be 15 m × 5.5 m, and field tests were carried out. Results show that the large spacing parameter for 24-m-high bench loosening blasting in Barun open-pit mine is efficient and economical in medium-hard rock blasting. This study provides a reference for the practical exploration of the expansion of high benches in open-pit mines in China. The calculation error of the corrected double exponential function is near the numerical simulation result. It is suitable for all kinds of professional designers.

Measurement Models for Carbon Dioxide Emission Factors of Passenger Cars Considering Characteristics of Roads and Traffic

In order to effectively control carbon dioxide emissions of motorized vehicles, it is very important to measure their carbon dioxide emission factors. The objective of this paper was to develop measurement models for the carbon dioxide emission factors of passenger cars. Road systems of downtown areas of four typical Chinese counties were explored and 12 types of basic road networks were recognized and defined. With PTV Vissim, microscopic traffic simulation models were set up for every type of basic road network, average speeds of the simulated cars were collected, and carbon dioxide emissions were calculated using MOVES (Motor Vehicle Emission Simulator) software. For model development, the paper put forth two compound explanatory variables: the weighted average of segment lengths and the sum of critical ratios of volume to saturation flow rate. Six functional relationships for the variables were tested and the double exponential function was proven to be the most appropriate. Finally, for each of the 12 types of basic road networks, a measurement model for carbon dioxide emission factors was calibrated using the double exponential function for the variables. The measurement models can be used to estimate the carbon dioxide emissions of passenger cars concerning potential improvement schemes impacting traffic demand and/or traffic supply.

Universality in COVID-19 spread in view of the Gompertz function

We demonstrate that universal scaling behavior is observed in the current coronavirus (SARS-CoV-2) spread, the COVID-19 pandemic, in various countries. We analyze the numbers of infected people who tested positive (cases) in 11 selected countries (Japan, USA, Russia, Brazil, China, Italy, Indonesia, Spain, South Korea, UK, and Sweden). By using a double exponential function called the Gompertz function, $f_\mathrm{G}(x)=\exp(-e^{-x})$, the number of cases is well described as $N(t)=N_0 f_\mathrm{G}(\gamma(t-t_0))$, where $N_0$, $\gamma$, and $t_0$ are the final number of cases, the damping rate of the infection probability, and the peak time of the daily number of new cases, $dN(t)/dt$, respectively. The scaled data of cases in most of the analyzed countries are found to collapse onto a common scaling function $f_\mathrm{G}(x)$ with $x=\gamma(t-t_0)$ being the scaling variable in the range of $f_\mathrm{G}(x)\pm 0.05$. The recently proposed indicator, the so-called $K$ value, the increasing rate of cases in one week, is also found to show universal behavior. The mechanism for the Gompertz function to appear is discussed from the time dependence of the produced pion numbers in nucleus–nucleus collisions, which is also found to be described by the Gompertz function.

Optimal PV Parameter Estimation via Double Exponential Function-Based Dynamic Inertia Weight Particle Swarm Optimization

Parameters associated with electrical equivalent models of the photovoltaic (PV) system play a significant role in the performance enhancement of the PV system. However, the accurate estimation of these parameters signifies a challenging task due to the higher computational complexities and non-linear characteristics of the PV modules/panels. Hence, an effective, dynamic, and efficient optimization technique is required to estimate the parameters associated with PV models. This paper proposes a double exponential function-based dynamic inertia weight (DEDIW) strategy for the optimal parameter estimation of the PV cell and module that maintains an appropriate balance between the exploitation and exploration phases to mitigate the premature convergence problem of conventional particle swarm optimization (PSO). The proposed approach (DEDIWPSO) is validated for three test systems; (1) RTC France solar cell, (2) Photo-watt (PWP 201) PV module, and (3) a practical test system (JKM330P-72, 310 W polycrystalline PV module) which involve data collected under real environmental conditions for both single- and double-diode models. Results illustrate that the parameters obtained from proposed technique are better than those from the conventional PSO and various other techniques presented in the literature. Additionally, a comparison of the statistical results reveals that the proposed methodology is highly accurate, reliable, and efficient.

Universality in COVID-19 spread in view of the Gompertz function

We demonstrate that universal scaling behavior is observed in the current coronavirus (COVID-19) spread in various countries. We analyze the numbers of infected people in selected eleven countries (Japan, USA, Russia, Brazil, China, Italy, Indonesia, Spain,South Korea, UK, and Sweden). By using the double exponential function called the Gompertz function, fG(x) = exp(−e−x), the number of infected people is well described as N(t) = N0fG(γ(t − t0)), where N0, γ and t0 are the final total number of infected people, the damping rate of the infection probability and the peak time of dN(t)/dt, respectively. The scaled data of infected people in most of the analyzed countries are found to collapse onto a common scaling function fG(x) with x = γ(t − t0) in the range of fG(x) ± 0.05. The recently proposed indicator so-called the K value, the increasing rate of infected people in one week, is also found to show universal behavior. The mechanism for the Gompertz function to appear is discussed from the time dependence of the produced pion numbers in nucleus-nucleus collisions, which is also found to be described by the Gompertz function.

Lump-type and interaction solutions to an extended (3 + 1)-dimensional Jimbo–Miwa equation

By using the Hirota bilinear method, we construct new lump-type solutions to an extended [Formula: see text]-dimensional Jimbo–Miwa equation, which describes certain [Formula: see text]-dimensional wave phenomena in physics. The presented solutions contain 10 arbitrary parameters and only need to satisfy four restrictive conditions to be analytic, thereby enriching the existing lump-type solutions. Moreover, we compute their interaction solutions with double exponential function waves, which include rogue wave solutions. Dynamical features of the obtained solutions are graphically exhibited.

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

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.

The finite representation property for composition, intersection, domain and range

We prove that the finite representation property holds for representation by partial functions for the signature consisting of composition, intersection, domain and range and for any expansion of this signature by the antidomain, fixset, preferential union, maximum iterate and opposite operations. The proof shows that, for all these signatures, the size of base required is bounded by a double-exponential function of the size of the algebra. This establishes that representability of finite algebras is decidable for all these signatures. We also give an example of a signature for which the finite representation property fails to hold for representation by partial functions.