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1 – 10 of 60J.I. Ramos and Carmen María García López
The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the…
Abstract
Purpose
The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.
Design/methodology/approach
An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.
Findings
The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.
Originality/value
The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.
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Geming Zhang, Lin Yang and Wenxiang Jiang
The purpose of this study is to introduce the top-level design ideas and the overall architecture of earthquake early-warning system for high speed railways in China, which is…
Abstract
Purpose
The purpose of this study is to introduce the top-level design ideas and the overall architecture of earthquake early-warning system for high speed railways in China, which is based on P-wave earthquake early-warning and multiple ways of rapid treatment.
Design/methodology/approach
The paper describes the key technologies that are involved in the development of the system, such as P-wave identification and earthquake early-warning, multi-source seismic information fusion and earthquake emergency treatment technologies. The paper also presents the test results of the system, which show that it has complete functions and its major performance indicators meet the design requirements.
Findings
The study demonstrates that the high speed railways earthquake early-warning system serves as an important technical tool for high speed railways to cope with the threat of earthquake to the operation safety. The key technical indicators of the system have excellent performance: The first report time of the P-wave is less than three seconds. From the first arrival of P-wave to the beginning of train braking, the total delay of onboard emergency treatment is 3.63 seconds under 95% probability. The average total delay for power failures triggered by substations is 3.3 seconds.
Originality/value
The paper provides a valuable reference for the research and development of earthquake early-warning system for high speed railways in other countries and regions. It also contributes to the earthquake prevention and disaster reduction efforts.
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Gopal Shruthi and Murugan Suvinthra
The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.
Abstract
Purpose
The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.
Design/methodology/approach
A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.
Findings
Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.
Originality/value
The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.
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Hussein Y.H. Alnajjar and Osman Üçüncü
Artificial intelligence (AI) models are demonstrating day by day that they can find long-term solutions to improve wastewater treatment efficiency. Artificial neural networks…
Abstract
Purpose
Artificial intelligence (AI) models are demonstrating day by day that they can find long-term solutions to improve wastewater treatment efficiency. Artificial neural networks (ANNs) are one of the most important of these models, and they are increasingly being used to forecast water resource variables. The goal of this study was to create an ANN model to estimate the removal efficiency of biological oxygen demand (BOD), total nitrogen (TN), total phosphorus (TP) and total suspended solids (TSS) at the effluent of various primary and secondary treatment methods in a wastewater treatment plant (WWTP).
Design/methodology/approach
The MATLAB App Designer model was used to generate the data set. Various combinations of wastewater quality data, such as temperature(T), TN, TP and hydraulic retention time (HRT) are used as inputs into the ANN to assess the degree of effect of each of these variables on BOD, TN, TP and TSS removal efficiency. Two of the models reflect two different types of primary treatment, while the other nine models represent different types of subsequent treatment. The ANN model’s findings are compared to the MATLAB App Designer model. For evaluating model performance, mean square error (MSE) and coefficient of determination statistics (R2) are utilized as comparative metrics.
Findings
For both training and testing, the R values for the ANN models were greater than 0.99. Based on the comparisons, it was discovered that the ANN model can be used to estimate the removal efficiency of BOD, TN, TP and TSS in WWTP and that the ANN model produces very similar and satisfying results to the APPDESIGNER model. The R-value (Correlation coefficient) of 0.9909 and the MSE of 5.962 indicate that the model is accurate. Because of the many benefits of the ANN models used in this study, it has a lot of potential as a general modeling tool for a range of other complicated process systems that are difficult to solve using conventional modeling techniques.
Originality/value
The objective of this study was to develop an ANN model that could be used to estimate the removal efficiency of pollutants such as BOD, TN, TP and TSS at the effluent of various primary and secondary treatment methods in a WWTP. In the future, the ANN could be used to design a new WWTP and forecast the removal efficiency of pollutants.
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This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and…
Abstract
Purpose
This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and uniqueness are proved. The authors divide the proof into two sections for the linear associated problem; the authors derive the a priori bound and demonstrate the operator range density that is generated. The authors solve the nonlinear problem by introducing an iterative process depending on the preceding results.
Design/methodology/approach
The functional analysis method is the a priori estimate method or energy inequality method.
Findings
The results show the efficiency of a priori estimate method in the case of time-fractional order differential equations with nonlocal conditions. Our results also illustrate the existence and uniqueness of the continuous dependence of solutions on fractional order differential equations with nonlocal conditions.
Research limitations/implications
The authors’ work can be considered a contribution to the development of the functional analysis method that is used to prove well-positioned problems with fractional order.
Originality/value
The authors confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.
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The initial value problem for a semi-linear high-order heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the…
Abstract
The initial value problem for a semi-linear high-order heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.
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Tarikul Islam and Armina Akter
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to…
Abstract
Purpose
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional
Design/methodology/approach
The rational fractional
Findings
Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.
Originality/value
The rational fractional
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