midpoint method
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Detritus ◽  
2021 ◽  
pp. 94-105
Author(s):  
Fabian Gievers ◽  
Achim Loewen ◽  
Michael Nelles

The pyrolysis of sewage sludge is an alternative method to recycle the contained nutrients, such as phosphorus, by material use of the resulting biochar. However, the ecological effects of pyrolysis are not easy to evaluate. Therefore, a life cycle assessment (LCA) was carried out to determine the environmental impact of sewage sludge pyrolysis and to compare it with the common method of sewage sludge incineration. In order to identify the most sustainable applications of the resulting biochar, four different scenarios were analyzed. The modeled life cycles include dewatering, drying and pyrolysis of digested sewage sludge and utilization paths of the by-products as well as various applications of the produced biochar and associated transports. The life cycle impact assessment was carried out using the ReCiPe midpoint method. The best scenario in terms of global warming potential (GWP) was the use of biochar in horticulture with net emissions of 2 g CO2 eq./kg sewage sludge. This scenario of biochar utilization can achieve savings of 78% of CO2 eq. emissions compared to the benchmark process of sewage sludge mono-incineration. In addition, no ecological hotspots in critical categories such as eutrophication or ecotoxicity were identified for the material use of biochar compared to the benchmark. Pyrolysis of digested sewage sludge with appropriate biochar utilization can therefore be an environmentally friendly option for both sequestering carbon and closing the nutrient cycle.


Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1103
Author(s):  
Felice Iavernaro ◽  
Francesca Mazzia

The paper presents fourth order Runge–Kutta methods derived from symmetric Hermite–Obreshkov schemes by suitably approximating the involved higher derivatives. In particular, starting from the multi-derivative extension of the midpoint method we have obtained a new symmetric implicit Runge–Kutta method of order four, for the numerical solution of first-order differential equations. The new method is symplectic and is suitable for the solution of both initial and boundary value Hamiltonian problems. Moreover, starting from the conjugate class of multi-derivative trapezoidal schemes, we have derived a new method that is conjugate to the new symplectic method.


BioResources ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. 3760-3770
Author(s):  
José Ferreira ◽  
Bruno Esteves ◽  
Ümit Ayata ◽  
Luisa Cruz-Lopes ◽  
Idalina Domingos

The forestry sector in Portugal faces important challenges, resulting in an increased incidence of fires and the action of pathogens, which puts the sustainability of forest resources at risk. Due to the economic, social, and environmental importance of forests, this work assessed the land use environmental impact of maritime pine and eucalypt standing in Portuguese forests. SimaPro software was used to translate the inventory table results into land use impact category. The ILCD 2011 Midpoint+ method was chosen to assess the “land use” environmental impact that focuses on soil quality and its indicator (kg carbon deficit), which describes the changes in soil organic matter associated with land interventions. The results showed that for the first rotation time, the land use impact category per cubic meter of maritime pine is 18423 kg C deficit and 23430 kg C deficit for eucalypt, which means that the land use impact category of eucalypt is 27% higher than the impact of maritime pine.


2021 ◽  
pp. 16-21
Author(s):  
Kirill Yu. Solomentsev ◽  
Vyacheslav I. Lachin ◽  
Aleksandr E. Pasenchuk

Several variants of half division two-dimensional method are proposed, which is the basis of a fundamentally new approach for constructing measuring instruments for sinusoidal or periodic electrical quantities. These measuring instruments are used in the diagnosis of electric power facilities. The most general variant, called midpoint method, is considered. The proposed midpoint method allows you to measure much smaller than using widespread methods, alternating currents or voltages, especially when changing the amplitude of the measured signal in very wide ranges, by 1–2 orders of magnitude. It is shown that using the midpoint method it is possible to suppress sinusoidal or periodic interference in the measuring path, in particular, to measure small alternating current when sinusoidal or periodic interference is 1–2 orders of magnitude higher than the useful signal. Based on the results of comparative tests, it was found that the current measuring device implementing the midpoint method is an order of magnitude more sensitive than the currently used high-precision measuring instruments.


2020 ◽  
Vol 491 (2) ◽  
pp. 124381
Author(s):  
Elkin Cárdenas ◽  
Rodrigo Castro ◽  
Willy Sierra

2020 ◽  
Vol 25 (2) ◽  
pp. 299-305
Author(s):  
Diana Marcela Devia Narváez ◽  
Fernando Mesa ◽  
German Correa-Vélez

This manuscript contains a detailed comparison between numerical solution methods of ordinary differential equations, which start from the Taylor series method of order 2, stating that this series hinders calculations for higher order derivatives of functions of several variables, so that the Runge Kutta methods of order 2 are implemented, which achieve the required purpose avoiding the cumbersome calculations of higher order derivatives. In this document, different variants of the Runge-Kutta methods of order 2 will be exposed from an introduction and demonstration of the connection of these with the Taylor series of order 2, these methods are: the method of Heun, the method of midpoint and the Ralston method. It will be observed from the solution of test differential equations its respective error with respect to the analytical solution, obtaining an error index dictated by the mean square error EMC. Through this document we will know the best numerical approximation to the analytical solution of the different PVI (initial value problems) raised, also fixing a solution pattern for certain problems, that is, the appropriate method for each type of problem will be stipulated. It was observed that the Ralston method presented greater accuracy followed by the midpoint method and the Heun method, in the other PVI it is observed that the midpoint method yields the best numerical solution since it has a very low EMC and difficult to reach by the other methods.  


Electronics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 434 ◽  
Author(s):  
Valery Andreev ◽  
Valerii Ostrovskii ◽  
Timur Karimov ◽  
Aleksandra Tutueva ◽  
Elena Doynikova ◽  
...  

In many tasks related to realistic neurons and neural network simulation, the performance of desktop computers is nowhere near enough. To overcome this obstacle, researchers are developing FPGA-based simulators that naturally use fixed-point arithmetic. In these implementations, little attention is usually paid to the choice of numerical method for the discretization of the continuous neuron model. In our study, the implementation accuracy of a neuron described by simplified Hodgkin–Huxley equations in fixed-point arithmetic is under investigation. The principle of constructing a fixed-point neuron model with various numerical methods is described. Interspike diagrams and refractory period analysis are used for the experimental study of the synthesized discrete maps of the simplified Hodgkin–Huxley neuron model. We show that the explicit midpoint method is much better suited to simulate the neuron dynamics on an FPGA than the explicit Euler method which is in common use.


2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Zeeshan Khan ◽  
Haroon Ur Rasheed ◽  
Saeed Islam ◽  
Sahib Noor ◽  
Waris Khan ◽  
...  

In this analysis, we introduced heat convective aspects of stagnation point movement of a magnetohydrodynamic (MHD) stream on a nonlinear oscillating plane with the impacts of velocity and heat slips with variable heat reservoir. By using some appropriate transformations, the governing differential equations are switched into an ordinary differential equation. The semianalytics technique called Homotpy Analysis Method (HAM) has been applied to evaluate the ordinary differential equations. For convergence achievement, a numerical method BVPh2-midpoint method is also applied and an outstanding agreement is found. The impacts of the governing constraints on flow, motion, and temperature distributions are investigated in detail. We observed that the temperature distribution increases with nonlinear heat reservoir parameter. Our results, in some limiting situations, matched well with previously published results, which approve that our obtained results are correct.


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