Accuracy contours in (nT, λ) space in electrochemical digital simulations

1991 ◽  
Vol 56 (1) ◽  
pp. 20-41 ◽  
Author(s):  
Dieter Britz ◽  
Merete F. Nielsen
Keyword(s):  
Finite Difference ◽  
Linear Sweep Voltammetry ◽  
Stability Factor ◽  
Dimensionless Time ◽  
Simulation Techniques ◽  
Rational Algorithm ◽  
The Stability ◽  
Transport Problems ◽  
Current Approximation ◽  
Digital Simulations

In finite difference simulations of electrochemical transport problems, it is usually tacitly assumed that λ, the stability factor Dδt/δx2, should be set as high as possible. Here, accuracy contours are shown in (nT, λ) space, where nT is he number of finite difference steps per unit (dimensionless) time. Examples are the Cottrell experiment, simple chronopotentiometry and linear sweep voltammetry (LSV) on a reversible system. The simulation techniques examined include the standard explicit (point- and box-) methods as well as Runge-Kutta, Crank-Nicolson, hopscotch and Saul’yev. For the box method, the two-point current approximation appears to be the most appropriate. A rational algorithm for boundary concentrations with explicit LSV simulations is discussed. In general, the practice of choosing as high a λ value when using the explicit techniques, is confirmed; there are practical limits in all cases.

Determining the Norton’s Equivalent Model of Distribution System with Distributed Generation (DG) for Stability Analysis

2019 ◽  
Vol 12 (2) ◽  
pp. 190-198
Author(s):  
Sunny Katyara ◽  
Lukasz Staszewski ◽  
Faheem Akhtar Chachar
Keyword(s):  
Distributed Generation ◽  
Normal Condition ◽  
Distribution System ◽  
Distribution Networks ◽  
Equivalent Model ◽  
Stability Factor ◽  
Matlab Simulation ◽  
The Stability ◽  
Stability Issues

Background: Since the distribution networks are passive until Distributed Generation (DG) is not being installed into them, the stability issues occur in the distribution system after the integration of DG. Methods: In order to assure the simplicity during the calculations, many approximations have been proposed for finding the system’s parameters i.e. Voltage, active and reactive powers and load angle, more efficiently and accurately. This research presents an algorithm for finding the Norton’s equivalent model of distribution system with DG, considering from receiving end. Norton’s model of distribution system can be determined either from its complete configuration or through an algorithm using system’s voltage and current profiles. The algorithm involves the determination of derivative of apparent power against the current (dS/dIL) of the system. Results: This work also verifies the accuracy of proposed algorithm according to the relative variations in the phase angle of system’s impedance. This research also considers the varying states of distribution system due to switching in and out of DG and therefore Norton’s model needs to be updated accordingly. Conclusion: The efficacy of the proposed algorithm is verified through MATLAB simulation results under two scenarios, (i) normal condition and (ii) faulty condition. During normal condition, the stability factor near to 1 and change in dS/dIL was near to 0 while during fault condition, the stability factor was higher than 1 and the value of dS/dIL was away from 0.

Yield Design of the Reinforced Embankment

2011 ◽  
Vol 368-373 ◽  
pp. 2804-2807
Author(s):  
Bing Zhang ◽  
Xiao Mou Wang
Keyword(s):  
Upper Bound ◽  
Design Approach ◽  
Stability Factor ◽  
Multiphase Model ◽  
Construction Process ◽  
Backfill Soil ◽  
Geotechnical Structures ◽  
The Stability ◽  
Kinematic Approach

A frequently used technique for improving the performance of geotechnical structures consists in incorporating into the backfill soil, during the construction process, regularly spaced thin reinforcing inclusions, called geotextile, geomembranes or geogrids. The stability of embankment, stabilized by reinforcing membranes, is investigated by means of a multiphase model developed in the framework of the yield design approach. By means of the kinematic approach, leading to upper bound estimates for the stability factor of the structure.

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

Efficient Two-dimensional Acoustic Wave Finite-Difference Numerical Simulation in Strongly Heterogeneous Media Using the Adaptive Mesh Refinement (AMR) Technique

Geophysics ◽  
2021 ◽  
pp. 1-76
Author(s):  
Chunli Zhang ◽  
Wei Zhang
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Adaptive Mesh Refinement ◽  
Heterogeneous Media ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Grid Spacing ◽  
Time Step ◽  
Velocity Models ◽  
The Stability

The finite-difference method (FDM) is one of the most popular numerical methods to simulate seismic wave propagation in complex velocity models. If a uniform grid is applied in the FDM for heterogeneous models, the grid spacing is determined by the global minimum velocity to suppress dispersion and dissipation errors in the numerical scheme, resulting in spatial oversampling in higher-velocity zones. Then, the small grid spacing dictates a small time step due to the stability condition of explicit numerical schemes. The spatial oversampling and reduced time step will cause unnecessarily inefficient use of memory and computational resources in simulations for strongly heterogeneous media. To overcome this problem, we propose to use the adaptive mesh refinement (AMR) technique in the FDM to flexibly adjust the grid spacing following velocity variations. AMR is rarely utilized in acoustic wave simulations with the FDM due to the increased complexity of implementation, including its data management, grid generation and computational load balancing on high-performance computing platforms. We implement AMR for 2D acoustic wave simulation in strongly heterogeneous media based on the patch approach with the FDM. The AMR grid can be automatically generated for given velocity models. To simplify the implementation, we employ a well-developed AMR framework, AMReX, to carry out the complex grid management. Numerical tests demonstrate the stability, accuracy level and efficiency of the AMR scheme. The computation time is approximately proportional to the number of grid points, and the overhead due to the wavefield exchange and data structure is small.

scholarly journals Spectrophotometric indicators of the stability of anthocyanin-containing extracts depending on the color of plant materials

2020 ◽  
Vol 31 (2) ◽  
pp. 88-92
Author(s):  
Vladimir Mikhailovich Koldaev ◽  
Artem Yurevich Manyakhin ◽  
Petr Semenovich Zorikov
Keyword(s):  
Hydrochloric Acid ◽  
Stability Factor ◽  
Plant Materials ◽  
Herbal Preparations ◽  
Violet Color ◽  
The Stability ◽  
Selection Of ◽  
Factor Coefficient ◽  
Anthocyanin Degradation

AbstractThis paper aims at spectrophotometric determination of changes in stability of extractable anthocyanins during drying of plant materials depending on their color. Raw and dried colored parts of 50 plant species from 25 families were used for the study. The extracts were prepared over 95% ethanol acidified with hydrochloric acid (pH ~ 1). The absorption spectra were registered within the range of 210 to 680 nm. The extinction variability factor, coefficient of intensity absorption relative and generalized stability factor were used to determine the anthocyanin degradation. The highest values of the stability factor were obtained for the extracts from fruit shells of burgundy or violet color within the range of 0.934±0.024 to 0.973±0.024, while the extracts from flower petals of the same care featured the stability factor that was 1.19 to 1.44 times less. The values of the stability factor of the extracts from black, red and blue materials are 1.15 to 1.19 times, 1.74 to 2.48 times and 4.65 to 4.84 times less respectively than those of the extracts from violet-burgundy materials. It is appropriate to apply the spectrophotometric factors of anthocyanins stability used in this study to selection of promising plants for industrial cultivation as material of anthocyanin-containing herbal preparations. The most stable anthocyanins are those of burgundy-purple and black fruits.

scholarly journals Qualifications for teachers and teachers of gifted students in Jeddah

2018 ◽  
Vol 2 (4) ◽  
Author(s):  
Ibtisam Rashad Abdullah Hameedah
Keyword(s):  
Random Sample ◽  
Gifted Students ◽  
Point Of View ◽  
Average Score ◽  
Stability Factor ◽  
Years Of Experience ◽  
Jeddah City ◽  
Study Population ◽  
Descriptive Approach ◽  
The Stability

This study aimed to identify the qualitative competencies of teachers and teachers of gifted students in Jeddah from their point of view and to indicate the extent of these competencies according to the variables of the study: gender, scientific qualification and years of experience. We have used the descriptive approach, as a questionnaire was developed to collect data, verified its validity and stability in the appropriate educational and statistical methods, and the value of the stability factor, Kronbach Alpha, (0.75). The study population is composed of all teachers and teachers of the gifted students in the schools of Jeddah city (70) teachers and teachers, a random sample was selected (40%). The results of the study showed that the qualitative competencies of teachers and teachers of gifted students came in a medium and an average score of (3.31) according to the Likert quintile scale. The results also showed that there were statistically significant differences between the estimations of the sample of the study of the qualitative competencies of teachers and gifted students in Jeddah For the sex variable, and the absence of differences attributed to the variable of scientific qualification, and years of experience.

scholarly journals A Finite-Difference Wavenumber-Time Domain Method for Sound Field Prediction in a Uniformly Moving Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Bichun Dong ◽  
Runmei Zhang ◽  
Chuanyang Yu ◽  
Huan Li
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Sound Pressure ◽  
Sound Field ◽  
Time Domain Method ◽  
Practical Significance ◽  
Moving Medium ◽  
Domain Method ◽  
Aero Engines ◽  
The Stability

Sound field prediction has practical significance in the control of noise generated by sources in a flow, for example, the noise in aero-engines and ventilation systems. Aiming at accurate and flexible prediction of time-dependent sound field, a finite-difference wavenumber-time domain method for sound field prediction in a uniformly moving medium is proposed. The method is based on the second-order convective wave equation, and the wavenumber-time domain representation of the sound pressure field on one plane is forward propagated via a derived recursive expression. In this paper, the recursive expression is first deduced, and then numerical stability and dispersion of the proposed method are analyzed, based on which the stability condition is given and the correction of dispersion related to the transition frequency is made. Numerical simulations are conducted to test the performance of the proposed method, and the results show that the method is valid and robust at different Mach numbers.

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