ACCURATE APPROXIMATION FOR THE CHLORINE TRANSPORT IN PIPES

2021 ◽  
Vol 25 (1) ◽  
pp. 115-126
Author(s):  
Yussri M. Mahrous
Keyword(s):  
Accurate Approximation

scholarly journals A Fuzzy Optimization Model for High-Speed Railway Timetable Rescheduling

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Li Wang ◽  
Yong Qin ◽  
Jie Xu ◽  
Limin Jia
Keyword(s):  
Optimization Model ◽  
High Speed ◽  
Fuzzy Optimization ◽  
Soft Constraints ◽  
Accurate Approximation ◽  
Total Delay ◽  
High Speed Rail ◽  
High Speed Railway ◽  
Tolerance Approach ◽  
Rail Line

A fuzzy optimization model based on improved symmetric tolerance approach is introduced, which allows for rescheduling high-speed railway timetable under unexpected interferences. The model nests different parameters of the soft constraints with uncertainty margin to describe their importance to the optimization purpose and treats the objective in the same manner. Thus a new optimal instrument is expected to achieve a new timetable subject to little slack of constraints. The section between Nanjing and Shanghai, which is the busiest, of Beijing-Shanghai high-speed rail line in China is used as the simulated measurement. The fuzzy optimization model provides an accurate approximation on train running time and headway time, and hence the results suggest that the number of seriously impacted trains and total delay time can be reduced significantly subject to little cost and risk.

ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE

2004 ◽  
Vol 04 (01) ◽  
pp. 63-76 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Hausdorff Dimension ◽  
Finite Subset ◽  
Continued Fraction ◽  
Cantor Set ◽  
Computational Method ◽  
Accurate Approximation ◽  
Natural Numbers ◽  
Important Special Case ◽  
The One ◽  
Special Case

Given a non-empty finite subset A of the natural numbers, let EA denote the set of irrationals x∈[0,1] whose continued fraction digits lie in A. In general, EA is a Cantor set whose Hausdorff dimension dim (EA) is between 0 and 1. It is shown that the set [Formula: see text] intersects [0,1/2] densely. We then describe a method for accurately computing dimensions dim (EA), and employ it to investigate numerically the way in which [Formula: see text] intersects [1/2,1]. These computations tend to support the conjecture, first formulated independently by Hensley, and by Mauldin & Urbański, that [Formula: see text] is dense in [0,1]. In the important special case A={1,2}, we use our computational method to give an accurate approximation of dim (E{1,2}), improving on the one given in [18].

Motion in frequency domain for harmonic balance simulation of electrical machines

2018 ◽  
Vol 37 (4) ◽  
pp. 1449-1460
Author(s):  
Markus Wick ◽  
Sebastian Grabmaier ◽  
Matthias Juettner ◽  
Wolfgang Rucker
Keyword(s):  
Steady State ◽  
Frequency Domain ◽  
Efficient Method ◽  
Harmonic Balance ◽  
Eddy Currents ◽  
Computational Effort ◽  
Electrical Machines ◽  
Accurate Approximation ◽  
Content Type ◽  
Magnetic Devices

Purpose The high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry. Design/methodology/approach The high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry. Findings The three-phase symmetry reduces the simulated geometry to the sixth part of one pole. The motion transforms to a frequency offset in the angular Fourier series decomposition. The calculation overhead of the Fourier integrals is negligible. The air impedance approximation increases the accuracy and yields a convergence speed of three iterations per decade. Research limitations/implications Only linear materials and two-dimensional geometries are shown for clearness. Researchers are encouraged to adopt recent harmonic balance findings and to evaluate the performance and accuracy of both formulations for larger applications. Practical implications This method offers fast-frequency domain simulations in the optimization process of rotating machines and so an efficient way to treat time-dependent effects such as eddy-currents or voltage-driven coils. Originality/value This paper proposes a new, efficient and accurate method to simulate a rotating machine in the frequency domain.

THE FISSION BARRIERS OF HEAVY AND EXOTIC NUCLEI

2010 ◽  
Vol 19 (04) ◽  
pp. 514-520 ◽  
Author(s):  
FEDIR IVANYUK ◽  
KRZYSZTOF POMORSKI
Keyword(s):  
Liquid Drop ◽  
Optimal Shape ◽  
Exotic Nuclei ◽  
Fission Barrier ◽  
Heavy Nuclei ◽  
Accurate Approximation ◽  
Barrier Heights ◽  
A Value ◽  
Fission Barriers ◽  
Experimental Values

We have calculated the liquid drop fission barriers of medium and heavy nuclei within the Lublin-Strasbourg-Drop model. Exploiting in addition the topographical theorem by Myers and Światecki we propose a simple but quite accurate approximation of the fission barrier heights. When comparing the r.m.s. deviation of approximated versus experimental values of fission barrier heights for known nuclei with Z > 70 a value 1.1 MeV is obtained which is comparable with the experimental uncertainties. The Strutinsky optimal shape method is generalized to the left-right asymmetric shapes of nuclei in order to investigate the influence of this degree of freedom on the barrier heights.

scholarly journals Comparative value of various methods of approximating the permanent wilting percentage

1969 ◽  
Vol 36 (2) ◽  
pp. 122-133
Author(s):  
M. A. Lugo López
Keyword(s):  
Puerto Rico ◽  
Organic Matter Content ◽  
Clay Content ◽  
Matter Content ◽  
Regression Equations ◽  
Accurate Approximation ◽  
Time Saving ◽  
Laboratory Equipment ◽  
Pressure Plate ◽  
Humid Region

Very accurate estimations of the permanent wilting percentage can be obtained for soils of all regions of Puerto Rico by use of regression equations based on the hygroscopic coefficient. Reliable estimates can also be obtained for humid-region soils by using the clay content as a basis. Attempts to correlate permanent wilting-percentage values with moisture equivalents and organic-matter content did not give such satisfactory results. The 15-atmosphere percentage as determined by using pressure plates gives an accurate approximation of permanent wilting-percentage values. It is time-saving, but initial expense in laboratory equipment is rather high. This approach is to be preferred whenever feasible. A regression equation is given relating pressure-plate values to the permanent wilting percentage. Whenever less precise estimates are acceptable and time is not a factor, advantage should be taken of the established correlation between the hygroscopic coefficient and the permanent wilting percentage.

scholarly journals WAVELESS APPROXIMATION THEORIES OF GRAVITY

2008 ◽  
Vol 17 (02) ◽  
pp. 265-273 ◽  
Author(s):  
JAMES A. ISENBERG
Keyword(s):  
Gravitational Field ◽  
Gravitational Radiation ◽  
Elliptic Equations ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Accurate Approximation ◽  
Time Step ◽  
Einstein Theory ◽  
Physical Systems ◽  
Theories Of Gravity

The analysis of a general multibody physical system governed by Einstein's equations is quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties — many coupled degrees of freedom, dynamic instability — are associated with the presence of gravitational waves. We have developed a number of "waveless approximation theories" (WAT's) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.

GROWTH INDEX AND MODIFIED GRAVITY

2011 ◽  
Vol 01 ◽  
pp. 228-233
Author(s):  
YUNGUI GONG
Keyword(s):  
Growth Rate ◽  
Dark Energy ◽  
Modified Gravity ◽  
Growth Index ◽  
Accurate Approximation ◽  
Energy Models ◽  
Λcdm Model ◽  
The Universe ◽  
Matter Energy ◽  
Matter Perturbation

The growth rate of matter perturbation and the expansion rate of the Universe can be used to distinguish modified gravity and dark energy models. Remarkably, the growth rate can be approximated as Ωγ. We discuss the dependence of the growth index γ on the dimensionless matter energy density Ω for a more accurate approximation of the growth factor. The observational data are used to fit different models. The data strongly disfavor the Dvali-Gabadadze-Porrati model. For the ΛCDM model, we find that [Formula: see text]. For the Dvali-Gabadadze-Porrati model, we find that [Formula: see text].

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