scholarly journals Numerical evaluation of a second-order water transfer term for variably saturated dual-permeability models

2004 ◽  
Vol 40 (7) ◽  
Author(s):  
J. Maximilian Köhne ◽  
Binayak P. Mohanty ◽  
Jirka Simunek ◽  
Horst H. Gerke
Keyword(s):  
Numerical Evaluation ◽  
Water Transfer ◽  
Second Order ◽  
Transfer Term

Second-order effects in URM walls subjected to compression and out-of-plane bending: From numerical evaluation to proposal of design procedures

2020 ◽  
Vol 209 ◽  
pp. 110130
Author(s):  
Marco Donà ◽  
Paolo Morandi ◽  
Massimiliano Minotto ◽  
Carlo Filippo Manzini ◽  
Francesca da Porto ◽  
...  
Keyword(s):  
Numerical Evaluation ◽  
Second Order ◽  
Order Effects ◽  
Design Procedures ◽  
Out Of Plane ◽  
Plane Bending ◽  
Second Order Effects

Numerical quadrature for computing of singular integrals

2015 ◽  
Vol 23 (2) ◽  
Author(s):  
Petr Stašek ◽  
Josef Kofron ◽  
Karel Najzar
Keyword(s):  
Numerical Evaluation ◽  
Singular Integrals ◽  
Second Order ◽  
Third Order ◽  
Rule Based ◽  
Numerical Examples ◽  
The Third ◽  
Hadamard Finite Part ◽  
Work First ◽  
Theoretical Results

AbstractThe paper is concerned with the superconvergence of numerical evaluation of Hadamard finite-part integral. Following the works [6-9], we studied the second-order and the third-order quadrature formulae of Newton-Cotes type and introduced new rules. The rule for the second-order gives the same convergence rate as the rule [6] but in more general cases, the rule for the third-order gives better results than the rule in [9] In this work, first we mention the main results on the superconvergence of the Newton-Cotes rules, we mention trapezoidal and Simpson’s rules and then we introduce a rule based on the cubic approximation. In the second part we describe important error estimates and in the last section we demonstrate theoretical results by numerical examples.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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