scholarly journals Modeling of Electromagnetic Fields in Parallel-Plane Structures: A Unified Contour-Integral Approach

2017 ◽  
Vol 26 (1) ◽  
pp. 1-9 ◽  
Author(s):  
M. Stumpf
Keyword(s):  
Electromagnetic Fields ◽  
Parallel Plane ◽  
Contour Integral ◽  
Integral Approach

scholarly journals Probability Calculations Within Stochastic Electrodynamics

2021 ◽  
Vol 8 ◽  
Author(s):  
Daniel C. Cole
Keyword(s):  
Electromagnetic Fields ◽  
First Principles ◽  
Quantum Electrodynamics ◽  
Zero Point ◽  
Probability Density Functions ◽  
Integral Approach ◽  
Multiple Points ◽  
Stochastic Electrodynamics ◽  
Dipole Oscillator ◽  
Weighted Paths

Several stochastic situations in stochastic electrodynamics (SED) are analytically calculated from first principles. These situations include probability density functions, as well as correlation functions at multiple points of time and space, for the zero-point (ZP) electromagnetic fields, as well as for ZP plus Planckian (ZPP) electromagnetic fields. More lengthy analytical calculations are indicated, using similar methods, for the simple harmonic electric dipole oscillator bathed in ZP as well as ZPP electromagnetic fields. The method presented here makes an interesting contrast to Feynman’s path integral approach in quantum electrodynamics (QED). The present SED approach directly entails probabilities, while the QED approach involves summing weighted paths for the wave function.

scholarly journals A contour integral approach to the computation of invariant pairs

2017 ◽  
Vol 681 ◽  
pp. 3-26
Author(s):  
Moulay Barkatou ◽  
Paola Boito ◽  
Esteban Segura Ugalde
Keyword(s):  
Contour Integral ◽  
Integral Approach

Application of XFEM to Model Stationary Crack and Crack Propagation for Pressure Containing Subsea Equipment

2016 ◽  
Author(s):  
Sam (Kwok Lun) Lee ◽  
David Martin
Keyword(s):  
Finite Element ◽  
Crack Propagation ◽  
Crack Growth ◽  
Displacement Field ◽  
Internal Surface ◽  
Contour Integral ◽  
Integral Approach ◽  
Thick Wall ◽  
Element Mesh ◽  
Integrity Assessment

The extended finite element method (XFEM) [1, 2] can approximate the discontinuous displacement field near cracks independently of the finite element mesh through the use of interpolation functions, which can describe the displacement field near cracks in the structure. Therefore, XFEM is appearing as an alternative to conventional contour integral method for crack growth analysis. Most benchmarks for XFEM in published literature were mostly for the through-wall crack or loadings were under tension or bending moment. Subsea equipment provided by FMC Technologies is used under the most extreme conditions of pressure and temperature. Due to the fact that most equipment in subsea is pressure containing, assessment of cracks and crack growth under pressure cycles is an essential part of the integrity assessment. The implementation of fracture mechanic based fatigue to analysis can extend equipment life while improving model accuracy. In this paper, crack growth modelling in a thick wall cylinder was performed by XFEM embedded in Abaqus [3]. The case study of semi-elliptical axial surface crack at internal surface was selected. The fracture and fatigue results based on LCF analysis were compared with contour integral approach and published experimental data [4]. One of the advantages of XFEM is it can easily accommodate changes in the crack propagation direction for mixed mode loading.

Unbiased estimation of particle number and sizes using the new stereological tools: the disector, the fractionator, the selector, and the nucleator — or just point-sampled intercepts

1988 ◽  
Vol 46 ◽  
pp. 428-429
Author(s):  
H.J.G. Gundersen
Keyword(s):  
Particle Number ◽  
Small Distance ◽  
Parallel Plane ◽  
Unbiased Estimation ◽  
Severe Problem ◽  
New Era ◽  
Size And Shape ◽  
Distinct Property ◽  
Sectioned Tissue

Previously, all stereological estimation of particle number and sizes were based on models and notoriously gave biased results, were very inefficient to use and difficult to justify. For all references to old methods and a direct comparison with unbiased methods see recent reviews.The publication in 1984 of the DISECTOR, the first unbiased stereological probe for sampling and counting 3—D objects irrespective of their size and shape, signalled the new era in stereology — and give rise to a number of remarkably simple and efficient techniques based on its distinct property: It is the only known way to obtain an unbiased sample of 3-D objects (cells, organelles, etc). The principle is simple: within a 2-D unbiased frame count or sample only cells which are not hit by a parallel plane at a known, small distance h.The area of the frame and h must be known, which might sometimes in itself be a problem, albeit usually a small one. A more severe problem may arise because these constants are known at the scale of the fixed, embedded and sectioned tissue which is often shrunken considerably.

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