A New and Simpler Formulation for Radiative Angle Factors

1963 ◽  
Vol 85 (2) ◽  
pp. 81-87 ◽  
Author(s):  
E. M. Sparrow
Keyword(s):  
Numerical Evaluation ◽  
Energy Exchange ◽  
Analytical Calculation ◽  
Additional Benefit ◽  
Finite Area ◽  
Reduced Order ◽  
Practical Utility ◽  
New Formulation ◽  
Superposition Theorem

A new representation for diffuse angle factors has been derived which replaces the usual area integrals by more tractable contour (i.e., line) integrals. The new formulation generally simplifies analytical calculation of angle factors. The advantages of the new representation are associated with the reduced order of the integrals (i.e., double reduced to single, quadruple reduced to double) which must be evaluated to calculate the angle factor. An additional benefit of the new representation is that integrals of simpler form are encountered than in the present representation. For the numerical evaluation of angle factors, the reduction in the order of the integrals should have great practical utility. In the case of energy exchange between an infinitesimal element and a finite area, a superposition theorem has been derived which permits results for certain basic surfaces to be linearly combined to yield angle factors for surfaces at other orientations. Several illustrations of the application of the new formulation are presented.

scholarly journals Influencing the Gradient of Material Properties by Gradation Extrusion

2015 ◽  
Vol 794 ◽  
pp. 166-173 ◽  
Author(s):  
Markus Bergmann ◽  
Andreas Sterzing ◽  
Dirk Landgrebe
Keyword(s):  
Material Properties ◽  
Numerical Evaluation ◽  
Analytical Calculation ◽  
Coarse Grained ◽  
Additional Material ◽  
Fine Grained ◽  
Extrusion Die ◽  
Large Gradient ◽  
Unique Method ◽  
The Relationship

Designing material characteristics by grain refinement using Severe Plastic Deformation (SPD) is an attractive way to create outstanding material properties. This paper presents a unique method which combines SPD and impact extrusion. The extrusion die is designed to create additional material deformation to a defined depth, resulting in a gradient from ultra-fine grained to coarse grained microstructure. Due to the large gradient the method is called gradation extrusion. The paper presents a new analytical calculation method and a numerical evaluation of the strain, showing the relationship between tool design and achievable effects and provides initial experimental results.

scholarly journals An improved reduced-order model for pressure drop across arterial stenoses

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258047
Author(s):  
Konstantinos G. Lyras ◽  
Jack Lee
Keyword(s):  
Pressure Drop ◽  
Reduced Order Model ◽  
Accurate Estimation ◽  
Classification Error ◽  
Fractional Flow ◽  
Order Model ◽  
Reduced Order ◽  
Flow Reserve ◽  
Proposed Model ◽  
New Formulation

Quantification of pressure drop across stenotic arteries is a major element in the functional assessment of occlusive arterial disease. Accurate estimation of the pressure drop with a numerical model allows the calculation of Fractional Flow Reserve (FFR), which is a haemodynamic index employed for guiding coronary revascularisation. Its non-invasive evaluation would contribute to safer and cost-effective diseases management. In this work, we propose a new formulation of a reduced-order model of trans-stenotic pressure drop, based on a consistent theoretical analysis of the Navier-Stokes equation. The new formulation features a novel term that characterises the contribution of turbulence effect to pressure loss. Results from three-dimensional computational fluid dynamics (CFD) showed that the proposed model produces predictions that are significantly more accurate than the existing reduced-order models, for large and small symmetric and eccentric stenoses, covering mild to severe area reductions. FFR calculations based on the proposed model produced zero classification error for three classes comprising positive (≤ 0.75), negative (≥ 0.8) and intermediate (0.75 − 0.8) classes.

scholarly journals Theoretical Description of the Coulomb Interaction by Padé-Jacobi Approximants

1994 ◽  
Vol 147 ◽  
pp. 606-611
Author(s):  
W. Stolzmann ◽  
T. Blöcker
Keyword(s):  
Coulomb Interaction ◽  
Numerical Evaluation ◽  
Theoretical Description ◽  
Helmholtz Energy ◽  
Coulomb Interactions ◽  
Many Body ◽  
New Formulation

AbstractCoulomb interactions for the Free Helmholtz energy and the pressure are studied in a partial new formulation which described more exactly the numerical evaluation of many body theories.

Monte Carlo Modelling of Secondary Electron Yield from Rough Surfaces

1990 ◽  
Vol 48 (1) ◽  
pp. 422-423
Author(s):  
John C. Russ
Keyword(s):  
Monte Carlo ◽  
Energy Loss ◽  
Secondary Electron ◽  
Secondary Electron Emission ◽  
Analytical Calculation ◽  
Mean Free Path ◽  
Single Scattering ◽  
High Energy ◽  
Secondary Electron Yield ◽  
Electron Yield

Monte-Carlo programs are well recognized for their ability to model electron beam interactions with samples, and to incorporate boundary conditions such as compositional or surface variations which are difficult to handle analytically. This success has been especially powerful for modelling X-ray emission and the backscattering of high energy electrons. Secondary electron emission has proven to be somewhat more difficult, since the diffusion of the generated secondaries to the surface is strongly geometry dependent, and requires analytical calculations as well as material parameters. Modelling of secondary electron yield within a Monte-Carlo framework has been done using multiple scattering programs, but is not readily adapted to the moderately complex geometries associated with samples such as microelectronic devices, etc.This paper reports results using a different approach in which simplifying assumptions are made to permit direct and easy estimation of the secondary electron signal from samples of arbitrary complexity. The single-scattering program which performs the basic Monte-Carlo simulation (and is also used for backscattered electron and EBIC simulation) allows multiple regions to be defined within the sample, each with boundaries formed by a polygon of any number of sides. Each region may be given any elemental composition in atomic percent. In addition to the regions comprising the primary structure of the sample, a series of thin regions are defined along the surface(s) in which the total energy loss of the primary electrons is summed. This energy loss is assumed to be proportional to the generated secondary electron signal which would be emitted from the sample. The only adjustable variable is the thickness of the region, which plays the same role as the mean free path of the secondary electrons in an analytical calculation. This is treated as an empirical factor, similar in many respects to the λ and ε parameters in the Joy model.

Psychoecological Systems Model for Participatory Community Action Research: Evidence of Validity and Practical Utility

2011 ◽  
Author(s):  
Roger N. Reeb ◽  
Susan F. Folger ◽  
Anne L. Steel ◽  
Sara E. Mason ◽  
Laura E. Stayton ◽  
...  
Keyword(s):  
Action Research ◽  
Research Evidence ◽  
Community Action ◽  
Practical Utility ◽  
Systems Model
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