Phonon focussing patterns: Calculation of response of finite area detectors to pulsed ballistic beams of dispersive and dispersionless phonons

1994 ◽  
Vol 96 (2) ◽  
pp. 213-222 ◽  
Author(s):  
Cz. Jasiukiewicz ◽  
T. Paszkiewicz ◽  
D. Lehmann
Keyword(s):  
Finite Area ◽  
Phonon Focussing

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.

Finite area element snow loading prediction - applications and advancements

1992 ◽  
Vol 42 (1-3) ◽  
pp. 1537-1548 ◽  
Author(s):  
Scott L. Gamble ◽  
Will W. Kochanski ◽  
Peter A. Irwin
Keyword(s):  
Finite Area ◽  
Area Element ◽  
Snow Loading

scholarly journals A Polyakov Formula for Sectors

2017 ◽  
Vol 28 (2) ◽  
pp. 1773-1839 ◽  
Author(s):  
Clara L. Aldana ◽  
Julie Rowlett
Keyword(s):  
Heat Kernel ◽  
Explicit Expression ◽  
Unit Area ◽  
Logarithmic Singularity ◽  
Conformal Factor ◽  
Opening Angle ◽  
Conformal Deformation ◽  
Finite Area ◽  
Different Parts

Abstract We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to a conformal deformation in the direction of a conformal factor with a logarithmic singularity at the origin. We compute explicitly all the contributions to this formula coming from the different parts of the sector. In the process, we obtain an explicit expression for the heat kernel on an infinite area sector using Carslaw–Sommerfeld’s heat kernel. We also compute the zeta-regularized determinant of rectangular domains of unit area and prove that it is uniquely maximized by the square.

A Systematic Computational Design System for Turbine Cascades, Airfoil Geometry and Blade-to-Blade Analysis

1983 ◽  
Author(s):  
Z.-Q. Ye
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Computational Design ◽  
Design System ◽  
Finite Area ◽  
Streamline Curvature ◽  
Boundary Layer Analysis ◽  
Curvature Analysis ◽  
Layer Analysis ◽  
Turbine Cascades

This paper describes a systematic computational design system for two-dimensional turbine cascades. The system includes a sequence of calculations in which airfoil profiles are designed from velocity diagram requirements and specified geometric parameters, followed by an inviscid global streamline curvature analysis, a magnified reanalysis around the leading edge, and a transitional profile boundary layer and wake mixing analysis. A finite area technique and a body-fitted mesh are used for the reanalysis. The boundary layer analysis is performed using the dissipation-integral method of Walz which has been modified in the present application. Several turbine airfoil profile geometry designs are presented. Also two sample cascade design cases and their calculated performance for a range of Mach numbers and incidence angles are given and discussed.

Chaotic advection by two interacting finite-area vortices

2001 ◽  
Vol 13 (4) ◽  
pp. 901-912 ◽  
Author(s):  
O. U. Velasco Fuentes
Keyword(s):  
Chaotic Advection ◽  
Finite Area
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