The transition matrix in prolate spheroidal coordinates

1984 ◽  
Vol 75 (S1) ◽  
pp. S53-S53
Author(s):  
Roger H. Hackman
Keyword(s):  
Transition Matrix ◽  
Prolate Spheroidal ◽  
Prolate Spheroidal Coordinates ◽  
Spheroidal Coordinates

Convective and Microwave Drying of Prolate Spheroidal Solids: Modeling and Simulation

2019 ◽  
Vol 391 ◽  
pp. 233-238
Author(s):  
E. Gomes da Silva ◽  
E. Santana de Lima ◽  
W.M. Paiva Barbosa de Lima ◽  
A.G. Barbosa de Lima ◽  
J.J. Silva Nascimento ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Heat Balance ◽  
Diffusion Theory ◽  
Microwave Drying ◽  
Drying Process ◽  
Balance Equations ◽  
Prolate Spheroidal ◽  
Moisture Migration ◽  
Prolate Spheroidal Coordinates ◽  
Spheroidal Coordinates

This paper focuses some fundamental aspects of combined convective and microwave drying of prolate spheroidal solids. A transient mathematical modeling based on the diffusion theory (mass and heat balance equations) written in prolate spheroidal coordinates was derived and the importance of this procedure on the analysis of the drying process of wet porous solid, is also presented. Results pointed to the behavior of the moisture migration and heating of the solid with different aspect ratio. Solids with higher area/volume relationships dry and heat faster.

Induced polarization in disseminated sulfide ores containing elongated mineralization

Geophysics ◽  
1981 ◽  
Vol 46 (9) ◽  
pp. 1258-1268 ◽  
Author(s):  
J. Wong ◽  
D. W. Strangway
Keyword(s):  
Electric Fields ◽  
Effective Conductivity ◽  
Dipole Moments ◽  
Two Component System ◽  
Prolate Spheroidal ◽  
Helmholtz Equations ◽  
Electrochemical Charge Transfer ◽  
Electrochemical Model ◽  
Prolate Spheroidal Coordinates ◽  
Spheroidal Coordinates

A disseminated sulfide ore is represented by a two‐component system in which metallically conducting prolate spheroidal particles (simulating elongated mineralization) are randomly scattered throughout an electrolytic host. The Helmholtz equations describing the spatial and frequency dependence of anions and cations in the electrolyte near the surface of a particle are solved in prolate spheroidal coordinates. Expressions for the frequency‐dependent dipole moment induced on the particle by external electric fields transverse or parallel to the long axis of the particle are found by examining boundary conditions related to electrochemical charge transfer between the metallic particle and the electrolyte. The dipole moments of individual particles can be used to determine the effective conductivity spectrum of the mixture as a whole via the simple Maxwell formula or a novel recursive calculation which is accurate for large‐volume fractions of particles. Examples of conductivity spectra from this electrochemical model incorporating elongated particles are presented, and comparison of results with appropriate experimental data indicates good agreement.

A Three-Dimensional Finite Element Method for Large Elastic Deformations of Ventricular Myocardium: II—Prolate Spheroidal Coordinates

1996 ◽  
Vol 118 (4) ◽  
pp. 464-472 ◽  
Author(s):  
K. D. Costa ◽  
P. J. Hunter ◽  
J. S. Wayne ◽  
L. K. Waldman ◽  
J. M. Guccione ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
Solution Time ◽  
Order Model ◽  
Prolate Spheroidal ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Prolate Spheroidal Coordinates ◽  
Spheroidal Coordinates

A three-dimensional finite element method for nonlinear finite elasticity is presented using prolate spheroidal coordinates. For a thick-walled ellipsoidal model of passive anisotropic left ventricle, a high-order (cubic Hermite) mesh with 3 elements gave accurate continuous stresses and strains, with a 69 percent savings in degrees of freedom (dof) versus a 70-element standard low-order model. A custom mixed-order model offered 55 percent savings in dof and 39 percent savings in solution time compared with the low-order model. A nonsymmetric 3D model of the passive canine LV was solved using 16 high-order elements. Continuous nonhomogeneous stresses and strains were obtained within 1 hour on a laboratory workstation, with an estimated solution time of less than 4 hours to model end-systole. This method represents the first practical opportunity to solve large-scale anatomically detailed models for cardiac stress analysis.

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