Three-dimensional analytical solution of the Laplace equation suitable for semiconductor detector design

1996 ◽  
Vol 43 (1) ◽  
pp. 256-265 ◽  
Author(s):  
A. Castoldi ◽  
E. Gatti ◽  
P. Rehak
Keyword(s):  
Analytical Solution ◽  
Laplace Equation ◽  
Semiconductor Detector ◽  
Three Dimensional ◽  
Detector Design

scholarly journals Analytical Solution of the Three-Dimensional Laplace Equation in Terms of Linear Combinations of Hypergeometric Functions

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3316
Author(s):  
Antonella Lupica ◽  
Clemente Cesarano ◽  
Flavio Crisanti ◽  
Artur Ishkhanyan
Keyword(s):  
Analytical Solution ◽  
Laplace Equation ◽  
Hypergeometric Functions ◽  
Three Dimensional ◽  
Linear Combinations ◽  
Elliptic Geometry ◽  
Parameter Values ◽  
Toroidal Geometry

We present some solutions of the three-dimensional Laplace equation in terms of linear combinations of generalized hyperogeometric functions in prolate elliptic geometry, which simulates the current tokamak shapes. Such solutions are valid for particular parameter values. The derived solutions are compared with the solutions obtained in the standard toroidal geometry.

scholarly journals The Hydromechanical Interplay in the Simplified Three-Dimensional Limit Equilibrium Analyses of Unsaturated Slope Stability

Geosciences ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 73
Author(s):  
Panagiotis Sitarenios ◽  
Francesca Casini
Keyword(s):  
Analytical Solution ◽  
Slope Stability ◽  
Slope Failure ◽  
Failure Modes ◽  
Pore Water Pressure ◽  
Limit Equilibrium ◽  
Water Pressure ◽  
Three Dimensional ◽  
Stability Limit ◽  
Smooth Transition

This paper presents a three-dimensional slope stability limit equilibrium solution for translational planar failure modes. The proposed solution uses Bishop’s average skeleton stress combined with the Mohr–Coulomb failure criterion to describe soil strength evolution under unsaturated conditions while its formulation ensures a natural and smooth transition from the unsaturated to the saturated regime and vice versa. The proposed analytical solution is evaluated by comparing its predictions with the results of the Ruedlingen slope failure experiment. The comparison suggests that, despite its relative simplicity, the analytical solution can capture the experimentally observed behaviour well and highlights the importance of considering lateral resistance together with a realistic interplay between mechanical parameters (cohesion) and hydraulic (pore water pressure) conditions.

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