The Dirichlet to Neumann Map for a Resistor Network

1991 ◽  
Vol 51 (4) ◽  
pp. 1011-1029 ◽  
Author(s):  
Edward B. Curtis ◽  
James A. Morrow
Keyword(s):  
Resistor Network ◽  
Dirichlet To Neumann Map

scholarly journals Calderón problem for Maxwell's equations in two dimensions

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Oleg Y. Imanuvilov ◽  
Masahiro Yamamoto
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Global Uniqueness ◽  
Calderón Problem ◽  
Dirichlet To Neumann Map

AbstractWe prove the global uniqueness in determination of the conductivity, the permeability and the permittivity of the two-dimensional Maxwell equations by the partial Dirichlet-to-Neumann map limited to an arbitrary subboundary.

On the perturbation of a uniform tiling with resistors

2016 ◽  
Vol 30 (24) ◽  
pp. 1650166 ◽  
Author(s):  
M. Q. Owaidat ◽  
J. H. Asad ◽  
Zhi-Zhong Tan
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Square Lattice ◽  
Resistor Network ◽  
Theoretical Results

The perturbation of a uniformly tiled resistor network by adding an edge (a resistor) to the network is considered. The two-point resistance on the perturbed tiling in terms of that on the perfect tiling is obtained using Green’s function. Some theoretical results are presented for an infinite modified square lattice. These results are confirmed experimentally by constructing an actual resistor lattice of size 13 × 13.

scholarly journals Atmospheric radiation boundary conditions for the Helmholtz equation

2018 ◽  
Vol 52 (3) ◽  
pp. 945-964 ◽  
Author(s):  
Hélène Barucq ◽  
Juliette Chabassier ◽  
Marc Duruflé ◽  
Laurent Gizon ◽  
Michael Leguèbe
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Acoustic Waves ◽  
Numerical Study ◽  
Outgoing Wave ◽  
Atmospheric Radiation ◽  
Angle Of Incidence ◽  
Radiation Boundary Conditions ◽  
Radiation Boundary ◽  
Dirichlet To Neumann Map

This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called atmospheric radiation boundary conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.

The Dirichlet-to-Neumann map for two-dimensional crack problems

2011 ◽  
Vol 200 (9-12) ◽  
pp. 1263-1271 ◽  
Author(s):  
Dorinamaria Carka ◽  
Mark E. Mear ◽  
Chad M. Landis
Keyword(s):  
Two Dimensional ◽  
Crack Problems ◽  
Dirichlet To Neumann Map

Minimum current in the two-component random resistor network

1992 ◽  
Vol 46 (19) ◽  
pp. 12137-12141 ◽  
Author(s):  
K. W. Yu ◽  
P. Y. Tong
Keyword(s):  
Random Resistor Network ◽  
Resistor Network ◽  
Two Component

scholarly journals Liouville's Theorem in the Radially Symmetric Case

2005 ◽  
Vol 48 (3) ◽  
pp. 405-408
Author(s):  
Richard Froese
Keyword(s):  
Short Proof ◽  
Symmetric Case ◽  
Ricatti Equation ◽  
Dirichlet To Neumann Map ◽  
Liouville’S Theorem

AbstractWe present a very short proof of Liouville's theorem for solutions to a non-uniformly elliptic radially symmetric equation. The proof uses the Ricatti equation satisfied by the Dirichlet to Neumann map.

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