scholarly journals Additional Boundary Condition for the Wire Medium

2006 ◽  
Vol 54 (6) ◽  
pp. 1766-1780 ◽  
Author(s):  
M.G. Silveirinha
Keyword(s):  
Boundary Condition ◽  
Additional Boundary Condition ◽  
The Wire

A scalar form of the complementary mild-slope equation

2010 ◽  
Vol 656 ◽  
pp. 407-416 ◽  
Author(s):  
YARON TOLEDO ◽  
YEHUDA AGNON
Keyword(s):  
Boundary Condition ◽  
Water Waves ◽  
Linear Time ◽  
Laboratory Data ◽  
Computational Effort ◽  
Scalar Equation ◽  
Scalar Form ◽  
Additional Boundary Condition ◽  
Mild Slope Equation ◽  
Pseudo Potential

Mild-slope (MS) type equations are depth-integrated models, which predict under appropriate conditions refraction and diffraction of linear time-harmonic water waves. Among these equations, the complementary mild-slope equation (CMSE) was shown to give better agreement with exact two-dimensional linear theory compared to other MS-type equations. Nevertheless, it has a disadvantage of being a vector equation, i.e. it requires solving a system of two coupled partial differential equations. In addition, for three-dimensional problems, there is a difficulty in constructing the additional boundary condition needed for the solution. In the present work, it is shown how the vector CMSE can be transformed into an equivalent scalar equation using a pseudo-potential formulation. The pseudo-potential mild-slope equation (PMSE) preserves the accuracy of the CMSE while avoiding the need of an additional boundary condition. Furthermore, the PMSE significantly reduces the computational effort relative to the CMSE, since it is a scalar equation. The accuracy of the new model was tested numerically by comparing it to laboratory data and analytical solutions.

scholarly journals Asymptotic Variational Formulae for Eigenvalues

1963 ◽  
Vol 6 (1) ◽  
pp. 15-25 ◽  
Author(s):  
C.A. Swanson
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Component ◽  
Differential Operators ◽  
Open Interval ◽  
Variational Problems ◽  
Elliptic Differential Operator ◽  
Additional Boundary Condition ◽  
Half Open Interval ◽  
Ordinary Differential Operators

The eigenvalues of a second order self-adjoint elliptic differential operator on Riemannian n-space R will be considered. Our purpose is to obtain asymptotic variational formulae for the eigenvalues under the topological deformations of (i) removing an ɛ -cell (and adjoining an additional boundary condition on the boundary component thereby introduced); and (ii) attaching an ɛ -handle, valid on a half-open interval 0 < ɛ ≤ ɛo. In particular the formulae will exhibit the non-analytic nature of the variation. Similar variational problems for singular ordinary differential operators have been considered by the writer in [3] and [4].

Capillary–gravity waves against a vertical cliff

1968 ◽  
Vol 64 (3) ◽  
pp. 827-832 ◽  
Author(s):  
B. A. Packham
Keyword(s):  
Boundary Condition ◽  
Surface Tension ◽  
Gravity Waves ◽  
Solid Boundary ◽  
Additional Boundary Condition ◽  
Additional Force ◽  
Sloping Beach ◽  
Effect Of Surface

In considering the problem of waves on a sloping beach, little regard seems to have been given to the effect of surface tension. Wehausen and Laitone (7) tend to attribute this to the fact that the additional force is small. This does not, of course, preclude the possibility that the effect may be appreciable in certain regions, and Longuet-Higgins (3), for example, has shown this to be the case near the crests for waves on the point of breaking. They also add, which is probably rather more pertinent, that difficulties arise when a solid boundary pierces the surface, since an additional boundary condition is required at the intersection, but give no indication as to what the boundary condition should be.

The Effect of Cross-sectional Geometry on ZT Enhancement in Rough Silicon Nanostructures

2010 ◽  
Vol 1267 ◽  
Author(s):  
Jyothi Swaroop Sadhu ◽  
Marc G Ghossoub ◽  
Sanjiv Sinha
Keyword(s):  
Thermal Conductivity ◽  
Boundary Condition ◽  
Cross Section ◽  
Silicon Nanowires ◽  
Silicon Nanostructures ◽  
Dramatic Reduction ◽  
Cross Sectional ◽  
The Wire ◽  
Phonon Localization ◽  
The Impact

AbstractThe dramatic reduction in the thermal conductivity of rough silicon nanowires is due to phonon localization in the wire resulting from multiple scattering of phonons from the rough walls. We report the dependence of thermal conductivity of the nanowires as a function of the surface roughness and the diameter of the wire by modeling the nanowire as a waveguide. In addition, we estimate the impact of boundary condition, dimensionality and cross section of rough wire on the thermal conductivity. This theoretical model gives insights for tailoring thermal conductivity and enhancing the ZT of silicon to 1 for its use in thermoelectrics

scholarly journals Additional boundary condition for a wire medium connected to a metallic surface

2008 ◽  
Vol 10 (5) ◽  
pp. 053011 ◽  
Author(s):  
Mário G Silveirinha ◽  
Carlos A Fernandes ◽  
Jorge R Costa
Keyword(s):  
Boundary Condition ◽  
Metallic Surface ◽  
Additional Boundary Condition
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