Plane wave diffraction by a wedge in a magnetoactive plasma under mixed boundary conditions and a ?thermodynamic paradox?

1985 ◽  
Vol 28 (3) ◽  
pp. 185-189
Author(s):  
M. S. Bobrovnikov ◽  
V. V. Fisanov
Keyword(s):  
Plane Wave ◽  
Boundary Conditions ◽  
Wave Diffraction ◽  
Mixed Boundary ◽  
Magnetoactive Plasma ◽  
Mixed Boundary Conditions ◽  
Plane Wave Diffraction

Diffraction of a plane wave by a half plane under mixed boundary conditions

1981 ◽  
Vol 59 (8) ◽  
pp. 974-984 ◽  
Author(s):  
T. C. Kaladhar Rao
Keyword(s):  
Plane Wave ◽  
Boundary Conditions ◽  
Half Plane ◽  
Infinite Series ◽  
Series Solution ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Condition ◽  
Neumann Condition ◽  
Transform Method

The problem of diffraction of a plane wave by a semi-infinite half plane with mixed boundary conditions (Dirichlet condition on one face and Neumann condition on the other) is solved by a direct and rather straightforward method. The infinite series solution and the far field are in agreement with the previous solutions obtained by the Lebedev–Kontorovich transform method as expected, as the two methods are basically equivalent. An alternate representation of the infinite series solution is presented which is valid for any type of incident field including cylindrical and spherical fields. This representation facilitates easy analysis of transient problems and the special case of an incident plane unit step function on the half plane is given as an example.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

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