Reciprocity relations in an isotropic compressible multifluid plasma

1976 ◽  
Vol 47 (7) ◽  
pp. 2918-2922 ◽  
Author(s):  
Takayuki Ishizone ◽  
Saburo Adachi ◽  
Yasuto Mushiake
Keyword(s):  
Reciprocity Relations ◽  
Multifluid Plasma

Reciprocity and Related Topics in Elastodynamics

2006 ◽  
Vol 59 (1) ◽  
pp. 13-32 ◽  
Author(s):  
Jan D. Achenbach
Keyword(s):  
Elasticity Theory ◽  
Elastic Body ◽  
19Th Century ◽  
Wave Motion ◽  
Review Article ◽  
Integral Representations ◽  
Time Harmonic ◽  
Reciprocity Relations ◽  
Elastic Systems ◽  
The 19Th Century

Reciprocity theorems in elasticity theory were discovered in the second half of the 19th century. For elastodynamics they provide interesting relations between two elastodynamic states, say states A and B. This paper will primarily review applications of reciprocity relations for time-harmonic elastodynamic states. The paper starts with a brief introduction to provide some historical and general background, and then proceeds in Sec. 2 to a brief discussion of static reciprocity for an elastic body. General comments on waves in solids are offered in Sec. 3, while Sec. 4 provides a brief summary of linearized elastodynamics. Reciprocity theorems are stated in Sec. 5. For some simple examples the concept of virtual waves is introduced in Sec. 6. A virtual wave is a wave motion that satisfies appropriate conditions on the boundaries and is a solution of the elastodynamic equations. It is shown that combining the desired solution as state A with a virtual wave as state B provides explicit results for state A. Basic elastodynamic states are discussed in Sec. 7. These states play an important role in the formulation of integral representations and integral equations, as shown in Sec. 8. Reciprocity in 1-D and full-space elastodynamics are discussed in Secs. 910, respectively. Applications to a half-space and a layer are reviewed in Secs. 1112. Section 13 is concerned with reciprocity of coupled acousto-elastic systems. The paper is completed with a brief discussion of reciprocity for piezoelectric systems. There are 61 references cited in this review article.

SEISMIC RECIPROCITY

Geophysics ◽  
1959 ◽  
Vol 24 (4) ◽  
pp. 681-691 ◽  
Author(s):  
Leon Knopoff ◽  
Anthony F. Gangi
Keyword(s):  
Scalar Product ◽  
Point Sources ◽  
Simple Experiment ◽  
Reciprocity Relations ◽  
Green's Tensor ◽  
Vector Case ◽  
Green’S Tensor

The reciprocity relationship describing the relations among the fields resulting from the interchange of point sources and receivers may be extended to the seismic case. Seismic reciprocity can be described either in terms of the scalar product of the vectors representing the excitation of the source and the field at the receiver, or in terms of a Green’s tensor describing these two quantities. Theoretical reciprocity relations give no information concerning reciprocity in the cases for which the scalar product vanishes. A simple experiment in the vector case demonstrates that reciprocity is not obtained when the scalar product of the two vectors vanishes.

Sign in / Sign up

Export Citation Format

Share Document