Computation of the anisotropic cubic elastic green's tensor function and the elastic energy coefficients of point defects in crystals

1976 ◽  
Vol 11 (3) ◽  
pp. 339-351 ◽  
Author(s):  
R.K. Leutz ◽  
R. Bauer
Keyword(s):  
Point Defects ◽  
Elastic Energy ◽  
Defects In Crystals ◽  
Tensor Function ◽  
Green's Tensor ◽  
Green’S Tensor

Contribution estimation of singular points in solving problems of radiation of HF VHF wire antennas arbitrarily located above the earth

2021 ◽  
Author(s):  
A.O. Perfilova
Keyword(s):  
Integral Equations ◽  
Singular Points ◽  
Tensor Function ◽  
Method Of Integral Equations ◽  
The Earth ◽  
Green's Tensor ◽  
The Wire ◽  
Wire Antennas ◽  
Green’S Tensor

The radiation solving the problem features of the wire antennas placed above the earth are considered. Based on the method of integral equations, the singular points contribution in solving radiation problems of the HF VHF wire antennas arbitrarily located above the earth is researched. The contribution of singular points is estimated depending on the frequency and parameters of the earth. It is shown that in the HF and VHF waves, their contribution of singular points is significant. The radiation solving the problem features of the wire antennas placed above the earth are considered. The value of elements of the Green’s tensor function is usually expressed in the Sommerfeld’s integrals form. The aim of this work is to estimate the contribution of singular points to the value of Sommerfeld’s integrals. Based on the method of integral equations, the singular points contribution in solving radiation problems of the HF VHF wire antennas arbitrarily located above the earth is researched. The contribution of singular points is estimated depending on the frequency and parameters of the earth. It is shown that in the HF and VHF waves, their contribution of singular points is significant.

Defects in Crystals

1968 ◽  
Vol 26 ◽  
pp. 244-245
Author(s):  
Kenneth R. Lawless
Keyword(s):  
Electron Microscope ◽  
Point Defects ◽  
Surface Defects ◽  
Chemical Properties ◽  
Material Point ◽  
Crystal Defects ◽  
Defects In Crystals ◽  
Irradiation Effects ◽  
Normal Lattice ◽  
Line Defects

One of the most important applications of the electron microscope in recent years has been to the observation of defects in crystals. Replica techniques have been widely utilized for many years for the observation of surface defects, but more recently the most striking use of the electron microscope has been for the direct observation of internal defects in crystals, utilizing the transmission of electrons through thin samples.Defects in crystals may be classified basically as point defects, line defects, and planar defects, all of which play an important role in determining the physical or chemical properties of a material. Point defects are of two types, either vacancies where individual atoms are missing from lattice sites, or interstitials where an atom is situated in between normal lattice sites. The so-called point defects most commonly observed are actually aggregates of either vacancies or interstitials. Details of crystal defects of this type are considered in the special session on “Irradiation Effects in Materials” and will not be considered in detail in this session.

scholarly journals Azimuthal Anchoring Strength in Photopatterned Alignment of a Nematic

Crystals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 675
Author(s):  
H. Nilanthi Padmini ◽  
Mojtaba Rajabi ◽  
Sergij V. Shiyanovskii ◽  
Oleg D. Lavrentovich
Keyword(s):  
Liquid Crystal ◽  
Point Defects ◽  
Elastic Energy ◽  
Separation Distance ◽  
Thin Layers ◽  
Uv Exposure ◽  
Surface Anchoring ◽  
Anchoring Strength ◽  
Spatially Varying

Spatially-varying director fields have become an important part of research and development in liquid crystals. Characterization of the anchoring strength associated with a spatially-varying director is difficult, since the methods developed for a uniform alignment are seldom applicable. Here we characterize the strength of azimuthal surface anchoring produced by the photoalignment technique based on plasmonic metamsaks. The measurements used photopatterned arrays of topological point defects of strength +1 and −1 in thin layers of a nematic liquid crystal. The integer-strength defects split into pairs of half-integer defects with lower elastic energy. The separation distance between the split pair is limited by the azimuthal surface anchoring, which allows one to determine the strength of the latter. The strength of the azimuthal anchoring is proportional to the UV exposure time during the photoalignment of the azobenzene layer.

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.

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