A direct method to calculate second-order two-dimensional terahertz spectroscopy in frequency-domain based on classical theory

2018 ◽  
Vol 11 (4) ◽  
pp. 413-418
Author(s):  
Feidi Xiang ◽  
Kejia Wang ◽  
Zhengang Yang ◽  
Jinsong Liu ◽  
Shenglie Wang
Keyword(s):  
Frequency Domain ◽  
Classical Theory ◽  
Terahertz Spectroscopy ◽  
Direct Method ◽  
Second Order ◽  
Two Dimensional ◽  
A Direct Method

Isoperimetric Problems in the Calculus of Variations

1952 ◽  
Vol 4 ◽  
pp. 257-280 ◽  
Author(s):  
William Karush
Keyword(s):  
Calculus Of Variations ◽  
Classical Theory ◽  
Indirect Method ◽  
Direct Method ◽  
Isoperimetric Problems ◽  
End Points ◽  
Sufficiency Theorems ◽  
Theory Of Fields ◽  
A Direct Method ◽  
Problem Of Bolza

We are concerned with establishing sufficiency theorems for minima of simple integrals of the parametric type in a class of curves with variable end points and satisfying isoperimetric side conditions. The results which are obtained involve no explicit assumptions of normality. Such results can be derived by transforming our problem to a problem of Bolza and using the latest developments in the theory of that problem. More recently [6] an indirect method of proof has been published. Our object is to present a direct method of proof without transformation of the problem which is based upon a generalization of the classical theory of fields.

scholarly journals Observation of strong helical excitons and unexpectedly giant Rashba splitting in single crystal two-dimensional Organic-Inorganic Halide Perovskites

2020 ◽  
Author(s):  
Andrivo Rusydi ◽  
Xiao Chi ◽  
Kai Leng ◽  
Runlai Li ◽  
Xiaojiang Yu ◽  
...  
Keyword(s):  
Single Crystal ◽  
Electric Fields ◽  
Direct Method ◽  
Two Dimensional ◽  
Spintronic Devices ◽  
Splitting Parameter ◽  
Halide Perovskites ◽  
Inversion Asymmetry ◽  
A Direct Method ◽  
Lead Halide

Abstract Two-dimensional (2D) organic-inorganic lead halide perovskites possess strong spin-orbit coupling, and in the presence of broken inversion symmetry, this may lead to helical excitons and Rashba splitting at the band extrema1-6. However, a direct and systematic measurement of the helical excitons and the Rashba parameter in the system is still lacking. Here, we report distinct two bright co-helical and two dark anti-helical excitons in single crystal ((CH3(CH2)3NH3)2(CH3NH3)n-1PbnI3n+1 (n = 1 to 4), where n determines quantum well (QW) thickness of inorganic layer7. By comprehensively analyzing the fine structure of helical excitons, we find that the Rashba splitting originates from surface inversion asymmetry and surface-normal electric fields, which are determined by the QW’s dielectric environment, n and temperature. The Rashba splitting parameter is found among the highest recorded of 2.66 and 2.5 eV∙Å for the conduction and valence band of n=1 Iodide, respectively, and reduces for n>1 Iodide. Our result shows the importance of helical excitons and Rashba splitting and presents a direct method to quantify the Rashba parameter in complex halide perovskites. We hope that our study inspires applications of QW materials in novel spintronic devices.

The gravity profile and its role in positioning the edge of a two‐dimensional faulted structure having an arbitrary vertical variation of density

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1097-1104 ◽  
Author(s):  
M. K. Paul ◽  
A. K. Goodacre
Keyword(s):  
Direct Method ◽  
Real Data ◽  
Theoretical Models ◽  
Seismic Profile ◽  
Two Dimensional ◽  
Lateral Variation ◽  
Straight Line ◽  
Gravity Interpretation ◽  
A Direct Method ◽  
Different Levels

It is shown analytically that as long as there is no lateral variation of density within a two‐dimensional faulted structure the value of gravity at any point on the upward extension of the fault remains constant. Consequently, this result leads to a direct method of gravity interpretation, where it is possible to delineate the edge of such a faulted structure by continuing the surface gravity values upward to different levels and then, by using suitable numerical techniques, find the desired resulting straight‐line gravity contour. The method has been verified using several theoretical models and applied to two sets of real data to demonstrate its usefulness. On a local scale, the Gloucester fault near Ottawa, Canada appears to be nearly vertical. On a larger scale, the gravity signature along the Southern Appalachian COCORP seismic profile can be explained by density jumps across a steeply dipping, major crustal discontinuity.

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