Role of the third-order elasticity modulus in stabilizing Na crystals at high pressures

2016 ◽  
Vol 80 (4) ◽  
pp. 484-490 ◽  
Author(s):  
M. A. Gufan
Keyword(s):  
High Pressures ◽  
Elasticity Modulus ◽  
Third Order ◽  
The Third

scholarly journals Volume derivatives of the Grüneisen parameter in the limit of infinite pressure

2019 ◽  
Vol 97 (1) ◽  
pp. 114-116 ◽  
Author(s):  
A. Dwivedi
Keyword(s):  
Boundary Condition ◽  
Fourth Order ◽  
Fundamental Theorem ◽  
High Pressures ◽  
Grüneisen Parameter ◽  
Third Order ◽  
Gruneisen Parameter ◽  
The Third ◽  
Properties Of Materials ◽  
Derivatives Of

Expressions have been obtained for the volume derivatives of the Grüneisen parameter, which is directly related to the thermal and elastic properties of materials at high temperatures and high pressures. The higher order Grüneisen parameters are expressed in terms of the volume derivatives, and evaluated in the limit of infinite pressure. The results, that at extreme compression the third-order Grüneisen parameter remains finite and the fourth-order Grüneisen parameter tends to zero, have been used to derive a fundamental theorem according to which the volume derivatives of the Grüneisen parameter of different orders, all become zero in the limit of infinite pressure. However, the ratios of these derivatives remain finite at extreme compression. The formula due to Al’tshuler and used by Dorogokupets and Oganov for interpolating the Grüneisen parameter at intermediate compressions has been found to satisfy the boundary condition at infinite pressure obtained in the present study.

The third-order polarizability γ of C60: The role of low-lying two-electron excited singlet states Ag and Hg

2000 ◽  
Vol 112 (15) ◽  
pp. 6603-6607 ◽  
Author(s):  
Yasushi Nomura ◽  
Takashi Miyamoto ◽  
Toshiki Hara ◽  
Susumu Narita ◽  
Tai-ichi Shibuya
Keyword(s):  
Excited Singlet ◽  
Third Order ◽  
The Third ◽  
Singlet States ◽  
Excited Singlet States

scholarly journals The Third Order in the Underground: Lay Organizations of the Ukrainian Greek Catholic Church in Precarpathian Region in the 1970s-1980s

2014 ◽  
Vol 1 (4) ◽  
pp. 73-82
Author(s):  
Oleg Zhernokleyev
Keyword(s):  
Catholic Church ◽  
Spiritual Life ◽  
Spiritual Practices ◽  
Third Order ◽  
The Third ◽  
Soviet Time ◽  
Structure And Activity

The paper highlights the role of communities of monks and nuns (the Third Orders) inthe structure and activity of the Ukrainian Greek Catholic Church (UGCC), which functionedunderground. It is emphasized that the historical roots of the Third Order are traced back to the13th century when spiritual life of specific lay communities was regulated by the Franciscan andthe Dominican Orders, and later, by the Carmelite Order. Between 1900 and 1930s lay communitiesof the UGCC became noticeably active. A characteristic example of their activity is the well knownRules for laypersons of the Basilian Order drawn by Metropolitan Archbishop Andrey Sheptytsky.In the 1970s (the Soviet time, when the UGCC worked underground), there appeared theRedemptorist and the Basilian Third Orders in Ivano-Frankivsk Oblast. Their members kept insafety different cult objects, held underground Divine Services, meetings, had spiritual practices,did catechesis, etc. On the whole, these lay communities had played an important role in theUGCC underground activity up till the late 1980s

scholarly journals The role of orthopedic surgery in the third-order emergency hospital of Kurume University.

1984 ◽  
Vol 33 (1) ◽  
pp. 283-286
Author(s):  
Osamu Sugiyama ◽  
Kanichiro Kiyonaga ◽  
Masaki Miyazaki ◽  
Koji Tanaka ◽  
Shiro Tahira ◽  
...  
Keyword(s):  
Orthopedic Surgery ◽  
Third Order ◽  
Emergency Hospital ◽  
The Third

Role of the band structure in determining the third-order susceptibility of semiconductor superlattices

1992 ◽  
Vol 45 (19) ◽  
pp. 11031-11035 ◽  
Author(s):  
M. J. Shaw ◽  
D. Ninno ◽  
B. M. Adderley ◽  
M. Jaros
Keyword(s):  
Band Structure ◽  
Semiconductor Superlattices ◽  
Third Order ◽  
The Third ◽  
Order Susceptibility

scholarly journals From a Mechanical Lagrangian to the Schrödinger Equation: A Modified Version of the Quantum Newton Law

2003 ◽  
Vol 18 (19) ◽  
pp. 3347-3368 ◽  
Author(s):  
A. Bouda
Keyword(s):  
Kinetic Term ◽  
Third Order ◽  
One Dimensional ◽  
The Third ◽  
Classical Potential ◽  
The One ◽  
Quantum Motion ◽  
Derivatives Of ◽  
Hamilton Jacobi Equation

In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a nonrelativistic spinless system. This Lagrangian is written as a difference between a function T, which represents the quantum generalization of the kinetic energy and which depends on the coordinate x and the temporal derivatives of x up the third order, and the classical potential V(x). The Hamiltonian is then constructed and the corresponding canonical equations are deduced. The function T is first assumed to be arbitrary. The development of T in a power series together with the dimensional analysis allow us to fix univocally the series coefficients by requiring that the well-known quantum stationary Hamilton–Jacobi equation be reproduced. As a consequence of this approach, we formulate the law of the quantum motion representing a new version of the quantum Newton law. We also analytically establish the famous Bohm relation [Formula: see text] outside the framework of the hydrodynamical approach and show that the well-known quantum potential, although it is a part of the kinetic term, plays really the role of an additional potential as assumed by Bohm.

scholarly journals Nonlinear Spectroscopy in the Condensed Phase: The Role of Duschinsky Rotations and Third Order Cumulant Contributions

2020 ◽  
Author(s):  
Tim Zuehlsdorff ◽  
Hanbo Hong ◽  
Liang Shi ◽  
Christine Isborn
Keyword(s):  
Excited State ◽  
Condensed Phase ◽  
Nonlinear Optical ◽  
Order Term ◽  
Optical Spectra ◽  
Cumulant Expansion ◽  
Third Order ◽  
The Third ◽  
Mode Mixing

First-principles modeling of nonlinear optical spectra in the condensed phase is highly challenging because both environment and vibronic interactions can play a large role in determining spectral shapes and excited state dynamics. Here, we compute two dimensional electronic spectroscopy (2DES) signals based on a cumulant expansion of the energy gap fluctuation operator, with a specific focus on analyzing mode mixing effects introduced by the Duschinsky rotation and the role of the third order term in the cumulant expansion for both model and realistic condensed phase systems. We show that for a harmonic model system, the third order cumulant correction captures effects introduced by a mismatch in curvatures of ground and excited state potential energy surfaces, as well as effects of mode mixing. We also demonstrate that 2DES signals can be accurately reconstructed from purely classical correlation functions using quantum correction factors. We then compute nonlinear optical spectra for the Nile red and Methylene blue chromophores in solution, assessing the third order cumulant contribution for realistic systems. We show that the third order cumulant correction is strongly dependent on the treatment of the solvent environment, revealing the interplay between environmental polarization and the electronic-vibrational coupling.

scholarly journals Nonlinear Spectroscopy in the Condensed Phase: The Role of Duschinsky Rotations and Third Order Cumulant Contributions

2020 ◽  
Author(s):  
Tim Zuehlsdorff ◽  
Hanbo Hong ◽  
Liang Shi ◽  
Christine Isborn
Keyword(s):  
Excited State ◽  
Condensed Phase ◽  
Nonlinear Optical ◽  
Order Term ◽  
Optical Spectra ◽  
Cumulant Expansion ◽  
Third Order ◽  
The Third ◽  
Mode Mixing

First-principles modeling of nonlinear optical spectra in the condensed phase is highly challenging because both environment and vibronic interactions can play a large role in determining spectral shapes and excited state dynamics. Here, we compute two dimensional electronic spectroscopy (2DES) signals based on a cumulant expansion of the energy gap fluctuation operator, with a specific focus on analyzing mode mixing effects introduced by the Duschinsky rotation and the role of the third order term in the cumulant expansion for both model and realistic condensed phase systems. We show that for a harmonic model system, the third order cumulant correction captures effects introduced by a mismatch in curvatures of ground and excited state potential energy surfaces, as well as effects of mode mixing. We also demonstrate that 2DES signals can be accurately reconstructed from purely classical correlation functions using quantum correction factors. We then compute nonlinear optical spectra for the Nile red and Methylene blue chromophores in solution, assessing the third order cumulant contribution for realistic systems. We show that the third order cumulant correction is strongly dependent on the treatment of the solvent environment, revealing the interplay between environmental polarization and the electronic-vibrational coupling.

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