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Mechanics of Short-Fiber-Reinforced Composites
Published in Sumit Sharma, Composite Materials, 2021
where Green tensor operator is Γijkl(x)=12[∂hikl∂xj(x)+∂hjkl∂xi(x)].
Statistical Wave Content of Radiative Transfer Theory
Published in L.A. Apresyan, Yu.A. Kravtsov, M.G. Edelev, Radiation Transfer, 2019
L.A. Apresyan, Yu.A. Kravtsov, M.G. Edelev
In the electromagnetic problem, the scalar amplitude us becomes the vector amplitude Es, and the operator G0 becomes the tensor operator G0 considered in Problem 3.24. Thus, instead of eqn (3.3.62) we have fω(n←n0)=−(1−n⊗n)Tkk04πE0,(3) where E0 is the polarization vector of the incident wave.
Gapless Superconductivity
Published in R. D. Parks, Superconductivity, 2018
where τxz is the stress tensor operator. A calculation similar to the one carried out above gives () αTsαTn=g(ql)∫0∞dω2Tcosh−2(ω2T)12(1+|u|2−1|u2−1|)
Nitrogen dioxide line shift coefficients induced by air pressure
Published in Molecular Physics, 2022
N. N. Lavrentieva, A. S. Dudaryonok
and denote the type of interaction (for instance, , correspond to dipole–quadrupole interaction, , correspond to quadrupole–quadrupole interaction). The transition moment is where is the reduced matrix elements of the irreducible tensor operator of rank . The functions are the complex resonance functions depending on the adiabaticity parameter where and are the frequencies of the collision-induced transitions in the absorbing and perturbing molecules, respectively, and the factors are chosen such as . We use for our calculations the resonance functions already averaged by relative speed [20] which were previously tabulated. The functions and are written similarly of [20].
Numerical study of hemodynamics in a complete coronary bypass with venous and arterial grafts and different degrees of stenosis
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2021
Shila Alizadehghobadi, Hasan Biglari, Hanieh Niroomand-Oscuii, Meisam H. Matin
where and P stand for the velocity and pressure fields in the blood, respectively, and D represents the tensor operator. µ and ρ are the dynamic viscosity and density of blood, respectively. The equation governing the structural equilibrium can be written in the form of: in which is the velocity component and is the Piola-Kirchhoff stress tensor and is the deformation. and are the vector of initial forces applied on the system and density, respectively. The governing equations (Eqs. (1)-(3)) are subject to the following boundary conditions at the fluid-structure interface: where and are the stress tensor for the fluid and the Cauchy stress tensor for the vessel wall, respectively, and is the normal vector. Eq. (4-a) represents the no-slip condition as well as the impermeability of the wall and Eqs. (4-b) and (4-c) stand for the continuity of the displacement and traction at the interface, respectively.
Quasi-relativistic study of nuclear electric quadrupole coupling constants in chiral molecules containing heavy elements
Published in Molecular Physics, 2020
Konstantin Gaul, Robert Berger
In this implementation, the large component is approximated as the ZORA wave function and terms involving the small component can be calculated by automatic generation of an approximate small component in the sense of ZORA: In the sense of our toolbox approach [7], the electronic EFG operator can be represented by the four component density function , a tensor operator , a scalar operator and no differential operator, where we have used the notation detailed in Ref. [7]. Within this notation, contributions to from the approximate ZORA two component number density functions and have to be evaluated. The contribution of the nuclear-nuclear repulsion was directly evaluated as written in Equation (3) and added subsequently to the electronic contribution to receive the NEQC tensor. For more details on our toolbox approach and the corresponding notation, we refer the reader to Ref. [7].