# Homogenization of second order energies on periodic thin structures

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Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without...

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Recent analysis of direct numerical simulations of compressible homogeneous shear flow turbulence has unraveled some of the energy transfer mechanisms responsible for the decrease of kinetic energy growth when the flow becomes more compressible. In this complementary study, attention is focused...

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The expansion of the exponential of a tensorial expression such as the interaction or pair correlation function between two nonspherical molecules 1, 2 is of the form âˆ‘mnl Î»mnl[uppercase_phi_synonym]mnl(12), where [uppercase_phi_synonym]mnl(12) are invariant tensorial expressions that...

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The Fourier transform of an irreducible spherical tensor is normally computed with the help of the Rayleigh expansion of a plane wave in terms of spherical Bessel functions and spherical harmonics. The angular integrations are then trivial. However, the remaining radial integral containing a...

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Density-functional theory (DFT) calculations of indirect nuclear magnetic resonance spin-spin coupling tensors J, with the anisotropic but symmetric parts being the particular concern, are carried out for a series of molecules with the linear response (LR) method. For the first time, the...

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The pressure tensor in a wedge-shaped cavity of a solid with dispersion forces is calculated. All four (three diagonal and one nondiagonal) components of the pressure tensor are calculated as functions of their positions inside the cavity. It is shown that these components satisfy the mechanical...

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Examines the construction of a nonlocal current density functional for magnetic responses. Comparison of the nonlocal current density functional with the local functionals; Capacity of nonlocal functionals to support net paramagnetism; Derivation of the full magnetic susceptibility and chemical...