China
Africa
Explore chapters and articles related to this topic
Vector Analysis and EM Waves
Published in Russell L. Herman, A Course in Mathematical Methods for Physicists, 2013
A special tensor is the Kronecker delta. () δ'βα=Λγαδδγ(Λ−1)βδ=Λγα(Λ−1)βγ=δβα.Linear combinations of tensors.
Introduction
Published in Saad A. Ragab, Hassan E. Fayed, Introduction to Finite Element Analysis for Engineers, 2018
Saad A. Ragab, Hassan E. Fayed
The Kronecker delta is defined such that δij = 1 if the index i is equal to the index j, and δij = 0 if i ≠ j. Thus, δ11 = δ22 = δ33 = 1, but δ12 = δ13 = δ23 = δ21 = δ31 = δ32 = 0. Note that δjj = δ11 + δ22 + δ33 = 3 because the index j is repeated.
Effect of Non-Uniform Vertical Excitations on Vertical Pounding Phenomenon in Continuous-Deck Curved Box Girder RC Bridges Subjected to Near-Source Earthquakes
Published in Journal of Earthquake Engineering, 2022
S. Tamaddon, M. Hosseini, A. Vasseghi
The symbol represents the Kronecker delta and is equal to . The equation can be expanded by inserting the dynamic displacements of Equations (7) and (8) into Equations (1) and (9) into Equation (2). Then, inserting Equations (12) and (13) into it and multiplying by and then integrating from to O for the beam OA. The equation expansion feature can also be used for the beam OB and pier CD. After expanding all three equations using the orthogonality condition (Equation 15), all terms on the left-hand side of equations will be zero except when n = m. So, for this case, one can write:
Thermodynamic factor of quaternary mixtures from Kirkwood–Buff integration
Published in Molecular Physics, 2020
Robin Fingerhut, Gerhard Herres, Jadran Vrabec
The general formalism for obtaining chemical potential derivatives from KBI was outlined by Ben-Naim [15]. The derivative of the chemical potential with respect to the particle number is given by with volume V, component indices i, j, a, b and total number of components in the mixture n. Note that indicates that all particle numbers are kept constant, except for . Equation (3) gives evidence that KBI are defined for open systems, like the ensemble, because the total number of molecules is not constant. The () matrix consists of the elements , where denotes the Kronecker delta. In Equation (3), are derivatives of the determinant with respect to , i.e. [15]. Note that matrix is symmetric because and thus .
Annular crack in a thermoelastic half-space
Published in Journal of Thermal Stresses, 2020
Now, the following Gegenbauer addition formula [55, Eq. (8.531 1)] are used to eliminate the radial variable r where is the Kronecker delta defined by