In an electrostatic field, all charge distributions and currents may be represented by a multipolar expansion using only electric and magnetic multipoles
. Instead, in a multipolar expansion of an electrodynamic field new terms appear.
"We found that electrons in crystals can collectively arrange to give rise not only to charge dipole units -- that is, pairings of positive and negative charges -- but also high-order multipoles
in which four or eight charges are brought together into a unit.
The intensity of the incident p-polarized field in comparison with the highest field intensity between the tip and the surface calculated in the used simplest dipole model in Rayleigh approximation is less than 2% and even smaller if multipoles
are taken into account.
Here, P is the number of multipoles
that controls the expanded form and the accuracy of the translation operator.
Many applications are found in different fields, such as; dynamical systems, electrical circuits with fractance, electrochemistry, multipoles
in electromagnetism, neurons in biology, the problems of viscoelasticity which be solved by Caputo, and many others.
Second, the move to a higher level of decomposition--as elements of the settlement scheme is not considered bipolar R, L, C elements, but three-phase multipoles
corresponding to the three-phase network elements.
Surface charts showing the distribution of the three dimensional borehole thermal resistance, calculated with ten multipoles
and Equation 8 under a variation of the pipe spacing and the grout thermal conductivity, were drawn for each GHE.
The translated probe coefficients [[sigma].sup.l.sub.nm] are basically the responses of the probe, located at r[??], to each of the multipoles
that compose the basis of vector spherical waves.
Instead, the interparticle interactions arise from multiple spatial directions and multipoles
are induced within the individual particles.
The microscopic EM theories developed by Jackson, Mazur, and Robinson (27), (29), (30) average multipoles
at a molecular level and replace the molecular multipoles
, with averaged point multipoles
usually located at the center-of-mass position.