Multipole structure and coordinate systems
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In this article, it was shown that for the case of two equal like electric charges, the coefficients of all higher multipoles vanish identically, even when the potential is given by a monopole term.Abstract:
Multipole expansions depend on the coordinate system, so that coefficients of multipole moments can be set equal to zero by an appropriate choice of coordinates. Therefore, it is meaningless to say that a physical system has a nonvanishing quadrupole moment, say, without specifying which coordinate system is used. (Except if this moment is the lowest non-vanishing one.) This result is demonstrated for the case of two equal like electric charges. Specifically, an adapted coordinate system in which the potential is given by a monopole term only is explicitly found, the coefficients of all higher multipoles vanish identically. It is suggested that this result can be generalized to other potential problems, by making equal coordinate surfaces adapt to the potential problem's equipotential surfaces.read more
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Journal ArticleDOI
Multipolar ordering in electro- and magnetostatic coupled nanosystems
Elena Y. Vedmedenko,N. Mikuszeit +1 more
TL;DR: An overview of mathematical definitions of multipole expansion and relations between different formulations is given and a general theoretical description of multipolar ordering on periodic two-dimensional lattices is presented.
Journal ArticleDOI
Multipolar scattering analysis of hybrid metal-dielectric nanostructures.
TL;DR: In this article, the evolution of the multipoles along with the spectra for a hybrid metal-dielectric nanoantenna, a Si cylinder and an Ag disk stacked one on top of another, as its dimensions are varied one by one.
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Shear and expansion evolution for dissipative fluids
S. Ahmad,A. Rehman Jami,Z. Aas +2 more
TL;DR: In this paper, the role of shear evolution equation in the modeling of relativistic spheres in f(R) gravity was analyzed and it was shown that non-static diagonally symmetric geometry is coupled with diagonal symmetry.
References
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Journal ArticleDOI
Methods of Theoretical Physics. By P.M. Morse and H. Feschbach. 2vols., Pp.xxii, 1978. 120s. each vol. 1953.(McGraw-Hill)
Book
Mathematical Methods for Physicists
TL;DR: In this article, the authors present a model for vector analysis based on the Calculus of Variations and the Sturm-Liouville theory, which includes the following: Curved Coordinates, Tensors.