Multipole Distributions and Hyper-Flux Fields
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916759137681408 |
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| author | Gol'dshtein, Vladimir Segev, Reuven |
| author_facet | Gol'dshtein, Vladimir Segev, Reuven |
| contents | We outline here a simple mathematical introduction to the notions of multipoles for a general extensive property $Π$ from the point of view of continuum mechanics. Classically, $Π$ is the electric charge, but the theory is not limited to electrostatics. The proposed framework allows a simple computation of the bound "charges" and bound multipoles of lower orders. In addition, if the property $Π$ has a potential function in the sense described below, a general expression for the mechanical force (power) functional acting on bodies containing the property is presented. Finally, using a similar viewpoint, we consider hyper-fluxes -- flux fields of tensorial order greater than one -- and show that moving multipoles (in particular, a moving dielectric) give rise to hyper-fluxes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_19559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multipole Distributions and Hyper-Flux Fields Gol'dshtein, Vladimir Segev, Reuven Mathematical Physics 70A05, 78A30 We outline here a simple mathematical introduction to the notions of multipoles for a general extensive property $Π$ from the point of view of continuum mechanics. Classically, $Π$ is the electric charge, but the theory is not limited to electrostatics. The proposed framework allows a simple computation of the bound "charges" and bound multipoles of lower orders. In addition, if the property $Π$ has a potential function in the sense described below, a general expression for the mechanical force (power) functional acting on bodies containing the property is presented. Finally, using a similar viewpoint, we consider hyper-fluxes -- flux fields of tensorial order greater than one -- and show that moving multipoles (in particular, a moving dielectric) give rise to hyper-fluxes. |
| title | Multipole Distributions and Hyper-Flux Fields |
| topic | Mathematical Physics 70A05, 78A30 |
| url | https://arxiv.org/abs/2505.19559 |