A Variational Approach to Electrostatics of Polarizable Heterogeneous Substances
We discuss equilibrium conditions for heterogeneous substances subject to electrostatic or magnetostatic effects. We demonstrate that the force-like aleph tensor ℵij and the energy-like beth tensor ℶij for polarizable deformable substances are divergence-free: ∇iℵij=0 and ∇iℶij=0. We introduce two...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/659127 |
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| author | Michael Grinfeld Pavel Grinfeld |
| author_facet | Michael Grinfeld Pavel Grinfeld |
| author_sort | Michael Grinfeld |
| collection | DOAJ |
| description | We discuss equilibrium conditions for heterogeneous substances subject
to electrostatic or magnetostatic effects. We demonstrate that the
force-like aleph tensor ℵij and the energy-like beth tensor ℶij for polarizable
deformable substances are divergence-free: ∇iℵij=0 and ∇iℶij=0.
We introduce two additional tensors: the divergence-free energy-like gimel
tensor ℷij for rigid dielectrics and the general electrostatic gamma tensor Γij which is not divergence-free.
Our approach is based on a logically consistent extension of the Gibbs
energy principle that takes into account polarization effects. While the
model is mathematically rigorous, we caution against the assumption that
it can reliably predict physical phenomena. On the contrary, clear models
often lead to conclusions that are at odds with experiment and therefore
should be treated as physical paradoxes that deserve the attention of the
scientific community. |
| format | Article |
| id | doaj-art-0c892ec8d8ee498b8aea29c1fabbf568 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-0c892ec8d8ee498b8aea29c1fabbf5682025-02-03T05:45:32ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/659127659127A Variational Approach to Electrostatics of Polarizable Heterogeneous SubstancesMichael Grinfeld0Pavel Grinfeld1Aberdeen Proving Ground, US Army Research Laboratory, Aberdeen, MD 21005-5066, USADrexel University, Philadelphia, PA 19104, USAWe discuss equilibrium conditions for heterogeneous substances subject to electrostatic or magnetostatic effects. We demonstrate that the force-like aleph tensor ℵij and the energy-like beth tensor ℶij for polarizable deformable substances are divergence-free: ∇iℵij=0 and ∇iℶij=0. We introduce two additional tensors: the divergence-free energy-like gimel tensor ℷij for rigid dielectrics and the general electrostatic gamma tensor Γij which is not divergence-free. Our approach is based on a logically consistent extension of the Gibbs energy principle that takes into account polarization effects. While the model is mathematically rigorous, we caution against the assumption that it can reliably predict physical phenomena. On the contrary, clear models often lead to conclusions that are at odds with experiment and therefore should be treated as physical paradoxes that deserve the attention of the scientific community.http://dx.doi.org/10.1155/2015/659127 |
| spellingShingle | Michael Grinfeld Pavel Grinfeld A Variational Approach to Electrostatics of Polarizable Heterogeneous Substances Advances in Mathematical Physics |
| title | A Variational Approach to Electrostatics of Polarizable Heterogeneous Substances |
| title_full | A Variational Approach to Electrostatics of Polarizable Heterogeneous Substances |
| title_fullStr | A Variational Approach to Electrostatics of Polarizable Heterogeneous Substances |
| title_full_unstemmed | A Variational Approach to Electrostatics of Polarizable Heterogeneous Substances |
| title_short | A Variational Approach to Electrostatics of Polarizable Heterogeneous Substances |
| title_sort | variational approach to electrostatics of polarizable heterogeneous substances |
| url | http://dx.doi.org/10.1155/2015/659127 |
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