Charge densities for conducting ellipsoids

Curtright, Thomas; Cao, Zikun; Huang, Sunxiang; Sarmiento, Julio S.; Subedi, Suresh C.; Tarrence, D A; Thapaliya, T. R.

doi:10.1088/1361-6404/ab806a

Cited by 5 publications

(9 citation statements)

References 13 publications

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“…Equation (29), which is the third key result of this paper, is derived in Appendix G. Interestingly, the surface charge density in Eq. ( 28) has the same functional form as the electrical charge distribution of an electrically charged conducting ellipsoid [46]. Figure 5 exhibits the curvature effect known from electrostatics: The greater the curvature of the surface, the greater the topological charge density.…”

Section: Pattern (Iv): Continous Surface Charge Distribution On An El...mentioning

confidence: 99%

Topological charge distributions of an interacting two-spin system

György

Varjas²,

Vrana³

et al. 2022

Phys. Rev. B

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Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the degeneracy points form a nodal loop or a nodal surface in the magnetic parameter space, similarly to such structures discovered in the band structure of topological semimetals. Key results of our work are that (1) we determine the topological charge distribution along these degeneracy geometries and (2) we show that these nonpointlike degeneracy patterns can be obtained not only by fine-tuning but they can be stabilized by spatial symmetries. Since simple spin systems such as the one studied here are ubiquitous in condensed-matter setups, we expect that our findings, and the physical consequences of these nontrivial degeneracy geometries, are testable in experiments with quantum dots, molecular magnets, and adatoms on metallic surfaces.

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Section: Pattern (Iv): Continous Surface Charge Distribution On An El...mentioning

confidence: 99%

Topological charge distributions of an interacting two-spin system

György

Varjas²,

Vrana³

et al. 2022

Phys. Rev. B

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“…To determine ρ ab , the direction of the electric field is needed. This direction is given by the bisector of the two straight lines from the focal points of the prolate spheroid to the observation point (Curtright et al, 2020). Using various trigonometric relations, which are given in Supporting Information S1, it can be derived that…”

Section: Model Descriptionmentioning

confidence: 99%

“…The electric field of a conducting ellipsoid has been derived analytically by Köhn and Ebert (2015) for the prolate spheroid case and by Curtright et al (2020) for arbitrary dimensions. The derivation of the electric field strength E yields…”

Section: Model Descriptionmentioning

confidence: 99%

“…To determine ρ ab , the direction of the electric field is needed. This direction is given by the bisector of the two straight lines from the focal points of the prolate spheroid to the observation point (Curtright et al., 2020). Using various trigonometric relations, which are given in Supporting Information , it can be derived that

{\rho }_{\text{ab}}=\frac{\sqrt{2}{{\rho }_{\mathrm{1}}}^{2}\sqrt{\frac{\left(4\sqrt{{a}^{2}-{b}^{2}}(a+r\mathrm{cos}(\theta ))+{{\rho }_{\mathrm{1}}}^{2}\right)\left(2ar\mathrm{cos}(\theta )+{b}^{2}+{\rho }_{\mathrm{1}}{\rho }_{\mathrm{2}}+{r}^{2}\right)}{{\rho }_{\mathrm{1}}{\rho }_{\mathrm{2}}}}}{{{\rho }_{\mathrm{1}}}^{2}+{\rho }_{\mathrm{1}}{\rho }_{\mathrm{2}}},

with ρ 1 and ρ 2 the straight lines from the two focal points of the ellipsoid to the observation point (see also supporting information ) given by

{\rho }_{1,\,2}=\sqrt{{r}^{2}+{\left(a\mp \sqrt{{a}^{2}-{b}^{2}}\right)}^{2}+2\left(a\mp \sqrt{{a}^{2}-{b}^{2}}\right)r\mathrm{cos}\theta }

…”

Section: Model Descriptionmentioning

confidence: 99%

See 1 more Smart Citation

A Model for Positive Corona Inception From Charged Ellipsoidal Thundercloud Hydrometeors

et al. 2022

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Lightning is observed to incept in thundercloud electric fields below the threshold value Ek for discharge initiation. To explain this, the local enhancement of the electric field by hydrometeors is considered. The conditions for the onset of positive corona discharges are studied in air for ellipsoidal geometries. A hydrometeor is simulated as an individual charged conductor in zero ambient field; there is only a field generated by the charge on the hydrometeor surface. By doing so, the feasibility of corona inception from ellipsoidal hydrometeors can be formulated based on the self‐sustaining condition of electron avalanches. For hydrometeor dimensions of a few millimeters and typical thundercloud pressure, values above 2.4 Ek are found for the onset electric field at the tip of the ellipsoid. From simulations the required ambient electric field for corona onset from an uncharged hydrometeor can then be derived. This results in values between 0.07 Ek and 0.8 Ek for semiaxes aspect ratios between 0.01 and 1. The charge required on the hydrometeor surface for corona onset for typical pressures is minimum for semiaxes aspect ratios increasing from 0.12 to 0.22 for decreasing hydrometeor volume from 42 to 4.2 mm3. For representative simulated hydrometeors, onset charges are between 495 and 2,430 pC. For a hydrometeor volume of 4.2 mm3 results are comparable to measured precipitation charges for aspect ratios between 0.16 and 0.32. From the results it is concluded that corona onset from ellipsoidal hydrometeors of a realistic volume can be achieved in thundercloud conditions for certain aspect ratios.

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“…Equation ( 26) is derived in Appendix G. Interestingly, the surface charge density in Eq. ( 26) has the same functional form as the electrical charge distribution of an electrically charged conducting ellipsoid [34]. Figure 5 exhibits the curvature effect known from electrostatics: the greater the curvature of the surface, the greater the topological charge density.…”

Section: Pattern (Iv): Continous Surface Charge Distribution On An El...mentioning

confidence: 99%

Topological charge distributions of an interacting two-spin system

Frank,

Varjas,

Vrana

et al. 2020

Preprint

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Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the degeneracy points form a nodal loop or a nodal surface in the magnetic parameter space, similarly to such structures discovered in the band structure of topological semimetals. We determine the topological charge distribution along these degeneracy geometries. We show that these non-point-like degeneracy patterns can be obtained not only by fine-tuning, but they can be stabilized by spatial symmetries. Since simple spin systems such as the one studied here are ubiquitous in condensed-matter setups, we expect that our findings, and the physical consequences of these nontrivial degeneracy geometries, are testable in experiments with quantum dots, molecular magnets, and adatoms on metallic surfaces.

show abstract

Charge densities for conducting ellipsoids

Cited by 5 publications

References 13 publications

Topological charge distributions of an interacting two-spin system

Topological charge distributions of an interacting two-spin system

A Model for Positive Corona Inception From Charged Ellipsoidal Thundercloud Hydrometeors

Topological charge distributions of an interacting two-spin system

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