2016
DOI: 10.1038/srep36918
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Conformal mapping for multiple terminals

Abstract: Conformal mapping is an important mathematical tool that can be used to solve various physical and engineering problems in many fields, including electrostatics, fluid mechanics, classical mechanics, and transformation optics. It is an accurate and convenient way to solve problems involving two terminals. However, when faced with problems involving three or more terminals, which are more common in practical applications, existing conformal mapping methods apply assumptions or approximations. A general exact me… Show more

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Cited by 10 publications
(5 citation statements)
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“…Based on a forward SC transformation, the upper half-plane of W-plane can then be transformed into a folded rectangle in another complex plane, namely, Q-plane, as shown in Fig. 2 e 30 . The dashed lines EE’ and E’F overlap, although they are drawn separately to show that the structure is closed.…”
Section: Resultsmentioning
confidence: 99%
“…Based on a forward SC transformation, the upper half-plane of W-plane can then be transformed into a folded rectangle in another complex plane, namely, Q-plane, as shown in Fig. 2 e 30 . The dashed lines EE’ and E’F overlap, although they are drawn separately to show that the structure is closed.…”
Section: Resultsmentioning
confidence: 99%
“…Many methods have been developed to correct the band-gap problem at a moderate computational cost, such as the DFT + U method, [62] meta-GGA-type TB-mBJ potentials, [63] the generalized Delta self-consistent-field method, [64] modification of pseudopotentials, [65] the DFT-1/2 method, [66] and the Wannier-Koopman method. [67] These methods have shown great successes in predicting the band gaps, but may also suffer from certain disadvantages like the lack of self-consistency, the absence of a total-energy formalism, and the ad hoc nature. Careful tests are always recommended when they are applied to a particular material of interest.…”
Section: Band Gapmentioning
confidence: 99%
“…These forces are defined in the appendix. The capacitance ( ), and electric field ( ), of the coplanar capacitors are also obtained by finite element analysis modelling from equations (A5) -(A7) reported in the appendix [30]. The increase in the relative permittivity of the space between coplanar capacitor electrodes when a particle enters their active volume space depends on the ratio between the particle aerodynamic volume and the volume of the active volume space between the charged electrodes and on the relative permittivity of the particle.…”
Section: B Theorymentioning
confidence: 99%