2013/04/24 by Titus Sandu, Sandu, Titus, George Boldeiu +3
Chemistry · Engineering · #Classical Physics (physics.class-ph) #Dielectric materials and actuators #Electrostatics and Colloid Interactions #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Microfluidic and Bio-sensing Technologies #Other Condensed Matter (cond-mat.other)
paper · pdf · doi:10.48550/arxiv.1304.6624
openalex publication_date 2013/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The capacitance of arbitrarily shaped objects is reformulated in terms of the Neumann-Poincaré operator. Capacitance is simply the dielectric permittivity of the surrounding medium multiplied by the area of the object and divided by the squared norm of the Neumann-Poincaré eigenfunction that corresponds to its largest eigenvalue. The norm of this eigenfunction varies slowly with shape changes and allows perturbative calculations. This result is also extended to capacitors. For axisymmetric geometries a numerical method provides excellent results against finite element method results. Two scale-invariant shape factors and the capacitance of nanowires and of membrane in biological cells are discussed.