Communications in Mathematical Sciences
Volume 15 (2017)
Generalized Shockley–Ramo theorem in electrolytes
Pages: 555 – 564
The charge motion in vacuum and the induced currents on the electrodes can be related through the Shockley–Ramo (SR) theorem. In this paper, we develop a generalized Shockley–Ramo (GSR) theorem, which could be used to study the motion of macro charged particles in electrolytes. It could be widely applied to biological and physical environments, such as the voltage-gated ion channels. With the procedure of renormalizing of charge and dipole, the generalized theorem provides a direct relationship between the induced currents and the macro charge velocity. Compared with the original Shockley–Ramo theorem, the generalized Shockley–Ramo theorem avoids integrating all the ionic flux, which could reduce the computational cost significantly.
hockley–Ramo theorem, electrolytes, charge renormalization, inverse problem
2010 Mathematics Subject Classification
35Q70, 82B21, 82C05, 92C30