TY - JOUR
T1 - GENERALIZED SHOCKLEY–RAMO THEOREM IN ELECTROLYTES
AU - LIU, PEI
AU - LIU, CHUN
AU - XU, ZHENLI
N1 - Funding Information:
∗Received: March 29, 2016; accepted (in revised form): August 13, 2016. Communicated by Jie Shen. The research of P. Liu and Z. Xu is supported by the NSFC (Grant Nos. 91130012 and 11571236), the Chinese Organization Department, and the HPC Center of Shanghai Jiao Tong University. The research of C. Liu is partially supported by NSF (Grant Nos. DMS-141200 and DMS-1216938). The authors also thank Prof. Bob Eisenberg for the valuable discussion and comments. P. Liu and Z. Xu would like to thank the Department of Mathematics of the Penn State University for hosting their visits and providing the great working environment.
Publisher Copyright:
© 2017. International Press. All rights reserved.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
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U2 - 10.4310/CMS.2017.v15.n2.a11
DO - 10.4310/CMS.2017.v15.n2.a11
M3 - Article
AN - SCOPUS:85099840235
VL - 15
SP - 555
EP - 564
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
SN - 1539-6746
IS - 2
ER -