Author
Kenneth S. Cole
Other affiliations: Bermuda Biological Station for Research, Marine Biological Laboratory, Harvard University ...read more
Bio: Kenneth S. Cole is an academic researcher from Columbia University. The author has contributed to research in topics: Electrical impedance & Wheatstone bridge. The author has an hindex of 23, co-authored 31 publications receiving 11590 citations. Previous affiliations of Kenneth S. Cole include Bermuda Biological Station for Research & Marine Biological Laboratory.
Papers
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TL;DR: In this paper, the locus of the dielectric constant in the complex plane was defined to be a circular arc with end points on the axis of reals and center below this axis.
Abstract: The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula e*−e∞=(e0−e∞)/[1+(iωτ0)1−α]. In this equation, e* is the complex dielectric constant, e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω=2π times the frequency, and τ0 is a generalized relaxation time. The parameter α can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis.If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result.If a dielectric satisfying Eq. (1) is represented by a three‐element electrical circuit, the mechanism responsible...
8,409 citations
TL;DR: In this paper, it was shown that the complex dielectric constant, e*, of many liquid and solid dielectrics is given by a single very general formula e*=e∞+(e0−e ∞)/[1+(iωτ0)1−α] In this equation e0 and e∞ are the ''static'' and ''infinite frequency'' dielectoric constants, ω = 2π times the frequency, τ 0 is a generalized relaxation time and α is a constant, 0 < α < 1 The transient current as a
Abstract: In the first paper of this series [J Chem Phys 9, 341 (1941)], it was shown that the complex dielectric constant, e*, of many liquid and solid dielectrics is given by a single very general formula e*=e∞+(e0−e∞)/[1+(iωτ0)1−α] In this equation e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω = 2π times the frequency, τ0 is a generalized relaxation time and α is a constant, 0 < α < 1 The transient current as a function of the time, t, after application of a unit constant potential difference has been calculated from this expression in series form For times much less than τ0, the time dependence is of the form (t/τ0)−α, and for times much greater than τ0, it is of the form (t/τ0)−(2—α) The transition between these extremes occurs for the range in which t is comparable with τ0 The total absorption charge, which is the integral of the exact expression, is always finite Although many transient data for dielectrics are of the predicted form, none have been taken over a suff
786 citations
373 citations
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TL;DR: This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre by putting them into mathematical form and showing that they will account for conduction and excitation in quantitative terms.
Abstract: This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre (Hodgkinet al, 1952,J Physiol116, 424–448; Hodgkin and Huxley, 1952,J Physiol116, 449–566) Its general object is to discuss the results of the preceding papers (Section 1), to put them into mathematical form (Section 2) and to show that they will account for conduction and excitation in quantitative terms (Sections 3–6)
19,800 citations
TL;DR: In this paper, the locus of the dielectric constant in the complex plane was defined to be a circular arc with end points on the axis of reals and center below this axis.
Abstract: The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula e*−e∞=(e0−e∞)/[1+(iωτ0)1−α]. In this equation, e* is the complex dielectric constant, e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω=2π times the frequency, and τ0 is a generalized relaxation time. The parameter α can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis.If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result.If a dielectric satisfying Eq. (1) is represented by a three‐element electrical circuit, the mechanism responsible...
8,409 citations
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
7,412 citations
TL;DR: In this article, it was shown that the electrical double-layer at a solid electrode does not in general behave as a pure capacitance but rather as an impedance displaying a frequency-independent phase angle different from 90°.
2,602 citations
TL;DR: In this paper, it was shown that the complex deformation of the same data can be represented by a function of same form but with different values for the constants, which can be interpreted as the decay of the distortion with time of the removal of stress field.
2,483 citations