The separation of the complex dielectric constant ? ( ? ) was reported in the original paper by Cole and Cole as follows:
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The dielectric constant and conductivity ( or simply the complex dielectric constant ) is dependent on the soil type and is a function of frequency.
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In this equation \ epsilon ^ * is the complex dielectric constant, { \ epsilon _ 0 } and \ epsilon _ \ infty are the " static " and " infinite frequency " dielectric constants, \ omega = 2 \ pi times the frequency, and \ tau _ 0 is a generalized relaxation time.
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His most influential papers have been " The Contribution of Excitons to the Complex Dielectric Constant of Crystals " ( 1958 ), describing the polariton; Electron transfer between biological molecules by thermally activated tunneling ( 1974 ), describing the quantum mechanics of long-range electron transfers; " Kinetic Proofreading : a New Mechanism for Reducing Errors in Biosynthetic Processes Requiring High Specificity " ( 1974 ); " Neural networks and physical systems with emergent collective computational abilities " ( 1982 ) ( known as the Hopfield Network ) and, with D . W . Tank, Neural computation of decisions in optimization problems ( 1985 ).
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