Cole element

Equation 9.27 describes an ideal conductance in parallel with a Fricke CPEp we may call it the parallel Cole element. Together with the series resistor Roo, they form a... 

In the impedance (Z-plot) Wessel diagram, the series resistance Roo of the Cole system moves the arc of the Cole element to the right along the real axis a distance equal to the value of Roo, and with no influence on the characteristic frequency (Figure 9.12). 

This is a Fricke CPEp in series with an ideal resistor we may call it the series Cole element. Together with the parallel conductance Go, they form the complete Cole parallel system. 

The term AR is found both in the Cole CPEp and the series resistance of Eq. 9.34. A change in a series resistance influences the value of the CPEp, so the series resistance is not a separate mechanism, but a part of the Cole polarisation mechanism. The ColeY equation does not allow an independent variable DC resistor in series with the CPEp. This limits the applicability of the ColeY equation in many real systems, because often series processes are processes independent of the CPEp. However, the parallel conductance Go of the ColeY equation is not correlated to AR, nor to x or flie a of the Zcoie- Go may therefore freely be regarded as an independent parallel conductance to the series Cole element. For example, in the skin, with sweat duct conductance in parallel with the... 

Restricting the value of Gyar (=1/R) so that it is equal to the Gi of the CPEp element, gives a special case with different properties. The impedance of such a Cole element is ... 

For lumped elements, e.g. resistors, capacitors or combinations of these elements, the differential equations, impedances and VSR are well-known [4]. Distributed elements, i.e. Warburg impedance. Constant Phase Element, or parallel connections like RCPE, also known as ZARC or Cole-Cole element, have non-integer exponents a of the complex frequency s in frequency domain. This corresponds to fractional differential equations in time domain and thus the calculation of the VSR requires fractional calculus, as can be seen in the following derivations. 

G.R. Cole et al, Fabrication of Uranium Oxide Fuel Elements , DuPont deNemours ... 

Henri Moissan, 1852-1907. Professor of chemistry at the ] cole Superieure de Pharmacie. The discoverer of the element fluorine. With his electric furnace he prepared many uncommon metals such as uranium, tungsten (wolfram), and vanadium. 

The nitrogen cycle is closely connected with the fluxes of hydrogen, sulfur, and other chemicals (Smith et al., 1998 Dimitroulopoulou and Marsh, 1997 Chapin et al., 2002 Rhee et al., 2005 Stevenson and Cole, 1999). Nitrogen and hydrogen react under great pressure and temperature in the presence of a catalyst to make ammonia. The study of correlations between the cycles of these elements is necessary to improve... 

Li, X., Coles, B.J., Ramsey, M.H. and Thornton, I. (1995a) Sequential extraction of soils for multi-element analysis by ICPAES. Chem. Geol., 124, 109-123. 

It has not been possible so far to establish that Cr is an essential element required by plants, however, addition of Cr to soils deficient in the element has been shown to increase growth rates and yields of potatoes, maize, rye, wheat or oats (Scharrer and Schropp, 1935 Huffman and Allaway, 1973 Bertrand and De Wolf, 1986). Nickel appears to be an essential element for plants (Farago and Cole, 1988). Zerner and coworkers (Dixon et al., 1975) demonstrated that urease isolated from jack bean (Canavalia ensiformis) was a nickel enzyme. Eskew et al. (1983) have shown that Ni is an essential micronutrient for legumes. Most plants contain nickel in the range 1 - 6 mg kg-1 (Vanselow, 1966 Hutchinson, 1981). The uptake of Ni is enhanced by low pH values, and available nickel increases at pH less than 6.5 as a consequence of the breakdown of Ni complexes in the soil with Fe and Mn oxides. Uptake of nickel by plants and questions of toxicity and tolerance have been reviewed by Farago and Cole (1988). Nickel toxicity toward plants has been reviewed by Vanselow (1966) and Hutchinson (1981). 

Sources of contamination in which excessive concentrations of elements may be brought about have been enumerated by a number of authors (Freedman and Hutchinson, 1981 Ernst and Joosse, 1983 Farago and Cole, 1988 Verkleij, 1993), and may be listed as follows ... 

The constant phase element (CPE) is a non-intuitive circuit element that was discovered in the course of investigations into responses from real systems. In general, a Nyquist plot (also called a Cole-Cole plot or complex impedance plane plot) should be a semicircle with the centre on the x-axis. However, the observed plot for some real systems was indeed the arc of a circle but with the centre located somewhere below the x-axis. Figure 4.1 shows the impedance spectra of a circuit of a resistor and a constant phase element connected in parallel. The centre of the semicircle is located at (l-n)x90° below the real axis. 

Cole DG, Kobierski LA, Konradi C, Hyman SE (1994) 6-Hydroxydopamine lesions of rat substantia nigra up-regulate dopamine-induced phosphorylation of the cAMP-response element-binding protein in striatal neurons. Proc Natl Acad Sci USA 97 9631-9635. 

It is possible to represent the entire electrochemical system including the instrumentation (potentiostat, etc.) as a single electrical circuit. The solution is usually spatially discretized into a network of resistance elements (see for example Coles et al., 1996). Double-layer charging can also be incorporated into these models by defining each element to contain a capacitor as well as a resistor. 

Allen, G.D., C. Chui, and B. Perry. Elements of Calculus. 2nd ed. Pacific Grove Brooks/Cole Publishing Co., 1989. Gowar, Norman. An Invitation to Mathematics. New York Oxford University Press, 1979. 

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