Watts, William

A year after receiving this document from Watt, William Pryce published his Minemlogia Cornubiensis, in which he stated that... 

Sec also Carnot, Nicolas Leonard Sadi Clausins, Rudolf Julius Emmanuel Culture and Energy Usage Ethical and Moral Aspects of Energy Use Gibbs, Jonah Willard Industiy and Business, History of Energy Use and Joule, James Prescott Kinetic Energy, Historical Evolution of the Use of Mayer, Julius Robert von Refining, History of Thomson, William Watt, James. 

This form is also known as the Williams-Watts functiont (145). It is a powerful yet simple form to use in fitting data, since it can accommodate any slope in the transition region. However, equation (40) cannot describe a complete master curve from glassy to rubbery state with a single value ofp. Instead, P (or m) is taken to be time (or temperature) dependent. 

A particular characteristic feature of dynamic processes in the vicinity of the glass transition is the ubiquity of the Kohlrausch-Williams-Watts (KWW) stretched exponential relaxation 1,7-9... 

Figure 21 Coherent intermediate scattering functions at the position of the amorphous halo versus time scaled by the a time, which is the time it takes the scattering function to decay by 70%. The thick gray line shows that the a-process can be fitted with a Kohlrausch-Williams-Watts (KWW) law.

Waters, William, 193 Watt, Charles, 45 Watts, Henry, 98, 101 Weber, Wilhelm, 45, 52 Weizmann, Chaim, 180, 180 n.75... 

Baker MJ, Giles MF, Garland CS, Muskett MJ, Rafeletos G, Smith SJ, Sunley JG, Watt RJ, Williams BL (1997) EP0752406 to BP Chemicals... 

Where p defines the shape of the hole energy spectrum. The relaxation time x in Equation 3 is treated as a function of temperature, nonequilibrium glassy state (5), crosslink density and applied stresses instead of as an experimental constant in the Kohlrausch-Williams-Watts function. The macroscopic (global) relaxation time x is related to that of the local state (A) by x = x = i a which results in (11)... 

Watts, R. R., R. J. Drago, R. G. Merrill, R. W. Williams, E. Perry, and J. Lewtas, Wood Smoke Impacted Air Mutagenicity and Chemical Analysis of Ambient Air in a Residential Area of Juneau, Alaska, JAPCA, 38, 652-660 (1988). 

More detailed accounts of alchemy in the middle ages can be found in William R. Newmans work on Geber, The Summa Perfectionis of Psetido-Geber (Leiden Brill, 1991). Excellent readings on the history of distillation can be found in Allen G. Debus, Fire Analysis and the Elements in the Sixteenth and the Seventeenth Centuries, Ann. Sci. 23 (1967), 127-147 and in Robert P. Multhauf, The Origins of Chemistry (New York Franklin Watts, 1967). 

The misnormalized data of Lee et al.16) was interpreted in terms of two discrete relaxation processes. It was proposed that the relaxation function should be represented as the sum of two Williams-Watts functions. The slope at short times was claimed to be equal to the / for the faster of the two processes. Numerical calculations and graphical representations of exact relaxation functions with parameters equal to those reported by Lee et al.16) were carried out. They did not look even qualitatively similar to their reported data. The slope at the shortest times must be related to a weighted sum of both of the /3 values for the sum of two WW functions. If it was desired to fit the data to a sum of two WW functions, then this could easily be carried out with a nonlinear least squares routine. In most cases it would not be possible to obtain statistically independent values of all six parameters, but at least no further errors would be introduced by faulty manipulations of the data. The graphical procedure of Lee et al.16) cannot be recommended as of any worth in this problem. 

Williams, G., Watts, D. C. Some aspects of dielectric relaxation of amorphous polymers including the effects of a hydrostatic pressure, in NMR Basic prindples and progress Vol. 4 (ed.) Diehl, P., Fluck, E., Kosfeld R., p. 271, Berlin, Springer-Verlag 1971... 

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