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Your search keyword '"Day, Stuart"' showing total 4 results
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4 results on '"Day, Stuart"'

3. Stability and local minimality of spherical harmonic twists $$u={\mathbf {Q}}(|x|) x|x|^{-1}$$u=Q(|x|)x|x|-1, positivity of second variations and conjugate points on $$\mathbf{SO}(n)$$SO(n)

Author

Day, Stuart and Taheri, Ali

Abstract

In this paper we discuss the stability and local minimising properties of spherical twists that arise as solutions to the harmonic map equation $$\begin{aligned} \mathbf{HME}[u;\, \mathbb {X}^n, \mathbb {S}^{n-1}] :=\left\{ \begin{array}{ll} \Delta u + |\nabla u|^2 u =0 &{} \qquad \text { in } \mathbb {X}^n, \\ |u|=1 &{}\qquad \text { in } \mathbb {X}^n , \\ u = \varphi &{}\qquad \text { on } \partial \mathbb {X}^n, \end{array}\right. \end{aligned}$$HME[u;Xn,Sn-1]:=Δu+|∇u|2u=0inXn,|u|=1inXn,u=φon∂Xn,by way of examining the positivity of the second variation of the associated Dirichlet energy. Here, following [31], by a spherical twist we mean a map $$u \in \mathscr {W}^{1,2}(\mathbb {X}^n, \mathbb {S}^{n-1})$$u∈W1,2(Xn,Sn-1)of the form $$x \mapsto {\mathbf {Q}}(|x|)x|x|^{-1}$$x↦Q(|x|)x|x|-1where $${\mathbf {Q}}={\mathbf {Q}}(r)$$Q=Q(r)lies in $$\mathscr {C}([a, b], \mathbf{SO}(n))$$C([a,b],SO(n))and $${\mathbb {X}}^n=\{x \in \mathbb {R}^n : a<|x|

Published
2024
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4. Low temperature oxidation of coal

Author

Day, Stuart J

Subjects
Other education not elsewhere classified
Abstract

The kinetics of oxidation of a high volatile bituminous coal have been studied at temperatures between 75 and 120 °C and particle sizes between 0.125 and 24 mm. The rate of oxidation was found to increase with increasing temperature yielding an activation energy of about 45 kJ/mol. At temperatures below about 75 °C the oxidation rate was essentially independent of the particle size but at higher temperatures, the rate tended to decrease with increasing particle size. For all of the temperatures examined, however, the rate remained independent of particle size if the particles were less than about 1 mm in diameter. This suggests that in those regimes where there is no particle size dependence, the overall rate of oxidation is under chemical control whereas in regions where the rate reduces with increasing particle diameter, diffusion becomes the rate limiting mechanism. -- Several oxidation rate models were tested against the experimental results. Of these, a modification of the shrinking core model in which each particle was assumed to be made up of many individual shrinking cores provided the best fit yielding excellent agreement with the measured rates. -- Moisture adsorption isotherms and the rate of moisture uptake by the coal were studied at temperatures between 10 and 60 °C and relative humidities ranging from about 10 to 100 percent. At all temperatures, moisture adsorption followed the Langmuir isotherm up to about 80 percent relative humidity but above this level the moisture content of the coal was substantially underestimated by the Langmuir model. An empirical model originally proposed by Henderson was found to provide a better fit over the full relative humidity range. The rate of moisture uptake increased with increasing relative humidity and temperature but decreased with increasing particle size. A rate model, similar in form to the shrinking core model, provided a very good fit to the experimental data and successfully predicted the effects of temperature, relative humidity and particle size on the rate of adsorption.

Published
2022
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