Diluted Networks of Nonlinear Resistors and Fractal Dimensions of Percolation Clusters

We study random networks of nonlinear resistors, which obey a generalized Ohm's law, $V\sim I^r$. Our renormalized field theory, which thrives on an interpretation of the involved Feynman Diagrams as being resistor networks themselves, is presented in detail. By considering distinct values of the nonlinearity r, we calculate several fractal dimensions characterizing percolation clusters. For the dimension associated with the red bonds we show that $d_{\scriptsize red} = 1/\nu$ at least to order {\sl O} (\epsilon^4), with $\nu$ being the correlation length exponent, and $\epsilon = 6-d$, where d denotes the spatial dimension. This result agrees with a rigorous one by Coniglio. Our result for the chemical distance, d_{\scriptsize min} = 2 - \epsilon /6 - [ 937/588 + 45/49 (\ln 2 -9/10 \ln 3)] (\epsilon /6)^2 + {\sl O} (\epsilon^3) verifies a previous calculation by one of us. For the backbone dimension we find D_B = 2 + \epsilon /21 - 172 \epsilon^2 /9261 + 2 (- 74639 + 22680 \zeta (3))\epsilon^3 /4084101 + {\sl O} (\epsilon^4), where $\zeta (3) = 1.202057...$, in agreement to second order in $\epsilon$ with a two-loop calculation by Harris and Lubensky.Comment: 29 pages, 7 figure

Critical Exponents for Diluted Resistor Networks

An approach by Stephen is used to investigate the critical properties of randomly diluted resistor networks near the percolation threshold by means of renormalized field theory. We reformulate an existing field theory by Harris and Lubensky. By a decomposition of the principal Feynman diagrams we obtain a type of diagrams which again can be interpreted as resistor networks. This new interpretation provides for an alternative way of evaluating the Feynman diagrams for random resistor networks. We calculate the resistance crossover exponent $\phi$ up to second order in $\epsilon=6-d$, where $d$ is the spatial dimension. Our result $\phi=1+\epsilon /42 +4\epsilon^2 /3087$ verifies a previous calculation by Lubensky and Wang, which itself was based on the Potts--model formulation of the random resistor network.Comment: 27 pages, 14 figure

Balancing Hardware Intensity in Microprocessor Pipelines

The evaluation of architectural tradeoffs is complicated by implications in the circuit domain which are typically not captured in the analysis but substantially affect the results. We propose a metric of hardware intensity, which is useful for evaluating issues that affect both circuits and architecture. Analyzing data for actual designs, we show how to measure the introduced parameters and discuss variations between observed results and common theoretical assumptions. For a power-efficient design, we derive relations for hardware intensity and supply voltage V under progressively more general situations and illustrate the use of these equations in simple examples. Then we establish a relation between the architectural energy-efficiency metric and hardware intensity, and we derive expressions for evaluating the effect of modifications at the microarchitectural level on processor frequency and power, assuming the optimal tuning of the pipeline. These relations will guide the architect to achieve an energy-optimal balance between architectural complexity and hardware intensity

Religious education, radicalisation and neoliberal governmentalities

The relevance of religion within the discipline and practice of education remains paramount, not only in understanding how social control operates in contemporary society, but also in addressing draconian measures intended to combat radicalisation in schools. With this in mind this chapter draws upon Foucault’s analysis of governmentality to explore how religious schooling and education facilitates the ‘governing of the soul’. It also explores Gane’s analytical development of this concept, while broadening the definition of religion to include policies and practices related to violent religious extremism. Consequently, through the lens of neoliberal governmentalities, it can be seen that elements of religion and education have been appropriated to introduce repressive social controls, which benefit neoliberal markets. In conclusion, it is maintained that these practices need to be challenged through the introduction of radical and critical, religion and ethics education