Accurate Adiabatic Connection Curve Beyond the Physical Interaction Strength

The adiabatic connection curve of density functional theory (DFT) is accurately calculated beyond the physical interaction strength for Hooke's atom, two interacting electrons in a harmonic well potential. Extrapolation of the accurate curve to the infinite coupling limit agrees well with the strictly correlated electron (SCE) hypothesis but the approach to this limit is more complex. The interaction strength interpolation is shown to be a good, but not perfect, fit to the adiabatic curve. Arguments about the locality of functionals and convexity of the adiabatic connection curve are examined in this regime.Comment: 7 pages, 5 figure

Hansard as an Aid to Statutory Interpretation in Canadian Courts from 1999 to 2010

This thesis employs qualitative and quantitative methods to provide a comprehensive picture o f the judicial use o f Hansard as an extrinsic aid to statutory interpretation in the courts of Canada from 1999 to 2010. The qualitative portion of the thesis examines all Supreme Court of Canada judgments in 2010 that make reference to Hansard and Hansard-like materials. The findings are compared with the findings of Professor Stéphane Beaulac, who studied the phenomenon in 1999. The quantitative portion ofthe research examines the prevalence and distribution ofjudgments that make reference to Hansard in the Courts throughout Canada from 1999 to 2010

Factorization of 3-point static structure functions in 3D Yukawa liquids

In many-body systems the convolution approximation states that the 3-point static structure function, $S^{(3)}(\textbf{k}_{1},\textbf{k}_{2})$, can approximately be "factorized" in terms of the 2-point counterpart, $S^{(2)}(\textbf{k}_{1})$. We investigate the validity of this approximation in 3-dimensional strongly-coupled Yukawa liquids: the factorization is tested for specific arrangements of the wave vectors $\textbf{k}_{1}$ and $\textbf{k}_{2}$, with molecular dynamics simulations. With the increase of the coupling parameter we find a breakdown of factorization, of which a notable example is the appearance of negative values of $S^{(3)}(\textbf{k}_{1},\textbf{k}_{2})$, whereas the approximate factorized form is restricted to positive values. These negative values -- based on the quadratic Fluctuation-Dissipation Theorem -- imply that the quadratic part of the density response of the system changes sign with wave number. Our simulations that incorporate an external potential energy perturbation clearly confirm this behavior