Who nominates judges? : Some issues underlying judicial appointments in South Africa

This article examines the importance and impact of the process of nomination on the appointment of judges in South Africa. The process of judicial appointment has changed dramatically following South Africa’s transition from apartheid to constitutional democracy. In the pre-constitutional era, appointments were made by the State President in Cabinet, with little or no external input beyond that elicited from a small political and legal elite

On the direct evaluation of the equilibrium distribution of clusters by simulation. II

We clarify some of the subtle issues surrounding the observational cluster method, a simulation technique for studying nucleation. The validity of the method is reaffirmed here. The condition of the compact cluster limit is quantified and its implications are elucidated in terms of the correct enumeration of configuration space

On the direct evaluation of the equilibrium distribution of clusters by simulation

An expression is derived that relates the average population of a particular type of cluster in a metastable vapor phase of volume Vtot to the probability, estimated by simulation, of finding this cluster in a system of volume V taken inside Vtot, where V<<Vtot. Correct treatment of the translational free energy of the cluster is crucial for this purpose. We show that the problem reduces to one of devising the proper boundary condition for the simulation. We then verify the result obtained previously for a low vapor density limit [J. Chem. Phys. 108, 3416 (1998)]. The difficulty implicit in our recent calculation [J. Chem. Phys. 110, 5249 (1999)], in which the approach in the former was generalized to higher vapor densities, is shown to be resolved by a method already suggested in that paper

Resonantly driven wobbling kinks

The amplitude of oscillations of the freely wobbling kink in the $\phi^4$ theory decays due to the emission of second-harmonic radiation. We study the compensation of these radiation losses (as well as additional dissipative losses) by the resonant driving of the kink. We consider both direct and parametric driving at a range of resonance frequencies. In each case, we derive the amplitude equations which describe the evolution of the amplitude of the wobbling and the kink's velocity. These equations predict multistability and hysteretic transitions in the wobbling amplitude for each driving frequency -- the conclusion verified by numerical simulations of the full partial differential equation. We show that the strongest parametric resonance occurs when the driving frequency equals the natural wobbling frequency and not double that value. For direct driving, the strongest resonance is at half the natural frequency, but there is also a weaker resonance when the driving frequency equals the natural wobbling frequency itself. We show that this resonance is accompanied by translational motion of the kink.Comment: 19 pages in a double-column format; 8 figure

Tracking shocked dust: state estimation for a complex plasma during a shock wave

We consider a two-dimensional complex (dusty) plasma crystal excited by an electrostatically-induced shock wave. Dust particle kinematics in such a system are usually determined using particle tracking velocimetry. In this work we present a particle tracking algorithm which determines the dust particle kinematics with significantly higher accuracy than particle tracking velocimetry. The algorithm uses multiple extended Kalman filters to estimate the particle states and an interacting multiple model to assign probabilities to the different filters. This enables the determination of relevant physical properties of the dust, such as kinetic energy and kinetic temperature, with high precision. We use a Hugoniot shock-jump relation to calculate a pressure-volume diagram from the shocked dust kinematics. Calculation of the full pressure-volume diagram was possible with our tracking algorithm, but not with particle tracking velocimetry.Comment: 10 pages, 8 figures, accepted for publication in Physics of Plasma

Minimum free-energy path of homogenous nucleation from the phase-field equation

The minimum free-energy path (MFEP) is the most probable route of the nucleation process on the multidimensional free-energy surface. In this study, the phase-field equation is used as a mathematical tool to deduce the minimum free-energy path (MFEP) of homogeneous nucleation. We use a simple square-gradient free-energy functional with a quartic local free-energy function as an example and study the time evolution of a single nucleus placed within a metastable environment. The time integration of the phase-field equation is performed using the numerically efficient cell-dynamics method. By monitoring the evolution of the size of the nucleus and the free energy of the system simultaneously, we can easily deduce the free-energy barrier as a function of the size of the sub- and the super-critical nucleus along the MFEP.Comment: 8 pages, 5 figures, Journal of Chemical Physics accepted for publicatio

Scaling properties of critical bubble of homogeneous nucleation in stretched fluid of square-gradient density-functional model with triple-parabolic free energy

The square-gradient density-functional model with triple-parabolic free energy is used to study homogeneous bubble nucleation in a stretched liquid to check the scaling rule for the work of formation of the critical bubble as a function of scaled undersaturation $\Delta\mu/\Delta\mu_{\rm spin}$, the difference in chemical potential $\Delta\mu$ between the bulk undersaturated and saturated liquid divided by $\Delta\mu_{\rm spin}$ between the liquid spinodal and saturated liquid. In contrast to our study, a similar density-functional study for a Lennard-Jones liquid by Shen and Debenedetti [J. Chem. Phys. {\bf 114}, 4149 (2001)] found that not only the work of formation but other various quantities related to the critical bubble show the scaling rule, however, we found virtually no scaling relationships in our model near the coexistence. Although some quantities show almost perfect scaling relations near the spinodal, the work of formation divided by the value deduced from the classical nucleation theory shows no scaling in this model even though it correctly vanishes at the spinodal. Furthermore, the critical bubble does not show any anomaly near the spinodal as predicted many years ago. In particular, our model does not show diverging interfacial width at the spinodal, which is due to the fact that compressibility remains finite until the spinodal is reached in our parabolic models.Comment: 10 pages, 10 figures, Journal of Chemical Physics accepted for publicatio

A Finite-Size Scaling Study of a Model of Globular Proteins

Grand canonical Monte Carlo simulations are used to explore the metastable fluid-fluid coexistence curve of the modified Lennard-Jones model of globular proteins of ten Wolde and Frenkel (Science, v277, 1975 (1997)). Using both mixed-field finite-size scaling and histogram reweighting methods, the joint distribution of density and energy fluctuations is analyzed at coexistence to accurately determine the critical-point parameters. The subcritical coexistence region is explored using the recently developed hyper-parallel tempering Monte Carlo simulation method along with histogram reweighting to obtain the density distributions. The phase diagram for the metastable fluid-fluid coexistence curve is calculated in close proximity to the critical point, a region previously unattained by simulation.Comment: 17 pages, 10 figures, 2 Table