Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Vertical toleration as a liberal ideal

This paper argues that the direct, vertical toleration of certain types of citizen by the Rawlsian liberal state is appropriate and required in circumstances in which these types of citizen pose a threat to the stability of the state. By countering the claim that vertical toleration is redundant given a commitment to the Rawlsian version of the liberal democratic ideal, and by articulating a version of that ideal that shows this claim to be false, the paper reaffirms the centrality of vertical toleration in the Rawlsian liberal account of state-citizen relations.

An ‘ideal’ form of decaying two-dimensional turbulence

In decaying two-dimensional Navier-Stokes turbulence, Batchelor's similarity hypothesis fails due to the existence of coherent vortices. However, it is shown that decaying two-dimensional turbulence governed by the Harney-Hasegawa-Mima (CHM) equation ∂/∂t (V^2 φ-λ^2 φ)+J(φ,∇^2 φ)=D where D is a damping, is described well by Batchelor's similarity hypothesis for wave numbers k ≪ λ (the so-called AM regime). It is argued that CHM turbulence in the AM regime is a more `ideal' form of two-dimensional turbulence than is Navier-Stokes turbulence itself.

Applying Jackson’s methodological ideal-types: problems of differentiation and classification

In The Conduct of Inquiry in International Relations, Patrick Jackson situates methodologies in International Relations in relation to their underlying philosophical assumptions. One of his aims is to map International Relations debates in a way that ‘capture[s] current controversies’ (p. 40). This ambition is overstated: whilst Jackson’s typology is useful as a clarificatory tool, (re)classifying existing scholarship in International Relations is more problematic. One problem with Jackson’s approach is that he tends to run together the philosophical assumptions which decisively differentiate his methodologies (by stipulating a distinctive warrant for knowledge claims) and the explanatory strategies that are employed to generate such knowledge claims, suggesting that the latter are entailed by the former. In fact, the explanatory strategies which Jackson associates with each methodology reflect conventional practice in International Relations just as much as they reflect philosophical assumptions. This makes it more difficult to identify each methodology at work than Jackson implies. I illustrate this point through a critical analysis of Jackson’s controversial reclassification of Waltz as an analyticist, showing that whilst Jackson’s typology helps to expose inconsistencies in Waltz’s approach, it does not fully support the proposed reclassification. The conventional aspect of methodologies in International Relations also raises questions about the limits of Jackson’s ‘engaged pluralism’.

The ideal self at play: the appeal of video games that let you be all you can be

Video games constitute a popular form of entertainment that allows millions of people to adopt virtual identities. In our research, we explored the idea that the appeal of games is due in part to their ability to provide players with novel experiences that let them “try on” ideal aspects of their selves that might not find expression in everyday life. We found that video games were most intrinsically motivating and had the greatest influence on emotions when players’ experiences of themselves during play were congruent with players’ conceptions of their ideal selves. Additionally, we found that high levels of immersion in gaming environments, as well as large discrepancies between players’ actual-self and ideal-self characteristics, magnified the link between intrinsic motivation and the experience of ideal-self characteristics during play.

The tragedy of non-ideal theory

This paper has three aims. First, it argues that the present use of ‘ideal theory’ is unhelpful, and that an earlier and apparently more natural use focusing on perfection would be preferable. Second, it has tried to show that revision of the use of the term would better expose two distinctive normative issues, and illustrated that claim by showing how some contributors to debates about ideal theory have gone wrong partly through not distinguishing them. Third, in exposing those two distinct normative issues, it has revealed a particular way in which ideal theory even under the more specific, revisionary definition will often be central to working out what to do in non-ideal circumstances. By clarifying the terms on which debates over ideal and non-ideal theory should take place, and highlighting the particular problems each deals with, it tries to clear the ground for turning to the actual problem, which is what to do in our non-ideal and often tragic circumstances.