Topological analysis of polymeric melts: Chain length effects and fast-converging estimators for entanglement length

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_e which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive and test new estimators which eliminate these systematic errors using information obtainable from the variation of entanglement characteristics with chain length. The new estimators produce accurate results for N_e from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.Comment: Major revisions. Developed near-ideal estimators which operate on multiple chain lengths. Now test these on two very different model polymers

Cosmological dynamics of scalar field with non-minimal kinetic term

We investigate dynamics of scalar field with non-minimal kinetic term. Nontrivial behavior of the field in the vicinity of singular points of kinetic term is observed. In particular, the singular points could serve as attractor for classical solutions.Comment: 6 pages, 3 figures, title is changed, some refs added, to be published in Gen. Rel. and Gra

Assessing the Democratic Legitimacy of the 2016 Brexit Referendum

This is the final version. Available from the publisher via the link in this recordThis contribution addresses the input legitimacy of the British EU membership referendum of June 2016. It considers who was given a vote in the first place, and whether those given a vote could make a reasonable choice in light of the campaign. More precisely, it assesses the following four criteria: the franchise, the presence of clarity, the amount and quality of information, and the quality of public debate, arguing that instances of direct democracy, such as referendums, require higher standards of civic behaviour from both elected representatives and voters than those required of representative democracy. The empirical analysis of these criteria shows that the referendum fell short regarding the first two criteria whilst it could have done better as regards the last two. The paper concludes by briefly discussing what can be learnt from this referendum for future referendums

Measuring the Hausdorff Dimension of Quantum Mechanical Paths

We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$. We find that all local potentials fall into the same universality class giving $d_{H}=2$ like the free motion. A velocity dependent action ($S \propto \int dt \mid \vec{v} \mid^{\alpha}$) in the path integral (e.g. electrons moving in solids, or Brueckner's theory of nuclear matter) yields $d_{H}=\frac{\alpha }{\alpha - 1}$ if $\alpha > 2$ and $d_{H}=2$ if $\alpha \leq 2$. We discuss the relevance of fractal pathes in solid state physics and in $QFT$, in particular for the Wilson loop in $QCD$.Comment: uuencoded and compressed shell archive file. 8 pages with 7 figure

Theoretical analysis of STM-derived lifetimes of excitations in the Shockley surface state band of Ag(111)

We present a quantitative many-body analysis using the GW approximation of the decay rate $\Gamma$ due to electron-electron scattering of excitations in the Shockley surface state band of Ag(111), as measured using the scanning tunnelling microscope (STM). The calculations include the perturbing influence of the STM, which causes a Stark-shift of the surface state energy $E$ and concomitant increase in $\Gamma$. We find $\Gamma$ varies more rapidly with $E$ than recently found for image potential states, where the STM has been shown to significantly affect measured lifetimes. For the Shockley states, the Stark-shifts that occur under normal tunnelling conditions are relatively small and previous STM-derived lifetimes need not be corrected.Comment: 4 pages, 3 figure

Differentiated integration as a fair scheme of cooperation (working paper)

This is the final version. Available from the European University Institute via the link in this recordIn the past few years, there have been few discussions about the future of the European Union (EU) that did not involve the topic of differentiated integration (DI), the process whereby some member states integrate further, while others temporarily or permanently opt out of specific policies. Pragmatically, DI has allowed European integration to proceed by both widening and deepening. Normatively, it has allowed for diverging national capacities and preferences to be accommodated. However, the growing acceptance that the EU’s future may lie in more institutional diversity leaves unanswered the question of the conditions under which DI could be accepted as a fair scheme of cooperation. This is the question addressed by this paper. Why is this an important question? First, if DI is perceived as unfair, it will not generate the support it needs to work and, to the contrary, might further nourish hard forms of Euroscepticism. Second, if the institutional design of DI is perceived to be unfair, it will fail in its purpose of reconciling member states who want to integrate to different degrees, and at different speeds. Third, it has often been suggested that DI allows member states to leave their fundamental disagreements about the nature and the finalité of the EU unresolved by recognising that they may proceed separately, with some moving forward whilst others hold back. However, DI can in fact contribute to creating new divisions and is itself an expression of divisions. Therefore, it is important to develop a more explicit understanding of the different notions of fairness that are involved in different designs of DI. Overall, fair design in DI matters because it ensures that DI contributes to greater acceptance of the EU rather than creating additional divisions. The paper explores two main approaches of international cooperation – statism and cosmopolitanism – and relates them to fairness in institutional design in DI

Differentiated integration as a fair scheme of cooperation

Differentiated integration (DI), whereby some MS opt out or are excluded from certain common EU policies for sovereignty or capacity reasons, may be thought to undermine the EU’s functioning as what John Rawls called a fair scheme of cooperation, grounded in norms of impartiality and reciprocity. However, we argue that different forms of DI can be compatible with either fair cooperation between states on the model of Rawls’ Law of Peoples or cooperation among citizens on the model of Rawls’ two principles of domestic justice. Meanwhile, the EU has features of both, being an international Union of states and a supra- and trans-national Union of citizens. We defend the coherence of this combination and contend that DI can provide a justified mechanism for ensuring fairness between states remains compatible with fairness between citizens both within and across states. Indeed it offers a potential model for other forms of international cooperation

Elastic and Plastic Behavior of Model Solids

A short ranged attractive (SHRAT) potential is employed here which is of the type of the effective two-particle interaction used in a variant of the ’embedded atom’ method for metals. Properties of the (pure) SHRAT model system in its gaseous, (metastable) liquid, and solid states have been computed earlier by molecular dynamics and, where possible, successfully compared with analytical  calculations, as well as with the behavior of real substances. After some remarks on scaling and reference values, elastic properties of the model metal are characterized by the bulk and shear moduli, and their corresponding Born-Green and fluctuation contributions. It is demonstrated that plastic flow implies significant structural changes, being reflected by the Born–Green contribution to the cubic shear modulus. Not only stick-slip behavior, but the detailed elastic response and plastic flow of the model solid is analyzed. In order to interpret and reproduce the simulated rheological quantities, a simple, but generalized Maxwell model is tested. Its tensorial generalization may be used in simulation schemes such as smoothed particle dynamics, which are applicable on length and time scales significantly larger than those accessible in molecular dynamics simulations