Higher order terms in multiscale expansions: a linearized KdV hierarchy

We consider a wide class of model equations, able to describe wave propagation in dispersive nonlinear media. The Korteweg-de Vries (KdV) equation is derived in this general frame under some conditions, the physical meanings of which are clarified. It is obtained as usual at leading order in some multiscale expansion. The higher order terms in this expansion are studied making use of a multi-time formalism and imposing the condition that the main term satisfies the whole KdV hierarchy. The evolution of the higher order terms with respect to the higher order time variables can be described through the introduction of a linearized KdV hierarchy. This allows one to give an expression of the higher order time derivatives that appear in the right hand member of the perturbative expansion equations, to show that overall the higher order terms do not produce any secularity and to prove that the formal expansion contains only bounded terms.Comment: arxiv version is already officia

A new criterion for the existence of KdV solitons in ferromagnets

The long-time evolution of the KdV-type solitons propagating in ferromagnetic materials is considered trough a multi-time formalism, it is governed by all equations of the KdV Hierarchy. The scaling coefficients of the higher order time variables are explicitly computed in terms of the physical parameters, showing that the KdV asymptotic is valid only when the angle between the propagation direction and the external magnetic field is large enough. The one-soliton solution of the KdV hierarchy is written down in terms of the physical parameters. A maximum value of the soliton parameter is determined, above which the perturbative approach is not valid. Below this value, the KdV soliton conserves its properties during an infinite propagation time

Cosmic Necklaces from String Theory

We present the properties of a cosmic superstring network in the scenario of flux compactification. An infinite family of strings, the (p,q)-strings, are allowed to exist. The flux compactification leads to a string tension that is periodic in 'p'. Monopoles, appearing here as beads on a string, are formed in certain interactions in such networks. This allows bare strings to become cosmic necklaces. We study network evolution in this scenario, outlining what conditions are necessary to reach a cosmologically viable scaling solution. We also analyze the physics of the beads on a cosmic necklace, and present general conditions for which they will be cosmologically safe, leaving the network's scaling undisturbed. In particular, we find that a large average loop size is sufficient for the beads to be cosmologically safe. Finally, we argue that loop formation will promote a scaling solution for the interbead distance in some situations.Comment: 14 pages, 5 figures; v3, typos corrected, comments added, published versio

Cutoff phenomenon for the simple exclusion process on the complete graph

We study the time that the simple exclusion process on the complete graph needs to reach equilibrium in terms of total variation distance. For the graph with n vertices and 1<<k<n/2 particles we show that the mixing time is of order (n/2)\log \min(k, \sqrt{n}), and that around this time, for any small positive epsilon the total variation distance drops from 1-epsilon to epsilon in a time window whose width is of order n (i.e. in a much shorter time). Our proof is purely probabilistic and self-contained.Comment: 16 pages, to appear in ALE

"Is My Crown Better than Your Euro? Exchange Rates and Public Opinion on the European Single Currency"

The No to the euro in referendums in Denmark and Sweden has been characterized as a public rebellion against an elite project and a sign of a general Euroscepticism among the citizens. However, it is often ignored that support for the euro fluctuates significantly over time in these countries, and hence analysing referendum outcomes simply in terms on static factors will provide only part of the explanation. In contrast to existing studies, this paper provides an analysis of the short-term dynamics in public support for the euro in the period leading up to the referendums. We thus address the question of why public attitudes towards monetary integration vary over time. We argue that at least part of the answer can be found in exchange rate fluctuations. Existing studies have neglected the fact that the national currency is not only a purely monetary indicator, but also carries symbolic weight. The public is therefore less likely to surrender their national currency when it is strong than when it is weak. They are also less willing to accept a replacement currency (e.g. the euro) when it is seen as weak vis-à-vis other world currencies. Our analysis of the two euro campaigns lends credence to our proposition that exchange rates matter. Moreover, we test impact of exchange rate changes on support of the euro using time series analysis. We find that the rapid fall in the value of the euro vis-à-vis the dollar contributed to the Danish rejection of the euro, whereas the strength of the Swedish currency made the Swedes more reluctant to relinquish their crown