A dimension-breaking phenomenon for water waves with weak surface tension

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength transverse perturbations. The key to these results is a formulation of the water wave problem as an evolutionary system in which the transverse horizontal variable plays the role of time, a careful study of the purely imaginary spectrum of the operator obtained by linearising the evolutionary system at a line solitary wave, and an application of an infinite-dimensional version of the classical Lyapunov centre theorem.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0941-

Three-Fold Diffraction Symmetry in Epitaxial Graphene and the SiC Substrate

The crystallographic symmetries and spatial distribution of stacking domains in graphene films on SiC have been studied by low energy electron diffraction (LEED) and dark field imaging in a low energy electron microscope (LEEM). We find that the graphene diffraction spots from 2 and 3 atomic layers of graphene have 3-fold symmetry consistent with AB (Bernal) stacking of the layers. On the contrary, graphene diffraction spots from the buffer layer and monolayer graphene have apparent 6-fold symmetry, although the 3-fold nature of the satellite spots indicates a more complex periodicity in the graphene sheets.Comment: An addendum has been added for the arXiv version only, including one figure with five panels. Published paper can be found at http://link.aps.org/doi/10.1103/PhysRevB.80.24140

Tackling the undeclared economy in the European Union: an evaluation of the tax morale approach

To evaluate a new approach towards tackling the undeclared economy which views participants as social actors rather than rational economic actors, this paper reports evidence from 27,563 face-to-face interviews conducted across the European Union during 2013. Multilevel logistic regression analysis reveals a strong association between participation in undeclared work and the level of tax morale. Finding that higher tax morale (and thus a lower propensity to engage in undeclared work) is strongly correlated with greater levels of state intervention but also with individual-level characteristics such as gender, age, education and employment status, the paper concludes not only by confirming a political economy approach and refuting modernization and neo-liberal explanations and remedies, but also by revealing for the first time the importance of solutions not so far considered, including improving educational attainment, older citizens mentoring for younger people, and improving women’s participation in the labour force

Discrete Routh Reduction

This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical $J_2$ correction, as well as the double spherical pendulum. The $J_2$ problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a nontrivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the noncanonical nature of the symplectic structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added, fixed typo

Renormalizing Partial Differential Equations

In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.Comment: 34 pages, Latex; [email protected]; [email protected]

Debt, economic growth and interest rates: An empirical study of the Swiss case, presenting a new long-term dataset: 1894-2014

Abstract In this paper, relations between public debt, economic growth, and long-term interest rates in Switzerland from 1894 to 2014 are examined. For this purpose, an original long-term dataset on the general gross public debt in Switzerland, namely the aggregation of the Confederation gross debt, the cantons’ gross debts, and the municipal gross debts, was reconstructed. Three different statistical approaches are performed to study relations between this aggregated debt, economic growth, and interest rates. The first consists of the study of correlations between GDP-weighted variables, the second is the study of the correlation between residuals of ARIMA time series models, and the last one studies vector autoregression (VAR) models, allowing us to test Granger causalities between variables. Every approach is performed on the whole time period but also on boom phases and recession phases independently. All the results suggest that the public debt during this period in Switzerland did not have a negative impact on economic growth and did not raise long-term interest rates

M3 money demand and excess liquidity in the euro area

Recent empirical studies have found evidence of unstable long run money demand functions if recent data are used. If the link between money balances and the macroeconomy is fragile, the rationale of monetary aggregates in the ECB strategy has to be doubted. In contrast we present a ``stable'' long run money demand relationship for M3 for the period 1983-2006. To obtain the result, the short run homogeneity restriction between money and prices is relaxed and a break in the income elasticity of money demand after 2001 is taken into account. Measures of excess liquidity do not show significant inflation pressures.The final publication is available at Springer via http://dx.doi.org/10.1007/s11127-010-9679-5. This publication was produced as part of the FINESS project, funded by the European Commission through the 7th Framework Programme under contract no. 217266 (http://www.finess-web.eu/)