Kinetic-growth self-avoiding walks on small-world networks

Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect, which gives finite values for its mean value . For random networks, this mean attrition length scales as a power of the network size, and diverges in the thermodynamic limit (large system size N). For small-world networks, we find a behavior that interpolates between those corresponding to regular lattices and randon networks, for rewiring probability p ranging from 0 to 1. For p < 1, the mean self-intersection and attrition length of kinetically-grown walks are finite. For p = 1, grows with system size as N^{1/2}, diverging in the thermodynamic limit. In this limit and close to p = 1, the mean attrition length diverges as (1-p)^{-4}. Results of approximate probabilistic calculations agree well with those derived from numerical simulations.Comment: 10 pages, 7 figure

Analysis for time discrete approximations of blow-up solutions of semilinear parabolic equations

We prove a posteriori error estimates for time discrete approximations, for semilinear parabolic equations with solutions that might blow up in finite time. In particular we consider the backward Euler and the Crank–Nicolson methods. The main tools that are used in the analysis are the reconstruction technique and energy methods combined with appropriate fixed point arguments. The final estimates we derive are conditional and lead to error control near the blow up time

From globalization to deglobalization: Zooming into trade. Bruegel Special Report

After decades of increasing globalization both in trade, capital flows but even people to people movements, it seems the trend has turned towards deglobalization. This article shows some evidence of the decrease in merchandise, capital and, to a lesser extent people to people flows. In addition, zooming into trade, the article offers an account of the importance of the strategic competition between the US and China to foster the deglobalization trend further. This is true for trade but even beyond in the tech and finance space. Finally, the demise of the WTO could be one of the most relevant turning points towards deglobalization, especially as far as trade is concerned. This should bring downward pressure to growth globally