Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.

Import competition from China and unemployment. An analysis using Spanish workers’micro-data.

In the period 1997-2011, import competition from China multiplied by five in the Spanish manufacturing sector. In this paper we analyze whether this severe increase in import competition from China is associated with a higher probability of becoming unemployed in the Spanish manufacturing sector. Linking industry-level data on imports with the working histories of 141,000 manufacturing workers, we show that import competition from China is positively associated with the probability of becoming unemployed. In particular, a standard deviation increase in import competition from China raises the probability of becoming unemployed between 0.8 and 3.5 percentage points, which represents between a 9% and a 44% increase relative to the unconditional probability of becoming unemployed. In contrast, we do not find any effect of import competition from China on manufacturing wages. Also, our estimations show that there is weak evidence of a positive association between a higher import competition from China and the probability of switching to an employment outside the manufacturing sector.