On the variational structure of breather solutions

In this paper we give a systematic and simple account that put in evidence that many breather solutions of integrable equations satisfy suitable variational elliptic equations, which also implies that the stability problem reduces in some sense to $(i)$ the study of the spectrum of explicit linear systems (\emph{spectral stability}), and $(ii)$ the understanding of how bad directions (if any) can be controlled using low regularity conservation laws. We exemplify this idea in the case of the modified Korteweg-de Vries (mKdV), Gardner, and sine-Gordon (SG) equations. Then we perform numerical simulations that confirm, at the level of the spectral problem, our previous rigorous results, where we showed that mKdV breathers are $H^2$ and $H^1$ stable, respectively. In a second step, we also discuss the Gardner and the Sine-Gordon cases, where the spectral study of a fourth-order linear matrix system is the key element to show stability. Using numerical methods, we confirm that all spectral assumptions leading to the $H^2\times H^1$ stability of SG breathers are numerically satisfied, even in the ultra-relativistic, singular regime. In a second part, we study the periodic mKdV case, where a periodic breather is known from the work of Kevrekidis et al. We rigorously show that these breathers satisfy a suitable elliptic equation, and we also show numerical spectral stability. However, we also identify the source of nonlinear instability in the case described in Kevrekidis et al. Finally, we present a new class of breather solution for mKdV, believed to exist from geometric considerations, and which is periodic in time and space, but has nonzero mean, unlike standard breathers.Comment: 55 pages; This paper is an improved version of our previous paper 1309.0625 and hence we replace i

Unemployment duration, unemployment benefits and recalls

We use administrative micro-data to investigate exits from unemployment of benefit recipients in Spain. Because the data allow us to distinguish between transitions to a new job and recall to the same employer, we apply a competing risks model with observed and unobserved heterogeneity. We are also able to control for the type of benefit received by the worker: insurance benefit or assistance benefit. We find significant differences between the new job hazard and the recall hazard. Both hazard rates increase around the time that insurance benefit elapses. We also find that when larger firms recall unemployed workers they tend to do so faster than smaller firms. In general, our results are consistent with predictions derived from search and implicit contract models. They highlight the importance of taking into account the possibility of recall in the analysis of unemployment duration among unemployment benefit recipients

Exits from unemployment : recall or new job

This paper studies transitions out of unemployment in Spain distinguishing between recall to the same employer and reemployment in a new job. We use a large sample of newly unemployed workers obtained from Social Security records for Spain. These data contain information about each individual's employer identy before and after the unemployment spell. A discrete-time duration model with competing risks of exits serves us to investigate the factors that influence the probabilities of leaving unemployment to return to the same employer or to find a new job with a different employer. We find that the route to exit unemployment is determinant to understand the influence of individual an job characteristics on the hazard rate, as well as the latter dependence on unemployment duration. The recall hazard rate exhibits positive duration dependence during the first months and negative duration dependence thereafter (it is larger for females), while the new-job hazard presents positive duration dependence (it is larger for males

Characterization of strain-induced precipitation in Inconel 718 superalloy

© 2016 ASM International Inconel 718 presents excellent mechanical properties at high temperatures, as well as good corrosion resistance and weldability. These properties, oriented to satisfy the design requirements of gas turbine components, depend on microstructural features such as grain size and precipitation. In this work, precipitation-temperature-time diagrams have been derived based on a stress relaxation technique and the characterization of precipitates by scanning electron microscopy. By using this methodology, the effect of strain accumulation during processing on the precipitation kinetics can be determined. The results show that the characteristics of precipitation are significantly modified when plastic deformation is applied, and the kinetics are slightly affected by the amount of total plastic deformation.Peer ReviewedPostprint (author's final draft

Dynamic recrystallization mechanisms and twining evolution during hot deformation of Inconel 718

The hot deformation behavior of an IN718 superalloy was studied by isothermal compression tests under the deformation temperature range of 950–1100 °C and strain rate range of 0.001–1 s-1 up to true strains of 0.05, 0.2, 0.4 and 0.7. Electron backscattered diffraction (EBSD) technique was employed to investigate systematically the effects of strain, strain rate and deformation temperature on the subgrain structures, local and cumulative misorientations and twinning phenomena. The results showed that the occurrence of dynamic recrystallization (DRX) is promoted by increasing strain and deformation temperature and decreasing strain rate. The microstructural changes showed that discontinuous dynamic recrystallization (DDRX), characterized by grain boundary bulging, is the dominant nucleation mechanism in the early stages of deformation in which DRX nucleation occurs by twining behind the bulged areas. Twin boundaries of nuclei lost their ¿3 character with further deformation. However, many simple and multiple twins can be also regenerated during the growth of grains. The results showed that continuous dynamic recrystallization (CDRX) is promoted at higher strains and large strain rates, and lower temperatures, indicating that under certain conditions both DDRX and CDRX can occur simultaneously during the hot deformation of IN718.Peer ReviewedPostprint (author's final draft

Twin-induced plasticity of an ECAP-processed TWIP steel

The TWIP steels show high strain hardening rates with high ductility which results in high ultimate tensile strength. This makes their processing by equal channel angular pressing very difficult. Up to now, this has only been achieved at warm temperatures (above 200 °C). In this paper, a FeMnCAl TWIP steel has been processed at room temperature and the resulted microstructure and mechanical properties were investigated. For comparison, the material has also been processed at 300 °C. The TWIP steel processed at room temperature shows a large increase in yield strength (from 590 in the annealed condition to 1295 MPa) and the ultimate tensile strength (1440 MPa) as a consequence of a sharp decrease in grain size and the presence within the grains of a high density of mechanical twins and subgrains. This dense microstructure results also in a loss of strain hardening and a reduction in ductility. The material processed at 300 °C is more able to accommodate deformation and has lower reduction in grain size although there is a significant presence of mechanical twins and subgrains produced by dislocation activity. This material reaches an ultimate tensile strength of 1400 MPa with better ductility than the room temperature material.Postprint (published version