Diffusion on a solid surface: anomalous is normal

We present a numerical study of classical particles diffusing on a solid surface. The particles motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic or a random two-dimensional potential. The model leads to a rich variety of different transport regimes, some of which correspond to anomalous diffusion such as has recently been observed in experiments and Monte Carlo simulations. We show that this anomalous behavior is controlled by the friction coefficient and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics.

Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Friction Stir Processing : a new microstructure improvement technique

In the present work, microstructure improvement using FSP (Friction Stir Processing) is studied. In the first part of the work, the microstructure improvement of as-cast A356 is demonstrated. Some tensile tests were applied to check the increase in ductility. However, the expected results couldn’t be achieved. In the second part, the microstructure improvement of a fusion weld in 1050 aluminium alloy is presented. Hardness tests were carried out to prove the mechanical propertyimprovements. In the third and last part, the microstructure improvement of 1050 aluminium alloy is achieved. A discussion of the mechanical property improvements induced by FSP is made. The influence of tool traverse speed on microstructure and mechanical properties is also discussed. Hardness tests and recrystallization theory enabled us to find out such influence

Constant coefficient tests for random coefficient regression

Random coefficient regression models have been applied in differentfields and they constitute a unifying setup for many statisticalproblems. The nonparametric study of this model started with Beranand Hall (1992) and it has become a fruitful framework. In thispaper we propose and study statistics for testing a basic hypothesisconcerning this model: the constancy of coefficients. The asymptoticbehavior of the statistics is investigated and bootstrapapproximations are used in order to determine the critical values ofthe test statistics. A simulation study illustrates the performanceof the proposals.