On the normal form of a system of differential equations with nilpotent linear part

We consider prenormal forms associated to generic perturbations of the system $\text{x}\text{?}\text{=2y,}\text{y}\text{?}\text{=3x}{}^2$. It is known that they have a formal normal form $\text{x}\text{?}\text{=2y+2x}\text{Δ}{}^1\text{,}\text{y}\text{?}\text{=3x}{}^2\text{+3y}\text{Δ}{}^1$, where $\text{Δ}{}^1\text{=x+A}{}_0\text{(y}{}^2\text{?x}{}^3\text{)}$ [Differential Equations 158 (1) (1999) 152–173]. We show that the series A₀ and the normalizing transformations are divergent, but 1-summable. To cite this article: M. Canalis-Durand, R. Schäfke, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

An adaptive Lagrange‐Galerkin method for the shallow‐water equations on the sphere

The shallow‐water equations on the sphere are compressible Navier‐Stokes equations that describe hydrostatic atmospheric dynamics. An adaptive Lagrange‐Galerkin method is applied on the spherical domain to develop a simplified global atmospheric model. Computational results show the experimental convergence of this numerical method.     

Quasiparticle and Cooper pair tenneling in small capacitance Josephson junctions

The tunneling of single electrons in small capacitance tunnel junctions is influenced by charging effects and by the fluctuations of the elecromagnetic environment. We study the effect of an external circuit with arbitrary impedance on the tunneling of quasiparticles and Cooper pairs in voltage driven Josephson junctions. We present results at finite temperatures and also consider an acdriven system.     

Fragmentation of gold projectiles: From evaporation to total disassembly

We have studied the fragmentation of Au projectiles interacting with targets of C, Al and Cu at an incident energy ofE/A=600 MeV. The employed inverse kinematics allowed a nearly complete detection of projectile fragments with chargeZ≧2. The recorded fragmentation events were sorted according to three observables, the multiplicityM _lp of light charged particles, the largest atomic numberZ _max within an event, and a new observable,Z _bound, representing the sum of the atomic numbersZ of all fragments withZ≧2. Using these observables, the impact parameter dependence of the fragmentation process was investigated. For all three targets, a maximum mean multiplicity of 3 to 4 intermediate mass fragments (IMFs) is observed. The corresponding impact parameters range from central collisions for theC target to increasingly peripheral collisions for the heavier targets. It is found that the correlation between the IMF multiplicity andZ _bound, extending from evaporation type processes (largeZ _bound) to the total disassembly of the projectile (smallZ _bound), is independent of the target nucleus. This universal behaviour may suggest an — at least partial — equilibration of the projectile fragment prior to its decay.     

Semiconductor saturable absorber mirror structures with low saturation fluence

We present two novel semiconductor saturable absorber mirror (SESAM) designs which can exhibit more than ten times lower saturation fluence than classical SESAM devices. Design considerations and characterization data are presented. These devices are particularly suited for passively mode-locked lasers with ultra-high repetition rates.     

How well do we understand the synthesis of heavy elements by heavy-ion induced fusion?

Experimental cross sections to synthesize heavy ion induced fusion reactions are confronted with calculations using the conventional picture of complete fusion after passing the barrier plus statistical deexcitation after complete equilibration. The sensitivity of the calculations to some of the parameters is demonstrated. Despite this sensitivity, a single parameter set is found that reproduces well the large body of data from experiments using actinide targets. By comparison, for the more symmetric entrance channels using targets around²⁰⁸Pb, we find a fusion hindrance that increases steeply with increasing compound nuclear charge. Predictions for a few reactions of future interest for the synthesis of heavy elements are also presented.     

Scanning tunneling spectroscopy of Ni/W(110): bcc and fcc properties in the second atomic layer

Nickel islands are grown on W(110) at elevated temperatures. Islands with a thickness of two layers are investigated with scanning tunneling microscopy. Spectroscopic measurements reveal that nanometer sized areas of the islands exhibit distinctly different apparent heights and dI/dVspectra. Spin polarized and paramagnetic band structure calculations indicate that the spectral features are due to fcc(111) and bcc(110) orientations of the Ni film, respectively.