Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity smaller than one

We prove the existence of a one-parameter family of self-similar solutions with time-dependent tails for Smoluchowski's coagulation equation, for a class of rate kernels $K(x,y)$ which are homogeneous of degree $\gamma\in(-\infty,1)$ and satisfy $K(x,1)\sim x^{-a}$ as $x\to 0$, for $a=1-\gamma$. In particular, for small values of a parameter $\rho>0$ we establish the existence of a positive self-similar solution with finite mass and asymptotics $A(t)x^{-(2+\rho)}$ as $x\to\infty$, with $A(t)\sim\rho t^\frac{\rho}{1-\gamma}$

Développement de circuits logiques programmables résistants aux alas logiques en technologie CMOS submicrométrique

The electronics associated to the particle detectors of the Large Hadron Collider (LHC), under construction at CERN, will operate in a very harsh radiation environment. Most of the microelectronics components developed for the first generation of LHC experiments have been designed with very precise experiment-specific goals and are hardly adaptable to other applications. Commercial Off-The-Shelf (COTS) components cannot be used in the vicinity of particle collision due to their poor radiation tolerance. This thesis is a contribution to the effort to cover the need for radiation-tolerant SEU-robust programmable components for application in High Energy Physics (HEP) experiments. Two components are under development: a Programmable Logic Device (PLD) and a Field-Programmable Gate Array (FPGA). The PLD is a fuse-based, 10-input, 8-I/O general architecture device in 0.25 micron CMOS technology. The FPGA under development is instead a 32x32 logic block array, equivalent to ~25k gates, in 0.13 micron CMOS. This work focussed also on the research for an SEU-robust register in both the mentioned technologies. The SEU-robust register is employed as a user data flip-flop in the FPGA and PLD designs and as a configuration cell as well in the FPGA design