Packing and Hausdorff measures of stable trees

In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of L\'evy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991) which corresponds to the Brownian case. We provide results for the whole stable trees and for their level sets that are the sets of points situated at a given distance from the root. We first show that there is no exact packing measure for levels sets. We also prove that non-Brownian stable trees and their level sets have no exact Hausdorff measure with regularly varying gauge function, which continues previous results from a joint work with J-F Le Gall (2006).Comment: 40 page

Rigidity and intermediate phases in glasses driven by speciation

The rigid to floppy transitions and the associated intermediate phase in glasses are studied in the case where the local structure is not fully determined from the macroscopic concentration. The approach uses size increasing cluster approximations and constraint counting algorithms. It is shown that the location and the width of the intermediate phase and the corresponding structural, mechanical and energetical properties of the network depend crucially on the way local structures are selected at a given concentration. The broadening of the intermediate phase is obtained for networks combining a large amount of flexible local structural units and a high rate of medium range order.Comment: 4 pages, 4 figure

Irreversible magnetization switching using surface acoustic waves

An analytical and numerical approach is developped to pinpoint the optimal experimental conditions to irreversibly switch magnetization using surface acoustic waves (SAWs). The layers are magnetized perpendicular to the plane and two switching mechanisms are considered. In precessional switching, a small in-plane field initially tilts the magnetization and the passage of the SAW modifies the magnetic anisotropy parameters through inverse magneto-striction, which triggers precession, and eventually reversal. Using the micromagnetic parameters of a fully characterized layer of the magnetic semiconductor (Ga,Mn)(As,P), we then show that there is a large window of accessible experimental conditions (SAW amplitude/wave-vector, field amplitude/orientation) allowing irreversible switching. As this is a resonant process, the influence of the detuning of the SAW frequency to the magnetic system's eigenfrequency is also explored. Finally, another - non-resonant - switching mechanism is briefly contemplated, and found to be applicable to (Ga,Mn)(As,P): SAW-assisted domain nucleation. In this case, a small perpendicular field is applied opposite the initial magnetization and the passage of the SAW lowers the domain nucleation barrier.Comment: 11 pages, 4 figure

Extending Elliptic Curve Chabauty to higher genus curves

We give a generalization of the method of "Elliptic Curve Chabauty" to higher genus curves and their Jacobians. This method can sometimes be used in conjunction with covering techniques and a modified version of the Mordell-Weil sieve to provide a complete solution to the problem of determining the set of rational points of an algebraic curve $Y$.Comment: 24 page

Combining leak--resistant arithmetic for elliptic curves defined over \F_p and RNS representation

In this paper we combine the residue number system (RNS) representation and the leak-resistant arithmetic on elliptic curves. These two techniques are relevant for implementation of elliptic curve cryptography on embedded devices.\\ % since they have leak-resistance properties. It is well known that the RNS multiplication is very efficient whereas the reduction step is costly. Hence, we optimize formulae for basic operations arising in leak-resistant arithmetic on elliptic curves (unified addition, Montgomery ladder) in order to minimize the number of modular reductions. We also improve the complexity of the RNS modular reduction step. As a result, we show how to obtain a competitive secured implementation.\\ Finally, %we recall the main advantages of the RNS representation, %especially in hardware and for embedded devices, and we show that, contrary to other approaches, ours takes optimally the advantage of a dedicated parallel architecture

Universal behavior of internal friction in glasses below T : anharmonicity vs relaxation

Comparison of the internal friction at hypersonic frequencies between a few K and the glass transition temperature Tg for various glasses brings out general features. At low temperature, internal friction is only weakly dependent on the material. At high temperature but still below Tg the internal friction for strong glasses shows a T-independent plateau in a very wide domain of temperature; in contrast, for fragile glass, a nearly linear variation of internal friction with T is observed. Anharmonicity appears dominant over thermally activated relaxational processes at high temperature.Comment: accepted in Physical Review

Effect of binder on performance of intumescent coatings

This study investigates the role of the polymeric binder on the properties and performance of an intumescent coating. Waterborne resins of different types (vinylic, acrylic, and styrene-acrylic) were incorporated in an intumescent paint formulation, and characterized extensively in terms of thermal degradation behavior, intumescence thickness, and thermal insulation. Thermal microscopy images of charred foam development provided further information on the particular performance of each type of coating upon heating. The best foam expansion and heat protection results were obtained with the vinyl binders. Rheological measurements showed a complex evolution of the viscoelastic characteristics of the materials with temperature. As an example, the vinyl binders unexpectedly hardened significantly after thermal degradation. The values of storage moduli obtained at the onset of foam blowing (melamine decomposition) were used to explain different intumescence expansion behaviors.Funding for this work was provided by FCT-Fundacao para a Ciencia e Tecnologia (Project PTDC/EQU-EQU/65300/2006), and by FEDER/QREN (project RHED) in the - framework of Programa Operacional Factor de Competitividade-COMPETE. Joana Pimenta thanks FCT for PhD Grant SFRH/BDE/33431/2008