Kolmogorov-Arnold-Moser Renormalization-Group Approach to the Breakup of Invariant Tori in Hamiltonian Systems

We analyze the breakup of invariant tori in Hamiltonian systems with two degrees of freedom using a combination of KAM theory and renormalization-group techniques. We consider a class of Hamiltonians quadratic in the action variables that is invariant under the chosen KAM transformations, following the approach of Thirring. The numerical implementation of the transformation shows that the KAM iteration converges up to the critical coupling at which the torus breaks up. By combining this iteration with a renormalization, consisting of a shift of resonances and rescalings of momentum and energy, we obtain a much more efficient method that allows to determine the critical coupling with high accuracy. This transformation is based on the physical mechanism of the breakup of invariant tori. We show that the critical surface of the transformation is the stable manifold of codimension one of a nontrivial fixed point, and we discuss its universality properties.Comment: 9 pages, 5 figures, RevTe

Thermo-gravimetric analysis as a tool for the optimisation of wood heat treatment parameters

9 pagesRetification is a heat treatment that decreases the swelling of wood and increases its resistance to fungal attack. It consists in a mild pyrolysis of wood (180°C-260°C) that takes place in a non oxidative atmosphere (nitrogen). The industrial development of retification requires optimisation of the treatment temperature and duration. In order to enhance the homogeneity of temperature in the furnace, and to avoid exothermic reaction, low temperatures seem to be preferable to high temperature. On the contrary, duration and temperature of treatment have to be high enough to provide good biological resistance and stabilization to the wood. However, high temperatures lead to a loss of mechanical strength. A question arises from these previous observations: is there any equivalence between a treatment of short time carried out at high temperature and a treatment of longer time at lower temperature? Answering this question can help to optimise rétification temperature and duration. The purpose of this study is to evaluate the relevance of a “time temperature equivalence” (TTE) for wood pyrolysis in the temperature range of retification. The principle of TTE is adapted from the study of wood viscoelastic properties. In this study, it is applied to the rate of anhydrous weight loss during wood pyrolysis. Thermo-gravimetric analysis (TGA) were performed on maritime pine (Pinus pinaster Ait.-) and beech (Fagus sylvatica) wood powder. Isothermal degradations were carried out at different temperatures ranging from 160°C to 260°C. A specific data analyse was carried out on the TGA derivative (DTG) in order to assess the relevance of the TTE in the temperature range of retification. It gave interpretable results for maritime pine, but not for beech. It showed that for maritime pine wood the TTE is confirmed from 200°C to 220°C, and not confirmed for temperatures superior to 230°C. An optimization of the temperature and time of treatment is thus possible

Modelling anhydrous weight loss of wood chips during torrefaction in a pilot kiln

International audienceBeech and spruce chips were torrefied in a batch rotating pilot kiln. For each torrefaction the temperature curve of the moving chips bed was recorded. The anhydrous weight loss (AWL) of each torrefaction was measured. Effect of torrefaction temperature and duration on the AWL was studied. In order to optimise short time torrefaction, models that can estimate the AWL from the chips temperature curve are required. Three phenomenological models were successfully applied. They all gave good correlations between experimental and calculated AWL. These three models can be employed to optimise industrial torrefaction. However, the more complex they are, the more difficult it is to understand their physical meaning. It is thus preferable to use simple model for the industrial control of torrefaction

Energy requirement for fine grinding of torrefied wood

International audienceThe purpose of this study is to investigate the influence of torrefaction on wood grinding energy. Wood chips were torrefied at different temperatures and durations. The energy required to obtain fine powder was measured. Particle size analyses were carried out on each powder sample. It is showed that torrefaction decreases both grinding energy and particle size distribution. A criterion to compare grindability of natural and torrefied wood is proposed. It takes into account both grinding energy and particle size distribution. It accounts the energy required for grinding particles to sizes inferior to 200 μm, for given grinding conditions. Torrefaction is characterised by the anhydrous weight loss (AWL) of wood. For AWL inferior to around 8%, grinding energy decreases fast. Over 8%, grinding energy decreases at a slow rate. Particle size distribution decreases linearly as the AWL increases. Both for spruce and beech, the grinding criterion is decreased of 93% when the AWL is around 28%

Etude physico-chimique d'un composite ciment-bois durant les premières heures d'hydratation.

3 pagesDans le domaine des nouveaux matériaux de construction, l'utilisation de composites à base ciment et de matériaux organiques devient essentiel. Elle permet d'améliorer ou de modifier les propriétés d'un ciment. Dans ce contexte, le matériau composite ciment-fibre de bois est extrêmement intéressant de par ses propriétés d'isolation phonique et acoustique ainsi que par sa faible masse spécifique. Le but de ce travail est de mieux comprendre les interactions chimiques entre le bois et le ciment ainsi que ces conséquences sur l'hydratation du ciment

Effect of torrefaction on grinding energy requirement for thin wood particle production

National audienceThe second generation biofuels exploits the lignocellulosic materials. The main advantage is to not compete with food chain. In the case of thermochemical means (gasification in an entrained flow reactor followed by Fischer-Tropsch synthesis), a grinding step is necessary to inject particles into the burner. The targeted particle size is about 200µm to reach a total conversion and to improve gas quality. Due to the plastic behaviour of the biomass, this step is strongly energy-consuming. Biomass torrefaction (thermal treatment lower than 300°C) is a way to decrease the grinding energy and to standardize materials (composition and moisture). Contrary to natural wood, torrefied wood has a brittle behaviour and a less mechanical strength. The aim of this study is to investigate the interest of torrefaction on wood grinding energy diminution. The torrefactions were carried out on beech and spruce, in an airtight rotating batch kiln under nitrogen. The effect of torrefaction temperature (160-300°C) and duration (5-60min), on weight loss, grinding energy and powder particles size were examined. The grinding energy was calculated by integration of the electric power of the grinder, which was measured by the means of a wattmeter. A grindability criterion, which took into account both grinding energy (E) and the volume fraction (X) of particles lower than the targeted size (200µm), was defined. Results showed a strong interest of torrefaction on the decrease in energy required for fine wood particle grinding. The grindability criterion could be reduced by 93% for treatments beyond 260°C. However, the global energy balance becomes less favourable. It is necessary to reach a compromise between the consumed energy by torrefaction and the decrease in grinding energy. According to the wood species, an optimum could be established around 10% of weight loss and around 85% of the grindability criterion diminution

Modification of cement hydration at early ages by natural and heated wood

International audienceHeat treatments of wood are widely used for the reduction of wood swelling and dimensional instability of wood-cement composites. The effect of natural and heated wood on the hydration of cement at early ages was investigated by isothermal calorimetry, thermogravimetry (TGA) and Fourier transform infrared (FTIR) spectroscopy. The addition of wood strongly delays and inhibits the hydration of the silicate phases. Consequently, the amount of portlandite is lower in composites than in neat cement. Approximately 30% of the inhibition of portlandite precipitation is due to an increase of calcium carbonate content in cement paste. The absorption of a part of water by wood produces a decrease in gypsum consumption. Nevertheless, the ettringite formation is not significantly affected since a diffusion of sulfate ions from wood occurs