Maximization of higher order eigenvalues and applications

The present paper is a follow up of our paper \cite{nS}. We investigate here the maximization of higher order eigenvalues in a conformal class on a smooth compact boundaryless Riemannian surface. Contrary to the case of the first nontrivial eigenvalue as shown in \cite{nS}, bubbling phenomena appear

Impacts of Winemaking Methods on Wastewaters and their Treatment

The volume, composition and organic load of wastewaters from five wineries producing white, rosé and red wines bythermovinification, as well as traditionally vinified red wines (75 000 hL to 240 000 hL wine), were studied in termsof the vinification methods used. Liquid-phase vinifications (white, rosé, thermovinification) produce wastewatersrich in sugars: 70% of the chemical oxygen demand (COD) when the must is treated, and flows depend on thedaily supply of grapes, representing 40 to 46% of the annual volume of wastewaters during the first month ofactivity (September). In contrast, solid-phase vinifications do not produce large quantities of waste at harvest, andwastewaters produced mainly during devatting are characterised by a predominance of ethanol (≤ 75% COD) andby staggered flows towards the second month (October), which are less intense (26.7 to 33.6%) and more spread out.The specific pollution coefficients of liquid-phase vinifications (5.18 to 6.04 kg COD/t grapes) are greater than thoseof solid-phase vinifications (3.82 kg COD/t grapes). The higher the winery’s liquid-phase vinification rate, the morethe maximal monthly volume of waste will be intense and early. These results should contribute to the improveddesign and management of winery wastewater treatments

H\"older regularity for weak solutions of H\"ormander type operators

Motivated by recent results on the (possibly conditional) regularity for time-dependent hypoelliptic equations, we prove a parabolic version of the Poincar\'e inequality, and as a consequence, we deduce a version of the classical Moser iteration technique using in a crucial way the geometry of the equation. The point of this contribution is to emphasize that one can use the {\sl elliptic} version of the Moser argument at the price of the lack of uniformity, even in the {\sl parabolic } setting. This is nevertheless enough to deduce H\"older regularity of weak solutions. The proof is elementary and unifies in a natural way several results in the literature on Kolmogorov equations, subelliptic ones and some of their variations

Low cost estimation of Wöhler and Goodman–Haigh curves of Ti-6Al-4V samples by considering the stress ratio effect

The stress ratio effect on the fatigue life of materials is a topic which have been studied by two different approaches. On the one hand, several experiments, performed under different stress ratios are necessary to estimate the corresponding Wöhler curves. Afterwards, these curves are considered to estimate the fatigue life under a particular stress range. On the other hand, fatigue failure criteria for fluctuating stress like the Goodman–Haigh relationship, are applied to estimate the stress amplitude for a constant fatigue life. Based on the Stüssi function, this paper presents a low cost model to estimate Wöhler curves and constant fatigue Goodman–Haigh diagrams. This procedure requires a set of tests performed under a particular stress ratio from LCF to HCF, and data from minimum two additional stress ranges for each subsequent stress ratio. An application on data from Ti-6Al-4V samples manufactured by selective laser melting (SLM) is presented

A coalescence model for freely decaying two-dimensional turbulence

We propose a ballistic coalescence model (punctuated-Hamiltonian approach) mimicking the fusion of vortices in freely decaying two-dimensional turbulence. A temporal scaling behaviour is reached where the vortex density evolves like $t^{-\xi}$. A mean-field analytical argument yielding the approximation $\xi=4/5$ is shown to slightly overestimate the decay exponent $\xi$ whereas Molecular Dynamics simulations give $\xi =0.71\pm 0.01$, in agreement with recent laboratory experiments and simulations of Navier-Stokes equation.Comment: 6 pages, 1 figure, to appear in Europhysics Letter

Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion

For a specific choice of the diffusion, the parabolic-elliptic Patlak-Keller-Segel system with non-linear diffusion (also referred to as the quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold phenomenon: there is a critical mass $M_c>0$ such that all the solutions with initial data of mass smaller or equal to $M_c$ exist globally while the solution blows up in finite time for a large class of initial data with mass greater than $M_c$. Unlike in space dimension 2, finite mass self-similar blowing-up solutions are shown to exist in space dimension $d?3$

Environmental Impacts of Tartaric Stabilisation Processes for Wines using Electrodialysis and Cold Treatment

The environmental impacts of the two tartaric stabilisation methods used for wines, electrodialysis andcold treatment, were studied by determining water consumption (for the process and cleaning), wasteproduced (organic load and the composition of wastewater and residues) and energy consumption, atthe pilot stage and in wineries. Thanks to an online treatment of electrodialysis brines by reverse osmosis(industrial facility that treats 30 hL wine/h), the recycling of permeates led to a 65% reduction in waterconsumption, the volume of which represented only 3.9% of the wine treated. When washing and cleaningwater from the ED-RO system was taken into account, overall water consumption was 5.5 L/hL wine. Thepresence of ethanol, due to an osmotic phenomenon with no loss of wine volume, and tartaric acid in thebrines contributes to the organic load of the brine, with a COD of close to 8.4 g O2/L. Overall electricalenergy consumption for stabilisation by electrodialysis (0.21 kWh/hL) turned out to be eight times lowerthan that of cold stabilisation. An evaluation of cold stabilisation effluents revealed that 66.6% of the CODdischarged came from the diatomaceous earth (DE), 21.8% from the washing of the filter and 11.4% fromthe washing of the cold treatment tank. The production of used DE was 2.64 g (wet weight)/L of wine, andthe ethanol present in the DE waste represented a loss in wine volume of 0.14 L/hL

Numerical renormalization group of vortex aggregation in 2D decaying turbulence: the role of three-body interactions

In this paper, we introduce a numerical renormalization group procedure which permits long-time simulations of vortex dynamics and coalescence in a 2D turbulent decaying fluid. The number of vortices decreases as $N\sim t^{-\xi}$, with $\xi\approx 1$ instead of the value $\xi=4/3$ predicted by a na\"{\i}ve kinetic theory. For short time, we find an effective exponent $\xi\approx 0.7$ consistent with previous simulations and experiments. We show that the mean square displacement of surviving vortices grows as $\sim t^{1+\xi/2}$. Introducing effective dynamics for two-body and three-body collisions, we justify that only the latter become relevant at small vortex area coverage. A kinetic theory consistent with this mechanism leads to $\xi=1$. We find that the theoretical relations between kinetic parameters are all in good agreement with experiments.Comment: 23 RevTex pages including 7 EPS figures. Submitted to Phys. Rev. E (Some typos corrected; see also cond-mat/9911032

Analytical results for random walk persistence

In this paper, we present the detailed calculation of the persistence exponent $\theta$ for a nearly-Markovian Gaussian process $X(t)$, a problem initially introduced in [Phys. Rev. Lett. 77, 1420 (1996)], describing the probability that the walker never crosses the origin. New resummed perturbative and non-perturbative expressions for $\theta$ are obtained, which suggest a connection with the result of the alternative independent interval approximation (IIA). The perturbation theory is extended to the calculation of $\theta$ for non-Gaussian processes, by making a strong connection between the problem of persistence and the calculation of the energy eigenfunctions of a quantum mechanical problem. Finally, we give perturbative and non-perturbative expressions for the persistence exponent $\theta(X_0)$, describing the probability that the process remains bigger than $X_0\sqrt{}$.Comment: 23 pages; accepted for publication to Phys. Rev. E (Dec. 98