Thermodynamical functions for a gas of point vortices

We formulate nonlinear integro-differential equation for the averaged collective Hamiltonian of a gas of interacting two-dimensional vortices, derive its analytical solution, and discuss the equilibrium, axially-symmetrical, probability distributions that are possible for such a model. We also theoretically prove that the probability distribution for a system of 2D point vortices takes a form similar to the Gibbs distribution, but point out that the physical fundamentals of such a system differ from the standard theory of interacting particles. Furthermore, we find thermodynamical functions for positive and negative “temperature” of the system, and point out that the states with positive “temperature” correspond to stationary bell-shape vortex distributions, while the states with negative “temperature” correspond to distributions localized near container walls. To cite this article: E. Bécu et al., C. R. Mecanique 336 (2008).     

Designing coalition-based fair and stable pricing mechanisms under private information on consumers’ reservation prices

We model the relation between an aggregator and consumers joining a coalition to reduce the risk resulting from the unpredictability of their base load demand, as a Stackelberg game formulated as a mathematical bilevel program with private information on the consumers’ reservation prices. At the upper-level of the Stackelberg game, the aggregator optimizes his daily price profile so as to reach a net targeted profit which is the maximum value guaranteeing that no consumer will leave the coalition - to contract with a conventional retailer considered here as a fixed alternative - while meeting fairness criterion imposed by the cost-sharing mechanism. At the lower-level, the consumers are asked to provide in day ahead an estimate of their base load hourly demand profile and to schedule their shiftable loads depending on the price signal sent by the aggregator. We provide algorithms that determine the unique price profile and consumer shiftable load schedules as functions of the reservation price estimates. The Stackelberg game between the aggregator and the consumers being repeated for a period of time, the aggregator has the possibility to update his estimates of the reservation prices relying on a feedback function which depends on the percentage of activated loads. A randomized algorithm for consumers’ reservation price learning based on regret minimization is provided. For four cost-sharing mechanisms such as uniform allocation, stand-alone cost, Shapley value, separable and non-separable costs, we determine the closed form of the aggregator’s optimal net targeted profit guaranteeing the stability of the coalition. We also determine conditions guaranteeing the core non-emptiness and prove that for a profit-maximizing aggregator, the stand-alone cost is always preferable to the Shapley value, which coincides with the uniform allocation. Furthermore, the optimal size of the coalition - in terms of the aggregator’s profit - can be determined analytically when the Shapley value is implemented as cost-sharing mechanism. The results are illustrated on a case study where we show that there exists an optimal net targeted profit below which the consumers energy bill is lower when joining the aggregator than with the conventional retailer. Coalition dynamics is also analyzed numerically depending on the consumer inertia in their energy supplier choice process, for each cost-sharing mechanism.     

Biofunctionalisation of colloidal gold nanoparticles via polyelectrolytes assemblies

Bioapplications of gold nanoparticles (Au NPs) have received significant attention due to their sensitive optical characteristics which depend on particle size and shape, state of aggregation and to surrounding (bio)chemical environment. In this review, we present an overview of several methods to synthesise stable colloidal Au NPs with focus on the use of the electrostatic assembly method of polyelectrolytes (PE) to functionalise Au NPs. This versatile method allows adjusting the thickness, chemical functions and the surface charge of the shells surrounding the Au NPs, thus the relevance of these features for the bioapplications of Au NPs involving surface-mediated processes is discussed. Moreover, because the PE used can be functionalised with organic fluorophores, drugs or antibodies yielding multifunctional nanocomposites useful for those applications, this review also provides an overview of the electrostatic assembly of functionalised PE onto Au NPs and their bioapplications.     

Cationic release behaviour of antimicrobial cellulose/silver nanocomposites

Silver nanoparticles (NPs) have received great attention, mainly due to their application as antimicrobial agents in diverse products, including textile- and paper-based materials. In this context, straightforward methodologies to monitor their cationic silver release capacity in diverse environments are required due to the rise of manufactured products containing silver NPs. Here, we describe the application of a potentiometric method based on a silver-selective electrode to monitor the kinetics of cationic release from cellulose/silver nanocomposites. We designed a set of experiments to apply this method to nanocomposites with several distinct types of cellulose matrices: vegetable, bacterial and nanofibrillated. The morphological features of the cellulose had a great influence on the distribution of silver NPs within the matrix as well as on the Ag⁺ release profiles. The cationic release profiles were interpreted based on common models, showing that, for the vegetal and bacterial cellulose nanocomposites, the kinetics is pseudo-first order, while for the nanofibrillated cellulose materials a model based on Fick’s power law provided the best fit.     

A hybrid neural model of ethanol production by Zymomonas mobilis

A hybrid neural model was developed for the alcoholic fermentation by Zymomonas mobilis. This model is composed by the mass-balance equations of the process and neural networks, which describe the kinetic rates. Strategies that combines scarce experimental data with approximate models of the process were used to generate new data for the training of the networks, minimizing the number of experiments required. The proposed hybrid neural methodology uses all the information avail able about the process to deal with the difficulties in the development of the model.     

A study of the intermolecular interactions of tolmetin/N-acetyl-l-tyrosine ethyl ester complex

The formation of tolmetin/N-acetyl-l-tyrosine ethyl ester (ATEE) complex has been reported by means of both theoretical and experimental studies, including quantum mechanical calculations as well as UV–vis absorption, fluorescence and time-resolved spectroscopy measurements. It has been found that the fluorescence of ATEE is quenched due to the formation of a non-fluorescent complex between ATEE and tolmetin in the ground state. The geometrical parameters of ATEE/tolmetin complex have been determined with the use of the DFT method applying the B3LYP correlation-exchange functional and 6-31G(d) basis set. The results of experiments indicated the static ATEE quenching by tolmetin. Additionally, the experimental and theoretically predicted Gibbs free energy of complexation has been calculated.     

Infrared digital reflective-holographic 3D shape measurements

We present a series of experiments to demonstrate digital holography on reflective objects at wavelength 10.6 μm of a CO₂ laser using a pyrocam array. Fresnel holograms of reflective objects are recorded by a Mach-Zehnder interferometer. We describe a method for improving the accuracy of the numerical reconstructions and for compensating the loss of resolution at longer wavelength by Fresnel reconstruction of digitally recorded infrared holograms.     

De-aggregation of polyfluorene derivative by blending with a series of poly(alkyl methacrylate)s with varying sidegroup sizes

A polyfluorene derivative of the PPV, poly(9,9′-n-dihexyl-2,7-fluorenedilvinylene-alt-1,4-phenylenevinylene), with a strong tendency to aggregation was blended with several members of a series composed by poly(alkyl methacrylate)s with the following substituents in the ester position: methyl, ethyl, isopropyl, isobutyl, n-butyl, and cyclohexyl. The de-aggregation effect in blends was studied by steady-state photoluminescence spectroscopy using several blend compositions. The efficiency of each dispersing phase was discussed in terms of the polymer miscibility, controlled by interaction parameters between the polyfluorene and every poly(alkyl methacrylate)s, here described using Hildebrand solubility parameters.