Validation of averaged equations for thermal vibrational convection in near-critical fluidsValidation d'équations moyennées pour l'étude de la convection vibrationnelle dans les fluides supercritiques.

Within an averaging approach, the governing equations and effective boundary conditions describing both the average and pulsation motion of a near-critical fluid subjected to high-frequency vibrations are obtained. Vibrations induce the non-homogeneities in average temperature. Owing to these non-homogeneities, the average flows can be generated even in isothermal cavity under weightlessness. These flows are examined for 1D and 2D configurations. The direct numerical simulations fulfilled earlier confirm the averaged model, we obtain the same flow structures by essentially smaller requirements for computational time. To cite this article: A.Vorobev et al., C. R. Mecanique 332 (2004).     

On the Reactivity of (−)‐(R)‐Carvone and (−)‐4aα,7α,7aβ‐Nepetalactone: Synthesis of New Heterocycles

The 1,3‐dipolar cycloaddition of 4‐chlorobenzonitrile oxide to the unsaturated system of (?)‐(R)‐carvone occurred exclusively at C(8) to give a new isoxazoline derivative. This derivative reacts with NH₂OH to yield a new heterocycle, observed for the first time. On the other hand, the addition of 4‐chlorobenzonitrile oxide to the unsaturated lactone (?)‐4aα,7α,7aβ‐nepetalactone gave, in a good yield, also a new heterocycle, again obtained for the first time. The terpenoid (?)‐(R)‐carvone and iridoid (?)‐4aα,7α,7aβ‐nepetalactone were isolated from Moroccan species Mentha viridis (L.) and Nepeta tuberosa (L.), respectively. The new heterocycles obtained were identified by combination of chromatographic and spectroscopic methods.     

H2 Convergence of Solutions of a Biharmonic Problem on a Truncated Convex Sector Near the Angle π

We consider a biharmonic problem Δ²u_ω = f_ω with Navier type boundary conditions u_ω = Δu_ω = 0, on a family of truncated sectors Ω_ω in ?² of radius r, 0 < r < 1 and opening angle ω, ω ∈ (2π/3, π] when ω is close to π. The family of right-hand sides (f_ω)_{ω∈(2π/3, π]} is assumed to depend smoothly on ω in L²(Ω_ω). The main result is that u_ω converges to u_π when ω → π with respect to the H²-norm. We can also show that the H²-topology is optimal for such a convergence result.

     

On shortest cocycle covers of graphs

A cocycle (resp. cycle) cover of a graph G is a family C of cocycles (resp. cycles) of G such that each edge of G belongs to at least one member of C. The length of C is the sum of the cardinalities of its members. While it is known (see [5, 6]) that every bridgeless graph G = (V, E) has a cycle cover of length not greater than $\text{5}\text{3}\text{|E|}$, it is shown that there exists no α < 2 such that every loopless graph G = (V, E) has a cocycle cover with length not greater than α |E|. To do this, cocycle covers of minimal length are determined for the complete graphs, thus solving a problem stated at the end of [6].     

A damped simple pendulum of constant amplitude

A simple pendulum acted on by gravity and subjected to a resistance proportional to the velocity of the bob is considered. If the length of the string and the mass of the bob are held constant, the amplitude of the bob decreases gradually because of the damping. We want to keep the maximum swing of the bob constant for all time; this we achieve by varying the length of the string, the mass of the bob or both. The key to the solution of our problem is a second-order nonlinear differential equation having arbitrary nonlinearity and an arbitrary coefficient function, for which we give the exact integral. We also give an application of this differential equation to a boundary-value problem for a nonlinear generalization of a hypergeometric equation.     

Approximation of the semigroup generated by the Hamiltonian of Reggeon field theory in Bargmann space

The Reggeon field theory is governed by a non-self adjoint operator constructed as a polynomial in A, A^*, the standard Bose annihilation and creation operators. In zero transverse dimension, this Hamiltonian acting in Bargmann space is defined by

Hλ^′,μ=λ^′A*2A²+μA^*A+iλA^*(A^*+A)A,     

Circuits with totally-fluctuating reactive elements

Summary Considered here first is a circuit consisting of resistanceR, inductanceL, capacitanceK, in series with a periodically variable capacitanceC(1 + cos t), with maximum value 2C and minimum value zero (i.e. open circuit). The exact solution of the Hill-type differential equation for the charge on the condensers is shown to be expressible in terms of associated Legendre functions of general degree and order. However, considerable analytical simplification is effected by appropriate choice of the value of capacitanceK, for then the solution (likewise exact) is in terms of more elementary functions. It is found that the value of the angular frequency , in relation to the circuit parameters, influences the character of the solution, which varies considerably with . Secondly, a lossless circuit consisting of a variable inductanceM(1+cos t), shunted by a fixed inductanceL and a capacitanceC, is considered. As before, appropriate choice ofL simplifies the solution functions. Actually, the circulating charge in the variable-inductance case has the same mathematical expression as that for the current in the variable-capacitance case.     

Determination of the Heat of Adsorption and Desorption of a Volatile Organic Compound Under Dynamic Conditions Using Fourier‐Transform Infrared Spectroscopy

Quantitative Fourier‐transform infrared spectroscopic analysis was used for the determination of adsorption capacity of a model volatile organic compound (VOC) under dynamic conditions. The analytical method used also offers the possibility of distinguishing between reversible and irreversible adsorption as well as further detection of adsorbed VOC transformation. The obtained adsorbed amounts have been used for the determination of the heat of adsorption and the activation energy of desorption using, respectively, isosteric and temperature programmed desorption methods. The approach has been applied to explore the potential use of local clay as an adsorbent material for VOC pollutants.     

Sorption/desorption study of strontium on Ain Oussera soils around the Es-Salam reactor facility

Four types of undisturbed soils around the Es-Salam reactor (Algeria) were used to evaluate the sorption behavior of strontium. The batch study was carried out under different experimental conditions. The kinetics were well fited by pseudosecond order model. Soils’s activation energies were 12.37, 14.76, 15.5 and 16.17 kJ mol⁻¹, corresponding to ion-exchange-type sorption. Sorption was exothermic (ΔH° < 0), spontaneous (ΔG° < 0) and favorable at low temperature. Competing cations, particularly Ca²⁺ reduce the Sr adsorption. Desorption reaction showed a higher value of Sr in the easily extractible phase indicating a relative availability of the element.