Strengthening the Connection between Science,Society and Environment to Develop Future French and European Bioeconomies: Cutting-Edge Research of VAALBIO Team at UCCS

The development of the future French and European bioeconomies will involve developing new green chemical processes in which catalytic transformations are key. The VAALBIO team (valorization of alkanes and biomass) of the UCCS laboratory (Unité de Catalyse et Chimie du Solide) are working on various catalytic processes, either developing new catalysts and/or designing the whole catalytic processes. Our research is focused on both the fundamental and applied aspects of the processes. Through this review paper, we demonstrate the main topics developed by our team focusing mostly on oxygen- and hydrogen-related processes as well as on green hydrogen production and hybrid catalysis. The social impacts of the bioeconomy are also discussed applying the concept of the institutional compass.     

On some recent proposals for testing macrorealism versus quantum mechanics

In order to evaluate its relevance, we reconsider critically the recent proposal by Leggett and Garg to test macrorealism against quantum mechanics by resorting to experiments involving noninvasive measurement processes on a SQUID. Our conclusion is that, in spite of the fact that the proposed experiment would neither constitute a test of macrorealism nor a test of macrocontextuality, a simplified form of it represents a (presumably) feasible experiment permitting a direct test of macroscopic quantum coherence. We also analyze the proposal from the point of view of the recent attempts to build up model theories allowing to take, within a purely quantum framework, a macrorealistic position about natural phenomena, i.e., the socalled dynamical reduction models and we stress that the proposed experiment has no relevance for the dynamical reduction program, as developed so far. However consideration of the SQUID system allows one to test other possible dynamical mechanisms leading to the objectification of macroproperties which could, in principle, be operative. We also briefly sketch experimental procedures to be followed to get all relevant information concerning macrocoherence.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Boundary blow-up for differential equations with indefinite weight

We obtain results of existence and multiplicity of solutions for the second-order equation x″+q(t)g(x)=0, with x(t) defined for all t∈]0,1[ and such that x(t)→+∞ as t→0⁺ and t→1⁻. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0,1].     

Permanence and Positive Periodic Solutions for Kolmogorov Competing Species Systems

We prove the existence of periodic solutions in a compact attractor of (R⁺)ⁿ for the Kolmogorov system x′_i = x_if_i(t, x₁, …, x_n), i = l, …, n in the competitive case. Extension to differential delay equations are con- sidered too. Applications are given to Lotka-Volterra systems with periodic coefficients.     

Trace Functionals for a Class of Pseudo-Differential Operators in R n

In this paper we define trace functionals on the algebra of pseudo-differential operators with cone-shaped exits to infinity. Furthermore, we improve the Weyl formula on the asymptotic distribution of eigenvalues and make use of it in order to establish inclusion relations between the interpolation normed ideals of compact operators in L ²(R ⁿ ) and the above operator classes.     

Poisson Geometrical Symmetries Associated to Non-Commutative Formal Diffeomorphisms

Let be the group of all formal power series starting with x with coefficients in a field of zero characteristic (with the composition product), and let F [ ] be its function algebra. In [BF] a non-commutative, non-cocommutative graded Hopf algebra was introduced via a direct process of disabelianisation of F [ ], taking the like presentation of the latter as an algebra but dropping the commutativity constraint. In this paper we apply a general method to provide four one-parameter deformations of , which are quantum groups whose semiclassical limits are Poisson geometrical symmetries such as Poisson groups or Lie bialgebras, namely two quantum function algebras and two quantum universal enveloping algebras. In particular the two Poisson groups are extensions of , isomorphic as proalgebraic Poisson varieties but not as proalgebraic groups.Acknowledgements. The author thanks Alessandra Frabetti and Loic Foissy for many helpful discussions.     

Diffraction-limited, 300-kW peak-power pulses from a coiled multimode fiber amplifier

We report a multimode, double-clad, Yb-doped fiber amplifier that produces diffraction-limited, 0.8-ns pulses with energies of 255 muJ and peak powers in excess of 300 kW at a repetition rate of ~8 kHz . Single-transverse-mode operation was obtained by bend-loss-induced mode filtering of the gain fiber.     

Spatial trapping of short pulses in Ti-indiffused LiNbO(3) waveguides

We show numerically and experimentally that spatial trapping can be induced in quadratic media even if the pump pulse's duration is shorter than the group-delay mismatch between fundamental wave and second-harmonic components. The influence of phase mismatch and pulse power on the trapping effect is discussed. Spatial, temporal, and spectral behaviors that accompany self-trapped propagation are highlighted.