Formal Verification of Numerical Programs: From C Annotated Programs to Mechanical Proofs

Numerical programs may require a high level of guarantee. This can be achieved by applying formal methods, such as machine-checked proofs. But these tools handle mathematical theorems while we are interested in C code, in which numerical computations are performed using floating-point arithmetic, whereas proof tools typically handle exact real arithmetic. To achieve this high level of confidence on C programs, we use a chain of tools: Frama-C, its Jessie plugin, Why and provers among Coq, Gappa, Alt-Ergo, CVC3 and Z3. This approach requires the C program to be annotated: each function must be precisely specified, and we prove the correctness of the program by proving both that it meets its specifications and that no runtime error may occur. The purpose of this paper is to illustrate, on various examples, the features of this approach.     

Linear viscoelastic properties of emulsions and suspensions with thermodynamic and hydrodynamic interactions

We present a new approach to describe the rheological properties of dispersions with non-hydrodynamic interactions (steric, electrostatic and Van der Waals interactions) in the linear viscoelastic domain. Our model is based on the calculation of additional stresses resulting from interaction potentials between spheres and Brownian motion. We start from the statistical mechanical approaches which have been developed by Batchelor and Green and later Lionberger and Russel, to model the viscoelastic properties of emulsions and suspensions. We have extended their calculations to the more general case of viscoelastic deformable inclusions in a viscoelastic matrix. Our contribution lies in the computation of the hydrodynamic functions involved in the term describing interaction stresses. This computation is based on Palierne's results on the deformation field around a viscoelastic inclusion embedded in a viscoelastic matrix. We have also rewritten the conservation equation in the case of interest, over the whole frequency domain. We finally express the complex shear modulus of the dispersion as the sum of two terms : Palierne's complex shear modulus gives the purely hydrodynamic contribution; the interaction contribution depends on both the hydrodynamic properties and the interaction potential.     

A Gibbs variational principle in space-time for infinite-dimensional diffusions

 We show that the set of stationary weak solutions for a class of infinite dimensional stochastic differential equations coincides with the set of shift invariant, space-time Gibbs fields for a certain potential. The key step consists in proving the Gibbs variational principle for space-time Gibbs fields. Received: 20 May 1999 / Revised version: 14 May 2001 / Published online: 11 December 2001     

High-efficiency single-mode Raman generation in a liquid-filled photonic bandgap fiber

Single-spatial-mode Raman generation in an ethanol-filled photonic bandgap fiber is demonstrated. Due to the limited bandwidth of the fiber, the generation is limited to the first Stokes order only, allowing high generated power without any visible decrease of the conversion efficiency. The realization of these two key properties opens the way to the realization of optimized compact nonlinear wavelength converters that will accommodate a large variety of usable liquids.     

Ion tree‐based structure elucidation of acetophenone dimers (AtA) from Acronychia pedunculata and their identification in extracts by liquid chromatography electrospray ionization LTQ‐Orbitrap mass spectrometry

Acronychia‐type acetophenones (AtA) is a chemical group of compounds of important structural and biological interest, abundant in Acronychia species. However, there are no data available for their characterization using mass spectrometry. In the current work, AtA have been investigated by multistage high resolution mass spectrometry and both electrospray ionization and atmospheric pressure chemical ionization, in positive and negative mode, were utilized for their structure elucidation and identification. The analysis of AtA using a linear ion trap‐Orbitrap analyzer enabled the structural determination of key fragment ions and cleavages, which can be used for the structural characterization thereof. A systematic nomenclature based on protonated and deprotonated fragment ions under collision‐induced dissociation conditions and decision trees for the structural determination of AtA are proposed. Furthermore, taking advantage of the characteristic fragmentation patterns, a selective Ultra High Performance Liquid Chromatography Electrospray Ionization multistage Mass Spectrometry (UHPLC‐ESI(‐)‐MSⁿ) method was developed and successfully applied for the dereplication of known AtA and the identification of potentially new ones in Acronychia extracts. Despite the structure similarity and the presence of isomers, accurate characterization of known and unknown AtA derivatives was possible. Copyright © 2015 John Wiley & Sons, Ltd.     

Fabrication of solid‐state nanopores and its perspectives

Nanofluidics is becoming an extensively developing technique in the field of bioanalytical chemistry. Nanoscale hole embed in an insulating membrane is employed in a vast variety of sensing platforms and applications. Although, biological nanopores have several attractive characteristics, in this paper, we focused on the solid‐state nanopores due to their advantages as high stability, possibility of diameter control, and ease of surface functionalizing. A detection method, based on the translocation of analyzed molecules through nanochannels under applied voltage bias and resistive pulse sensing, is well established. Nevertheless, it seems that the new detection methods like measuring of transverse electron tunneling using nanogap electrodes or optical detection can offer significant additional advantages. The aim of this review is not to cite all related articles, but highlight the steps, which in our opinion, meant important progresses in solid‐state nanopore analysis.     

Surface and Structural Investigation of a MnOx Birnessite‐Type Water Oxidation Catalyst Formed under Photocatalytic Conditions

Catalytically active MnO_x species have been reported to form in situ from various Mn‐complexes during electrocatalytic and solution‐based water oxidation when employing cerium(IV) ammonium ammonium nitrate (CAN) oxidant as a sacrificial reagent. The full structural characterization of these oxides may be complicated by the presence of support material and lack of a pure bulk phase. For the first time, we show that highly active MnO_x catalysts form without supports in situ under photocatalytic conditions. Our most active ⁴MnO_x catalyst (～0.84 mmol O₂ mol Mn^?1 s^?1) forms from a Mn₄O₄ bearing a metal–organic framework. ⁴MnO_x is characterized by pair distribution function analysis (PDF), Raman spectroscopy, and HR‐TEM as a disordered, layered Mn‐oxide with high surface area (216 m²g^?1) and small regions of crystallinity and layer flexibility. In contrast, the ^SMnO_x formed from Mn²⁺ salt gives an amorphous species of lower surface area (80 m²g^?1) and lower activity (～0.15 mmol O₂ mol Mn^?1 s^?1). We compare these catalysts to crystalline hexagonal birnessite, which activates under the same conditions. Full deconvolution of the XPS Mn2p_3/2 core levels detects enriched Mn³⁺ and Mn²⁺ content on the surfaces, which indicates possible disproportionation/comproportionation surface equilibria.     

Towards new molecular photocatalysts for CO2 reduction: photo-induced electron transfer versus CO dissociation within [Os(NN)(CO)2Cl2] Complexes

Optical excitation in the visible region of trans-(Cl)-[Os(bpy)(CO)(2)Cl(2)] (bpy=2,2'-bipyridine; C1) and trans-(Cl)-[Os(dmbpy)(CO)(2)Cl(2)] (dmbpy=4,4'-dimethyl 2,2'-bipyridine; C2) is known to induce the common CO dissociation reaction. However, the quantum yield of the reactions is less than 0.15, although C1 and C2 display pronounced photoluminescence in the visible region at room temperature with a lifetime of few tens of nanoseconds. Taking into account the characteristics of their emitting state, we have investigated the capability of C1 and C2 to act as a photosensitiser in redox reactions in different solvents (MeCN, PrCN and DMF). The efficient oxidation and reduction of both complexes under continuous irradiation in the presence of a sacrificial electron acceptor or donor is reported here. The photo-induced transformations and the nature of the resulting compounds were analysed by UV/Vis and IR spectroscopies and cyclic voltammetry. Photo-induced oxidation of C1 and C2 leads to the corresponding monocarbonyl oxidised species, whereas photo-induced reduction under argon leads mainly to the formation of the corresponding Os-bonded molecular wires P1 and P2 after exchange of two electrons associated with the loss of two chloro ligands. The chemical yield of the latter reaction (around 65%) becomes quantitative by adding [Ru(bpy)(3)](2+) as an external redox photosensitiser. This behaviour has been used to photocatalyse the two electron, two proton conversion of CO(2) to CO. Turnover numbers (TON) of 11.5 and 19.5 have been obtained respectively for C1 and C2 after 4.5 h of irradiation under CO(2) in DMF with triethanolamine as the electron donor. TON can be slightly increased by adding [Ru(bpy)(3)](2+) to the solution.