Pierre Turq,an inspirational scientist in charge and at interfaces

Pierre Turq has made decisive contributions to the theory and to the multiscale simulation of charged systems, such as molten salts, electrolyte solutions and colloidal suspensions, in the bulk, at interfaces and under confinement. His research line focussed on dynamical properties and was characterised by constant efforts to connect his theoretical work to both experiments and practical applications. In this article, his colleagues and former students pay a tribute to his past and current research interests by illustrating some recent developments accomplished in his laboratory.     

On well-posedness for some dispersive perturbations of Burgers' equation

We show that the Cauchy problem for a class of dispersive perturbations of Burgers' equations containing the low dispersion Benjamin–Ono equation

${?}_{t}u?D_x^{\alpha }{?}_{x}u={?}_x(u^2),0<\alpha \le 1,$

is locally well-posed in $H^s(\mathbb{R})$ when $s>s_{\alpha }:=\frac{3}{2}?\frac{5\alpha }{4}$. As a consequence, we obtain global well-posedness in the energy space $H^{\frac{\alpha }{2}}(\mathbb{R})$ as soon as $\frac{\alpha }{2}>s_{\alpha }$, i.e. $\alpha >\frac{6}{7}$.     

Optical sectioning in wide-field microscopy obtained by dynamic structured light illumination and detection based on a smart pixel detector array

Optical sectioning in wide-field microscopy is achieved by illumination of the object with a continuously moving single-spatial-frequency pattern and detecting the image with a smart pixel detector array. This detector performs an on-chip electronic signal processing that extracts the optically sectioned image. The optically sectioned image is directly observed in real time without any additional postprocessing.     

Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms

We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant α. Our result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron pairs. We also prove that the density of any minimizer is an L ¹ function and compute the effective charge of the system, recovering the usual renormalization of charge: the physical coupling constant is related to α by the formula α_phys ≃ α(1 + 2α/(3π) log Λ)⁻¹, where Λ is the ultraviolet cut-off. We eventually prove an estimate on the highest number of electrons which can be bound by a nucleus of charge Z. In the nonrelativistic limit, we obtain that this number is  ≤  2Z, recovering a result of Lieb. This work is based on a series of papers by Hainzl, Lewin, Séré and Solovej on the mean-field approximation of no-photon QED.     

Practical use of variational principles for modeling water waves

This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a ‘relaxed’ variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is particularly suitable for the construction of approximate water wave models, since it allows more freedom while preserving a variational structure. The advantages of this relaxed formulation are illustrated with various examples in shallow and deep waters, as well as arbitrary depths. Using subordinate constraints (e.g., irrotationality or free surface impermeability) in various combinations, several model equations are derived, some being well-known, other being new. The models obtained are studied analytically and exact traveling wave solutions are constructed when possible.     

Polyphenols from Dichrostachys cinerea Fruits Anti-Inflammatory,Analgesic, and Antioxidant Capacity in Freund’s Adjuvant-Induced Arthritic Rat Model

Dichrostachys cinerea (L.) Wigth & Arn. (DC) is widely used in traditional medicine against several inflammatory diseases, especially rheumatoid arthritis, because of its antioxidant and anti-inflammatory effects. This study aimed to characterize the polyphenol-rich DC fruit extracts and investigate the analgesic, anti-inflammatory, and antioxidant effects in a rat inflammation model induced by complete Freund’s adjuvant (CFA). Water and ethanolic extracts were characterized using liquid chromatography coupled with mass spectrometry (LC-MS), Fourier-transform infrared (FTIR) spectroscopy, and gas chromatography coupled with mass spectrometry (GC-MS). The polyphenol-rich extracts were administered in three different concentrations for 30 days. Pain threshold, thermal hyperalgesia, edema, and serum biomarkers specific to inflammatory processes or oxidative stress were evaluated. Both extracts were rich in polyphenolic compounds, mainly flavan-3-ols, proanthocyanidins, and flavone glycosides, which had important in vitro antioxidant capacity. DC fruit extracts administration had the maximum antinociceptive and anti-inflammatory effects after one day since the CFA injection and showed promising results for long-term use as well. The measurement of pro-inflammatory cytokines, cortisol, and oxidative stress parameters showed that DC extracts significantly reduced these parameters, being dose and extract-type dependent. These results showed potential anti-inflammatory, analgesic, and antioxidative properties and revealed the necessity of using a standardized polyphenolic DC extract to avoid result variability.     

Comprehensive two-dimensional gas chromatography for enhanced analysis of naphthas: new column combination involving permethylated cyclodextrin in the second dimension

A new column association using comprehensive two-dimensional gas chromatography for the detailed molecular analysis of hydrocarbon mixtures is reported in this paper. In order to compare the impact of two different secondary columns, a novel column combination relying on a GC x 2GC system was used. This system is based on a non-polar first column (PONA) combined with both a permethylated beta-cyclodextrin (beta-Dex 120) stationary phase and a polysilphenylensiloxane (BPX 50) in the second dimension. Compared to BPX 50 stationary phase, the implementation of beta-cyclodextrin columns as the second dimension was found to improve the resolution between paraffins and naphthenes in the naphtha range but not in the middle distillate range. Attempts to improve the results and to understand the interaction mechanism remained unsuccessful. Therefore, the benefits of the beta-Dex 120-column are only demonstrated on heavy naphtha cut for the quantitation of hydrocarbons.     

A microfluidic device based on droplet storage for screening solubility diagrams

This work describes a new microfluidic device developed for the rapid screening of solubility diagrams. In several parallel channels, hundreds of nanolitre volume droplets of a given solution are first stored with a gradual variation in the solute concentration. Then, the application of a temperature gradient along these channels enables us to read directly and quantitatively phase diagrams, concentration vs. temperature. We show, using a solution of adipic acid, that we can measure ten points of the solubility curve in less than 1 hr and with only 250 microL of solution.