A nonalgebraic patchwork

Itenberg and Shustin’s pseudoholomorphic curve patchworking is in principle more flexible than Viro’s original algebraic one. It was natural to wonder if the former method allows one to construct nonalgebraic objects. In this paper we construct the first examples of patchworked real pseudoholomorphic curves in Σ _n whose position with respect to the pencil of lines cannot be realized by any real algebraic curve of the same bidegree. Both authors are very grateful to the Max Planck Institute für Mathematik in Bonn for its financial support and excellent working conditions.     

Dynamics of optically excited electrons in the conducting polymer PEDT:PSS

Femtosecond time-resolved two-photon photoemission spectroscopy is employed to study the dynamics of the non-equilibrium electron distribution in the conducting polymer poly(3,4-ethylene-dioxythiophene): poly-(styrenesulfonate) (PEDT:PSS) film following optical excitation at 2.1 eV. We found that the electron thermalization occurs on a ultrafast timescale of around 60 fs analogous to the relaxation times of optically excited electrons in Au(111).     

Biodegradable polymeric nanoformulation based on the antiprotozoal canthin-6-one

The efficacy of antiprotozoal agents against intracellular infections is very often limited by an almost negligible access to the cellular level where the pathogens are hidden. As a result, high doses of the chemotherapy agents are needed to be administered, but the great incidence of severe adverse drug effects generally leads to pharmacotherapy failure. To enhance the pharmacological effect of the antiprotozoal and antifungal canthin-6-one, loading into biodegradable poly(octylcyanoacrylate) nanoparticles has been considered. The preparation of canthin-6-one nanoformulation (average size ≈170 nm) has been performed by a single-absorption procedure with high drug loading and little burst release as determined by RP-HPLC. Further characterization of this nanoformulation has been carry out by electrophoretic measurements, analysis of the surface thermodynamics of the nanoparticles, and ¹H-NMR analysis. Nanoparticles loaded with canthin-6-one were characterized by a significant hydrophobicity and a great surface electrical charge under physiological conditions. These are two key physicochemical factors determining recognition by the reticuloendothelial system, resulting in a fast intracellular uptake by infected phagocytes. It is expected that this nanoformulation offers potential applications for an efficient canthin-6-one delivery to intracellular infections.     

Simulations of kinetic electrostatic electron nonlinear (KEEN) waves with variable velocity resolution grids and high-order time-splitting

KEEN waves are non-stationary, nonlinear, self-organized asymptotic states in Vlasov plasmas. They lie outside the precepts of linear theory or perturbative analysis, unlike electron plasma waves or ion acoustic waves. Steady state, nonlinear constructs such as BGK modes also do not apply. The range in velocity that is strongly perturbed by KEEN waves depends on the amplitude and duration of the ponderomotive force generated by two crossing laser beams, for instance, used to drive them. Smaller amplitude drives manage to devolve into multiple highly-localized vorticlets, after the drive is turned off, and may eventually succeed to coalesce into KEEN waves. Fragmentation once the drive stops, and potential eventual remerger, is a hallmark of the weakly driven cases. A fully formed (more strongly driven) KEEN wave has one dominant vortical core. But it also involves fine scale complex dynamics due to shedding and merging of smaller vortical structures with the main one. Shedding and merging of vorticlets are involved in either case, but at different rates and with different relative importance. The narrow velocity range in which one must maintain sufficient resolution in the weakly driven cases, challenges fixed velocity grid numerical schemes. What is needed is the capability of resolving locally in velocity while maintaining a coarse grid outside the highly perturbed region of phase space. We here report on a new Semi-Lagrangian Vlasov-Poisson solver based on conservative non-uniform cubic splines in velocity that tackles this problem head on. An additional feature of our approach is the use of a new high-order time-splitting scheme which allows much longer simulations per computational effort. This is needed for low amplitude runs. There, global coherent structures take a long time to set up, such as KEEN waves, if they do so at all. The new code’s performance is compared to uniform grid simulations and the advantages are quantified. The birth pains associated with weakly driven KEEN waves are captured in these simulations. Canonical KEEN waves with ample drive are also treated using these advanced techniques. They will allow the efficient simulation of KEEN waves in multiple dimensions, which will be tackled next, as well as generalizations to Vlasov-Maxwell codes. These are essential for pursuing the impact of KEEN waves in high energy density plasmas and in inertial confinement fusion applications. More generally, one needs a fully-adaptive grid-in-phase-space method which could handle all small vorticlet dynamics whether pealing off or remerging. Such fully adaptive grids would have to be computed sparsely in order to be viable. This two-velocity grid method is a concrete and fruitful step in that direction.     

Comprehensive combinatory standard correction: a calibration method for handling instrumental drifts of gas chromatography-mass spectrometry systems

The current work describes a new method, the comprehensive combinatory standard correction (CCSC), for the correction of instrumental signal drifts in GC-MS systems. The method consists in analyzing together with the products of interest a mixture of n selected internal standards, and in normalizing the peak area of each analyte by the sum of standard areas and then, select among the summation operator sigma(p = 1)(n)C(n)p possible sums, the sum that enables the best product discrimination. The CCSC method was compared with classical techniques of data pre-processing like internal normalization (IN) or single standard correction (SSC) on their ability to correct raw data from the main drifts occurring in a dynamic headspace-gas chromatography-mass spectrometry system. Three edible oils with closely similar compositions in volatile compounds were analysed using a device which performance was modulated by using new or used dynamic headspace traps and GC-columns, and by modifying the tuning of the mass spectrometer. According to one-way ANOVA, the CCSC method increased the number of analytes discriminating the products (31 after CCSC versus 25 with raw data or after IN and 26 after SSC). Moreover, CCSC enabled a satisfactory discrimination of the products irrespective of the drifts. In a factorial discriminant analysis, 100% of the samples (n = 121) were well-classified after CCSC versus 45% for raw data, 90 and 93%, respectively after IN and SSC.     

Spontaneous Biomimetic Formation of (±)‐Dictazole B under Irradiation with Artificial Sunlight

Guided by biosynthetic considerations, the total synthesis of dictazole B is reported for the first time. Experimental evidence for an easy access to challenging cyclobutane alkaloids of marine origin, which are often postulated to be biosynthetic precursors of more complex structures, is provided.     

Dynamic uniaxial extension of elastomers at constant true strain rate

Elastomers are widely used for damping components in various industrial contexts because of their remarkable dissipative properties: they can bear severe mechanical loading conditions, i.e., high strain rates and large strains. Depending on the strain rate, the mechanical response of these materials can vary from purely rubber-like to glassy. In the intermediate strain rate range (1-100/s), uniaxial extension experiments are classically conducted at constant nominal strain rate. We present here a new experimental methodology to investigate the mechanical response of soft materials at constant true strain rate in the intermediate strain rate range. For this purpose, the displacement imposed on the specimen by the tensile machine is an exponential function of time. A high speed servo-hydraulic machine is used to perform experiments at strain rates ranging from 0.01 to 100/s. A specific specimen is designed in order to achieve a uniform strain field (and thus a uniform stress field). Furthermore, an instrumented aluminium bar is used to measure the applied force; which overcomes the difficulties due to dynamic effects. Simultaneously, a high speed camera enables the measurement of strain in the sample using a point tracking technique. Finally, the method is applied to determine the stress-strain curve of an elastomer for both loading and unloading responses up to a stretch ratio λ = 2.5; the influence of the true strain rate on both stiffness and dissipation of the material is then discussed.