Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes

We review various generalizations of the notion of Lie algebras, in particular those appearing in the recently proposed Bagger-Lambert-Gustavsson model, and study their interrelations. We find that Filippov's n-Lie algebras are a special case of strong homotopy Lie algebras. Furthermore, we define a class of homotopy Maurer-Cartan equations, which contains both the Nahm and the Basu-Harvey equations as special cases. Finally, we show how the super Yang-Mills equations describing a Dp-brane and the Bagger-Lambert-Gustavsson equations supposedly describing M2-branes can be rewritten as homotopy Maurer-Cartan equations, as well.Comment: 1+28 page

On the Time-Evolution of Resonant Triads in Rotational Capillary-Gravity Water Waves

We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume a constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero we recover the well known integrable three-wave system

Dissolution and phosphate-induced transformation of ZnO nanoparticles in synthetic saliva probed by AGNES without previous solid-liquid separation. Comparison with UF-ICP-MS

The variation over time of free Zn2+ ion concentration in stirred dispersions of ZnO nanoparticles (ZnO NPs) prepared in synthetic saliva at pH 6.80 and 37 degrees C was followed in situ (without solid liquid separation step) with the electroanalytical technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping). Under these conditions, ZnO NPs are chemically unstable due to their reaction with phosphates. The initial stage of transformation (around 5-10 h) involves the formation of a metastable solid (presumably ZnHPO4), which later evolves into the more stable hopeite phase. The overall decay rate of ZnO NPs is significantly reduced in comparison with phosphate-free background solutions of the same ionic strength and pH. The effective equilibrium solubilities of ZnO (0.29-0.47 mg.L-1), as well as conditional excess-ligand stability constants and fractional distributions of soluble Zn species, were determined in the absence and presence of organic components. The results were compared with the conventional ultrafiltration and inductively coupled plasma-mass spectrometry (UF-ICP-MS) methodology. AGNES proves to be advantageous in terms of speed, reproducibility, and access to speciation information. KeywordsThis work was supported by the Spanish Ministry MINECOunder Grant No. CTM2016-78798 and European UnionSeventh Framework Programme FP7-NMP.2012.1.3-3 underGrant No. 310584 (NANoREG). FQ gratefully acknowledgesa grant from AGAUR

THE LOAD-CARRYING CAPACITY FOR SOME TUBULAR REACTORS AND STRESS CONCENTRATION

The purpose of this paper was to evaluate the state of stress and the stress concentration in the main critical junctions of a tubular reactor. Additional two numerical analyses were developed to identify the critical junctions of reactor due to the main loads: temperature gradient and internal pressure. One analysis is based on the extension of classical thin shell theory and the flexibility matrix method and the second on the finite element method (FEM), by the package COSMOS/M Designer II. Comparative experimental study based on recording the strains at selected surface positions, for different values of the reaction loads, was done using strain gauges. The analyses reveal a reasonable accuracy of the results and accurate positioning of the critical junctions. The loads are variable, so that the study may give a primary estimation on the fatigue design and analysis

Dynamics of trace metal sorption by an ion-exchange chelating resin described by a mixed intraparticle/film diffusion transport model. The Cd/Chelex case

The time-evolution of Cd2+ ion sorption by Chelex 100 resin was studied in batch experiments as a function of time, pH, ionic strength, stirring rate, mass of resin and initial metal ion concentration. In the experimental conditions, the amount of resin sites are in excess with respect to the amount of metal ion, leading to extensive depletion of metal in bulk solution when equilibrium is reached. The data were described using a mixed control mass transport model in finite volume conditions (MCM) that includes explicitly both intraparticle and film diffusion steps. Exact numerical computations and a new approximate analytical expression of this model are reported here. MCM successfully predicts the influence of pH and ionic strength on the experimental Cd(II)/Chelex kinetic profiles (which cannot be justified by a pure film diffusion controlled mechanism) with a minimum number of fitting parameters. The overall diffusion coefficient inside the resin was modelled in terms of the Donnan factor and the resin/cation binding stability constant. The values of the latter coefficient as a function of pH and ionic strength were estimated from the Gibbs-Donnan model. Even though MCM is numerically more involved than models exclusively restricted to film or intraparticle diffusion control, it proves to be accurate in a wider range of values of the mass transfer Biot number and solution/resin metal ratios.The authors gratefully acknowledge support for this research from the Spanish Ministry MINECO (Projects CTM2013-48967 and CTM2016-78798) and by the “Comissionat d'Universitats i Recerca de la Generalitat de Catalunya” (2014SGR1132). FQ acknowledges a grant from AGAUR

THEORETICAL AND EXPERIMENTAL STUDIES ON DISKS CENTRIFUGAL SEPARATORS

The paper presents an extension of classical thin shell theory to those with moderate thickness, having simplex order h/R ≤ 0.2 ... 0.33. The application of the flexibility matrix method is studied to realise a computerised analysis of centrifugal disks separators for the influence of the central load Fa induced for assembling the bowl and for the critical area junctions. In the first time, the separator's bowl is divided in structural elements; each of the structural elements is at first considered separately and then the global generalised forces and bending moments are obtained from the displacement compatibility conditions at each element junction. Comparative experimental investigations based on recording surface strains at selected locations of the bowl performed with strain gauges reveal a reasonable agreement. The main features of the method as, (1) reasonable accuracy of the results, (2) reasonable positioning of the critical junctions, (3) low computational cost, give a real possibility in the design work

Affine invariant conditions for the topological distinction of quadratic systems with a critical point of the 4th multiplicity

The affine invariant partition of the set of quadratic systems with one finite singular point of the 4th multiplicity with respect to different topological classes is accomplished. The conditions corresponding to this partition are semi-algebraic, i.e. they are expressed as equalities or inequalities between polynomials