Stratification of the Radiation Field Inside a Photobioreactor During Microalgae Growth

Light availability is a main issue in autotrophic growth of photosynthetic microorganisms. The change of the suspended cells concentration and that of their chlorophylls content during microalgal growth alters the optical properties of the aqueous suspension. This brings about changes in the properties of the radiation field inside the reactor. In this work, we have computed the evolution in time of the local volumetric rate of absorption of photons inside a photobioreactor by means of a Monte Carlo simulation algorithm previously developed. From this study, we have computed two operational variables that are useful tools for the analysis, performance comparison, optimization and scaling up of photobioreactors: the average rate of photon absorption and the volumetric distribution function of photons absorption rates. Based on these two variables, it is possible to systematically quantify the degree of stratification of the culture medium, which is a decisive aspect that hampers the reactor efficiency regarding the energy usage for biomass production.     

A Simple Strategy to Improve the Accuracy of the Injection Step in Batch Injection Analysis Systems with Amperometric Detection

In this study, we describe for the first time the application of an internal standard method to compensate for random errors associated with the injection procedure in batch injection analysis (BIA) systems with multiple pulse amperometric detection. A sequence of potential pulses was selected in such a way that the internal standard (IS) compound was detected individually at one potential pulse and both the IS and analyte, were detected at another potential pulse. The current ratio (I_IS+analyte/I_IS) was used in the construction of the calibration curve and then to compensate for random errors. The use of disposable syringes or manual pipettes in BIA systems increases the robustness of the method and dispenses with skilled operators.     

The first metals in Mendeleiev’s table: further arguments to place He above Ne and not above Be

In a recent paper in this Journal, one of us argued against placing He above Be in Mendeleiev’s system of the elements. In it the goal was to dispute the notion that in Mendeleiev’s system of the elements the location of He should in fact lie above Be, which has a very similar electronic configuration, rather than above the noble gas column. That paper was based on rather old, Hartree–Fock limit studies on the strikingly limited non-additive contributions in the He₃ and He₄ systems in contrast with the much larger non-additivity obtained for the Be₃, Be₄ and Be₅ oligomers. In a recent benchmark multireference Averaged Quadratic Coupled Cluster results on Be₂ and Be₃ we showed that the delocalized non-additive contribution comprises 94 % of the binding energy of Be₃. Here we use this and other pertinent information (drawn from the same paper) to conclude that He may not be associated with Be in Mendeleiev’s Table, despite their quite similar spectroscopic ground states. Furthermore, we use the new results to show that the large non-additivity implies that less than 2 % of the Be₃ binding is located in each Be pair contained within the Be trimer. The rest of the interaction energy is necessarily delocalized over all three Be atoms. This might actually announce the bulk properties (i.e. “the electron gas”) that in solid-state physics explain the large electric and heat conduction for the solid Be metal. Thus, in the case of beryllium the metallic characteristics are already evident in Be₃, a far cry from the monoatomic helium gas.     

A-posteriori KAM theory with optimal estimates for partially integrable systems

In this paper we present a-posteriori KAM results for existence of d-dimensional isotropic invariant tori for n-DOF Hamiltonian systems with additional $n?d$ independent first integrals in involution. We carry out a covariant formulation that does not require the use of action-angle variables nor symplectic reduction techniques. The main advantage is that we overcome the curse of dimensionality avoiding the practical shortcomings produced by the use of reduced coordinates, which may cause difficulties and underperformance when quantifying the hypotheses of the KAM theorem in such reduced coordinates. The results include ordinary and (generalized) iso-energetic KAM theorems. The approach is suitable to perform numerical computations and computer assisted proofs.     

Aminomethyl Transfer (Mannich) Reactions Between an O-Triethylsilylated Hemiaminal and Anilines,RnC6H5−nNH2 Leading to New Diamines,Triamines, Imines,or 1,3,5-Triazines Dependent upon Substituent R

The reactions of the Mannich reagent Et₃SiOCH₂NMe₂ ( 1 ) with a variety of anilines (mono-substituted RC₆H₄NH₂, R=H, 4-CN, 4-NO₂, 4-Ph, 4-Me, 4-MeO, 4-Me₂N; di-substituted R₂C₆H₃NH₂, R₂=3,5-(CH₃)₂, 3,5-(CF₃)₂; tri-substituted R₃C₆H₂NH₂, R₃=3,5-Me₂-4-Br and a “super bulky” aniline (Ar*NH₂) [Ar*=2,6-bis(diphenylmethyl)-4-tert-butylphenyl]) led to the formation of a range of products dependent upon the substituent. With electron-withdrawing substituents, previously unknown diamines, RC₆H₄NH(CH₂NMe₂) [R=CN ( 2 a ), NO₂ ( 2 b )] and R₂C₆H₃NH(CH₂NMe₂) [R₂=3,5-(CF₃)₂ ( 2 c) ] were formed. Further reaction of 2 a , b , c with 1 yielded the corresponding triamines RC₆H₄N(CH₂NMe₂)₂ (R=CN ( 3 a ), NO₂ ( 3 b ) and R₂C₆H₃N(CH₂NMe₂)₂, R₂=3,5-(CF₃)₂ ( 3 c ). The new polyamines were characterized by NMR spectroscopy, and for 2 a , 2 c _, and 3 c , by single crystal XRD. In the case of electron-donating groups, R=4-OMe, 4-NMe₂, 4-Me, 3,5-Me₂, 3,5-Me₂-4-Br, and for R=4-Ph, the reactions with 1 immediately led to the formation of the related 1,3,5-triazines, R=4-MeO ( 5 a ), 4-Me₂N ( 5 b ), 4-Me ( 5 c ), 3,5-Me₂ ( 5 d ), 3,5-Me₂-4-Br ( 5 e ), 4-Ph ( 5 f ), 4-Cl ( 5 g ). The “super bulky” aniline rapidly produced a single product, namely the corresponding imine Ar*N=CH₂ ( 4 ) which was also characterized by single crystal XRD. Imine 4 is both thermally and oxidatively stable. All reactions are very fast, thus based upon the presence of Si we are tempted to denote the reactions of 1 as examples of “Silick” chemistry.