Quantification of free auxins in semi-hardwood plant cuttings and microshoots by dispersive liquid–liquid microextraction/microwave derivatization and GC/MS analysis

Several studies have suggested that differences in the natural rooting ability of plant cuttings could be attributed to differences in endogenous auxin levels. Hence, during rooting experiments, it is important to be able to routinely monitor the evolution of endogenous levels of plant hormones. This work reports the development of a new method for the quantification of free auxins in auxin-treated Olea europaea (L.) explants, using dispersive liquid–liquid microextraction (DLLME) and microwave assisted derivatization (MAD) followed by gas chromatography/mass spectrometry (GC/MS) analysis. Linear ranges of 0.5–500 ng mL 1 and 1–500 mg mL 1 were used for the quantification of indole-3-acetic acid (IAA) and indole-3-butyric acid (IBA), respectively. Determined by serial dilutions, the limits of detection (LOD) and quantification (LOQ) were 0.05 ng mL 1 and 0.25 ng mL 1, respectively for both compounds. When using the calibration curve for determination, the LOQ corresponded to 0.5 ng mL 1 (IAA) and 0.5 mg mL 1 (IBA). The proposed method proved to be substantially faster than other alternatives, and allowed free auxin quantification in real samples of semi-hardwood cuttings and microshoots of two olive cultivars. The concentrations found in the analyzed samples are in the range of 0.131–0.342 mg g 1 (IAA) and 20–264 mg g 1 (IBA).

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of-reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced-assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.