A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement

We propose an alternative crack propagation algo- rithm which effectively circumvents the variable transfer procedure adopted with classical mesh adaptation algo- rithms. The present alternative consists of two stages: a mesh-creation stage where a local damage model is employed with the objective of defining a crack-conforming mesh and a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation which is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered scheme for standard equilibrium and screened Poisson equa- tions is used in this second stage. Element subdivision is based on edge split operations using a constitutive quantity (damage). To assess the robustness and accuracy of this algo- rithm, we use five quasi-brittle benchmarks, all successfully solved.

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).