Lie-Poincaré transformations and a reduction criterion in Landau theory

In the Landau theory of phase transitions one considers an effective potential Φ whose symmetry group G and degree d depend on the system under consideration; generally speaking, Φ is the most general G-invariant polynomial of degree d. When such a Φ turns out to be too complicate for a direct analysis, it is essential to be able to drop unessential terms, i.e., to apply a simplifying criterion. Criteria based on singularity theory exist and have a rigorous foundation, but are often very difficult to apply in practice. Here we consider a simplifying criterion (as stated by Gufan) and rigorously justify it on the basis of classical Lie-Poincaré theory as far as one deals with fixed values of the control parameter(s) in the Landau potential; when one considers a range of values, in particular near a phase transition, the criterion has to be accordingly partially modified, as we discuss. We consider some specific cases of group G as examples, and study in detail the application to the Sergienko-Gufan-Urazhdin model for highly piezoelectric perovskites.     

Excess noise generation during spectral broadening in a microstructured fiber

We observe that nanojoule femtosecond pulses that are spectrally broadened in a microstructured fiber acquire excess noise. The excess noise is manifested as an increase in the noise floor of the rf spectrum of the photocurrent from a photodetector illuminated by the pulse train from the laser oscillator. Measurements are made of the intensity dependence of the excess noise for both 100 fs and sub-10 fs pulses. The excess noise is very strong for 100 fs pulses, but barely measurable for sub-10 fs pulses. A rigorous quantum treatment of the nonlinear propagation of ultrashort pulses predicts that, for a fixed generated bandwidth, the amount of excess noise decreases with pulse duration, in agreement with the experimental results.     

Determination of manganese in brain samples by slurry sampling graphite furnace atomic absorption spectrometry

A simple procedure for the determination of manganese in different sections of human brain samples by graphite furnace atomic absorption spectrometry has been developed. Brain sections included cerebellum, hypothalamus, frontal cortex, vermix and encephalic trunk. Two sample preparation procedures were evaluated, namely, slurry sampling and microwave-assisted acid digestion. Brain slurries (2% w/v) could be prepared in distilled, de-ionized water, with good stability for up to 30 min. Brain samples were also digested in a domestic microwave oven using 5 ml of concentrated HNO₃. A mixed palladium+magnesium nitrate chemical modifier was used for thermal stabilization of the analyte in the electrothermal atomizer up to pyrolysis temperatures of 1300 °C, irrespective of the matrix. Quantitation of manganese was conducted in both cases by means of aqueous standards calibration. The detection limits were 0.3 and 0.4 ng ml⁻¹ for the slurry and the digested samples, respectively. The accuracy of the procedure was checked by comparing the results obtained in the analysis of slurries and digested brain samples, and by analysis of the NIST Bovine Liver standard reference material (SRM 1577a). The ease of slurry preparation, together with the conventional set of analytical and instrumental conditions selected for the determination of manganese make such methodology suitable for routine clinical applications.     

Asymmetric synthesis of 4,4-disubstituted-2-imidazoli-dinones: potent NK1 antagonists

[structure: see text] A highly efficient and practical synthesis of 4,4-Disubstituted-2-Imidazolidinones utilizing a "self-reproduction of the center of chirality" strategy is described.     

Glycidol syntheses and valorizations: Boosting the glycerol biorefinery

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Breaking of permutation symmetry and diagonal group action: Nielsen model and the standard model as low-energy limit

We point out that, on the basis of a theorem by L. Michel, every model based on the symmetryG ... G has a generic low-energy limit the breaking to diagonal action, i.e., toG. This applies in particular to the proposal by Nielsen to consider such a model withG the standard model group.