Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.

Dynamical evolution of Saturn's F ring dust particles

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Exploring S-type orbits in the Pluto-Charon binary system

This work generates, through a sample of numerical simulations of the restricted three-body problem, diagrams of semimajor axis and eccentricity which defines stable and unstable zones for particles in S-type orbits around Pluto and Charon. Since we consider initial conditions with 0 <= e <= 0.99, we found several new stable regions. We also identified the nature of each one of these newly found stable regions. They are all associated to families of periodic orbits derived from the planar circular restricted three-body problem. We have shown that a possible eccentricity of the Pluto-Charon system slightly reduces, but does not destroy, any of the stable regions.

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.

In Vitro Evaluation Of Sun Protection Factor And Stability Of Commercial Sunscreens Using Mass Spectrometry.

Sunlight exposure causes several types of injury to humans, especially on the skin; among the most common harmful effects due to ultraviolet (UV) exposure are erythema, pigmentation and lesions in DNA, which may lead to cancer. These long-term effects are minimized with the use of sunscreens, a class of cosmetic products that contains UV filters as the main component in the formulation; such molecules can absorb, reflect or diffuse UV rays, and can be used alone or as a combination to broaden the protection on different wavelengths. Currently, worldwide regulatory agencies define which ingredients and what quantities must be used in each country, and enforce companies to conduct tests that confirm the Sun Protection Factor (SPF) and the UVA (Ultraviolet A) factor. Standard SPF determination tests are currently conducted in vivo, using human subjects. In an industrial mindset, apart from economic and ethical reasons, the introduction of an in vitro method emerges as an interesting alternative by reducing risks associated to UV exposure on tests, as well as providing assertive analytical results. The present work aims to describe a novel methodology for SPF determination directly from sunscreen formulations using the previously described cosmetomics platform and mass spectrometry as the analytical methods of choice.

Effect of the kappa-casein gene polymorphism, breed and seasonality on physicochemical characteristics, composition and stability of bovine milk

The objective of this study was to evaluate the effect of genetic polymorphism of kappa-casein, breed and seasonality on the physicochemical characteristics, composition and stability of milk in commercial dairy herds. A total of 879 milk and blood samples were collected from 603 Holstein and 276 Girolando cows, obtained during rainy and dry seasons. Milk samples were analyzed to determine the physicochemical characteristics, composition and ethanol stability, while blood samples were subjected to polymerase chain reaction to identify the kappa-casein genotype. The frequencies of genotypes AA, AB and BB of k-casein were respectively, 66.83, 31.84 and 1.33% for Holstein, and 71.38, 27.90 and 0.72% for the Girolando cows, respectively. The A allele was more frequent than the B allele, both for Holstein (0.827 and 0.173) and Girolando cows (0.853 and 0.147), respectively. Cows of AB and BB genotypes showed a higher milk fat content compared to the AA genotype. There was an interaction between breed and seasonality on the concentration of milk urea with higher values for Holstein and Girolando cows in the rainy and dry season, respectively. The levels of lactose, total solids, crude protein, true protein, casein and the casein:true protein ratio were higher during the dry season, while during the rainy season, the somatic cell count and milk urea concentration were higher. There was no association between milk stability and k-casein genotypes, but Holstein cows showed higher milk stability than Girolando cows, and milk was more stable during the rainy season than during the dry season.

Obtaining and stability verification of superconducting phases of the Nb-Al and Nb-Sn systems by mechanical alloying and low-temperature heat treatments

The development of Nb(3)Al and Nb(3)Sn superconductors is of great interest for the applied superconductivity area. These intermetallics composites are obtained normally by heat treatment reactions at high temperature. Processes that allow formation of the superconducting phases at lower temperatures (<1000 degrees C), particularly for Nb(3)Al, are of great interest. The present work studies phase formation and stability of Nb(3)Al and Nb(3)Sn superconducting phases using mechanical alloying (high energy ball milling). Our main objective was to form composites near stoichiometry, which could be transformed into the superconducting phases using low-temperature heat treatments. High purity Nb-Sn and Nb-Al powders were mixed to generate the required superconducting phases (Nb-25at.%Sn and Nb-25at.%Al) in an argon atmosphere glove-box. After milling in a Fritsch mill, the samples were compressed in a hydraulic uniaxial press and encapsulated in evacuated quartz tubes for heat treatment. The compressed and heat treated samples were characterized using X-ray diffractometry. Microstructure and chemical analysis were accomplished using scanning electron microscopy and energy dispersive spectrometry. Nb(3)Al XRD peaks were observed after the sintering at 800 degrees C for the sample milled for 30 h. Nb(3)Sn XRD peaks could be observed even before the heat treatment. (C) 2009 Elsevier B.V. All rights reserved.

ADAPTABILITY AND STABILITY OF SOYBEAN GENOTYPES UNDER DIFFERENT TIMES OF SOWING

This study aimed to evaluate the average behavior, the genotype x environment (GxE), adaptability and stability of seven soybean cultivars at three sowing dates in Uberlandia-MG. The tests were conducted at Capim Branco Farm, belonging to the Federal University of Uberlandia. Sowing was held on october 29 (1st season), november 24 (2nd season) and december 17 (3rd season) 2007. The experimental design was a randomized, seven genotypes (UFUS Xavante, UFUS Riqueza, UFUS Guarani, UFUS Milionaria, Msoy 8001, Msoy 8411 and Msoy 8914) with three replications in each of three sowing dates. Means were compared by Tukey test at 5% probability. Analysis of adaptability and phenotypic stability of genotypes was performed using the Eberhart and Russell (1966), Lin and Binns (1988) modified by Carneiro (1998) and centroid (NASCIMENTO et al., 2009). For grain yield, the cultivar UFUS Xavante was classified as specific adaptability to environment and high stability. The other cultivars were classified as being of general adaptability. For oil content, the cultivars Msoy 8914 and UFUS Xavante behaved as high stability and was classified as having high adaptability. For the character content of protein, all cultivars behaved as wide adaptability and low stability.

UV-Derivative Spectrophotometric and Stability-Indicating High-Performance Liquid Chromatographic Methods for Determination of Simvastatin in Tablets

A stability-indicating high-performance liquid chromatographic (HPLC) and a second-order derivative spectrophotometric (UVDS) analytical methods were validated and compared for determination of simvastatin in tablets. The HPLC method was performed with isocratic elution using a C18 column and a mobile phase composed of methanol:acetonitrile:water (60:20:20, v/v/v) at a flow rate of 1.0 ml/min. The detection was made at 239 nm. In UVDS method, methanol and water were used in first dilution and distilled water was used in consecutive dilutions and as background. The second-order derivative signal measurement was taken at 255 nm. Analytical curves showed correlation coefficients > 0.999 for both methods. The quantitation limits (QL) were 2.41 mu g/ml for HPLC and 0.45 mu g/ml for UVDS, respectively. Intra and inter-day relative standard deviations were < 2.0 %. Statistical analysis with t- and F-tests are not exceeding their critical values demonstrating that there is no significant difference between the two methods at 95 % confidence level.

Characterization and stability study of a water-in-oil microemulsion incorporating quercetin

Background: The effectiveness of a water/oil (w/o) microemulsion containing quercetin against ultraviolet B radiation (UVB) induced damage was recently demonstrated by our group. However, during the development of new pharmaceutical products, the evaluation of percutaneous absorption and in vivo effectiveness should be accompanied by evaluation of stability parameters as an integral part of the process. Objective: The aim was to investigate the stability of the final microemulsion formulation considering the temperature ranges of storage and application. Methods: The physical, chemical, and functional stability of this formulation under different conditions of storage during 12 months and the photostability of quercetin incorporated into this system over UVB exposure for 7 days were evaluated. Results: Although the results indicated a notable physical stability of the w/o microemulsions during the experimental period under all employed conditions, in both, the chemical and functional studies, a significant loss of quercetin content and antioxidant activity was found after 6 months of storage at 30 degrees C/70% relative humidity and after 2 months at 40 degrees C/70% relative humidity. The photostability study results demonstrated that the incorporation of quercetin into the w/o microemulsion maintained the previously demonstrated photostability of this flavonoid under forced exposure to UVB irradiation. Conclusion: Thus, this work demonstrates that special storage conditions (at 4 +/- 2 degrees C) are necessary to maintain the functionality of the w/o microemulsion containing quercetin and mainly emphasizes the importance of studying physical, chemical, and functional parameters at the same time during stability evaluation of active principles.

Influence of Phase Inversion on the Formation and Stability of One-Step Multiple Emulsions

A novel method of preparation of water-in-oil-in-micelle-containing water (W/O/W(m)) Multiple emulsions using the one-step emulsification method is reported. These multiple emulsions were normal (not temporary) and stable over a 60 day test period. Previously, reported multiple emulsion by the one-step method were abnormal systems that formed at the inversion point of simple emulsion (where there is an incompatibility in the Ostwald and Bancroft theories, and typically these are O/W/O systems). Pseudoternary phase diagrams and bidimensional process-composition (phase inversion) maps were constructed to assist in process and composition optimization. The surfactants used were PEG40 hydrogenated castor oil and sorbitan oleate, and mineral and vegetables oils were investigated. Physicochemical characterization studies showed experimentally, for the First time, the significance of the ultralow surface tension point oil multiple emulsion formation by one-step via phase inversion processes. Although the significance of ultralow surface tension has been speculated previously, to the best of our knowledge, this is the first experimental confirmation. The multiple emulsion system reported here was dependent not only upon the emulsification temperature, but also upon the component ratios, therefore both the emulsion phase inversion and the phase inversion temperature were considered to fully explain their formation. Accordingly, it is hypothesized that the formation of these normal multiple emulsions is not a result of a temporary incompatibility (at the inversion point) during simple emulsion preparation, as previously reported. Rather, these normal W/O/W(m) emulsions are a result of the simultaneous occurrence of catastrophic and transitional phase inversion processes. The formation of the primary emulsions (W/O) is in accordance with the Ostwald theory and the formation of the multiple emulsions (W/O/W(m)) is in agreement with the Bancroft theory.

Thickness and stability of adsorbed film in cylindrical mesopores

The adsorbed film in small cylindrical mesopores is studied by using MCM-41 samples of uniform cylindrical channels as model systems. It is found that at a given relative pressure, the smaller the pore radius, the thicker the adsorbed film is, as postulated by Broekhoff and De Beer. Thermodynamics analysis established that the stability of the adsorbed film is determined by interface curvature and the potential of interaction between adsorbate and adsorbent. A semiempirical equation is proposed to describe the state of stable adsorbed films in cylindrical mesopores. It is also shown to be useful in calculations of pore size distributions of mesoporous solids.

Complexes of 1-thia-4,7,10-triazacyclododecane ([12]aneN(3)S) - Synthesis, structure and stability constants

The 12-membered macrocyclic ligand 1-thia-4,7, 10-triazacyclododecane ([12]aneN(3)S) has been synthesised, although upon crystallization from acetonitrile a product in which carbon dioxide had added to one secondary amine in the macrocyclic ring (H[12]aneN(3)SCO(2). H2O) was isolated and subsequently characterised by X-ray crystallography. The protonation constants for [12]aneN(3)S and stability constants with Zn(II), Pb(II), Cd(II) and Cu(II) have been determined either potentiometrically or spectrophotometrically in aqueous solution, and compared with those measured or reported for the ligands 1-oxa-4,7,10-triazacyclododecane ([12]aneN(3)O) and 1,4,7,10-tetraazacyclododecane ([12]aneN(4)). The magnitudes of the stability constants are consistent with trends observed previously for macrocyclic ligands as secondary amine donors are replaced with oxygen and thioether donors although the stability constant for the [Hg([12]aneN(4))](2+) complex has been estimated from an NMR experiment to be at least three orders of magnitude larger than reported previously. Zinc(II), mercury(II), lead(II), copper(II) and nickel(II) complexes of [12]aneN(3)S have been isolated and characterised by X-ray crystallography. In the case of copper(II), two complexes [Cu([12]aneN(3)S)(H2O)](ClO4)(2) and [Cu-2([12]aneN(3)S)(2)(OH)(2)](ClO4)(2) were isolated, depending on the conditions employed. Molecular mechanics calculations have been employed to investigate the relative metal ion size preferences of the [3333], asym-[2424] and sym-[2424] conformation isomers. The calculations predict that the asym-[2424] conformer is most stable for M-N bond lengths in the range 2.00-2.25 Angstrom whilst for the larger metal ions the [3333] conformer is dominant. The disorder seen in the structure of the [Zn([12]aneN(3)S)(NO3)](+) complex is also explained by the calculations. (C) 1999 Elsevier Science Ltd. All rights reserved.

FURTHER INSIGHTS TOWARD VITAMIN C DETERMINATION AND STABILITY. PROPOSAL OF A NEW QUANTIFICATION METHOD

This work aimed at an evaluation of the classical iodine method for quantification of vitamin C (L-ascorbic acid) in fruit juices, as well as at a search into the stability of this so popular vitamin under different conditions of pH, temperature and light exposition, in addition to a proposal of a new quantification method. Our results point to the persistent reversibility of the blue color of the starch-triiodide complex at the end point when using the classical iodine titration, and the overestimation of the true vitamin concentration in fruit juices. A new quantification method is proposed in order to overcome this problem. Surprising conclusions were obtained regarding the controversial stability of L-ascorbic acid toward atmospheric oxygen, at low pH, even in fruit juice and at room temperature, showing that the major problem concerned with aging of fruit juices is proliferation of microorganisms rather than expontaneous oxidation of L-ascorbic acid.