Continuation of travelling‐wave solutions of the Navier–Stokes equations

An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first‐order pseudospectral semi‐implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton–Raphson solver and is shown to be highly efficient in performing this task, even when high‐resolution grids are used. This method is well suited to three‐dimensional calculations in cylindrical or spherical geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

Physical aging of a polyetherimide: Creep and DSC measurements

Creep and differential scanning calorimetry (DSC) measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures ranged from 160°C to T_g with aging times ranging from 10 min to 8 days. The only measurable effect of physical aging on the short-time creep curves is a shift of the creep compliance to longer times. Andrade plots of the compliance versus the cube root of time are linear at short times with the slope β decreasing with increasing aging time to a constant value once equilibrium is reached. Log β³ is related directly to the degree to which the creep curves shift to longer times with physical aging, and is used in this work as a measure of physical aging. A reduced curve of log β³ versus log aging time is obtained for the aging temperatures investigated by appropriate vertical and horizontal shifts. The enthalpy change during aging increases linearly with the logarithm of the aging time, t_a, leveling off at equilibrium at values which increase with decreasing aging temperature. Hence, both nonequilibrium and equilibrium temperature shift factors can be calculated from the DSC data. Good agreement is observed between the equilibrium temperature shift factors obtained from the creep and DSC data. The temperature dependence of the nonequilibrium temperature shift factors is found to be an order of magnitude smaller than that of the equilibrium shift factors. The time scales to reach equilibrium for enthalpy and for mechanical measurements are found to be the same within experimental error. © 1995 John Wiley & Sons, Inc.     

On a class of graphs with prescribed mean curvature

We study a class of quasilinear elliptic equations on the unit ball of ℝ ⁿ in the divergence form ∑ _j=1 ⁿ D _j{G(|x|²,|Du|²)D _j u} =H(|x|) and get estimates on the boundary by using a modified barrier-function technique of Bernstein. We establish a maximum principle for the gradients of solutions and get a global gradient estimate. We prove that solutions with constant boundary condition must be radial. Finally, we apply these results to graphs {(x,u(x)):x∈H ⁿ } whereu:H ⁿ →ℝ is a smooth map of then-hyperbolic spaceH ⁿ =B(0,1) with the metric to get the existence of graphs with radial prescribed mean curvature.     

Determination of the enantiomeric composition of guest molecules by chemometric analysis of the UV-visible spectra of cyclodextrin guest-host complexes

Multivariate statistical techniques were applied to the UV spectra of a series of solutions at pH 12 containing a fixed concentration (30 mM) of beta-cyclodextrin (beta-CD) and a fixed concentration (15 mM) of 2-phenylglycine (phi-Gly) with various known enantiomeric compositions. Multivariate correlation of the spectral data for the solutions containing the phi-Gly/beta-CD guest-host complexes with the known enantiomeric composition of the phi-Gly samples was accomplished by partial-least-squares regression. When the multivariate model was used to predict the enantiomeric purity of a test set of samples over the mol fraction range of 0.5-0.9 R-phi-Gly, the average magnitude of the relative errors in the mol fraction determination of enantiomeric composition was 3%. A plot of the enantiomeric composition predicted by the model versus the known enantiomeric composition of the calibration set gave a straight line with a correlation coefficient of 0.955, a slope of 1.05, and an offset of 5.61 x 10-4.     

Solubility of Triethylamine in Tetraethylammonium Chloride Aqueous Solutions from 20 to 35°C

Solubilities of triethylamine in aqueous tetraethylammonium chloride solutions were measured at 20, 25, and 35°C. The molalities in Et₄NCl of the aqueous solvents ranged from 0.03 to 1 mol-kg^–1. The data were evaluated from density measurements using a vibrating-tube densimeter. At each temperature, least-squares method was used to fit experimental density data points to double polynomial equations of various degrees. Triethylamine molalities of the saturated aqueous phases were estimated by extrapolation from those equations. Experimental data were interpreted in terms of hydrophobic and electrostatic perturbed domains in the hydration shells of the noneleceory and of the cation of the salt, as a function of temperature and salt concentration. The conclusions obtained are consistent with previous volumetric studies.     

The Genus Cetraria s. str.—A Review of Its Botany,Phytochemistry, Traditional Uses and Pharmacology

The genus Cetraria s. str. (Parmeliaceae family, Cetrarioid clade) consists of 15 species of mostly erect brown or greenish yellow fruticose or subfoliose thallus. These Cetraria species have a cosmopolitan distribution, being primarily located in the Northern Hemisphere, in North America and in the Eurasia area. Phytochemical analysis has demonstrated the presence of dibenzofuran derivatives (usnic acid), depsidones (fumarprotocetraric and protocetraric acids) and fatty acids (lichesterinic and protolichesterinic acids). The species of Cetraria, and more particularly Cetraria islandica, has been widely employed in folk medicine for the treatment of digestive and respiratory diseases as decoctions, tinctures, aqueous extract, and infusions. Moreover, Cetraria islandica has had an important nutritional and cosmetic value. These traditional uses have been validated in in vitro and in vivo pharmacological studies. Additionally, new therapeutic activities are being investigated, such as antioxidant, immunomodulatory, cytotoxic, genotoxic and antigenotoxic. Among all Cetraria species, the most investigated by far has been Cetraria islandica, followed by Cetraria pinastri and Cetraria aculeata. The aim of the current review is to update all the knowledge about the genus Cetraria covering aspects that include taxonomy and phylogeny, morphology and distribution, ecological and environmental interest, phytochemistry, traditional uses and pharmacological properties.     

Folding Free Energy Determination of an RNA Three-Way Junction Using Fluctuation Theorems

Nonequilibrium work relations and fluctuation theorems permit us to extract equilibrium information from nonequilibrium measurements. They find application in single-molecule pulling experiments where molecular free energies can be determined from irreversible work measurements by using unidirectional (e.g., Jarzynski’s equality) and bidirectional (e.g., Crooks fluctuation theorem and Bennet’s acceptance ratio (BAR)) methods. However, irreversibility and the finite number of pulls limit their applicability: the higher the dissipation, the larger the number of pulls necessary to estimate ΔG within a few kBT. Here, we revisit pulling experiments on an RNA three-way junction (3WJ) that exhibits significant dissipation and work-distribution long tails upon mechanical unfolding. While bidirectional methods are more predictive, unidirectional methods are strongly biased. We also consider a cyclic protocol that combines the forward and reverse work values to increase the statistics of the measurements. For a fixed total experimental time, faster pulling rates permit us to efficiently sample rare events and reduce the bias, compensating for the increased dissipation. This analysis provides a more stringent test of the fluctuation theorem in the large irreversibility regime.     

The role of nanocellulose fibers, starch and chitosan on multipolysaccharide based films

Thin nanocomposite films of thermoplastic starch, chitosan and cellulose nanofibers (bacterial cellulose or nanofibrillated cellulose) were prepared for the first time by solvent casting of water based suspensions of the three polysaccharides. The role of the different bioploymers on the final properties (thermal stability, transparency, mechanical performance and antimicrobial activity) of the films was related with their intrinsic features, contents and synergic effects resulting from the establishment of interactions between them. Thermoplastic starch displays an important role on the thermal stability of the films because it is the most stable polysaccharide; however it has a negative impact on the mechanical performance and transparency of the films. The addition of chitosan improves considerably the transparency (up to 50 % transmittance for 50 % of chitosan, in respect to the amount of starch), mechanical performance and antimicrobial properties (at least 25 % of chitosan and no more than 10 % of cellulose nanofibers are required to observe bacteriostatic or bactericidal activity) but decrease their thermal stability. The incorporation of cellulose nanofibers had the strongest positive impact on the mechanical properties of the materials (increments of up to 15 and 30 MPa on the Young′s modulus and Tensile strength, respectively, for films with 20 % of BC or NFC). Nonetheless, the impact in thermal stability and mechanical performance of the films, promoted by the addition of chitosan and cellulose nanofibres, respectively, was higher than the expected considering their percentage contents certainly because of the establishment of strong and complex interactions between the three polysaccharides.