Existence and Ergodicity for the Two-Dimensional Stochastic Magneto-Hydrodynamics Equations

The paper proves the existence of solutions to the magneto-hydrodynamics equations driven by random exterior forcing terms both in the velocity and in the magnetic field. The existence and uniqueness of an invariant measure is also obtained via coupling methods.     

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.     

Reaction of bis(phosphine)(hydrotris(3,5-dimethylpyrazolyl)borato)rhodium(I) with phenylacetylene,p-nitrobenzaldehyde,and triphenyltin hydride: structures of [Rh(Tp)(PPh(3))(2)], [Rh(Tp)(H)(C(2)Ph)(P(4-C(6)H(4)F)(3))], [Rh(Tp)(H)(COC(6)H(4)-4-NO(2))(PPh(3))], and [Rh(Tp)(H)(SnPh(3))(PPh(3))

The complexes [Rh(Tp)(PPh(3))(2)] (1a) and [Rh(Tp)(P(4-C(6)H(4)F)(3))(2)] (1b) combine with PhC(2)H, 4-NO(2)-C(6)H(4)CHO and Ph(3)SnH to give [Rh(Tp)(H)(C(2)Ph)(PR(3))] (R = Ph, 2a; R = 4-C(6)H(4)F, 2b), [Rh(Tp)(H)(COC(6)H(4)-4-NO(2))(PR(3))] (R = Ph, 3a), and [Rh(Tp)(H)(SnPh(3))(PR(3))] (R = Ph, 4a; R = 4-C(6)H(4)F, 4b) in moderate to good yield. Complexes 1a, 2b, 3a, and 4a have been structurally characterized. In 1a the Tp ligand is bidentate, in 2b, 3a, and 4a it is tridentate. Crystal data for 1a: space group P2(1)/c; a = 11.9664(19), b = 21.355(3), c = 20.685(3) A; beta = 112.576(7) degrees; V = 4880.8(12) A(3); Z = 4; R = 0.0441. Data for 2b: space group P(-)1; a = 10.130(3), b = 12.869(4), c = 17.038(5) A; alpha = 78.641(6), beta = 76.040(5), gamma = 81.210(6) degrees; V = 2100.3(11) A(3); Z = 2; R = 0.0493. Data for 3a: space group P(-)1; a = 10.0073(11), b = 10.5116(12), c = 19.874(2) A; alpha = 83.728(2), beta = 88.759(2), gamma = 65.756(2) degrees; V =1894.2(4) A(3); Z = 2; R = 0.0253. Data for 4a: space group P2(1)/c; a = 15.545(2), b = 18.110(2), c = 17.810(2) A; beta = 95.094(3) degrees; V = 4994.1(10) A(3); Z = 4; R = 0.0256. NMR data ((1)H, (31)P, (103)Rh, (119)Sn) are also reported.     

Correlation between Small-Angle X-ray Scattering spectra and apparent diffusion coefficients in the study of structure and interaction of sodium taurodeoxycholate micelles

Small-Angle X-ray Scattering (SAXS) and Dynamic Light Scattering (DLS) measurements were carried out on aqueous micellar solutions of the ionic biological detergent sodium taurodeoxycholate (NaTDC). Apparent diffusion coefficients (D(app)) and SAXS spectra of NaTDC 0.1 M solutions at different ionic strengths (0.1-0.3 M NaCl) were reported. A comparative analysis of SAXS spectra and D(app) data was performed to infer information on particle structure and interaction potential. Uniform particles with a spherical, an oblate, and a prolate symmetry were used to model the micelles in the data interpretation. A hard-core interaction shell of suitable thickness and a screened Coulomb potential of the electric double layer (EDL potential) were alternatively used to represent the long-range repulsive tail of the interaction potential. The Percus Yevick and the Rescaled Mean Spherical Approximation were applied. To compare the data of the two techniques, for each sample, a D(app) was calculated from the SAXS best-fitting geometrical parameters and interparticle structure factor of the micelles. Hence, a fitting procedure involving both the scattering and D(app) data was performed. The interpretation of SAXS spectra does not allow the discrimination between the oblate and the prolate symmetries of the aggregates. On the other hand, the comparison of calculated and experimental D(app) values indicates that the prolate ellipsoid is better suited to represent the micelle shape. Moreover, the agreement between calculated and experimental D(app) values is sensitively better at the lowest NaCl concentration when the EDL potential is used. A rodlike micellar growth and a progressive screening of the electrostatic interactions is testified by the trends of best-fitting parameters as a function of the added electrolyte.     

Mesomorphic behaviour and TSDC measurements of ortho-metallated palladium(II) and platinum(II) complexes with S,O-donor co-ligands

A series of ortho-metallated Pd and Pt complexes containing an imine ligand carrying three alkoxy chains and N-benzoylthiourea derivatives as co-ligands were prepared and their liquid crystalline properties investigated. Their structures were assigned based on elemental analysis, IR and ¹H NMR spectroscopy, whereas thermal properties were investigated by differential scanning calotimetry and polarising optical microscopy. All the compounds exhibit monotropic transitions involving nematic and smectic A phases, with the mesomorphic behaviour strongly related to the type of N-benzoylthiourea as well as the metal centre used. The thermally stimulated depolarisation current technique was employed to determine the conduction mechanism, phase transition temperature and the activation energies for one of the ortho-metallated Pd complexes.     

New high-pressures vapor-liquid equilibrium data for the carbon dioxide + 2-methyl-2-propanol binary system

New vapor-liquid equilibria (VLE) data at 323.15, 333.15, 343.15, and 353.15 K and pressures up to 112.9 bar are reported for the carbon dioxide + 2-methyl-2-propanol system. The experimental method used in this work was a static analytical method with liquid and vapor phases sampling using a rapid online sampler injector (ROLSI?) coupled to a gas chromatograph (GC) for analysis. Measured VLE data and literature data for carbon dioxide + 2-methyl-2-propanol system were modeled with the Soave-Redlich-Kwong (SRK) cubic equation of state with classical van der Waals (two-parameter conventional mixing rule, 2PCMR) mixing rules. A single set of interaction parameters that lead to a correct phase behavior was used in this work to model the new VLE data and critical points of the mixtures in a wide range of temperature and pressure. The SRK prediction results were compared to the new data measured in this study and to available literature data.

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Stabilization of the Gurtin–MacCamy population system

We consider the classical Gurtin–MacCamy system describing the growth and spread of an age structured population and show that the steady states are actually stabilizable by a controller v = v(a, t) acting on an age interval [a ₁, a ₂].