Inhomogeneous ‘longitudinal’ plane waves in a deformed elastic material

By definition, a homogeneous isotropic compressible Hadamard material has the property that an infinitesimal longitudinal homogeneous plane wave may propagate in every direction when the material is maintained in a state of arbitrary finite static homogeneous deformation. Here, as regards the wave, homogeneous means that the direction of propagation of the wave is parallel to the direction of eventual attenuation; and longitudinal means that the wave is linearly polarized in a direction parallel to the direction of propagation. In other words, the displacement is of the form u = ncos k(n · x – ct), where n is a real vector. It is seen that the Hadamard material is the most general one for which a longitudinal inhomogeneous plane wave may also propagate in any direction of a predeformed body. Here, inhomogeneous means that the wave is attenuated, in a direction distinct from the direction of propagation; and longitudinal means that the wave is elliptically polarized in the plane containing these two directions, and that the ellipse of polarization is similar and similarly situated to the ellipse for which the real and imaginary parts of the complex wave vector are conjugate semi-diameters. In other words, the displacement is of the form u = {S exp i(S · x – ct)}, where S is a complex vector (or bivector). Then a Generalized Hadamard material is introduced. It is the most general homogeneous isotropic compressible material which allows the propagation of infinitesimal longitudinal inhomogeneous plane circularly polarized waves for all choices of the isotropic directional bivector. Finally, the most general forms of response functions are found for homogeneously deformed isotropic elastic materials in which longitudinal inhomogeneous plane waves may propagate with a circular polarization in each of the two planes of central circular section of the ⁿ -ellipsoid, where is the left Cauchy-Green strain tensor corresponding to the primary pure homogeneous deformation.     

Stability of a Steady Viscous Incompressible Flow Past an Obstacle

We derive a sufficient condition for stability of a steady solution of the Navier–Stokes equation in a 3D exterior domain Ω. The condition is formulated as a requirement on integrability on the time interval (0, +∞) of a semigroup generated by the linearized problem for perturbations, applied to a finite family of certain functions. The norm of the semigroup is measured in a bounded sub-domain of Ω. We do not use any condition on “smallness” of the basic steady solution.      

Existence of Solutions with the Prescribed Flux of the Navier–Stokes System in an Infinite Cylinder

The existence and uniqueness of a solution to the nonstationary Navier–Stokes system having a prescribed flux in an infinite cylinder is proved. We assume that the initial data and the external forces do not depend on x₃ and find the solution (u, p) having the following form

On the macroscopic dynamics induced by a model wave-particle collision operator

The macroscopic dynamics of a kinetic equation involving a model wave-particle collision operator of plasma physics is investigated. The Chapman-Enskog asymptotics is first considered in the framework of a hydrodynamic scaling. The obtained macroscopic model still involves a kinetic variable, the particle energy in the rest frame of the fluid, but shares similarities with the compressible Navier-Stokes equation of gas dynamics. Then a diffusive scaling is examined under the hypothesis of small perturbations of a global equilibrium. In this case, the macroscopic model couples the usual incompressible Navier-Stokes with a diffusion equation for the energy distribution function of the particles, constrained by an extended version of the Boussinesq relation. In both cases, the effect of a Lorentz force term is developed, in the perspective of plasma physical modelling. Received June 16, 1997     

Singularities in the Density Gradient

The compressible steady state Navier–Stokes system with viscosity is considered on a plane polygonal domain. It is shown that if a solution satisfies certain reasonable regularity conditions, and if the velocity is non-zero and points into the domain at a vertex of the polygon, then the gradient of the density either becomes infinite or has a jump discontinuity at each point of the streamline emanating from the vertex.     

1-(2′,2′,2′-Trifluoroethyl)-4-phosphopyrazoles: Synthese et Etude Spectroscopique ir et RMN 1H, 13C, 19F,et 31P

Seven new 1-fluorinated-4-phosphopyrazoles 2 have been prepared in 60–94% yield by cyclization of N-(2′,2′,2′-trifluoroethyl) phosphonyl β-hydrazones 1 with triethyl orthoformate in the presence of acetic acid. The IR data, the ¹H, ¹³C, ¹⁹F, ³¹P chemical shifts and coupling constants of the compounds 2 are reported.     

POLY(10-UNDECENOIC ACID) AND SOME OF ITS DERIVATIVES

Commercially available 10-undecenoic acid was esterified with 2,5-dimethylphenol. After the supply of ester was properly complexed, it was polymerized in quantities and in high yield to high molcular polymers. The polymeric esters were hydrolyzed with base to the acid salt, which were converted to the acids. Reactions with 1,1′-carbonyldiimidazole gave polyethylene-based polymeric imidazolids.     

Intermolecular interactions of formic acid with benzene: Energy decomposition analyses with ab initio MP2 and double‐hybrid density functional computations

The intermolecular interactions of formic acid (HCOOH) with benzene (C₆H₆) have been investigated using localized molecular orbital energy decomposition analyses (LMO‐EDA) with ab initio MP2 and several double‐hybrid density functionals. The molecular geometries of five HCOOH…C₆H₆ complexes and corresponding benchmark total interaction energies at the CCSD(T)/CBS level are taken from literature (Zhao et al., J. Chem. Theory Comput. 2009, 5, 2726). According to the results of LMO‐EDA with the MP2 method, the dispersion energies are found to be as important as the electrostatic energies for the total interaction energies of the five HCOOH…C₆H₆ complexes. Based on LMO‐EDA with the double‐hybrid density functionals of B2PLYP, B2K‐PLYP, B2T‐PLYP, and B2GP‐PLYP computations, two new parameters for the framework of B2PLYP are extrapolated. These two new parameters are tested with other 10 complexes involving C₆H₆ (Crittenden, J. Phys. Chem. A 2009, 113, 1663), and they perform well on predicting the corresponding total interaction energies. Interestingly, these two new parameters for the framework of B2PLYP also perform well on the noncovalent complexation energies database (NCCE31/05) developed by Truhlar's group (Zhao and Truhlar, J. Phys. Chem. A 2005, 109, 5656). Therefore, these two new parameters appear to be suitable for investigating the noncovalent interactions, and they are denoted as B2N‐PLYP, where N stands for the noncovalent interaction. This study is expected to provide new insight into the derivation of double‐hybrid density functionals for studying the noncovalent interactions. © 2013 Wiley Periodicals, Inc.     

Conjugated Polymers-Based Ternary Hybrid toward Unique Photophysical Properties

The improvement of optical and optoelectronic properties of the individual poly [2-methoxy-5- (2-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV), poly[2-methoxy-5-(3,7-dimethyl-octyloxy)-1,4-phenylenevinylene]–End capped with Dimethyl phenyl (OC1C10–PPV–DMP), and poly (9,9′-di- n -octylfluorenyl-2,7-diyl) (F8) was revealed by blending them in ternary hybrid with optimal ratio (F8/2 wt.% MEH-PPV/2 wt.% OC1C10–PPV–DMP). All individual and optimal ternary solutions were prepared via the solution-blending method followed by depositing them onto glass and ITO substrates using spin-coating technique. The semi-crystalline phase of the ternary hybrid and the strong mixing between the conjugated polymers were evidenced by observing the X-ray diffraction patterns that related to F8 into the hybrid diffractogram. The optical and optoelectronic properties of all prepared thin films were investigated in terms of absorption and emission spectra, Commission International d′Eclairage (CIE) coordinates, and current–voltage (I-V) characterizations. Emission peaks at the entire range of visible spectrum can be revealed from the ternary hybrid of the three individual conjugated polymers, producing white emission as evidenced from the emission spectrum and CIE coordinates of the hybrid. Among all fabricated organic light-emitting diodes (OLEDs) devices, the ternary hybrid-based-OLED revealed the best performance in terms of current and turn-on voltage.     

Push-Pull Structures Based on 2-Aryl/thienyl Substituted Quinazolin-4(3H)-ones and 4-Cyanoquinazolines

Design and synthesis of 2-(aryl/thiophen-2-yl)quinazolin-4(3H)-ones and 4-cyano-2-arylquinazolines with Et₂N-, Ph₂N- or carbazol-9-yl- electron donating fragment are described. The key photophysical properties of these compounds have been studied by UV/Vis absorption and fluorescence spectroscopy in solvents of different polarity (toluene and MeCN). 2-(Aryl/thiophen-2-yl)quinazolin-4(3H)-ones show fluorescence in blue-green region in toluene solution with quantum yields up to 89% in the case of 2-(4’-N,N-diphenylamino[1,1’-biphenyl]-4-yl)-quinazolin-4(3H)-one. Moreover, triphenylamino derivative based on quinazolin-4(3H)-one with para-phenylene linker displays the highest quantum yield of 40% in powder. The fluorescence QY of Et₂N and Ph₂N derivatives decrease when going from toluene to MeCN solution, whereas carbazol-9-yl counterparts demonstrate strengthening of intensity that emphasizes the strong influence of donor fragment nature on photophysical properties. 4-Cyanoquinazolines are less emissive in both solvents, as well as, in solid state. The introduction of cyano group into position 4 leads to orange/red colored powder and dual emission bands. Some molecules demonstrate the increase in emission intensity upon addition of water to MeCN solution. According to frontier molecular orbitals (HOMO, LUMO) calculations, the energy gap of 4-cyanoquinazoline decreases by more than 1 eV compared to quinazolin-4-one, that is consistent with experimental data.