The scalar Oseen operator − Δ + ∂/2202<Emphasis Type="Italic">x</Emphasis><Subscript>1</Subscript> in ℝ<Superscript>2</Superscript>

This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in L ^p theory.     

An STM study of the localized atomic reaction of 1,2- and 1,4-dibromoxylene with Si(1 1 1)-7 × 7

Thermal reactions of 1,2- and 1,4-dibromoxylene (1,2- and 1,4-diBrXy) with Si(1 1 1)-7 × 7 were investigated by STM at room temperature under UHV conditions. Reaction led to the formation of single adsorbed Br-atoms or pairs of Br-atoms, in a ratio approx. 3:1 for both reagents. Experimental results were interpreted in terms of ‘parent-mediated’ (halogen atom accompanied by organic residue), and ‘daughter-mediated’ (no accompanying organic residue) reaction dynamics. Both mechanisms contributed to the bromination of the silicon surface in comparable amounts. For pairs of bromine atoms the Br–Br separation had a most probable value of 7.6 Å for 1,2-diBrXy, and 11.5 Å for 1,4-diBrXy. This separation was in each case greater than that in the diBrXy parent molecule by a few angstroms. For parent-mediated reaction the dynamics were revealed in detail by the STM images which gave the vectorial location of the halogen-atom products (distance and angle of the daughter atoms) relative to the prior location and alignment of the adsorbed parent molecule. Both reagents, 1,2- and 1,4-diBrXy, were found to be less reactive than the corresponding dibromobenzenes studied earlier in this laboratory [S. Dobrin et al., Surf. Sci. 561 (2004) 11], in both parent- and daughter-mediated modes.     

Surface acoustic waves in the GHz range generated by periodically patterned metallic stripes illuminated by an ultrashort laser pulse.

The photoelastic response of periodic arrays of stripes attached to the surface of a substrate and illuminated by an ultrashort laser pulse were investigated. The samples were gold arrays on silicon and aluminum arrays either on crystalline quartz or on silicon. The metallic stripes had submicrometer lateral dimensions and the spatial periods ranged from about 1 microm up to 5 microm. The substrate being transparent (quartz) or slightly absorbing (silicon) at the laser wavelength (lambda = 750 nm), a laterally modulated thermal stress is generated near the surface of the substrate when a light pulse illuminates the structure. The studies of vibrations involved by the subsequent relaxation processes show that surface acoustic waves at frequency as high as about 5 GHz are excited with the samples consisting of aluminum stripes. In the case of the aluminum samples with the largest lateral spatial periods (aluminum on quartz), the surface acoustic wave propagates outside the illuminated area. In the case of the gold samples, a normal mode of individual bars is observed instead. Experimental evidence shows that these behaviors are mainly governed both by the lateral spatial period of the structure and by the density of the metal.     

Inverse determination of the heat transfer characteristics on a circular plane fin in a finned-tube bundle

In this work, we present the numerical results of the average heat transfer coefficients, $ \overline{{h_{\varphi } }} $ , over a circular plane fin in a finned-tube bundle for both aligned and staggered arrangements as well as the fin efficiency and the heat flux dissipated from the whole fin. The study covers a wide range of Reynolds number (2 × 10³–3 × 10⁴), for three different positions of the finned tube inside the heat exchanger. The temperature distribution on the fins surfaces was obtained experimentally using infrared thermography technique. The predicted values of the heat transfer coefficient were obtained numerically using the finite element method in conjunction with the conjugate gradient algorithm and the measured temperatures.     

Clipped time autocorrelation function of intensity fluctuations for a non gaussian field

Numerical results for the single and double clipped autocorrelation functions of intensity fluctuations of squared intensity of gaussian-exponential field are reported and compared with the unclipped ones.     

Theoretical study of the electronic structure of MCH(2)(+)(M=Fe,Co,Ni)

State of the art coupled cluster (CC) methods are applied to accurately characterize the ground state electronic structure and photoelectron spectra of transition metal carbene ions MCH(2) (+) (M=Fe, Co, and Ni). The geometries and energies of the lowest energy quartet, triplet, and doublet electronic states as well as several low-lying vertical excitation energies of FeCH(2) (+), CoCH(2) (+), and NiCH(2) (+) are reported. The excitation energies are computed using the equation-of-motion CC and for states of different symmetries, by the energy differences of single reference ground and excited states (Delta-CC). The latter employ several reference states; the unrestricted Hartree-Fock, restricted open shell Hartree-Fock, and unrestricted Kohn-Sham. We conclude that the (2)A(1) electronic ground state of NiCH(2) (+) is separated by about 30.0 kJ/mol from the next highest state, and the lowest (4)B(1) and (4)B(2) states of FeCH(2) (+) as well as the (3)A(2) and (3)A(1) states of CoCH(2) (+) are nearly degenerate. The presence of metal-pi*(MCH(2)) charge transfer states with significant oscillator strengths in the visible/near-UV energy domain of the theoretical spectra of FeCH(2) (+) and CoCH(2) (+) are at the origin of the photofragmentation of these compounds observed after irradiation between 310 and 360 nm.     

Ion induced dipole clusters H(n)- (3 ≤ n-odd ≤ 13): density functional theory calculations of structure and energy

We investigate anew the possible equilibrium geometries of ion induced dipole clusters of hydrogen molecular ions, of molecular formula H(n)(-) (3 ≤ n-odd ≤ 13). Our previous publications [Sapse, A. M.; et al. Nature 1979, 278, 332; Rayez, J. C.; et al., J. Chem. Phys. 1981, 75, 5393] indicated these molecules would have a shallow minimum and adopt symmetrical geometries that accord with the valence shell electron pair repulsion (VSEPR) rules for geometries defined by electron pairs surrounding a central point of attraction. These earlier calculations were all based upon Hartree-Fock (HF) calculations with a fairly small basis of atomic functions, except for the H3(-) ion for which configuration interaction (CI) calculations were carried out. A related paper [Hirao, K.; et al., Chem. Phys. 1983, 80, 237] carried out similar calculations on the same clusters, finding geometries similar to our earlier calculations. However, although that paper argued that the stabilization energy of negative ion clusters H(n)(-) is small, vibration frequencies for the whole set of clusters was not reported, and so a definitive assertion of a true equilibrium was not present. In this paper we recalculate the energetics of the ion induced dipole clusters using density function theory (DFT) B3LYP method calculations in a basis of functions (6-311++G(d,p)). By calculating the vibration frequencies of the VSEPR geometries, we prove that in general they are not true minima because not all the resulting frequencies correspond to real values. By searching the energy surface of the B3LYP calculations, we find the true minimum geometries, which are surprising configurations and are perhaps counterintuitive. We calculate the total energy and binding energy of the new geometries. We also calculate the bond paths associated with the quantum theory of atoms in molecules (QTAIM). The B3LYP/6-311++G(d,p) results, for each molecule, deliver bond paths that radiate between each polarized H2 molecule and the polarizing H(-) ion.