A model for transitional plane Couette flow

A simplified model of plane Couette flow is derived by means of a cross-stream (y) Galerkin expansion in terms of trigonometric functions appropriate for idealized stress-free boundary conditions at the plates. A set of partial differential equations is obtained, governing the in-plane (x–z) space-dependence of a velocity field taken in the form: u=U₀(x,z,t)+[1+U₁(x,z,t)]sin(πy/2), v=V₁(x,z,t)cos(πy/2), w=W₀(x,z,t)+W₁(x,z,t)sin(πy/2). Beyond Lorenz-like Waleffe's modeling (Waleffe 1997), this Swift–Hohenberg type of approach is expected to give an access to the microscopic mechanism of spatiotemporal intermittency typical of the transition to turbulence in plane Couette flow (Pomeau 1986, Bergé et al. 1998).     

Synthesis of homologously pure bacteriochlorophyll-e and f analogues from BChls-c/d via transformation of the 7-methyl to formyl group and self-aggregation of synthetic zinc methyl bacteriopheophorbides-c/d/e/f in non-polar organic solvent

Homologously pure methyl bacteriopheophorbides-e and f (BPhes-e/f_M) were prepared from modification of naturally occurring bacteriochlorophylls-c and d (BChls-c/d), respectively, by transformation of the methyl to formyl group at the 7-position. The absolute configuration of the 1-hydroxyethyl group at the 3-position of (Zn-)BPhes-e/f_M was determined from comparison with structurally known BChl-c/d epimers. Visible spectra of synthetic (Zn-)BPhe-c/d/e/f_M showed that the 7¹-oxidation and the 8²/12¹/20-methylation affected Soret, Q_x and Q_y bands of both the monomeric (in a polar organic solvent) and oligomeric species (in a non-polar solvent).     

Molar excess volumes of ternary mixtures of nonelectrolytes

Molar excess volumes V^E_ijk of methylenebromide i + pyridine j + β-picoline (k, cyclohexane (i) + pyridine (j) + β-picoline(K), benzene(i)+toluene(j)+1,2-dichloroethane(k), benzene(i) + 0-xylene(j) + 1,2-dichloroethane(k) and benzene(i) + p-xylene(j) + 1,2-dichloroethane(k) mixtures have been determined dilatometrically at 298.15 K. The data have been examined in terms of Sanchez and Lacombe theory and the graph-theoretical approach, and it is found that they are described well by the latter. Self- and cross-volume interaction coefficients V_jk, V_jjk and V_jkk, etc., have also been evaluated and the values utilised to study molecular interactions between the jth and kth molecular species in the presence of the ith in these i + j + k mixtures.     

Theoretical and experimental analysis of the fine structure and hyperfine structure in the configurations 5p6s and 5p6p of the antimony II spectrum

From 17 transitions in the singly ionized Sb II spectrum the hyperfine structure (A andB splitting constants) of the complete excited configurations 5p6s and 5p6p were determined by means of optical interference spectroscopy. In addition, a theoretical analysis both of the fine structure and also of the hyperfine structure was carried out (in the case of 5p6p of the general typenpn′p for the first time in literature). For the 3 levels 5p6p ³ P ₁, 5p7p ³ D ₂ and 5p6p ¹ P ₁ a different classification was found and consistent values for the fine structure parameters, mixing coefficients and single electron hyperfine structure splitting parametersa _nl ^ik andb _nl ^ik were obtained. The three new determinations in Sb II of the quadrupole moment (in barn) of¹²¹Sb (Q(5p6s)=?0.55(5);Q(5p6p)=?0.57(5) from the 5p-electron andQ(5p6p)=?0.7(2) from the 6p-electron) are well agreeing with each other but differ to former values from SbI. The core polarization and isotope shift of the lines, however, are compatible with our former results in SbI.     

On the line intensity ratios of prominent Si II,Si III,and Si IV multiplets

Line intensities of singly, doubly and triply ionized silicon (Si II, Si III, and Si IV, respectively) belonging to the prominent higher multiplets, are of interest in laboratory and astrophysical plasma diagnostics. We measured these line intensities in the emission spectra of pulsed helium discharge. The Si II line intensity ratios in the 3s3p²²D–3s²4p²P^o, 3s²3d²D–3s²4f²F^o, and 3s²4p²P^o–3s²4d²D transitions, the Si III line intensity ratios in the 3s3d³D–3s4p³P^o, 3s4p³P^o–3s4d³D, 3s4p³P^o–3s5s³S, 3s4s³S–3s4p³P^o, and 3s4f³F^o–3s5g³G transitions, and the Si IV line intensity ratios in the 4p²P^o–4d²D and 4p²P^o–5s²S transitions were obtained in a helium plasma at an electron temperature of about 17,000 ± 2000 K. Line shapes were recorded using a spectrograph and an ICCD camera as a highly-sensitive detection system. The silicon atoms were evaporated from a Pyrex discharge tube designed for the purpose. They represent impurities in the optically thin helium plasma at the silicon ionic wavelengths investigated. The line intensity ratios obtained were compared with those available in the literature, and with values calculated on the basis of available transition probabilities. The experimental data corresponded well with line intensity ratios calculated using the transition probabilities obtained from a Multi Configuration Hartree–Fock approximation for Si III and Si IV spectra. We recommend corrections of some Si II transition probabilities.     

Hardness evaluation of cured urea–formaldehyde resins with different formaldehyde/urea mole ratios using nanoindentation method

To understand the influence of formaldehyde/urea (F/U) mole ratio on the properties of urea–formaldehyde (UF) resins, this study investigated hardness of cured UF resins with different F/U mole ratios using a nanoindentation method. The traditional Brinell hardness (H_B) method was also used for comparison. The H_B of cured UF resin films with different F/U mole ratios was determined after exposing the films to different post-curing temperatures. The nanoindentation method was employed for these films to measure Meyer hardness (H_M) and reduced modulus (E_r) which have been used to calculate the elastic modulus (E_s) of cured UF resins. As the F/U mole ratio decreased, the H_B decreased continuously, indicating a less rigid network structure in low F/U mole ratio UF resins. The higher the post-curing temperature, the greater the value of H_B. The H_M value also showed a similar trend as a function of F/U mole ratio. However, the E_r and E_s did not show a consistent trend as exhibited by H_M and H_B. Both H_M and E_r showed much greater variation in the coefficient of variation (COV) at lower F/U mole ratios 1.0 and 1.2, indicating a more heterogeneous composition of these resins. Linear relationships between H_M and E_r indicate that heterogeneity of the surface composition of samples contributes greatly to variations in the measured values. This variability is discussed in terms of crystal structures present in the cured UF resins of low F/U mole ratios.     

A methodology to define the Cubic Equation of State of a simple fluid

A method to define the Cubic Equation of State (CES) of a simple substance is presented in this work. CES is constructed with only three parameters of the fluid, namely, the critical compressibility Z_c≡P_cv_c/RT_c, the acentric factor ω ≡ − log  (P^(sat)/P_c) − 1 (where P^(sat) is the saturated vapor pressure), and the saturated vapor volume v^(sat) at the temperature T^(sat)/T_c = 0.7 (where T_c is the critical temperature, v_c is the critical volume, and P_c is the critical pressure). The resulting CES is unique for each substance and, in general, it is different from other known CES in the literature.     

Identification of new lines in the beam-foil spectrum of B II–IV

Ten, six, and twenty-one new lines appearing in the beam-foil spectra of boron (30–200 nm) have been identified in B II, B III, and B IV, respectively. Energies have been determined with higher accuracy than obtained before for the 2p3s ¹ P ⁰, 2s6d ³ D, 2p3p ³ D, 2p3p ³ S, 2p3p ³ P, and 2p3p ¹ D terms in B II. First energy values are also reported for the 2s6d ¹ D and 2s7d ³ D terms in B II.     

Hyperfine structure in the configurations4f 4 6s 2 and4f 4 5d 6s of Nd I

The high resolution laser-atomic-beam technique was used to investigate the hyperfine structure in Nd I 4f ⁴6s ^{2 5} I,⁵ F,⁵ S and 4f ⁴5d6s ⁷ L,⁷ K,⁷ I,⁷ H. The metastable states were populated by an arc discharge burning in the atomic beam. The measured hyperfine constantsA andB of the levels of 4f ⁴6s ² and 4f ⁴5d6s allow a parametric analysis to be performed using the effective tensor operator formalism. The experimental radial integrals of the 4f and 5d electrons fit with those of the other lanthanides. The 4f radial integrals are in agreement with values of optimized Hartree-Fock-Slater calculations. The spectroscopic quadrupole moments of¹⁴³Nd and¹⁴⁵Nd are deduced from the 4f parameters:Q _I =?0.610(21) b and ?0.314(12) b, respectively. TheQ _I resulting from the 5d parameter are in satisfactory agreement with these values. The hyperfine anomaly due to thes electron in 4f ⁴5d 6s amounts to about 1%.     

Efficient and practical synthesis of both enantiomers of 6-silyloxy-3-pyranone derivatives

Lipase catalyzed kinetic resolution of racemic cis-6-(tert-butyldimethylsilyloxy)-3,6-dihydro-2H-pyran-3-ol (rac)-1 was achieved in high enantiomeric excess. Transesterification of (rac)-1 with vinylacetate in ^tBuOMe yielded the alcohol (3S,6R)-1 in 99.0% ee, whereas (3R,6S)-1 was obtained, in 99.0% ee, by the lipase catalyzed ester hydrolysis of acetate (3R,6S)-2, which was obtained along with the transesterification. Both (3S,6R)-1 and (3R,6S)-1 were subjected to oxidation to provide the corresponding 6-silyloxy-3-pyranone (6R)-3 and (6S)-3, respectively. Application to the synthesis of 7, which is the key intermediate of asymmetric synthesis of pseudomonic acid A 9 is also described.     

Semiclassical variational study of size effects in neutral and charged jellium droplets

An analytic expression for the total energy of metallic clusters composed ofN identical atoms of valencev and with net chargeQ is obtained by means of a variational solution of the Thomas-Fermi-Weizsäcker energy density functional within the spherical jellium model. The minimum energy is given as an expansion in decreasing powers of the cluster radiusR=r _s Z ^1/3, withZ=vN andr _s the radius per electron of the bulk metal. The coefficients are obtained as functions ofr _s . Terms of volume (R ³), surface (R ²), curvature (R), constant (R ⁰), (1/R) and (1/R ²) are clearly separated in the formula, as well as the different contributions (kinetic, coulombic and exchange-correlation) to each of them. The asymptotic values (R→∞) for the work functions,W(r _s ), and surface energies σ(r _s ), are compared to analogous semiclassical and Kohn-Sham calculations of jellium-like surfaces and to the experimental values. The size dependent behaviour of chemical potentials, μ(R), electron affinities,AF(R), and ionization potentials,IP(R), are easily obtained for any kind of metallic clusters. In particular we discuss the Coulomb and quantum corrections to the coefficients β, δ in the asymptotic formulae:IP?W+β/R andAF?W+δ/R.     

Fine tuning of the structure of phosphine–phosphoramidites: application for rhodium-catalyzed asymmetric hydrogenations

Diastereomers of (4-(diphenylphosphino)pentan-2-yl)-N-isopropyl-{dinaphtho[2,1-d:1′,2′-f][1,3,2]dioxa-phosphepin-2-yl}-4-amine, (S)-(2S,4S)-1, and (S)-(2R,4R)-3; the octahydro derivative 4 of (S)-(2S,4S)-1, and derivative 2 of (S)-(2S,4S)-1 containing a 1,3-propanediyl backbone, have been synthesized and used for rhodium-catalyzed asymmetric hydrogenations of prochiral olefins in order to study the role of the stereogenic elements in the backbone and in the terminal moiety. The central chirality in the bridge has been found to determine the configuration of the product with a cooperative effect from the terminal groups. Excellent ee’s (up to 99.9%) were obtained in the hydrogenation of methyl (Z)-α-acetamidocinnamate using a rhodium complex with the matched arrangement (S)-(2S,4S)-1. The hydrogenation is accomplished in a highly enantioselective manner by using green solvents such as propylene carbonate.     

Moderate generation of sulfenylnitrenes from novel N-sulfenylsulfodiimides

N-Sulfenylated sulfodiimides were first prepared by the reaction of S,S-diphenyl-N-tosylsulfodiimide with arenesulfenyl chlorides under the basic conditions. Thermolysis of S,S-diphenyl-N-(2-nitrophenylsulfenyl)- and S,S-diphenyl-N-(2,4-dinitrophenylsulfenyl)sulfodiimides in the presence of olefins proceeded at 50-80 °C to give the corresponding deiminated S,S-diphenyl-N-tosylsulfimide and N-sulfenylaziridines in very good yields. 2,4-Dinitrophenyl-sulfenylnitrene was trapped by trans- and cis-1-phenylpropenes stereospecifically. The thermolysis temperature of the N-sulfenylsulfodiimides was found to be lower than N-sulfenylsulfoximide and higher than N-sulfenyliminosulfonium salt and very effective to trap the sulfenylnitrene to give the N-sulfenylaziridines in very good yields.     

Fuzzy Symmetry Characteristics of Propadine Molecule

The fuzzy symmetry characteristics for the internal-rotation of propadine were analyzed using the fuzzy symmetry theory for molecule and molecular orbital (MO). In the process of rotation, three different symmetry point groups D_2h, D_2d, and D₂ were considered. Using the D_4h point group, which is the minimal point group including all symmetry elements of D_2h, D_2d, and D₂, we can analyze the fuzzy symmetry for this process. The elements included in D_4h point group can be classified to four subsets: (i) G0—it includes all the elements in D₂ point group, also belongs to all the above three point groups of D_2h, D_2d, and D₂; (ii) G1—it includes the elements in D_2h point group, but not in D_2d point group; (iii) G2—it includes the elements in D_2d point group, but not in D_2h point group; (iv) G3—it includes the elements in D_4h point group, but not in D_2h or D_2d point group. On the basis of the above four subsets, we analyzed the membership functions and the regularity of variation in MOs for the internal-rotation of propadine.     

Copper(I) catalysis: Synthesis of N,N′-diarylated and N-aryl,N′-formylated chiral C2-symmetric diamines

Chiral N,N′-diaryl C₂-symmetric diamines and N-aryl,N′-formyl-trans-(1R,2R)-diaminocyclohexane are readily accessed by copper catalyzed N,N′-diarylation and N-aryl,N′-formylation of trans-(1R,2R)-diaminocyclohexane with aryl bromides. N,N′-diarylation using (R)-1,1′-binaphthyl-2,2′-diamine and iodobenzene gave the corresponding (R)-N,N′-diphenyl-1,1′-binaphthyl-2,2′-diamine derivative in 83% yield.     

Crystal Structures of Three Framework Alkali Metal Uranyl Phosphate Hydrates

Three homeotypic hydrated alkali metal uranyl phosphates, A₂(UO₂)[(UO₂)(PO₄)]₄(H₂O)₂, A=Cs (CsUP), Rb (RbUP), K (KUP), were synthesized by hydrothermal methods. Intensity data were collected at room temperature using MoKα radiation and a CCD-based area detector. Their crystal structures were solved by Patterson (CsUP) and direct (RbUP, KUP) methods and refined by full-matrix least-squares techniques to agreement indices (CsUP, RbUP, KUP) wR₂=0.048, 0.230, 0.072 for all data, and R1=0.023, 0.078, 0.038 calculated for 5338, 4738, 4514 unique observed reflections (∣F_o∣≥4σ_F), respectively. The compound CsUP is orthorhombic, space group Cmc2₁, Z=4, a=14.854(1), b=13.879(1), c=12.987(1) Å, V=2677.5(3) ų. Both RbUP and KUP are monoclinic, space group Cm, but are presented in the unconventional pseudo-orthorhombic space group Fm11 to facilitate comparison with CsUP and to allow a model for RbUP that includes the effects of pseudo-merohedral twinning. RbUP is monoclinic, space group Fm11, Z=4, a=15.72(2), b=13.84(1), c=13.05(1) Å, α=90.39°(2), V=2839(5) ų; KUP is monoclinic, space group Fm11, Z=4, a=15.257(1), b=13.831(1), c=13.007(1) Å, α=91.760°(1), V=2743.4(3) ų. The structures consist of sheets of phosphate tetrahedra and uranyl pentagonal bipyramids, with composition [(UO₂)(PO₄)]⁻, that are topologically identical to the uranyl silicate sheets in uranophane-beta. These sheets are connected by a uranyl pentagonal bipyramid in the interlayer that shares corners with two phosphate tetrahedra on each of two adjacent sheets and whose fifth equatorial vertex is an H₂O group, resulting in an open framework with alkali metal cations in the larger cavities of the structures. Where CsUP and RbUP have two alkali metal positions and a H₂O group in these cavities, KUP has four K atoms and two H₂O groups, all of which are partially occupied, in the interstitial sites.     

Hyperfine structure of the resonance lines of53Cr and lifetimes of some excited states of the Cr I spectrum

The hyperfine structure of the⁵³Cr resonance linesa ⁷ S ₃ ?z ⁷ P _2,3,4 has been investigated by means of laser saturation spectroscopy. By comparison of the experimental signal curves with theoretically computed spectra the hitherto unknown sign of the magnetic hyperfine coupling constant in thea ⁷ S ₃ ground state of⁵³Cr could be determined unambigiously to be negative. Further the signs of the hfs coupling constants in thez ⁷ P states — so far only evaluated by theoretical reasoning — could be confirmed. Additionally the lifetimes of the statesz ⁷ P,z ⁵ P,f ⁷ D,z ⁵ F,e ⁷ D ₅ andy ⁵ P ₃ in the Cr I spectrum have been determined from the fluorescence decay after pulsed laser excitation.     

Helicity of N,N′-diaryl-trans-1,2-diaminocyclohexane derivatives. Implications for molecular helicity manipulations

Derivatives of trans-1,2-diaminocyclohexane (DACH), useful as chiral ligands, scaffolds and building blocks, differ in their conformation. The conformation of N,N′-diaryl-DACH derivatives was studied by the semiempirical and DFT computational methods and by exciton-coupled circular dichroism. It was found that, contrary to M-helical N,N′-diimine, N,N′-diimide and N,N′-diamide derivatives, the aromatic residues in N,N′-diphenyl derivatives are oriented to form a P-helix for the (R,R)-DACH absolute configuration. The helicity of the bis-aryl system is modified in the case of 1-naphthyl or 2-naphthyl derivatives. Further switching of helicity has been demonstrated by either protonation or mono-N-acetylation of N,N′-diaryl DACH derivatives.     

Copolymerization of acrylic acid to nylon-6 by trapped radicals—I. Vapour phase grafting

Film of nylon-6 has been γ-irradiated in vacuo to various doses D. Grafting has been effected by subsequent exposure in vacuo to vapour at 50° of composition 9.1 wt% acrylic acid and 90.9 wt% water. Determinations have been made of total vapour uptake as well as the individual swellings due to monomer and water. For D ? ca. 2 Mrad, the initial rate of grafting R_g increased with D in accord with R_g ∝ D^β with β = 0.45 ± 0.05, thus suggesting bimolecular chain termination. However, for D ? ca. 2 Mrad, there is no further increase in R_g. This is attributed in part to the fact that the radical yield is proportional to dose only for D ? ca. 2.5 Mrad. Diffusion controlled grafting has been predicted elsewhere to be characterized by β = 0.67. Grafting proceeds from the surface and the initial stages are concluded to be essentially free from diffusion control, since (a) β ≠ 0.67, (b) the rate of uptake of monomer vapour >R_g and (c) a large change in film thickness yields only a very small change in R_g.     

Engineering of Yeast Old Yellow Enzyme OYE3 Enables Its Capability Discriminating of (E)-Citral and (Z)-Citral

The importance of yeast old yellow enzymes is increasingly recognized for direct asymmetric reduction of (E/Z)-citral to (R)-citronellal. As one of the most performing old yellow enzymes, the enzyme OYE3 from Saccharomyces cerevisiae S288C exhibited complementary enantioselectivity for the reduction of (E)-citral and (Z)-citral, resulting in lower e.e. value of (R)-citronellal in the reduction of (E/Z)-citral. To develop a novel approach for the direct synthesis of enantio-pure (R)-citronellal from the reduction of (E/Z)-citral, the enzyme OYE3 was firstly modified by semi-rational design to improve its (R)-enantioselectivity. The OYE3 variants W116A and S296F showed strict (R)-enantioselectivity in the reduction of (E)-citral, and significantly reversed the (S)-enantioselectivity in the reduction of (Z)-citral. Next, the double substitution of OYE3 led to the unique variant S296F/W116G, which exhibited strict (R)-enantioselectivity in the reduction of (E)-citral and (E/Z)-citral, but was not active on (Z)-citral. Relying on its capability discriminating (E)-citral and (Z)-citral, a new cascade reaction catalyzed by the OYE3 variant S296F/W116G and glucose dehydrogenase was developed, providing the enantio-pure (R)-citronellal and the retained (Z)-citral after complete reduction of (E)-citral.