Investigation of ultra wideband multi-channel dichroic beamsplitters from 0.3 to 52µm

The development of a set of multi-channel dichroics which includes a 6 channel dichroic operating over the wavelength region from 0.3 to 52µm is described. In order to achieve the optimum performance, the optical constants of PbTe, Ge and CdTe coatings in the strongly absorptive region have been determined by use of a new iterative method using normal incidence reflectance measurement of the multilayer together with initial values of energy gap Eg and infinite refractive index n for the semiconductor model. The design and manufacture of the dichroics is discussed and the final results are presented.

Time-resolved gas-phase kinetic study of the germylene addition reaction, CH3C CCH3

Time-resolved kinetic studies of the reaction of germylene, GeH2, generated by laser. ash photolysis of 3,4-dimethyl-1-germacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reaction with 2-butyne, CH3C CCH3. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at five temperatures in the range 300-556 K. The second order rate constants obtained by extrapolation to the high pressure limits at each temperature, fitted the Arrhenius equation: log(k(infinity)/cm(3) molecule(-1) s(-1)) = (-10.46 +/- 10.06) + (5.16 +/- 10.47) kJ mol(-1)/ RT ln 10 Calculations of the energy surface of the GeC4H8 reaction system were carried out employing the additivity principle, by combining previous quantum chemical calculations of related reaction systems. These support formation of 1,2-dimethylvinylgermylene (rather than 2,3-dimethylgermirene) as the end product. RRKM calculations of the pressure dependence of the reaction are in reasonable agreement with this finding. The reactions of GeH2 with C2H2 and with CH3CRCCH3 are compared and contrasted.

Gas-phase kinetics of chlorosilylene reactions. I. ClSiH + Me3SiH: absolute rate measurements and theoretical calculations for prototype Si−H insertion reactions

Time-resolved studies of chlorosilylene, CISiH, generated by the 193 nm laser flash photolysis of 1-chloro-1-silacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reaction with trimethylsilane, Me3SiH, in the gas phase. The reaction was studied at total pressures up to 100 torr (with and without added SF6) over the temperature range 297-407 K. The rate constants were found to be pressure independent and gave the following Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-13.97 +/- 0.25) + (12.57 +/- 1.64) kJ mol(-1)/RT In 10. The Arrhenius parameters are consistent with a mechanism involving an intermediate complex, whose rearrangement is the rate-determining step. Quantum chemical calculations of the potential energy surface for this reaction and also the reactions of CISiH with SiH4 and the other methylsilanes support this conclusion. Comparisons of both experiment and theory with the analogous Si-H insertion processes of SiH2 and SiMe2 show that the main factor causing the lower reactivity of ClSiH is the secondary energy barrier. The calculations also show the existence of a novel intramolecular H-atom exchange process in the complex of ClSiH with MeSiH3.

Direct time-resolved study of the kinetics of the reaction of silylene with phenylsilane in the gas phase. Does SiH2 react with the aromatic ring?

Laser flash photolysis studies of silylene, SiH2, generated by the 193 nm laser flash photolysis phenylsilane, PhSiH3, have been carried out to obtain rate constants for its bimolecular reaction with PhSiH3 itself, in the gas phase. The reaction was studied in SF6 (mostly at 10 Torr total pressure) over the temperature range 298-595 K. The rate constants (also found to be pressure independent) gave the following Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-9.92 +/- 0.04) + (3.31 +/- 0.27) kJ mol(-1)/RT ln 10 Similar investigations of the reaction of silylene with benzene, C6H6, (295-410 K) gave data suggestive of the fact that SiH2 might be reacting with photochemical products of C6H6 as well as with C6H6 itself. However, in the latter system, apparent rate constants were sufficiently low to indicate that in the reaction of SiH2 with PhSiH3 addition to the aromatic ring was unlikely to be in excess of 3% of the total. Quantum chemical calculations of the energy surface for SiH2 + C6H6 indicate that 7-silanorcaradiene and 7-silacycloheptatriene are possible products but that PhSiH3 formation is unlikely. RRKM calculations suggest that 7-silanorcaradiene should be the initial product but that it cannot be collisionally stabilized under experimental conditions

Dimetallic complexes of macrocycles with two rigid dibenzofuran units as receptors for detection of anionic substrates

The hexaazamacrocycles [28](DBF)2N6 {cyclo[bis(4,6-dimethyldibenzo[b,d]furaniminoethyleneiminoethylene]} and [32](DBF)2N6 {cyclo[bis(4,6-dimethyldibenzo[b,d]furaniminopropyleneiminopropylene]} form stable dinuclear copper(II) complexes suitable to behave as receptors for several anionic substrates. These two receptors were used to study the binding interactions with several substrates, such as imidazole (Him) and some carboxylates [benzoate (bz−), oxalate (ox2−), malonate (mal2−), phthalate (ph2−), isophthalate (iph2−), and terephthalate (tph2−)] by spectrophotometric titrations and EPR spectroscopy in MeOH (or H2O):DMSO (1:1 v/v) solution. The largest association constant was found for ox2− with Cu2[32](DBF)2N64+, whereas for the aromatic dicarboxylate anions the binding constants follow the trend ph2− > iph2− > tph2−, i.e. decrease with the increase of the distance of the two binding sites of the substrate. On the other hand, the large blue shift of 68 nm observed by addition of Him to Cu2[32](DBF)2N64+ points out for the formation of the bridged CuimCu cascade complex, indicating this receptor as a potential sensor for the detection and determination of imidazole in solution. The X-band EPR spectra of the Cu2[28](DBF)2N64+ and Cu2[32](DBF)2N6]4+ complexes and the cascade complexes with the substrates, performed in H2O:DMSO (1:1 v/v) at 5 to 15 K, showed that the CuCu distance is slightly larger than the one found in crystal state and that this distance increases when the substrate is accommodated between the two copper centres. The crystal structure of [Cu2[28](DBF)2N6(ph)2]·CH3OH was determined by X-ray diffraction and revealed the two copper centres bridged by two ph2− anions at a Cu···Cu distance of 5.419(1) Å. Each copper centre is surrounded by three carboxylate oxygen atoms from two phthalate anions and three contiguous nitrogen atoms of the macrocycle in a pseudo octahedral coordination environment.

Magnetic coupling in trinuclear partial cubane copper(II) complexes with a hydroxo bridging core and peripheral phenoxo bridges from NNO donor Schiff base ligands

Three new trinuclear copper(II) complexes, [(CuL1)(3)(mu(3)-OH)](ClO4)(2)center dot 3.75H(2)O (1), [(CuL2)(3)(mu(3)-OH)](ClO4)(2) (2) and [(CuL3)(3)(mu(3)-OH)](BF4)(2)center dot 0.5CH(3)CN (3) have been synthesized from three tridentate Schiff bases HL1, HL2, and HL3 (HL1 = 2-[(2-amino-ethylimino)-methyl]-phenol, HL2 = 2-[(2-methylamino-ethylimino)-methyl]-phenol and HL3 = 2-[1-(2-dimethylamino-ethylimino)-ethyl]-phenol). The complexes are characterized by single-crystal X-ray diffraction analyses, IR, UV-vis and EPR spectroscopy, and variable-temperature magnetic measurements. All the compounds contain a partial cubane [Cu3O4] core consisting of the trinuclear unit [(CuL)(3)(mu(3)-OH)](2+) together with perchlorate or fluoroborate anions. In each of the complexes, the three copper atoms are five-coordinated with a distorted square-pyramidal geometry except in complex 1, in which one of the Cu-II ions of the trinuclear unit is six-coordinate being in addition weakly coordinated to one of the perchlorate anions. Variable-temperature magnetic measurements and EPR spectra indicate an antiferromagnetic exchange coupling between the CuII ions of complexes 1 and 2, while this turned out to be ferromagnetic for complex 3. Experimental values have been fitted according to an isotropic exchange Hamiltonian. Calculations based on Density Functional Theory have also been performed in order to estimate the exchange coupling constants in these three complexes. Both sets of values indicate similar trends and specially calculated J values establish a magneto-structural correlation between them and the Cu-O-Cu bond angle, in that the coupling is more ferromagnetic for smaller bond angle values.

Evolution of coronal mass ejection morphology with increasing heliocentric distance. II. In Situ observations

Interplanetary coronal mass ejections (ICMEs) are often observed to travel much faster than the ambient solar wind. If the relative speed between the two exceeds the fast magnetosonic velocity, then a shock wave will form. The Mach number and the shock standoff distance ahead of the ICME leading edge is measured to infer the vertical size of an ICME in a direction that is perpendicular to the solar wind flow. We analyze the shock standoff distance for 45 events varying between 0.5 AU and 5.5 AU in order to infer their physical dimensions. We find that the average ratio of the inferred vertical size to measured radial width, referred to as the aspect ratio, of an ICME is 2.8 ± 0.5. We also compare these results to the geometrical predictions from Paper I that forecast an aspect ratio between 3 and 6. The geometrical solution varies with heliocentric distance and appears to provide a theoretical maximum for the aspect ratio of ICMEs. The minimum aspect ratio appears to remain constant at 1 (i.e., a circular cross section) for all distances. These results suggest that possible distortions to the leading edge of ICMEs are frequent. But, these results may also indicate that the constants calculated in the empirical relationship correlating the different shock front need to be modified; or perhaps both distortions and a change in the empirical formulae are required.

Adapting the International System of Units to the twenty-first century

We review the proposal of the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM), currently being considered by the General Conference on Weights and Measures (Conférences Générales des Poids et Mesures, CGPM), to revise the International System of Units (Le Système International d’Unitès, SI). The proposal includes new definitions for four of the seven base units of the SI, and a new form of words to present the definitions of all the units. The objective of the proposed changes is to adopt definitions referenced to constants of nature, taken in the widest sense, so that the definitions may be based on what are believed to be true invariants. In particular, whereas in the current SI the kilogram, ampere, kelvin and mole are linked to exact numerical values of the mass of the international prototype of the kilogram, the magnetic constant (permeability of vacuum), the triple-point temperature of water and the molar mass of carbon-12, respectively, in the new SI these units are linked to exact numerical values of the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant, respectively. The new wording used expresses the definitions in a simple and unambiguous manner without the need for the distinction between base and derived units. The importance of relations among the fundamental constants to the definitions, and the importance of establishing a mise en pratique for the realization of each definition, are also discussed.

Molybdate and tungstate transfer by rat ileum competitive inhibition by sulphate

For both MoO42− and WO42− the maximum rate of uptake by the small intestine of the rat (studied in vitro using the everted sac technique) occurs in the lower ileum. Kinetic constants, derived by a least squares procedure, are compared with those previously obtained for SO42− transport. For both and , , with only small differences between sacs IV and V. Mutual inhibition of MoO42− and WO42− transport and inhibition of both by SO42− are competitive processes. This is shown by the generally good agreement between values and derived values and by V values in the presence and absence of the inhibiting species. The three ions SO42−, MoO42− and WO42− are probably transferred across the intestine by a common carrier system. Implications for the sulphate-molybdenum interaction in molybdosis are discussed.

Sulphate transport by rat ileum. Effect of molybdate and other anions

Kinetic constants for SO42− transport by upper and lower rat ileum in vitro have been determined by computer fitting of rate vs concentration data obtained using the everted sac technique. MoO42− inhibition of this transport is competitive, and kinetic constants for the inhibition were similarly determined. Transport is also inhibited by the anions WO42−, S2O32− and SeO42−, in the order . These anions have no effect on the transport of l-valine. Low SO42− transport rates were observed in sacs from animals fed a high-molybdenum diet. The significance of the results with respect to the problem of molybdate toxicity in animals is discussed, and related to the known protective effect of SO42−.

Conformational modulation of sequence recognition in synthetic macromolecules

The different triplet sequences in high molecular weight aromatic copolyimides comprising pyromellitimide units ("I") flanked by either ether-ketone ("K") or ether-sulfone residues ("S") show different binding strengths for pyrene-based tweezer-molecules. Such molecules bind primarily to the diimide unit through complementary π-π-stacking and hydrogen bonding. However, as shown by the magnitudes of 1H NMR complexation shifts and tweezer-polymer binding constants, the triplet "SIS" binds tweezer-molecules more strongly than "KIS" which in turn bind such molecules more strongly than "KIK". Computational models for tweezer-polymer binding, together with single-crystal X-ray analyses of tweezer-complexes with macrocyclic ether-imides, reveal that the variations in binding strength between the different triplet sequences arise from the different conformational preferences of aromatic rings at diarylketone and diarylsulfone linkages. These preferences determine whether or not chain-folding and secondary π−π-stacking occurs between the arms of the tweezermolecule and the 4,4'-biphenylene units which flank the central diimide residue.

Equidistributing Meshes with Constraints

Adaptive methods which “equidistribute” a given positive weight function are now used fairly widely for selecting discrete meshes. The disadvantage of such schemes is that the resulting mesh may not be smoothly varying. In this paper a technique is developed for equidistributing a function subject to constraints on the ratios of adjacent steps in the mesh. Given a weight function $f \geqq 0$ on an interval $[a,b]$ and constants $c$ and $K$, the method produces a mesh with points $x_0 = a,x_{j + 1} = x_j + h_j ,j = 0,1, \cdots ,n - 1$ and $x_n = b$ such that\[ \int_{xj}^{x_{j + 1} } {f \leqq c\quad {\text{and}}\quad \frac{1} {K}} \leqq \frac{{h_{j + 1} }} {{h_j }} \leqq K\quad {\text{for}}\, j = 0,1, \cdots ,n - 1 . \] A theoretical analysis of the procedure is presented, and numerical algorithms for implementing the method are given. Examples show that the procedure is effective in practice. Other types of constraints on equidistributing meshes are also discussed. The principal application of the procedure is to the solution of boundary value problems, where the weight function is generally some error indicator, and accuracy and convergence properties may depend on the smoothness of the mesh. Other practical applications include the regrading of statistical data.

Plane wave approximation in linear elasticity

We consider the approximation of solutions of the time-harmonic linear elastic wave equation by linear combinations of plane waves. We prove algebraic orders of convergence both with respect to the dimension of the approximating space and to the diameter of the domain. The error is measured in Sobolev norms and the constants in the estimates explicitly depend on the problem wavenumber. The obtained estimates can be used in the h- and p-convergence analysis of wave-based finite element schemes.

Electrospun supramolecular polymer fibres

The electrospinning of urethane based low molecular weight polymers differing only in the nature of the hydrogen bonding end-groups has been investigated. For the end-groups with the lowest binding constants at maximum solubility only droplets, are produced at the electrode; in contrast, increasing the binding constant of the end-group results in electrospun fibres being produced. The properties of the fibres produced are subject to changes in solvent, concentration and temperature. Typical diameters for these fibres were found to be some 10 s of μm, rather than the sub-micron dimensions often produced in electrospinning systems. Such diameters are related to the high initial concentrations required; this also may influence the rate of solvent removal and preferential surface solidification which feature in these examples. A simple theoretical model is used to relate the association constant to the molecular weight required for fibre formation; significantly lower levels of association are required for higher molecular weight macromonomers compared to smaller molecular systems.

The asymptotic behavior of densities related to the supremum of a stable process

If X is a stable process of index α∈(0, 2) whose Lévy measure has density cx−α−1 on (0, ∞), and S1=sup0x)∽Aα−1x−α as x→∞ and P(S1≤x)∽Bα−1ρ−1xαρ as x↓0. [Here ρ=P(X1>0) and A and B are known constants.] It is also known that S1 has a continuous density, m say. The main point of this note is to show that m(x)∽Ax−(α+1) as x→∞ and m(x)∽Bxαρ−1 as x↓0. Similar results are obtained for related densities.