Laser amplifier design

Often one wants a laser amplifier system to produce an output pulse of a specific form, e.g., time shape, energy, etc. Given any potential amplifier configuration one needs to find the proper input pulse which, when propagated through the amplifier system, results in the desired output pulse. Efficient operation of the amplifier (large energy extraction) usually implies that the response of the laser medium is nonlinear, which makes such a calculation very tedious if attempted on a hit and miss basis. Here we discuss a procedure which enables one to systematically generate the proper input pulse. Once the input is known it is straightforward to determine whether the amplifier configuration is suitable.     

Constant Sustainable Consumption Rate in Optimal Growth with Exhaustible Resources

The problem of optimal growth with an exhaustible resource deposit under R. M. Solow's criterion of maximum sustainable consumption rate, previously formulated as a minimum-resource-extraction problem, is shown to be a Mayer-type optimal-control problem. The exact solution of the relevant firstorder necessary conditions for optimality is derived for a Cobb-Douglas production function, whether or not the constant unit resource extraction cost vanishes. The related problem of maximizing the terminal capital stock over an unspecified finite planning period is investigated for the development of more efficient numerical schemes for the solution of multigrade-resource deposit problems. The results for this finite-horizon planning problem are also important from a theoretical viewpoint, since they elucidate the economic content of the optimal growth paths for infinite-horizon problems.     

There is no roughening singularity at finite temperature

It is shown, for any non-zero temperature and finite coupling, that there are large transverse fluctuations in the electric flux tubes connecting quark-antiquark pairs. For large $\text{q}\text{q}$ separation L, the average distance of the flux tube from its equilibrium position diverges like $\text{√}\text{L}$. Hence the flux tube is rough. The consequent absence of a roughening singularity may imply that rotational invariance and the continuum limit are approached more gradually than at zero temperature.     

EFFECTS OF SOG ON DPP-RECEPTOR BINDING

Concentration gradients of morphogens are known to be instrumental in cell signaling and tissue patterning. Of interest here is how the presence of a competitor of BMP ligands affects cell signaling. The effects of Sog on the binding of Dpp with cell receptors are analyzed for dorsal-ventral morphogen gradient formation in vertebrate and Drosophila embryos. This prototype system includes diffusing ligands, degradation of morphogens, and cleavage of Dpp-Sog complexes by Tolloid to free up Dpp. Simple and biologically meaningful necessary and sufficient conditions for the existence of a steady state gradient configuration are established, and existence theorems are proved. For high Sog production rates (relative to the Dpp production rate), it is found that the steady state configuration exhibits a more intense Dpp-receptor concentration near the dorsal midline. Numerical simulations of the evolution of the system show that, beyond some threshold Sog production rate, the transient Dpp-receptor concentration at the dorsal midline would become more intense than that of the steady state, before subsiding and approaching a nonuniform steady state of lower magnitude. The magnitude of the transient concentration has been found to increase by several fold with increasing Sog production rate. The highly intense Dpp activity at and around the dorsal midline is consistent with available experimental observations and other analytical studies.     

Sterically hindered diazonium salts for the grafting of a monolayer on metals

An organic monolayer is obtained on Cu, Au, and SiH by electrografting 3,5-bis-tert-butyl benzenediazonium tetrafluoroborate, as evidenced by cyclic voltammetry, IR-ATR, and ellipsometry. This results from the bulky groups at the 3,5-positions that sterically hinder the growth of the layer.     

New egg-shaped fullerenes: non-isolated pentagon structures of Tm3N@C(s)(51 365)-C84 and Gd3N@C(s)(51 365)-C84

Although there are 51 568 non-IPR and 24 IPR structures for C84, the egg-shaped endohedral fullerenes Tm3N@C(s)(51 365)-C84 and Gd3N@C(s)(51 365)-C84 utilize the same non-IPR cage structure as found initially for Tb3N@C(s)(51 365)-C84.     

Dinuclear iron complexes based on parallel beta-diiminato binding sites: syntheses, structures and reaction with O2

With the background that certain natural systems utilize two Fe(II) centres in their prosthetic groups for the activation of O2, a ligand system containing two parallel beta-diiminato binding sites linked by a xanthene backbone ([RXanthdim]2- with residues R = 2,3-dimethylphenyl and 2,4-difluorophenyl at the iminato units, respectively) was investigated with respect to its Fe(II) coordination chemistry in order to study O(2) activation reactions. Hence, the corresponding lithium salts were treated with FeCl2 to yield the complexes [Me2C6H3Xanthdim]Fe2Cl3(Li(thf)3), and [F2C6H3Xanthdim]Fe2Cl3(Li(thf)3), , respectively, each of which comprises Cl-Fe(micro-Cl)Fe-Cl(Li(thf)3) units. and indeed readily react with O2 to give the oxides [RXanthdim]Fe2Cl2O containing Fe(III)-O-Fe(III) moieties. Due to the electron withdrawing F atoms reacts more slowly than . The molecular structures of , and [Me2C6H3Xanthdim]Fe2Cl2O, , as determined by single crystal X-ray diffraction are discussed, and an investigation concerning their magnetic properties revealed an antiferromagnetic coupling of the two iron centres in all complexes; naturally, the strongest coupling is observed for .     

Cu-Bound Formates are Main Reaction Intermediates during CO2 Hydrogenation to Methanol over Cu/ZrO2

Cu/ZrO₂ is a promising catalyst for the hydrogenation of CO₂ to methanol. Reaction pathways involving formates or hydroxycarbonyls have been proposed. We show here that three different types of formates can be observed under reaction conditions at 220 °C and 3 bar, one being located on metallic Cu and two others being bound to ZrO₂. The surface concentrations of formates were determined through calibration curves and their reactivity measured during chemical transient experiments. The Cu-bound formate represented only about 7 % of surface formates, but exhibited a higher reactivity and was found to be the only formate that could account for all the production of methanol. Copper is thus not there only to activate H₂, but also bears other crucial intermediates. This work reemphasizes that fully quantitative IR analyses and transient methods are required to unravel the role of surface species.     

Structural studies of TcO2 by neutron powder diffraction and first-principles calculations

Crystalline technetium dioxide was prepared and for the first time its crystal structure determined by neutron powder diffraction. In addition, electronic structure calculations using density functional theory were performed to further elucidate the bonding mechanisms in TcO2. The crystal structure determined by Rietveld analysis with the NPD data is of a distorted rutile type, similar to that of MoO2; space group P21/c, a = 5.6891(1), b = 4.7546(1), c = 5.5195(1) A, and beta = 121.453(1) degrees . The NPD analysis also establishes a new neutron scattering length of 6.00(3) fm for 99Tc. Our results clearly show metal-metal bonding between Tc pairs along the edge-sharing chains of TcO6 octahedra. The Tc-Tc bond was found to be 2.622(1) A from NPD profile analysis and 2.59 A from first-principles DFT calculations. The bond is somewhat longer than expected from earlier predictions, suggesting that the nature of the Tc-Tc interaction is weaker than anticipated for the Tc(IV) cation with three outer electrons. The NPD results supported by the DFT calculations suggest that the filling of antibonding orbitals and the influence of the crystal field stabilization of the d3 Tc cations lead to more regular TcO6 octahedra and diminish the metal-metal bond strength compared with closely related oxides such MoO2 and WO2.