Anion-directed template synthesis and hydrolysis of mono-condensed Schiff base of 1,3-pentanediamine and o-hydroxyacetophenone in Ni-II and Cu-II complexes

Bis(o-hydroxyacetophenone)nickel(II) dihydrate, on reaction with 1,3-pentanediamine, yields a bis-chelate complex [NiL2]center dot 2H(2)O (1) of mono-condensed tridentate Schiff base ligand HL {2-[1-(3-aminopentylimino)ethyl]phenol}. The Schiff base has been freed from the complex by precipitating the Nil, as a dimethylglyoximato complex. HL reacts smoothly with Ni(SCN)(2)center dot 4H(2)O furnishing the complex [NiL(NCS)] (2) and with CuCl2 center dot 2H(2)O in the presence of NaN3 or NH4SCN producing [CuL(N-3)](2) (3) or [CuL(NCS)] (4). On the other hand, upon reaction with Cu(ClO4)(2)center dot 6H(2)O and Cu(NO3)(2)center dot 3H(2)O, the Schiff base undergoes hydrolysis to yield ternary complexes [Cu(hap)(pn)(H2O)]ClO4 (5) and [Cu(hap)(pn)(H2O)]NO3 (6), respectively (Hhap = o-hydroxyacetophenone and pn = 1,3-pentanediamine). The ligand HL undergoes hydrolysis also on reaction with Ni(ClO4)(2)center dot 6H(2)O or Ni(NO3)(2)center dot 6H(2)O to yield [Ni(hap)(2)] (7). The structures of the complexes 2, 3, 5, 6, and 7 have been confirmed by single-crystal X-ray analysis. In complex 2, Ni-II possesses square-planar geometry, being coordinated by the tridentate mono-negative Schiff base, L and the isothiocyanate group. The coordination environment around Cu-II in complex 3 is very similar to that in complex 2 but here two units are joined together by end-on, axial-equatorial azide bridges to result in a dimer in which the geometry around Cu-II is square pyramidal. In both 5 and 6, the Cu-II atoms display the square-pyramidal environment; the equatorial sites being coordinated by the two amine groups of 1,3-pentanediamine and two oxygen atoms of o-hydroxyacetophenone. The axial site is coordinated by a water molecule. Complex 7 is a square-planar complex with the Ni atom bonded to four oxygen atoms from two hap moieties. The mononuclear units of 2 and dinuclear units of 3 are linked by strong hydrogen bonds to form a one-dimensional network. The mononuclear units of 5 and 6 are joined together to form a dimer by very strong hydrogen bonds through the coordinated water molecule. These dimers are further involved in hydrogen bonding with the respective counteranions to form 2-D net-like open frameworks. ((C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008).

Different supramolecular hydrogen bond structures and significant changes in magnetic properties in dinuclear mu(2)-1,1-N-3 copper(II) complexes with very similar tridentate Schiff base blocking ligands

Three new basal-apical, mu(2)-1,1-azide bridged complexes, [CuL1(N-3)](2) (1), [CuL2(N-3)](2) (2) and [CuL3(N-3)]2 (3) with very similar tridentate Schiff base blocking ligands [L-1=N-(3-aminopropyl) salicylaldimine, L-2=7-amino-4-methyl-5-azahept-3-en-2-one and L-3=8-amino-4-methyl-5-azaoct-3-en-2-one) have been synthesised and their molecular structures determined by X-ray crystallography. In complex 1, there is no inter-dimer H-bonding. However, complexes 2 and 3 form two different supramolecular structures in which the dinuclear entities are linked by strong H-bonds giving one-dimensional systems. Variable-temperature (300-2 K) magnetic susceptibility measurements and magnetization measurements at 2 K reveal that complexes 1 and 2 have antiferromagnetic coupling while 3 has ferromagnetic coupling which is also confirmed by EPR spectra at 4-300 K. Magnetostructural correlations have been made taking into consideration both the azido bridging ligands and the existence of intermolecular hydrogen bonds in complexes 2 and 3.

Supramolecular hydrogen-bond structures and magnetic interactions in basal-apical, dinuclear, azide-bridged copper(II) complexes

The synthesis, characterisation, X-ray single crystal structures and magnetic properties of three new basal-apical mu(2)-1,1-azide-bridged complexes [(CuLN3)-N-1](2) (1), [(CuLN3)-N-2](2) (2) and [(CuLN3)-N-3](2) (3) with very similar tridentate Schiff-base blocking ligands {HL1 = N-[2-(ethylamino) ethyl] salicylaldimine; HL2 = 7-(ethylamino)-4-methyl-5-azahept-3-en-2-one; HL3 = 7-amino-4-methyl-5-azaoct-3-en-2-one} have been reported [complex 1: monoclinic, P2(1)/c, a = 8.390(2), b = 7.512(2), c = 19.822(6) Angstrom, beta = 91.45(5)degrees; complex 2: monoclinic, P2(1)/c, a = 8.070(9), b = 9.787(12), c = 15.743(17) A, beta = 98.467(10)degrees; complex 3: monoclinic, P2(1)/n, a = 5.884(7), b = 16.147(18), c = 11.901(12) Angstrom, beta = 90.050(10)degrees]. The structures consist of neutral dinuclear entities resulting from the pairing of two mononuclear units through end-on azide bridges connecting an equatorial position of one copper centre to an axial position of the other, The copper ions adopt a (4+1) square-based geometry in all the complexes. In complex 2, there is no inter-dimer hydrogen-bonding. However, complexes 1 and 3 form two different supramolecular structures in which the dinuclear entities are linked by H-bonds giving one-dimensional systems. Variable temperature (300-2 K) magnetic-susceptibility measurements and magnetisation measurements at 2 K reveal that all three complexes have antiferromagnetic coupling. Magneto-structural correlations have been made taking into consideration both the azido bridging ligands and the existence of intermolecular hydrogen bonds. ((C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2004).

Cu-II acetate complexes involving N,N,O donor Schiff base ligands: Mono-atomic oxygen bridged dimers and alternating chains of the dimers and Cu-2(OAc)(4)

Two tridentate N,N,O donor Schiff bases, HL1 (4-(2-ethylamino-ethylimino)-pentan-2-one) and HL2 (3-(2-amino-propylimino)-1-phenyl-butan-1-one) on reaction with Cu-II acetate in presence of triethyl amine yielded two basal-apical, mono-atomic acetate oxygen-bridging dimeric copper(II) complexes, [Cu2L21(OAc)(2)] (1), [Cu2L22(OAc)(2)] (2). Whereas two other similar tridentate ligands HL3 (4-(2-amino-propylimino)-pentane-2-one) and HL3 (3-(2-amino-ethylimino)-1-phenyl-butan-1-one) under the same conditions produced a mixture of the corresponding dinners and a one-dimensional alternating chain of the dimer and copper acetate moiety, [Cu4L23(OAc)(6)](n) (3) and [Cu4L24(OAc)(6)](n) (4), formed by a very rare mu(3) bridging mode of the acetate ion. All four complexes (1-4) have been characterized by X-ray crystallography. The isotropic Hamiltonian, H = -JS(1)S(2) has been used to interpret the magnetic data. Magnetic measurements of 1 and 2 in the temperature range 2-300 K reveal a very weak antiferromagnetic coupling for both complexes U = -0.56 and -1.19 cm(-1) for 1 and 2, respectively). (C) 2008 Elsevier Ltd. All rights reserved.

A similarity solution for a shock reflection problem in isentropic gas dynamics

A one-dimensional shock-reflection test problem in the case of slab, cylindrical, or spherical symmetry is discussed. The differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankie-Hugoniot shock relations.

Similarity solutions of the shallow water equations

A one-dimensional shock (bore) reflection problem is discussed for the two-dimensional shallow water equations with cylindrical symmetry. The differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankine-Hugoniot shock relations.

Prediction of supercritical flow in open channels

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. A linearised problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Similarity solutions for multicomponent flows

A one-dimensional shock-reflection test problem in the case of slab, cylindrical or spherical symmetry is discussed for multi-component flows. The differential equations for a similarity solution are derived and then solved numerically in conjunction with the Rankine-Hugoniot shock relations.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Using Doppler radar with a simple explicit microphysics model to diagnose problems with ice sublimation depth-scales in forecast models

Several previous studies have attempted to assess the sublimation depth-scales of ice particles from clouds into clear air. Upon examining the sublimation depth-scales in the Met Office Unified Model (MetUM), it was found that the MetUM has evaporation depth-scales 2–3 times larger than radar observations. Similar results can be seen in the European Centre for Medium-Range Weather Forecasts (ECMWF), Regional Atmospheric Climate Model (RACMO) and Météo-France models. In this study, we use radar simulation (converting model variables into radar observations) and one-dimensional explicit microphysics numerical modelling to test and diagnose the cause of the deep sublimation depth-scales in the forecast model. The MetUM data and parametrization scheme are used to predict terminal velocity, which can be compared with the observed Doppler velocity. This can then be used to test the hypothesis as to why the sublimation depth-scale is too large within the MetUM. Turbulence could lead to dry air entrainment and higher evaporation rates; particle density may be wrong, particle capacitance may be too high and lead to incorrect evaporation rates or the humidity within the sublimating layer may be incorrectly represented. We show that the most likely cause of deep sublimation zones is an incorrect representation of model humidity in the layer. This is tested further by using a one-dimensional explicit microphysics model, which tests the sensitivity of ice sublimation to key atmospheric variables and is capable of including sonde and radar measurements to simulate real cases. Results suggest that the MetUM grid resolution at ice cloud altitudes is not sufficient enough to maintain the sharp drop in humidity that is observed in the sublimation zone.

A self-structured adaptive decision feedback equalizer

In a decision feedback equalizer (DFE), the structural parameters, including the decision delay, the feedforward filter (FFF), and feedback filter (FBF) lengths, must be carefully chosen, as they greatly influence the performance. Although the FBF length can be set as the channel memory, there is no closed-form expression for the FFF length and decision delay. In this letter, first we analytically show that the two-dimensional search for the optimum FFF length and decision delay can be simplified to a one-dimensional search and then describe a new adaptive DFE where the optimum structural parameters can be self-adapted.

Flexible MMSE DFE using length and LAG adaptation

This paper investigates how to choose the optimum tap-length and decision delay for the decision feedback equalizer (DFE). Although the feedback filter length can be set as the channel memory, there is no closed-form expression for the feedforward filter length and decision delay. In this paper, first we analytically show that the two dimensional search for the optimum feedforward filter length and decision delay can be simplified to a one dimensional search, and then describe a new adaptive DFE where the optimum structural parameters can be self-adapted.

Dispersion of a point-source release of a passive scalar through an urban-like array for different wind directions

The dispersion of a point-source release of a passive scalar in a regular array of cubical, urban-like, obstacles is investigated by means of direct numerical simulations. The simulations are conducted under conditions of neutral stability and fully rough turbulent flow, at a roughness Reynolds number of Reτ = 500. The Navier–Stokes and scalar equations are integrated assuming a constant rate release from a point source close to the ground within the array. We focus on short-range dispersion, when most of the material is still within the building canopy. Mean and fluctuating concentrations are computed for three different pressure gradient directions (0◦ , 30◦ , 45◦). The results agree well with available experimental data measured in a water channel for a flow angle of 0◦ . Profiles of mean concentration and the three-dimensional structure of the dispersion pattern are compared for the different forcing angles. A number of processes affecting the plume structure are identified and discussed, including: (i) advection or channelling of scalar down ‘streets’, (ii) lateral dispersion by turbulent fluctuations and topological dispersion induced by dividing streamlines around buildings, (iii) skewing of the plume due to flow turning with height, (iv) detrainment by turbulent dispersion or mean recirculation, (v) entrainment and release of scalar in building wakes, giving rise to ‘secondary sources’, (vi) plume meandering due to unsteady turbulent fluctuations. Finally, results on relative concentration fluctuations are presented and compared with the literature for point source dispersion over flat terrain and urban arrays. Keywords Direct numerical simulation · Dispersion modelling · Urban array

Virtual landmarking for locality aware peer IDs

In Peer-to-Peer (P2P) networks, it is often desirable to assign node IDs which preserve locality relationships in the underlying topology. Node locality can be embedded into node IDs by utilizing a one dimensional mapping by a Hilbert space filling curve on a vector of network distances from each node to a subset of reference landmark nodes within the network. However this approach is fundamentally limited because while robustness and accuracy might be expected to improve with the number of landmarks, the effectiveness of 1 dimensional Hilbert Curve mapping falls for the curse of dimensionality. This work proposes an approach to solve this issue using Landmark Multidimensional Scaling (LMDS) to reduce a large set of landmarks to a smaller set of virtual landmarks. This smaller set of landmarks has been postulated to represent the intrinsic dimensionality of the network space and therefore a space filling curve applied to these virtual landmarks is expected to produce a better mapping of the node ID space. The proposed approach, the Virtual Landmarks Hilbert Curve (VLHC), is particularly suitable for decentralised systems like P2P networks. In the experimental simulations the effectiveness of the methods is measured by means of the locality preservation derived from node IDs in terms of latency to nearest neighbours. A variety of realistic network topologies are simulated and this work provides strong evidence to suggest that VLHC performs better than either Hilbert Curves or LMDS use independently of each other.