Structural and magnetic studies of Schiff base complexes of nickel(ii) nitrite: change in crystalline state, ligand rearrangement and a very rare μ-nitrito-1κO:2κN:3κO′ bridging mode

Four new nickel(II) complexes, [Ni2L2(NO2)2]·CH2Cl2·C2H5OH, 2H2O (1), [Ni2L2(DMF)2(m-NO2)]ClO4·DMF (2a), [Ni2L2(DMF)2(m-NO2)]ClO4 (2b) and [Ni3L¢2(m3-NO2)2(CH2Cl2)]n·1.5H2O (3) where HL = 2-[(3-amino-propylimino)-methyl]-phenol, H2L¢ = 2-({3-[(2-hydroxy-benzylidene)-amino]-propylimino}-methyl)-phenol and DMF = N,N-dimethylformamide, have been synthesized starting with the precursor complex [NiL2]·2H2O, nickel(II) perchlorate and sodium nitrite and characterized structurally and magnetically. The structural analyses reveal that in all the complexes, NiII ions possess a distorted octahedral geometry. Complex 1 is a dinuclear di-m2-phenoxo bridged species in which nitrite ion acts as chelating co-ligand. Complexes 2a and 2b also consist of dinuclear entities, but in these two compounds a cis-(m-nitrito-1kO:2kN) bridge is present in addition to the di-m2-phenoxo bridge. The molecular structures of 2a and 2b are equivalent; they differ only in that 2a contains an additional solvated DMF molecule. Complex 3 is formed by ligand rearrangement and is a one-dimensional polymer in which double phenoxo as well as m-nitrito-1kO:2kN bridged trinuclear units are linked through a very rare m3-nitrito-1kO:2kN:3kO¢ bridge. Analysis of variable-temperature magnetic susceptibility data indicates that there is a global weak antiferromagnetic interaction between the nickel(II) ions in four complexes, with exchange parameters J of -5.26, -11.45, -10.66 and -5.99 cm-1 for 1, 2a, 2b and 3, respectively

Standardized test to evaluate numerical weather prediction algorithms

In order to assist in comparing the computational techniques used in different models, the authors propose a standardized set of one-dimensional numerical experiments that could be completed for each model. The results of these experiments, with a simplified form of the computational representation for advection, diffusion, pressure gradient term, Coriolis term, and filter used in the models, should be reported in the peer-reviewed literature. Specific recommendations are described in this paper.

Anion-directed template synthesis and hydrolysis of mono-condensed Schiff base of 1,3-pentanediamine ando-hydroxyacetophenone in NiII and CuII Complexes

Bis(o-hydroxyacetophenone)nickel(II) dihydrate, on reaction with 1,3-pentanediamine, yields a bis-chelate complex [NiL2]·2H2O (1) of mono-condensed tridentate Schiff baseligand HL {2-[1-(3-aminopentylimino)ethyl]phenol}. The Schiff base has been freed from the complex by precipitating the NiII as a dimethylglyoximato complex. HL reacts smoothly with Ni(SCN)2·4H2O furnishing the complex [NiL(NCS)] (2) and with CuCl2·2H2O in the presence of NaN3 or NH4SCN producing [CuL(N3)]2 (3) or [CuL(NCS)] (4). On the other hand, upon reaction with Cu(ClO4)2·6H2O and Cu(NO3)2·3H2O, 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)2·6H2O or Ni(NO3)2·6H2O 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, NiII possesses square-planar geometry, being coordinated by the tridentate mono-negative Schiff base, L and the isothiocyanate group. The coordination environment around CuII 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 CuII is square pyramidal. In both 5 and 6, the CuII 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.

Correlation between Fourier series expansion and Hückel orbital theory

The Fourier series can be used to describe periodic phenomena such as the one-dimensional crystal wave function. By the trigonometric treatements in Hückel theory it is shown that Hückel theory is a special case of Fourier series theory. Thus, the conjugated π system is in fact a periodic system. Therefore, it can be explained why such a simple theorem as Hückel theory can be so powerful in organic chemistry. Although it only considers the immediate neighboring interactions, it implicitly takes account of the periodicity in the complete picture where all the interactions are considered. Furthermore, the success of the trigonometric methods in Hückel theory is not accidental, as it based on the fact that Hückel theory is a specific example of the more general method of Fourier series expansion. It is also important for education purposes to expand a specific approach such as Hückel theory into a more general method such as Fourier series expansion.

Assessing levels of uncertainty in recent temperature time series

We examine to what degree we can expect to obtain accurate temperature trends for the last two decades near the surface and in the lower troposphere. We compare temperatures obtained from surface observations and radiosondes as well as satellite-based measurements from the Microwave Soundings Units (MSU), which have been adjusted for orbital decay and non-linear instrument-body effects, and reanalyses from the European Centre for Medium-Range Weather Forecasts (ERA) and the National Centre for Environmental Prediction (NCEP). In regions with abundant conventional data coverage, where the MSU has no major influence on the reanalysis, temperature anomalies obtained from microwave sounders, radiosondes and from both reanalyses agree reasonably. Where coverage is insufficient, in particular over the tropical oceans, large differences are found between the MSU and either reanalysis. These differences apparently relate to changes in the satellite data availability and to differing satellite retrieval methodologies, to which both reanalyses are quite sensitive over the oceans. For NCEP, this results from the use of raw radiances directly incorporated into the analysis, which make the reanalysis sensitive to changes in the underlying algorithms, e.g. those introduced in August 1992. For ERA, the bias-correction of the one-dimensional variational analysis may introduce an error when the satellite relative to which the correction is calculated is biased itself or when radiances change on a time scale longer than a couple of months, e.g. due to orbit decay. ERA inhomogeneities are apparent in April 1985, October/November 1986 and April 1989. These dates can be identified with the replacements of satellites. It is possible that a negative bias in the sea surface temperatures (SSTs) used in the reanalyses may have been introduced over the period of the satellite record. This could have resulted from a decrease in the number of ship measurements, a concomitant increase in the importance of satellite-derived SSTs, and a likely cold bias in the latter. Alternately, a warm bias in SSTs could have been caused by an increase in the percentage of buoy measurements (relative to deeper ship intake measurements) in the tropical Pacific. No indications for uncorrected inhomogeneities of land surface temperatures could be found. Near-surface temperatures have biases in the boundary layer in both reanalyses, presumably due to the incorrect treatment of snow cover. The increase of near-surface compared to lower tropospheric temperatures in the last two decades may be due to a combination of several factors, including high-latitude near-surface winter warming due to an enhanced NAO and upper-tropospheric cooling due to stratospheric ozone decrease.

Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part I: gravity wave forcing

Parameterization schemes for the drag due to atmospheric gravity waves are discussed and compared in the context of a simple one-dimensional model of the quasi-biennial oscillation (QBO). A number of fundamental issues are examined in detail, with the goal of providing a better understanding of the mechanism by which gravity wave drag can produce an equatorial zonal wind oscillation. The gravity wave–driven QBOs are compared with those obtained from a parameterization of equatorial planetary waves. In all gravity wave cases, it is seen that the inclusion of vertical diffusion is crucial for the descent of the shear zones and the development of the QBO. An important difference between the schemes for the two types of waves is that in the case of equatorial planetary waves, vertical diffusion is needed only at the lowest levels, while for the gravity wave drag schemes it must be included at all levels. The question of whether there is downward propagation of influence in the simulated QBOs is addressed. In the gravity wave drag schemes, the evolution of the wind at a given level depends on the wind above, as well as on the wind below. This is in contrast to the parameterization for the equatorial planetary waves in which there is downward propagation of phase only. The stability of a zero-wind initial state is examined, and it is determined that a small perturbation to such a state will amplify with time to the extent that a zonal wind oscillation is permitted.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part II: combined effects of gravity waves and equatorial planetary waves

This study examines the effect of combining equatorial planetary wave drag and gravity wave drag in a one-dimensional zonal mean model of the quasi-biennial oscillation (QBO). Several different combinations of planetary wave and gravity wave drag schemes are considered in the investigations, with the aim being to assess which aspects of the different schemes affect the nature of the modeled QBO. Results show that it is possible to generate a realistic-looking QBO with various combinations of drag from the two types of waves, but there are some constraints on the wave input spectra and amplitudes. For example, if the phase speeds of the gravity waves in the input spectrum are large relative to those of the equatorial planetary waves, critical level absorption of the equatorial planetary waves may occur. The resulting mean-wind oscillation, in that case, is driven almost exclusively by the gravity wave drag, with only a small contribution from the planetary waves at low levels. With an appropriate choice of wave input parameters, it is possible to obtain a QBO with a realistic period and to which both types of waves contribute. This is the regime in which the terrestrial QBO appears to reside. There may also be constraints on the initial strength of the wind shear, and these are similar to the constraints that apply when gravity wave drag is used without any planetary wave drag. In recent years, it has been observed that, in order to simulate the QBO accurately, general circulation models require parameterized gravity wave drag, in addition to the drag from resolved planetary-scale waves, and that even if the planetary wave amplitudes are incorrect, the gravity wave drag can be adjusted to compensate. This study provides a basis for knowing that such a compensation is possible.

Motion planning of autonomous vehicles in a non-autonomous vehicle environment without speed lanes

Planning is one of the key problems for autonomous vehicles operating in road scenarios. Present planning algorithms operate with the assumption that traffic is organised in predefined speed lanes, which makes it impossible to allow autonomous vehicles in countries with unorganised traffic. Unorganised traffic is though capable of higher traffic bandwidths when constituting vehicles vary in their speed capabilities and sizes. Diverse vehicles in an unorganised exhibit unique driving behaviours which are analysed in this paper by a simulation study. The aim of the work reported here is to create a planning algorithm for mixed traffic consisting of both autonomous and non-autonomous vehicles without any inter-vehicle communication. The awareness (e.g. vision) of every vehicle is restricted to nearby vehicles only and a straight infinite road is assumed for decision making regarding navigation in the presence of multiple vehicles. Exhibited behaviours include obstacle avoidance, overtaking, giving way for vehicles to overtake from behind, vehicle following, adjusting the lateral lane position and so on. A conflict of plans is a major issue which will almost certainly arise in the absence of inter-vehicle communication. Hence each vehicle needs to continuously track other vehicles and rectify plans whenever a collision seems likely. Further it is observed here that driver aggression plays a vital role in overall traffic dynamics, hence this has also been factored in accordingly. This work is hence a step forward towards achieving autonomous vehicles in unorganised traffic, while similar effort would be required for planning problems such as intersections, mergers, diversions and other modules like localisation.

Ternary erbium chromium sulfides : structural relationships and magnetic properties

Single crystals of four erbium-chromium sulfides have been grown by chemical vapor transport using iodine as the transporting agent. Single-crystal X-ray diffraction reveals that in Er(3)CrS(6) octahedral sites are occupied exclusively by Cr(3+) cations, leading to one-dimensional CrS(4)(5-) chains of edge-sharing octahedra, while in Er(2)CrS(4), Er(3+), and Cr(2+) cations occupy the available octahedral sites in an ordered manner. By contrast, in Er(6)Cr(2)S(11) and Er(4)CrS(7), Er(3+) and Cr(2+) ions are disordered over the octahedral sites. In Er(2)CrS(4), Er(6)Cr(2)S(11), and Er(4)CrS(7), the network of octahedra generates an anionic framework constructed from M(2)S(5) slabs of varying thickness, linked by one-dimensional octahedral chains. This suggests that these three phases belong to a series in which the anionic framework may be described by the general formula [M(2n+1)S(4n+3)](x-), with charge balancing provided by Er(3+) cations located in sites of high-coordination number within one-dimensional channels defined by the framework. Er(4)CrS(7), Er(6)Cr(2)S(11), and Er(2)CrS(4) may thus be considered as the n = 1, 2, and infinity members of this series. While Er(4)CrS(7) is paramagnetic, successive magnetic transitions associated with ordering of the chromium and erbium sub-lattices are observed on cooling Er(3)CrS(6) (T(C)(Cr) = 30 K; T(C)(Er) = 11 K) and Er(2)CrS(4) (T(N)(Cr) = 42 K, T(N)(Er) = 10 K) whereas Er(6)Cr(2)S(11) exhibits ordering of the chromium sub-lattice only (T(N) = 11.4 K).

A study of the microstructure and condition of thin sheets of painting support ivory using SEM and ESEM

This paper outlines a study of the microstructure of thin sheets of ivory used as a painting support for portrait miniatures. Warping of the ivory support is one of the main problems commonly found in portrait miniatures from the late eighteenth century and early nineteenth century. Portrait miniatures from this period are painted on very thin sheets of ivory that are often only 0.2 mm in thickness. Warping can lead to cracking of the ivory and can also accentuate flaking of the paint layer. The problem of warping in ivory has thus been of long-term interest to conservators who deal with portrait miniatures, including those at the Victoria and Albert (V&A) Museum. The causes of warping are complex. However, it should be noted that artists normally stuck the thin ivory sheets onto paper or card before commencing the painting. The possible causes of warping therefore are thought to relate to the differential reactions of the ivory/adhesive/paper or card layers to changes in relative humidity (RH). It is well known that ivory is hygroscopic and anisotropic.1 However, only a few scientific studies have been carried out related to this subject and systematic analyses of the morphological and microstructural changes due to changes in RH or moisture in such thin sheets of ivory have yet to be investigated.

A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

Comments on some recent measurements of anomalously steep N2O and O3tracer spectra in the stratospheric surf zone

Recent aircraft measurements, primarily in the extratropics, of the horizontal variance of nitrous oxide (N2O) and ozone (O3) in the middle stratosphere indicate that horizontal spectra of the tracer variance scale nearly as k−2, where k is the spatial wavenumber along the aircraft flight track [Strahan and Mahlman, 1994; Bacmeister et al., 1996]. This spectral scaling has been regarded as inconsistent with the accepted picture of stratospheric tracer motion; large-scale quasi-two-dimensional tracer advection typically yields a k−1 scaling (i.e., the classical Batchelor spectrum). In this paper it is argued that the nearly k−2 scaling seen in the measurements is a natural outcome of quasi-two-dimensional filamentation of the polar vortex edge. The accepted picture of stratospheric tracer motion can thus be retained: no additional physical processes are needed to account for deviations from the Batchelor spectrum. Our argument is based on the finite lifetime of tracer filaments and on the “singularity spectrum” associated with a one-dimensional field composed of randomly spaced jumps in concentration.