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

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.

ATD: a multiplatform for semiautomatic 3-D detection of kidneys and their pathology in real time

This research presents a novel multi-functional system for medical Imaging-enabled Assistive Diagnosis (IAD). Although the IAD demonstrator has focused on abdominal images and supports the clinical diagnosis of kidneys using CT/MRI imaging, it can be adapted to work on image delineation, annotation and 3D real-size volumetric modelling of other organ structures such as the brain, spine, etc. The IAD provides advanced real-time 3D visualisation and measurements with fully automated functionalities as developed in two stages. In the first stage, via the clinically driven user interface, specialist clinicians use CT/MRI imaging datasets to accurately delineate and annotate the kidneys and their possible abnormalities, thus creating “3D Golden Standard Models”. Based on these models, in the second stage, clinical support staff i.e. medical technicians interactively define model-based rules and parameters for the integrated “Automatic Recognition Framework” to achieve results which are closest to that of the clinicians. These specific rules and parameters are stored in “Templates” and can later be used by any clinician to automatically identify organ structures i.e. kidneys and their possible abnormalities. The system also supports the transmission of these “Templates” to another expert for a second opinion. A 3D model of the body, the organs and their possible pathology with real metrics is also integrated. The automatic functionality was tested on eleven MRI datasets (comprising of 286 images) and the 3D models were validated by comparing them with the metrics from the corresponding “3D Golden Standard Models”. The system provides metrics for the evaluation of the results, in terms of Accuracy, Precision, Sensitivity, Specificity and Dice Similarity Coefficient (DSC) so as to enable benchmarking of its performance. The first IAD prototype has produced promising results as its performance accuracy based on the most widely deployed evaluation metric, DSC, yields 97% for the recognition of kidneys and 96% for their abnormalities; whilst across all the above evaluation metrics its performance ranges between 96% and 100%. Further development of the IAD system is in progress to extend and evaluate its clinical diagnostic support capability through development and integration of additional algorithms to offer fully computer-aided identification of other organs and their abnormalities based on CT/MRI/Ultra-sound Imaging.

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

On the use of a time sequence of surface pressures in four-dimensional data assimilation

The possibility of using a time sequence of surface pressure observations in four-dimensional data assimilation is being investigated. It is shown that a linear multilevel quasi-geostrophic model can be updated successfully with surface data alone, provided the number of time levels are at least as many as the number of vertical levels. It is further demonstrated that current statistical analysis procedures are very inefficient to assimilate surface observations, and it is shown by numerical experiments that the vertical interpolation must be carried out using the structure of the most dominating baroclinic mode in order to obtain a satisfactory updating. Different possible ways towards finding a practical solution are being discussed.

Problems in four-dimensional data assimilation

With the introduction of new observing systems based on asynoptic observations, the analysis problem has changed in character. In the near future we may expect that a considerable part of meteorological observations will be unevenly distributed in four dimensions, i.e. three dimensions in space and one in time. The term analysis, or objective analysis in meteorology, means the process of interpolating observed meteorological observations from unevenly distributed locations to a network of regularly spaced grid points. Necessitated by the requirement of numerical weather prediction models to solve the governing finite difference equations on such a grid lattice, the objective analysis is a three-dimensional (or mostly two-dimensional) interpolation technique. As a consequence of the structure of the conventional synoptic network with separated data-sparse and data-dense areas, four-dimensional analysis has in fact been intensively used for many years. Weather services have thus based their analysis not only on synoptic data at the time of the analysis and climatology, but also on the fields predicted from the previous observation hour and valid at the time of the analysis. The inclusion of the time dimension in objective analysis will be called four-dimensional data assimilation. From one point of view it seems possible to apply the conventional technique on the new data sources by simply reducing the time interval in the analysis-forecasting cycle. This could in fact be justified also for the conventional observations. We have a fairly good coverage of surface observations 8 times a day and several upper air stations are making radiosonde and radiowind observations 4 times a day. If we have a 3-hour step in the analysis-forecasting cycle instead of 12 hours, which is applied most often, we may without any difficulties treat all observations as synoptic. No observation would thus be more than 90 minutes off time and the observations even during strong transient motion would fall within a horizontal mesh of 500 km * 500 km.

Extensivity of two-dimensional turbulence

This study is concerned with how the attractor dimension of the two-dimensional Navier–Stokes equations depends on characteristic length scales, including the system integral length scale, the forcing length scale, and the dissipation length scale. Upper bounds on the attractor dimension derived by Constantin, Foias and Temam are analysed. It is shown that the optimal attractor-dimension estimate grows linearly with the domain area (suggestive of extensive chaos), for a sufficiently large domain, if the kinematic viscosity and the amplitude and length scale of the forcing are held fixed. For sufficiently small domain area, a slightly “super-extensive” estimate becomes optimal. In the extensive regime, the attractor-dimension estimate is given by the ratio of the domain area to the square of the dissipation length scale defined, on physical grounds, in terms of the average rate of shear. This dissipation length scale (which is not necessarily the scale at which the energy or enstrophy dissipation takes place) can be identified with the dimension correlation length scale, the square of which is interpreted, according to the concept of extensive chaos, as the area of a subsystem with one degree of freedom. Furthermore, these length scales can be identified with a “minimum length scale” of the flow, which is rigorously deduced from the concept of determining nodes.

Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence

We study two-dimensional (2D) turbulence in a doubly periodic domain driven by a monoscale-like forcing and damped by various dissipation mechanisms of the form νμ(−Δ)μ. By “monoscale-like” we mean that the forcing is applied over a finite range of wavenumbers kmin≤k≤kmax, and that the ratio of enstrophy injection η≥0 to energy injection ε≥0 is bounded by kmin2ε≤η≤kmax2ε. Such a forcing is frequently considered in theoretical and numerical studies of 2D turbulence. It is shown that for μ≥0 the asymptotic behaviour satisfies ∥u∥12≤kmax2∥u∥2, where ∥u∥2 and ∥u∥12 are the energy and enstrophy, respectively. If the condition of monoscale-like forcing holds only in a time-mean sense, then the inequality holds in the time mean. It is also shown that for Navier–Stokes turbulence (μ=1), the time-mean enstrophy dissipation rate is bounded from above by 2ν1kmax2. These results place strong constraints on the spectral distribution of energy and enstrophy and of their dissipation, and thereby on the existence of energy and enstrophy cascades, in such systems. In particular, the classical dual cascade picture is shown to be invalid for forced 2D Navier–Stokes turbulence (μ=1) when it is forced in this manner. Inclusion of Ekman drag (μ=0) along with molecular viscosity permits a dual cascade, but is incompatible with the log-modified −3 power law for the energy spectrum in the enstrophy-cascading inertial range. In order to achieve the latter, it is necessary to invoke an inverse viscosity (μ<0). These constraints on permissible power laws apply for any spectrally localized forcing, not just for monoscale-like forcing.

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).

Co3(SO4)3(OH)2[enH2]: a newS= 3/2 Kagome-type layered sulfate with a unique connectivity

The Kagome lattice, comprising a two-dimensional array of corner-sharing equilateral triangles, is central to the exploration of magnetic frustration. In such a lattice, antiferromagnetic coupling between ions in triangular plaquettes prevents all of the exchange interactions being simultaneously satisfied and a variety of novel magnetic ground states may result at low temperature. Experimental realization of a Kagome lattice remains difficult. The jarosite family of materials of nominal composition AM3(SO4)2(OH)6 (A = monovalent cation; M= Fe3+, Cr3+), offers perhaps one of the most promising manifestations of the phenomenon of magnetic frustration in two dimensions. The magnetic properties of jarosites are however extremely sensitive to the degree of coverage of magnetic sites. Consequently, there is considerable interest in the use of soft chemical techniques for the design and synthesis of novel materials in which to explore the effects of spin, degree of site coverage and connectivity on magnetic frustration.

On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteria

The energy-Casimir stability method, also known as the Arnold stability method, has been widely used in fluid dynamical applications to derive sufficient conditions for nonlinear stability. The most commonly studied system is two-dimensional Euler flow. It is shown that the set of two-dimensional Euler flows satisfying the energy-Casimir stability criteria is empty for two important cases: (i) domains having the topology of the sphere, and (ii) simply-connected bounded domains with zero net vorticity. The results apply to both the first and the second of Arnold’s stability theorems. In the spirit of Andrews’ theorem, this puts a further limitation on the applicability of the method. © 2000 American Institute of Physics.

Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.

The stability of a two-dimensional vorticity filament under uniform strain

The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ < 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ e 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.

Inhomogeneous two-dimensional turbulence in the atmosphere

Faced with the strongly nonlinear and apparently random behaviour of the energy-containing scales in the atmosphere, geophysical fluid dynamicists have attempted to understand the synoptic-scale atmospheric flow within the context of two-dimensional homogeneous turbulence theory (e.g. FJØRTOFT [1]; LEITH [2]). However atmospheric observations (BOER and SHEPHERD [3] and Fig.1) show that the synoptic-scale transient flow evolves in the presence of a planetary-scale, quasi-stationary background flow which is approximately zonal (east-west). Classical homogeneous 2-D turbulence theory is therefore not strictly applicable to the transient flow. One is led instead to study 2-D turbulence in the presence of a large-scale (barotropically stable) zonal jet inhomogeneity.