Studies in werner clathrates. Part 2. Structures of bis (isothiocyanato) tetra (4-phenylpyridine) nickel (II)· 4-dimethylsulphoxide,bis (isothiocyanato) tetra (3-methylpyridine) nickel (II)· chloroform and bis (isothiocyanato) tetra (3,5-dimethylpyridine) nickel (II)

The structures of Ni(NCS)₂(4-PhPy)₄·4DMSO and Ni(NCS)₂(3-MePy)₄·CHCl₃ have been elucidated. Movement of guest molecules through channels in the host structure was simulated by potential energy calculations. Ni(NCS)₂(3,5-diMePy)₄ does not form inclusion compounds. An intra-molecular potential energy study shows that theortho-hydrogens on the 3,5-dimethylpyridine ligands control the conformation of the molecule. The same result is obtained with the 4-methylpyridine ligand, which suggests that the extent of rotation of substituted pyridines about the Ni–N bounds is not a factor governing clathrate formation. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82030 (43 pages).     

Integrability of the classical[\bar \psi _i \psi _i ]_2^2 and[\bar \psi _i \psi _i ]_2^2 - [\bar \psi _i \gamma _5 \psi _i ]_2^2 interactions

We study the interaction ofN classical two-dimensional massless Fermi fields through the symmetric couplings \([\bar \psi _i \psi _i ]^2 \) or \([\bar \psi _i \psi _i ]^2 - [\bar \psi _i \gamma _5 \psi _i ]^2 \) . We explicitly show complete integrability in the casesN=1, 2, using the inverse scattering method. The fields occuring in the associated linear eigenvalue problem and evolution equation are simply related to the fundamental fields Ψ _i that satisfy the original non-linear equations. ForN>2, calculations become very involved, but there is no doubt that the system remains completely integrable, reducing to appropriate generalizations of the sine- and sinh-Gordon equation, a situation analogous to Pohlmeyer's discussion in a somewhat similar problem: the two-dimensional non-linear σ-model. Finally, all the explicit analytic solutions that we have worked out in the present framework are identical to those found by Dashen et al., and Shei, in a semiclassical treatment of the fully quantum mechanical version of these models. This leads us to conjecture that the quantum theory also shares most of the features of completely integrable systems, like the massive Thirring model.     

Thermal properties and volume fraction of the boundary interphase in metal-filled epoxies

Summary A previous study (1) on the thermomechanical behaviour of metal-filled Epoxies led us to conclude that the concept of the boundary interphase is a very useful tool for describing quantitatively the quality of adhesion between the matrix and the filler particles. It was shown that this interphase exists in reality and is an area between filler and matrix, which contains both areas of adsorption interaction in polymer surface layers into filler particles, as well as an area of mechanical imperfections.In the present paper, under the assumption that the interphase is homogeneous and isotropic, exhibiting perfect adhesion with both main phases, a theory was developed to describe the thermomechanical behaviour of this interphase.Thermal expansion coefficients and volume fraction of the interphase of a large number of composites were determined and the effect of various parameters, such as temperature, volume fraction of filler and particle size, were examined for specimens exhibiting imperfect as well as perfect adhesion between matrix and filler.With 12 figures and 1 table     

Convection-enhanced diffusion for random flows

We analyze the effective diffusivity of a passive scalar in a two-dimensional, steady, incompressible random flow that has mean zero and a stationary stream function. We show that in the limit of small diffusivity or large Peclet number, with convection dominating, there is substantial enhancement of the effective diffusivity. Our analysis is based on some new variational principles for convection diffusion problems and on some facts from continuum percolation theory, some of which are widely believed to be correct but have not been proved yet. We show in detail how the variational principles convert information about the geometry of the level lines of the random stream function into properties of the effective diffusivity and substantiate the result of Isichenko and Kalda that the effective diffusivity behaves likeɛ ^3/13 when the molecular diffusivityɛ is small, assuming some percolation-theoretic facts. We also analyze the effective diffusivity for a special class of convective flows, random cellular flows, where the facts from percolation theory are well established and their use in the variational principles is more direct than for general random flows.     

Time and direction of arrival detection and filtering for imaging in strongly scattering random media

We study detection and imaging of small reflectors in heavy clutter, using an array of transducers that emits and receives sound waves. Heavy clutter means that multiple scattering of the waves in the heterogeneous host medium is strong and overwhelms the arrivals from the small reflectors. Building on the adaptive time-frequency filter of [Borcea et al, SIIMS 2011;4(3)], we propose a robust method for detecting the direction of arrival of the direct echoes from the small reflectors, and suppressing the unwanted clutter backscatter. This improves the resolution of imaging. We illustrate the performance of the method with realistic numerical simulations in a non-destructive testing setup.     

The elastic modulus of particulate composites using the concept of a mesophase

A theoretical model for the evaluation of the elastic modulus in particulate composites has been developed. The method takes into account the existence of a mesophase between main phases, which constitutes an important parameter influencing the behaviour of a composite material. This layer between the matrix and filler develops different physico-chemical properties from those of the constituent phases and variable ones along its thickness. The effect of the progressive variation of the elastic modulus of the mesophase on the modulus of the composite was estimated by applying various simple laws of variation. Convenient laws of variation were introduced, varying from a simple one, assuming a linear law, to a more refined one using a parabolic law. Experimental results with particulates, based on iron-filled epoxy composites, compared satisfactorily with other models. However, the model based on a parabolic law was superior to all others on physical grounds.List of symbols E elastic modulus - v Poisson's ratio - volume fraction - r radius - V volume - K bulk modulus - r thickness of mesophase - parameter which depends on the sudden changes of the heat capacity for the filled and unfilled polymer C _p ^f and C _p ⁰