This study considers a 3D basic unit-cell proposed for auxetic and non-auxetic foams namely the elongated hexagonal dodecahedron deforming through changes in angle between its ligaments (idealised hinging model). This structure was studied in detail for the potential of exhibiting negative Poisson's ratio and/or negative compressibility by means of a method based on standard force-field molecular modelling technique, termed as Empirical Modelling Using Dummy Atoms (EMUDA). The mechanical properties obtained from this method were then compared to a previously published analytical model of this structure [Grima J N, CaruanaGauci R, Attard D, and Gatt R 2012, Proc. Roy. Soc. A 468 3121], and found to be in good agreement with each other. The results showed that this system can exhibit zero Poisson's ratios in one of its planes and positive or negative Poisson's ratios in other planes, depending on the geometry of the model. It was also shown that under certain conditions, negative linear andÃ³r area compressibility was also exhibited.
This paper investigates the suitability of the General Utility Lattice Program (GULP) for studying auxetic materials at the molecular level. GULP is a force-field based molecular modelling package which incorporates the 'core-shell' model for simulating polarisability. A validation procedure was performed where the capability of GULP to reproduce the structural and mechanical properties of SOD (a zeolite for which the single crystalline elastic constants have been experimentally measured). It was found that not all GULP libraries (force-fields) could reproduce these properties, although the 'Catlow 1992' and 'Sauer 1997' libraries were found the produce good results. These libraries were then used to study the all-silica forms of various 'presumably auxetic' zeolites. The simulations generally confirmed the conclusions reported in earlier studies, and in particular, the fibrous zeolites THO, NAT and EDI where once again shown to be auxetic in the (001) plane. A study was also performed aimed at assessing the effect of interstitial species on the mechanical properties of NAT where it was shown that these species reduce the auxetic effect. This is very significant as once again we have confirmed the potential of these materials as molecular level auxetics, and hopefully, these results will result in generating more interest into the fascinating materials which could be used in many practical applications (e.g. tuneable molecular sieves).
A novel solution of the free convection boundary problem is represented in analytical form for velocity and temperature for an isothermal vertical plate, as an example. These fields are built as a Taylor Series in the x coordinate with coeffiients as functions of the vertical coordinate (y). We restrict ourselves by cubic approximation for both functions. The basic Navier-Stokes and Fourier-Kirchhoffequations and boundary conditions give links between coeffiients and connected with free convection heat transfer phenomenon which define the analytical form of the solution as a function of the Grashof number only. In the solution the non zero velocity of a fluid flow through a leading edge of the plate is taken into account. The solution in the form of velocity and temperature profiles is numerically evaluated and illustrated for air.
We consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon number of finite and point receivers. Application to the LIDAR problem and X-ray beam scattering for orthogonal and inclined to a layer is considered.
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