Non-projectability of polytope skeleta

We investigate necessary conditions for the existence of projections of polytopes that preserve full k-skeleta. More precisely, given the combinatorics of a polytope and the dimension e of the target space, what are obstructions to the existence of a geometric realization of a polytope with the given combinatorial type such that a linear projection to e-space strictly preserves the k-skeleton. Building on the work of Sanyal (2009), we develop a general framework to calculate obstructions to the existence of such realizations using topological combinatorics. Our obstructions take the form of graph colorings and linear integer programs. We focus on polytopes of product type and calculate the obstructions for products of polygons, products of simplices, and wedge products of polytopes. Our results show the limitations of constructions for the deformed products of polygons of Sanyal and Ziegler (2010) and the wedge product surfaces of Rörig and Ziegler (2011) and complement their results.     

A comparative study of electronic structure and bonding in transition metal monocarbides

The structural, electronic, elastic and bonding properties of four transition metal carbides, ScC, YC (group III), VC and NbC (group V), have been investigated systematically using the first principles density functional theory (DFT). The full potential linearized augmented plane wave (FP-LAPW) method with the generalized gradient approximation (GGA) for the exchange correlation has been used for the calculation of the total energy. The ground state properties, such as equilibrium lattice constant, bulk modulus, are computed and compared with theoretical and experimental data. The electronic and bonding patterns of the two groups of compounds have been analyzed quantitatively and compared with the available data. It is clear from band structures that all the four transition metal monocarbides are metallic in nature. Analysis of elastic constants reveals that the carbides of group III are ductile in nature while those of group V are brittle.     

Electronic structure and magnetism of disordered bcc Fe alloys

We study the electronic structure and magnetic properties of disordered bcc Co_xFe_1-x, Cr_xFe_1-x and Mn_xFe_1-x alloys in their ferromagnetic phases using the Augmented Space Recursion (ASR) technique coupled with the tight-binding linearized muffin tin orbital (TB-LMTO) method. We calculate the density of states and magnetic moment of these alloys to show the variation upon alloying Fe with the other neighbouring 3d transition metals using arguments based on charge transfer, exchange splitting and hybridization effects. Received 10 April 2001 and Received in final form 15 August 2001     

Irrotational Bianchi V viscous fluid cosmology with heat flux

The irrotational Bianchi V cosmological model under the influence of both shear and bulk viscosity, together with heat flux, has been studied. Exact solutions for the model are obtained with three assumptions of which the first two relate the matter density, shear scalar, and expansion scalar and the third is a barotropic equation of state, connecting the matter density and thermodynamic pressure. The properties of the solutions are studied and the temperature distribution is also given explicitly. It has been observed that along with the viscosity, heat flux further adds to the rate of entropy increase.     

High pressure behavior of NpSe and NpTe

The high pressure behavior and pressure induced structural phase transition of two neptunium monochalcogenides have been investigated by using a three body potential approach. The calculated compression curves and the values of different high pressure behavior for NpSe and NpTe are presented and have been discussed and compared with the experimental values wherever available. The accuracy of the present approach in reproducing the phase transition pressure and high pressure behavior for these compounds are in general good agreement with the measured data. For NpSe and NpTe, the phase transition pressures for going from NaCl to CsCl phase have been observed at 22.4 and 14.2 GPa, respectively.     

Effect of radiation on hydromagnetic vertical channel flow

The effect of radiation on the combined free and forced convection flow of an electrical conducting viscous fluid through an open-ended vertical channel in slip flow regime and permeated by a constant magnetic field in transverse direction has been considered. The temperature on the walls has been supposed to vary linearly with distance. On the assumption of optically thin limit, the expressions for velocity, induced magnetic field, temperature, flow rate and the heat transfer coefficient due to thermal conduction are obtained and the influence of radiation on these solutions are shown either graphically or in tabulated forms.Notation x, y, z cartesian coordinates - v velocity - 2L distance between the channel walls - B ₀ applied magnetic field - B induced magnetic field - T temperature - p pressure - density - magnetic permeability - v kinematic coefficient of viscosity - conductivity of the fluid - g acceleration due to gravity - coefficient of volume expansion - thermal diffusivity of the fluid - c _p specific heat at constant pressure - q_R radiative heat flux - k absorption coefficient - e _b Plank function - T 0 reference temperature - N vertical temperature gradient - M= B₀L[/(v)]^1/2 Hartmann number - R _a=gNL⁴/(v) Rayleigh number - P_m = magnetic Prandtl number - 2d₁, 2d₂ thickness of the walls - ₁, ₂ conductivities of the walls     

MHD laminar thin-film flow along a vertcal wall

An accelerating magnetohydrodynamic laminar flow of an electrically conducting fluid under the influence of gravity and in presence of transverse magnetic field is investigated in the paper. Using a cubic polynomial for the velocity profile inside the boundary layer, the momentum integral equation is solved numerically by Runge-Kutta method to determine the boundary layer thickness and the corresponding film thickness is then calculated for the entrance region. The effect of magnetic field on these solutions is shown in graphical form.List of symbols u, v local velocity components - p pressure - density - kinematic viscosity - viscosity= - electrical conductivity - g acceleration due to gravity - U _s (x) inviscid core velocity - h(x) film thicknes - (x) boundary layer thickness - M Hartmann number - B ₀ external magnetic field The authors remain thankful to the referee for some helpful criticisms.