Semigroups of transcendental entire functions and their dynamics

We investigate the dynamics of semigroups of transcendental entire functions using Fatou–Julia theory. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroups. We provide some condition for connectivity of the Julia set of the transcendental semigroups. We also study finitely generated transcendental semigroups, abelian transcendental semigroups and limit functions of transcendental semigroups on its invariant Fatou components.     

OVERLAPPING CONTROL VOLUME APPROACH FOR CONVECTION–DIFFUSION PROBLEMS

This paper introduces a finite volume method to solve 2D steady state convection–diffusion problems on structured non-orthogonal grids. Overlapping control volumes (OCV) are used to discretize the physical domain and the governing equations are solved without transformation. An isoparametric formulation is used to compute diffusion and for upwinding. Four test problems are solved using this and other schemes. The modelling of diffusion in OCV seems very effective even on distorted meshes. The convection modelling in OCV is found to be second-order-accurate, like QUICK, on regular meshes. Although its accuracy is slightly inferior to the latter on rectangular grids, its faster convergence gives it a better overall performance. On non-orthogonal grids, OCV gives better accuracy for a large and practical range of Peclet numbers than does QUICK applied to the transformed equations using the conventional five-point diffusion modelling. The results obtained also demonstrate that the scheme reduces false diffusion to a considerable extent in comparison with the power-law scheme.     

A new temperature-dependent equation of state of solids

In the present paper, a temperature-dependent equation of state (EOS) of solids is discussed which is found to be applicable in high-pressure and high-temperature range. Present equation of state has been applied in 18 solids. The calculated data are found in very good agreement with the data available from other sources.     

Measurement of peak fluence of neutron beams using Bi-fission detectors

Fission fragments and other charged particles leave tracks of permanent damage in most of the insulating solids. Damage track detectors are useful for personal dosimeters and for flux/dose determination of high-energy particles from accelerators or cosmic rays. A detector that has its principal response at nucleon energy above 50 MeV is provided by the fission of Bi-209. Neutrons produce the largest percentage of hadron dose in most high-energy radiation fields. In these fields, the neutron spectrum is typically formed by low-energy neutrons (evaporation spectrum) and high-energy neutrons (knock-on spectrum). We used Bi-fission detectors to measure neutron peak fluence and compared the result with the calculated value of neutron peak fluence. For the exposure to 100 MeV we have used the iThemba Facility in South Africa.     

B s data at Tevatron and possible new physics

The new physics (NP) is parametrized with four model-independent quantities: the magnitudes and phases of the dispersive part M ₁₂ and the absorptive part ??₁₂ of the NP contribution to the effective Hamiltonian. We constrain these parameters using the four observables ??M _s, ????_s, the mixing phase $\beta_\mathrm{s}^{J/\psi\phi}$ and $A^b_{\rm sl}$ . This formalism is extended to include charge-parity-time reversal (CPT) violation, and it is shown that CPT violation by itself, or even in the presence of CPT-conserving NP without an absorptive part, helps only marginally in the simultaneous resolution of these anomalies.     

Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity

The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle θ. A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.     

First-principle study of nanostructures of functionalized graphene

We present first-principle calculations of 2D nanostructures of graphene functionalized with hydrogen and fluorine, respectively, in chair conformation. The partial density of states, band structure, binding energy and transverse displacement of C atoms due to functionalization (buckling) have been calculated within the framework of density functional theory as implemented in the SIESTA code. The variation in band gap and binding energy per add atom have been plotted against the number of add atoms, as the number of add atoms are incremented one by one. In all, 37 nanostructures with 18C atoms, 3 × 3 × 1 (i.e., the unit cell is repeated three times along x-axis and three times along y-axis) supercell, have been studied. The variation in C–C, C–H and C–F bond lengths and transverse displacement of C atoms (due to increase in add atoms) have been tabulated. A large amount of buckling is observed in the carbon lattice, 0.0053–0.7487 Å, due to hydrogenation and 0.0002–0.5379 Å, due to fluorination. As the number of add atoms (hydrogen or fluorine) is increased, a variation in the band gap is observed around the Fermi energy, resulting in change in behaviour of nanostructure from conductor to semiconductor/insulator. The binding energy per add atom increases with the increase in the number of add atoms. The nanostructures with 18C+18H and 18C+18F have maximum band gap of 4.98 eV and 3.64 eV, respectively, and binding energy per add atom –3.7562 eV and –3.3507 eV, respectively. Thus, these nanostructures are stable and are wide band-gap semiconductors, whereas the nanostructures with 18C+2H, 18C+4H, 18C+4F, 18C+8F, 18C+10F and 18C+10H atoms are small band-gap semiconductors with the band gap lying between 0.14 eV and 1.72 eV. Fluorine being more electronegative than hydrogen, the impact of electronegativity on band gap, binding energy and bond length is visible. It is also clear that it is possible to tune the electronic properties of functionalized graphene, which makes it a suitable material in microelectronics.