Radiative transfer in fine structures of solar prominences

In the first part we used Ambartsumains method of addition of layers to show that various problems of radiative transfer in a plane-parallel inhomogeneous atmosphere may be reduced to the solution of the cauchy problems for linear differential equations. The idea of the approach is that we start with the determining of the reflection and transmission coefficients of an atmosphere by solving the initial-value problem for a set of linear differential equations of the first order. After that the internal radiation field is found immediately without solving any new equation.There are some solar prominence fine structures which are not observable. Thus, we need to use theoretical methods to study their geometric and physical properties. It is believed that observed intensities and their fluctuations are related to such fine structures in the line of sight. Regarding the fact that the spectrum line corresponding to the transition will not be sharp and will have a spread in frequency that can be described by absorption profiles. So, the second part of the present study is an attempt to determine the intensity fluctuations in the frequency-dependent case with different absorption profiles such as Doppler, Voigt and Lorentz profiles. It became evident that the intensity fluctuations vary with absorption profile and optical depth variations in the line of sight. It should be noted that the present study focuses on the LTE absorbing atmosphere.     

The photocatalytic mechanism of BiOI with oxygen vacancy and iodine self-doping

The photocatalytic mechanism of BiOI with an oxygen vacancy and iodine self-doping is investigated by studying their structural, electronic and optical properties. The results of the first-principle calculations indicate that the utilization of the visible light region is broadened, and thus the photocatalytic performance is improved, via introducing an oxygen vacancy or I dopant. Among them, I-Bi doped BiOI shows the best photocatalytic performance, and it is also the preferred one of the three structures due to its better stability. The occurrence of I-Bi or I-I interactions in the original double iodine layer along with the introduction of I dopant leads to a planar localization of the photocatalytic mechanism. Then it is expected that the photo-generated carriers will transfer to the catalyst surface more easily; the photocatalytic activity of BiOI relies on the planar localization to a great degree.     

Turbulent structures in an optimal Taylor–Couette flow between concentric counter-rotating cylinders

The turbulent structures formed in a Taylor–Couette (TC) flow established between two concentric counter-rotating cylinders were explored numerically. The shear Reynolds number was set to Re_shear = 8000 and the radius ratio was set to r_i/r_o = 0.5. An optimal flow corresponding to the maximal angular velocity transport between the cylinders was selected for the TC flow. The mean velocity profile reached its steepest value near the cylinders in the optimal TC flow. The streamwise velocity correlations at the outer cylinder in the gap exceeded those at the inner cylinder. The large convective transport of angular velocity in the gap generated a maximal angular velocity flux to achieve the optimal flow. The angular velocity flux generated by the momentum source exceeded that generated by the momentum sink. The vorticity dispersion was larger near the inner cylinder than near the outer cylinder, but vorticity stretching near the outer cylinder exceeded than that near the inner cylinder. The skin friction coefficient budgets were plotted using the velocity–vorticity correlation. The vortex stretching contributions dominated the skin friction budgets. The area near the inner cylinder was populated by stronger vortices, but their population density was smaller than the population density of the vortices near the outer cylinder. The probability density functions of the wall-normal and streamwise velocity fluctuations delineated the presence of the large wall-normal velocity fluctuations near the outer cylinder.     

Comparison of subwavelength focusing properties of diffraction and Fresnel zone plate plasmonic planar lenses

The subwavelength focusing properties of diffractive plasmonic planar lenses (DPLs) and Fresnel zone plate plasmonic planar lenses (FZPs) have been compared in this paper. To that end, we use the same lens material, incident wavelength, thickness and focal length for comparison. Both DPLs and FZPs consist of central circular slits surrounded by transparent and opaque zones and can get clear focusing performances. By using the rigorous electromagnetic numerical method, the fields in the focal region are analyzed in detail, and our results demonstrate that FZP can generate higher transmission efficiency, and higher peak field intensity at the focal plane. Focusing polarization properties of the lens illuminated by linearly polarized state, are calculated and analyzed also. The numerical results show that both the DPL and the FZP produce asymmetrical focal spot distributions with a low f-number. To the FZP, the full-width at half-maximum (FWHM) varies from 256 nm (along y-axis) to 516 nm(along x-axis) and to the DPL, the FWHM varies from 256 nm(along y-axis) to 580 nm(along x-axis), respectively. But for a high f-number, the asymmetrical performance of the focal spot will be reduced due to complicated electromagnetical field interferences and micro waveguide effect. Otherwise, the DPL can get a higher depolarization effect than the FZP does.     

Growth mode and novel structure of ultra-thin KCl layers on the Si(1 0 0)-2 × 1 surface

This study investigates ultra-thin potassium chloride (KCl) films on the Si(1 0 0)-2 × 1 surfaces at near room temperature. The atomic structure and growth mode of this ionic solid film on the covalent bonded semiconductor surface is examined by synchrotron radiation core level photoemission, scanning tunneling microscopy and ab initio calculations. The Si 2p, K 3p and Cl 2p core level spectra together indicate that adsorbed KCl molecules at submonolayer coverage partially dissociate and that KCl overlayers above one monolayer (ML) have similar features in the valance band density of states as those of the bulk KCl crystal. STM results reveal a novel c(4 × 4) structure at 1 ML coverage. Ab initio calculations show that a model that comprises a periodic pyramidal geometry is consistent with experimental results.     

Separation of Variables for Bi-Hamiltonian Systems

We address the problem of the separation of variables for the Hamilton–Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called N manifolds, to give intrisic tests of separability (and Stäckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel'fand–Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.     

Integer linear programming formulation of the material requirements planning problem

Lot sizing procedures for discrete and dynamic demand form a distinct class of inventory control problems, usually referred to asmaterial requirements planning. A general integer programming formulation is presented, covering an extensive range of problems: single-item, multi-item, and multi-level optimization; conditions on lot sizes and time phasing; conditions on storage and production capacities; and changes in production and storage costs per unit. The formulation serves as a uniform framework for presenting a problem and a starting point for developing and evaluating heuristic and tailor-made optimum-seeking techniques.