Topogenous and Nearness Structures on Categories

We introduce topogenous orders on a general category and demonstrate that they are equivalent to neighbourhood operators and subsume both closure and interior operators. By looking at the basic properties of so-called strict morphisms relative to a topogenous order the ease of working with their axioms and the concurrent generalisation of both interior and closure is evident. In closing we consider Herrlich’s concept of nearness in a category and how it interacts with topogenous orders and syntopogenous structures.     

Effects of temperature gradient induced nanoparticle motion on conduction and convection of fluid

The continuous synthesis of nickel nanoparticles (NiNPs) in a static microchannel T-mixer by the reduction of NiCl₂·6H₂O in the presence of ethylene glycol without a stabilizing/capping agent was investigated. The nanoparticles were formed in accordance with the modified polyol process with hydrazine used as a reducing agent and NaOH as a catalyst for nanoparticle formation. The reaction mechanism for NiNP formation was investigated in batch with the help of Fourier transform infrared spectroscopy and X-ray diffraction (XRD) techniques. Parameters were found for reducing reaction times from 60 to 1?min. The effects of temperature (60?C120?°C) and NaOH concentration (0.1 and 0.5?M) on batch-processed particle characteristics were also studied using XRD, transmission electron microscope and electron microprobe analysis. Average particle size was reduced from 9.2?±?2.9 to 5.4?±?0.9?nm at higher temperature and NaOH concentration. Adaptation of this chemistry to a static microchannel T-mixer for continuous synthesis resulted in smooth, spherical particles. Increases in the reaction temperature from 120 to 130?°C resulted in a narrow size distribution of 5.3?±?1?nm and also resulted in magnetic properties of 5.1?emu/g (saturation magnetization), 1.1?emu/g (remanent magnetization), and 62?Oe (coercivity).     

Local structure reconstruction in hydrogenated amorphous silicon from angular correlation and synchrotron diffraction studies

Hydrogenated amorphous silicon (a-Si:H) is a widely used thin film semiconductor material which is still incompletely understood. It is generally assumed to form a continuous random network, with a high concentration of coordination defects (dangling bonds), which are hydrogen terminated. Neither the exact nature of these sites nor the degree of medium range order has been fully determined. In this paper, we present the first results for the local structure, from a combined study using angular correlation of positron annihilation radiation (ACAR) and synchrotron radiation diffraction. Reciprocal space information is obtained directly, for the mesoscale structure and the local defect structure, from the orientation dependent diffraction and 2D-ACAR patterns, respectively. Furthermore, inversion of both patterns yields a comparison of real space information through maps of the silicon-silicon pair correlation function and the electron-positron autocorrelation function B^2γ(r). From this information, it is possible to identify the dominant structural defect as a vacancy-size dangling bond cluster, around which the network strain is fully relaxed.     

A monotone scheme for Hamilton–Jacobi equations via the nonstandard finite difference method

A usual way of approximating Hamilton–Jacobi equations is to couple space finite element discretization with time finite difference discretization. This classical approach leads to a severe restriction on the time step size for the scheme to be monotone. In this paper, we couple the finite element method with the nonstandard finite difference method, which is based on Mickens' rule of nonlocal approximation. The scheme obtained in this way is unconditionally monotone. The convergence of the new method is discussed and numerical results that support the theory are provided. Copyright © 2009 John Wiley & Sons, Ltd.     

Transitive quasi-uniform structures depending on a parameter

Aequationes mathematicae - In a category $${\mathcal {C}}$$ with an ( $${\mathcal {E}}$$ , $${\mathcal {M}}$$ )-factorization structure for morphisms, we prove that any subclass $${\mathcal {N}}$$...