The 1‐2‐3‐Conjecture for Hypergraphs

A weighting of the edges of a hypergraph is called vertex‐coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e. every edge contains at least two vertices with different weighted degrees. In this article, we show that such a weighting is possible from the weight set for all hypergraphs with maximum edge size and not containing edges solely consisting of identical vertices. The number is best possible for this statement.     

An iterative approach to graph irregularity strength

An assignment of positive integer weights to the edges of a simple graph G is called irregular if the weighted degrees of the vertices are all different. The irregularity strength, s(G), is the maximal edge weight, minimized over all irregular assignments, and is set to infinity if no such assignment is possible. In this paper, we take an iterative approach to calculating the irregularity strength of a graph. In particular, we develop a new algorithm that determines the exact value s(T) for trees T in which every two vertices of degree not equal to two are at distance at least eight.     

Thermochemistry of thermal plasma chemical reactions. Part II. A survey of synthesis routes for silicon nitride production

Feasibility routes for thermal plasma production of silicon nitride powders are explored. First, a collation of the various proposed systems from the extant literature is examined. Reactant systems investigated include free silicon, silicon monoxide, silicon dioxide, silicon tetrachloride, silane, and other organosilicon precursors, along with various nitriding and reducing species. The reaction yields of these systems are brought to a common denominator by thermodynamic analysis and a first-step introduction of nucleation kinetics including comparisons against published experiments and the authors' own research. In particular, it is observed that the formation of liquid-phase free silicon in the neighborhood of 2500 K is quite detrimental to silicon nitride yield, and furthermore, a high supersaturation of silicon should always be avoided.     

A note on cycle spectra of line graphs

We show that line graphs G=L(H) with σ₂(G)≥7 contain cycles of all lengths k, 2rad(H)+1≤k≤c(G). This implies that every line graph of such a graph with 2rad(H)≥Δ(H) is subpancyclic, improving a recent result of Xiong and Li. The bound on σ₂(G) is best possible.     

Obituary for Professor Mikhail F. Zhukov

Plasma Chemistry and Plasma Processing -     

Claw‐free 3‐connected P11‐free graphs are hamiltonian

We show that every 3‐connected claw‐free graph which contains no induced copy of P₁₁ is hamiltonian. Since there exist non‐hamiltonian 3‐connected claw‐free graphs without induced copies of P₁₂ this result is, in a way, best possible. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 111–121, 2004     

Modeling of RF plasma torch with a metallic tube inserted for reactant injection

Flow, temperature, and electromagnetic (EM) fields in a radio-frequency thermal plasma torch designed for the preparation of superconducting powders or films have been analysed by using a new two-dimensional modeling approach with the electric field intensity as the fundamental EM field variable. The insertion of a stainless steel injection tube into the torch leads to large induction currents in this tube. Although such large induction currents cause pronounced changes of the EM fields near the injection tube, flow and temperature fields are little affected. There exists only one large toroidal vortex in the upper part of the present torch, while the maximum temperature appears at an off-axis location within the coil region.     

Determination of the arc-root position in a DC plasma torch

The behavior of an arc operated in the nontransferred mode with a conical-shaped cathode and a nozzle-shaped anode is studied by applying general tyro-dimensional conservation equations and auxiliary relations for the simulation of arc channel flows. The position of the arc-root attachment at the anode surface is determined by using Steenbeck's minimum principle, which postulates a minimum arc voltage for a given current and certain given boundary conditions. The overall effects of the anode-arc root on the plasma flow are, studied by comparing the results with those of the transferred mode of operation. Specific arc-channel diameters are chosen in the simulation in order to verify flit, numerical model through comparisons with experimental results. The results show that Steenbeck's minimum principle is useful for determining the position of the arc-root attachment at the anode surface. Application of this method for control of the arc-anode attachment may be valuable in the design and operation of plasma spray torches to avoid jet instabilities.     

Process study of thermal plasma chemical vapor deposition of diamond,part I: Substrate material,temperature, and methane concentration

Effects of process parameters on diamond film synthesis in DC thermal plasma jet reactors are discussed including substrate material, methane concentration and substrate temperature. Diamond has been deposited on silicon, molybdenum, tungsten, tantalum, copper, nickel, titanium, and stainless steel. The adhesion of diamond film to the substrate is greatly affected by the type of substrate used. It has been found that the methane concentration strongly affects the grain size of the diamond films. Increased methane concentrations result in smaller grain sizes due to the increased number of secondary nucleations on the existing facets of diamond crystals. Substrate temperature has a strong effect on the morphology of diamond films. With increasing substrate temperature, the predominant orientation of the crystal growth planes changes from the (111) to the (100) planes. Studies of the variation of the film quality across the substrate due to the nonuniformity of thermal plasma jets indicate that microcrystalline graphite formation starts at the corners and edges of diamond crystals when the conditions become unfavorable for diamond deposition.     

Diamond synthesis by DC thermal plasma CVD at 1 atm

Diamond crystals and films have been success full y synthesized by DC thermal plasma jet CVD at a pressure of I atrn. A novel triple torch plasma reactor has been used to generate a convergent plasma volume to entrain the participating gases. Three coalescing plasma jets produces! by this reactor direct the dissociated and ionized gaseous species onto ( 100) silicon wafer substrates where the diamond grows. In a typical 10-min run, depending on the method of .substrate preparation, either microcrystals with sizes up to 8 m or continuous films with thicknesses of 1–2 m have been obtained. X-ray diffraction, scanning electron microscopy, and Raman spectroscopy have been used for the characterization of the crystals and of the films.