The Gauss image of entire graphs of higher codimension and Bernstein type theorems

Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori estimates for the harmonic Gauss map. The required conditions here are more general than in previous work and they therefore enable us to improve substantially previous results for the Lawson–Osseman problem concerning the regularity of minimal submanifolds in higher codimension and to derive Bernstein type results.     

Analytic aspects of the Toda system: I. A Moser‐Trudinger inequality

In this paper, we analyze solutions of the open Toda system and establish an optimal Moser‐Trudinger type inequality for this system. Let Σ be a closed surface with area 1 and K = (a_ij)_{N × N} the Cartan matrix for SU(N + 1), i.e., We show that has a lower bound in (H¹(Σ))^N if and only if This inequality is optimal. As a direct consequence, if M_j < for 4π for j = 1, 2, …, N, Φ_M has a minimizer u that satisfies © 2001 John Wiley & Sons, Inc.     

Precoloring Extension of Co-Meyniel Graphs

The pre-coloring extension problem consists, given a graph G and a set of nodes to which some colors are already assigned, in finding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs. We answer a question of Hujter and Tuza by showing that “PrExt perfect” graphs are exactly the co-Meyniel graphs, which also generalizes results of Hujter and Tuza and of Hertz. Moreover we show that, given a co-Meyniel graph, the corresponding contracted graph belongs to a restricted class of perfect graphs (“co-Artemis” graphs, which are “co-perfectly contractile” graphs), whose perfectness is easier to establish than the strong perfect graph theorem. However, the polynomiality of our algorithm still depends on the ellipsoid method for coloring perfect graphs. C.N.R.S. Final version received: January, 2007     

Modeling of the submicron particles formation and initial layer ash deposition during high temperature oxy-coal combustion

The future use of coal as a fuel for power generation in the US depends on the availability of financially viable technologies for capture and storage of CO₂ emissions from power plants. Key second-generation candidates for CO₂ capture include high temperature and pressurized oxy-firing of coal, which has the potential to increase efficiency, lower capital costs, avoid air ingress and reduce oxygen requirements. However, unquantified challenges, such as flame behavior, heat transfer, ash transformation, ash deposition and char oxidation, still exist for those technologies. This study specifically focuses on the formation of submicron particles and initial layer ash deposition during high temperature oxy-coal combustion. Previous work has shown that the initial layer deposits are mainly formed of submicron size ash aerosols transported by thermophoresis. Unfortunately, the importance of submicron particle deposition has not received much attention, probably due to the insignificant deposit mass and difficulty in prediction of the submicron particles formation. In this work, models including mineral matter vaporization model, scavenging model and deposition model are developed and applied into a three-dimensional CFD framework to predict the submicron particles formation and subsequent initial layer deposits formation. The model results are comparable to experimental data. The merits of this work are that it has led to the development of a novel approach to predict both submicron particle formation and initial layer ash deposition during oxy-coal combustion.     

The roles of added chlorine and sulfur on ash deposition mechanisms during solid fuel combustion

The focus of this paper is on effects of chlorine and sulfur on coal ash deposition rates, under practically relevant but systematically controlled combustion conditions. This problem is important, not so much for coal, but to understand and predict deposition rates for biomass combustion where chlorine contents can be high. To this end, ash deposition rates on a controlled temperature surface were measured for controlled amounts of chlorine and sulfur added to a pulverized coal, doped with potassium and burned in a 100 kW rated combustion rig. Previous work with 35 tests on 11 coal, biomass and petroleum coke fuels burned under a range of operating conditions had strongly suggested that the deposition rate of the tightly bound inside deposits was independent of the ash aerosol composition, and depended only on PM₁ in the flue gas. The loosely bound outside deposition rate was dependent primarily on the total alkali content in the flue gas. The new results using chlorine added to the fuel (in the form of ammonium chloride) required these previous conclusions to be drastically revised. They showed that chlorine, not alkali alone, had large effects on the deposition rate of the inside deposits, which now were orders of magnitude higher than without chlorine addition, and did not fit previous (multi-fuel) correlations with PM₁. Sulfur addition, together with chlorine, did not affect deposition rates much, although it did lower the chlorine content of the deposit. These results are interpreted in terms of the ash aerosol size segregated composition, which was also measured, and potential sulfation reactions within the deposit.     

Editorial

On behalf of your students your colleagues, and your friends     

Ultrafine ash aerosols from coal combustion: Characterization and health effects

Ultrafine coal fly-ash particles, defined here as those with diameters less than 0.5 μm, typically comprise less than 1% of the total fly-ash mass. These particles are formed primarily through ash vaporization, nucleation, and coagulation/condensation mechanisms, which lead to compositions notably different compared to other fine or coarse particle fractions formed by fragmentation. Whereas previous studies have focused on health effects of particulate matter with aerodynamic diameters less than 2.5 μm (PM_2.5) (including both vaporization and fragmentation modes), this paper reports results of interdisciplinary research focused on both characterization and health effects of primary ultrafine coal ash aerosols alone. Ultrafine, fine, and coarse ash particles were segregated and collected from a coal burned in a 20 kW laboratory combustor and two additional coals burned in an externally heated drop tube furnace. Extracted samples from both combustors were characterized by transmission electron microscopy (TEM), wavelength dispersive X-ray fluorescence (WD-XRF) spectroscopy, Mossbauer spectroscopy, and X-ray absorption fine structure (XAFS) spectroscopy. Pulmonary inflammation was characterized by albumin concentrations in mouse lung lavage fluid after instillation of collected particles in saline solutions and a single direct inhalation exposure. Results indicate that coal ultrafine ash sometimes, but not always, contains significant amounts of carbon, probably soot originating from coal tar volatiles, depending on coal type and combustion device. Surprisingly, XAFS results revealed the presence of chromium and thiophenic sulfur in the ultrafine ash particles. Although the single direct inhalation study failed to reveal significant health effects, the instillation results suggested potential lung injury, the severity of which could be correlated with the carbon (soot) content of the ultrafines. Further, this increased toxicity is consistent with theories in which the presence of carbon mediates transition metal (i.e., Fe) complexes, as revealed in this work by TEM and XAFS spectroscopy, promoting reactive oxygen species, oxidation–reduction cycling, and oxidative stress.     

Chaos synchronization in networks of coupled maps with time-varying topologies

Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex networks both analytically and numerically. The temporal variation is rather general and formalized as being driven by a metric dynamical system. Four network models are discussed in detail in which the interconnections between vertices vary through time randomly. These models are: 1) i.i.d. sequences of random graphs with fixed wiring probability, 2) groups of graphs with random switches between the individual graphs, 3) graphs with temporary random failures of nodes, and 4) the meet-for-dinner model where the vertices are randomly grouped. We show that the temporal variation and randomness of the connection topology can enhance synchronizability in many cases; however, there are also instances where they reduce synchronizability. In analytical terms, the Hajnal diameter of the coupling matrix sequence is presented as a measure for the synchronizability of the graph topology. In topological terms, the decisive criterion for synchronization of coupled chaotic maps is that the union of the time-varying graphs contains a spanning tree.