Large deviations from a macroscopic scaling limit for particle systems with Kac interaction and random potential

We consider a lattice gas in a periodic d-dimensional lattice of width γ⁻¹, γ>0, interacting via a Kac's type interaction, with range and strength γ^d, and under the influence of a random one body potential given by independent, bounded, random variables with translational invariant distribution. The system evolves through a conservative dynamics, i.e. particles jump to nearest neighbor empty sites, with rates satisfying detailed balance with respect to the equilibrium measures. In [M. Mourragui, E. Orlandi, E. Saada, Macroscopic evolution of particles systems with random field Kac interactions, Nonlinearity 16 (2003) 2123–2147] it has been shown that rescaling space as γ⁻¹ and time as γ⁻², in the limit γ→0, for dimensions d3, the macroscopic density profile ρ satisfies, a.s. with respect to the random field, a non-linear integral partial differential equation, having the diffusion matrix determined by the statistical properties of the external random field. Here we show an almost sure (with respect to the random field) large deviations principle for the empirical measures of such a process. The rate function, which depends on the statistical properties of the external random field, is lower semicontinuous and has compact level sets.     

On the extremal values of the second largest Q-eigenvalue

We study extremal graphs for the extremal values of the second largest Q-eigenvalue of a connected graph. We first characterize all simple connected graphs with second largest signless Laplacian eigenvalue at most 3. The second part of the present paper is devoted to the study of the graphs that maximize the second largest Q-eigenvalue. We construct families of such graphs and prove that some of theses families are minimal for the fact that they maximize the second largest signless Laplacian eigenvalue.     

Numerical simulation of generalized newtonian blood flow past a couple of irregular arterial stenoses

This paper looked at the numerical investigations of the generalized Newtonian blood flow through a couple of irregular arterial stenoses. The flow is treated to be axisymmetric, with an outline of the stenoses obtained from a three dimensional casting of a mild stenosed artery, so that the flow effectively becomes two‐dimensional. The Marker and Cell (MAC) method is developed for the governing unsteady generalized Newtonian equations in staggered grid for viscous incompressible flow in the cylindrical polar co‐ordinates system. The derived pressure‐Poisson equation was solved using Successive‐Over‐Relaxation (S.O.R.) method and the pressure‐velocity correction formulae have been derived. Computations are performed for the pressure drop, the wall shear stress distribution and the separation region. The presented computations show that in comparison to the corresponding Newtonian model the generalized Newtonian fluid experiences higher pressure drop, lower peak wall shear stress and smaller separation region. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 960–981, 2011     

High temperature shock-tube study of the reaction of gallium with ammonia

The gas-phase reaction of Ga atoms with NH(3) was studied behind reflected shock waves in the temperature range of 1380 to 1870 K at pressures of 1.4 to 4.0 bar. Atomic-resonance-absorption spectroscopy (ARAS) at 403.299 nm was applied for the time-resolved determination of the Ga-atom concentration. Trimethylgallium (Ga(CH(3))(3)) was used as a precursor of Ga atoms. After the initial increase in Ga concentration due to Ga(CH(3))(3) decomposition, the Ga concentration decreases rapidly in the presence of NH(3). For the simulation of the measured Ga-atom concentration profiles from the studied reaction, additional knowledge about the thermal decomposition of Ga(CH(3))(3) is required. The rate coefficient k(4) of the reaction Ga + NH(3) → products (R4) was determined from the Ga-atom concentration profiles under pseudo-first-order assumption and found to be k(4)(T) = 10(14.1±0.4) exp(-11?900 ± 700 K/T) cm(3) mol(-1) s(-1) (error limits at the one standard deviation level). No significant pressure dependence was noticeable within the scatter of the data at the investigated pressure range.     

Inkjet printing of inorganic sol–gel ink and control of the geometrical characteristics

In this article we have shown the possibility to inkjet an ink on glass substrates for high resolution or on large area by varying the geometrical characteristics such as the dried droplet diameter and the line width. We formulated an inorganic sol–gel ink based on tetraethyl orthosilicate with a suitable mixture of organic solvents and investigated the thermal stability of the ink. The influence of the applied voltage during the jetting process as well as the surface free energy of the coated glass substrates were studied for tailoring the droplet diameter and line width of the dried inkjet-print.     

p-Type behaviour of electrodeposited ZnO:Cu films

Cu-doped ZnO (ZnO:Cu) thin films and ZnO/ZnO:Cu homojunction devices were electrodeposited on conductive glass substrates in a non-aqueous electrolyte containing Cu and Zn salts. The Cu content of the films is proportional to the Cu/Zn precursor ratio in the deposition electrolyte. ZnO:Cu was found to be of a hexagonal wurtzite structure with (002) preferred orientation. A transition from n-type to p-type was observed for ZnO:Cu films with a Cu/Zn ratio higher than 2% as inferred from the change in the direction of the photocurrent. The rectifying characteristics shown by homojunction devices further confirm the p-type conductivity of ZnO:Cu layers.     

k-Domination and k-Independence in Graphs: A Survey

In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs. For a positive integer k, a subset S of vertices in a graph G = (V, E) is k-dominating if every vertex of V − S is adjacent to at least k vertices in S. The subset S is k-independent if the maximum degree of the subgraph induced by the vertices of S is less or equal to k − 1. In this paper we survey results on k-domination and k-independence.     

Dominator Colorings in Some Classes of Graphs

A dominator coloring is a coloring of the vertices of a graph such that every vertex is either alone in its color class or adjacent to all vertices of at least one other class. We present new bounds on the dominator coloring number of a graph, with applications to chordal graphs. We show how to compute the dominator coloring number in polynomial time for P ₄-free graphs, and we give a polynomial-time characterization of graphs with dominator coloring number at most 3.