An (m+1)-step iterative method of convergence order (m+2) for linear complementarity problems

In this paper, we present an (m+1)-step iterative method of convergence order (m+2) for solving linear complementarity problems. The proposed iterative method is simple and easy to construct, and requiring only third Fréchet differentiation. Computational efficiency in its general form is discussed and a comparison between the efficiency of the proposed method and existing ones is made. The performance is tested through numerical experiments on some test problems.     

The influence of strongly reducing conditions on strong metal-support interactions in Cu/ZnO catalysts used for methanol synthesis

A systematic series of binary and ternary copper catalysts was investigated using the methanol synthesis reaction at atmospheric pressure. Strong metal-support interactions between copper and zinc oxide induced by strongly reducing conditions were probed by the adsorption of carbon monoxide, which was monitored qualitatively and quantitatively by a combination of microcalorimetry, temperature-programmed desorption experiments and Fourier transform infrared spectroscopy. For the zinc oxide-containing catalysts, the pretreatment in flowing carbon monoxide at 493 K resulted in a severe decoration of the copper metal particles with ZnOx adspecies, whereas after methanol synthesis at 493 K the state of the copper was essentially identical to that seen after hydrogen reduction. Copper was always found to be present in its zero-valent state.     

Nonequilibrium critical behavior in unidirectionally coupled stochastic processes

Phase transitions from an active into an absorbing, inactive state are generically described by the critical exponents of directed percolation (DP), with upper critical dimension d(c)=4. In the framework of single-species reaction-diffusion systems, this universality class is realized by the combined processes A-->A+A, A+A-->A, and A-->0. We study a hierarchy of such DP processes for particle species A,B,..., unidirectionally coupled via the reactions A-->B, ...(with rates mu(AB),...). When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents beta(i) which are markedly reduced at each hierarchy level i> or =2. This scenario can be understood on the basis of the mean-field rate equations, which yield beta(i)=1/2(i-1) at the multicritical point. Using field-theoretic renormalization-group techniques in d=4-epsilon dimensions, we identify a new crossover exponent phi, and compute phi=1+O(epsilon(2)) in the multicritical regime (for small mu(AB)) of the second hierarchy level. In the active phase, we calculate the fluctuation correction to the density exponent on the second hierarchy level, beta(2)=1/2-epsilon/8+O(epsilon(2)). Outside the multicritical region, we discuss the crossover to ordinary DP behavior, with the density exponent beta(1)=1-epsilon/6+O(epsilon(2)). Monte Carlo simulations are then employed to confirm the crossover scenario, and to determine the values for the new scaling exponents in dimensions d< or =3, including the critical initial slip exponent. Our theory is connected to specific classes of growth processes and to certain cellular automata, and the above ideas are also applied to unidirectionally coupled pair annihilation processes. We also discuss some technical as well as conceptual problems of the loop expansion, and suggest some possible interpretations of these difficulties.     

Literatur

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